Left Termination proof of /tmp/tmp

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

0 Prolog

↳1 PrologToPrologProblemTransformerProof (⇒, 673 ms)

↳2 Prolog

↳3 PrologToPiTRSProof (⇒, 182 ms)

↳4 PiTRS

↳5 DependencyPairsProof (⇔, 454 ms)

↳6 PiDP

↳7 DependencyGraphProof (⇔, 11 ms)

↳8 AND

    ↳9 PiDP

        ↳10 UsableRulesProof (⇔, 0 ms)

        ↳11 PiDP

        ↳12 PiDPToQDPProof (⇔, 0 ms)

        ↳13 QDP

        ↳14 QDPSizeChangeProof (⇔, 4 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

(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(g,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\nT1 is ground\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\nT1 is ground\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: true | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 1 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 2 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 3 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\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\nT1 is ground\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(T6, T2, T7), SCOPE: 1, CLAUSE: 1 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 2 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 3 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: true | delete(T10, T2, T11), SCOPE: 1, CLAUSE: 2 | delete(T10, T2, T11), SCOPE: 1, CLAUSE: 3 | delete(T10, T2, T11), SCOPE: 1, CLAUSE: 4\n\nT10 is ground\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: delete(T6, T2, T7), SCOPE: 1, CLAUSE: 2 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 3 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\nT7 is ground\nX10 is free\nX11 is free\ndelete(T6, T2, T7) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: delete(T10, T2, T11), SCOPE: 1, CLAUSE: 2 | delete(T10, T2, T11), SCOPE: 1, CLAUSE: 3 | delete(T10, T2, T11), SCOPE: 1, CLAUSE: 4\n\nT10 is ground\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: delmin(T22, T20, T21) | delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 3 | delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 4\n\nT17 is ground\nT20 is ground\nT18 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: delete(T10, T2, T11), SCOPE: 1, CLAUSE: 3 | delete(T10, T2, T11), SCOPE: 1, CLAUSE: 4\n\nT10 is ground\nT11 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T10, 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(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 3 | delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 4\n\nT17 is ground\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(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 3 | delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 4\n\nT17 is ground\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(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 3 | delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 4\n\nT17 is ground\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(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 3 | delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 4\n\nT17 is ground\nT20 is ground\nT18 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 3\n\nT17 is ground\nT20 is ground\nT18 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 4\n\nT17 is ground\nT20 is ground\nT18 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: ','(less(T121, T122), delete(T121, T126, T125))\n\nT121 is ground\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(T121, T122)\n\nT121 is ground\nT122 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: delete(T121, T126, T125)\n\nT121 is ground\nT125 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: less(T121, T122), SCOPE: 4, CLAUSE: 7 | less(T121, T122), SCOPE: 4, CLAUSE: 8\n\nT121 is ground\nT122 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: less(T121, T122), SCOPE: 4, CLAUSE: 7\n\nT121 is ground\nT122 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: less(T121, T122), SCOPE: 4, CLAUSE: 8\n\nT121 is ground\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(T140, T141)\n\nT140 is ground\nT141 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: ','(less(T159, T158), delete(T158, T163, T162))\n\nT158 is ground\nT159 is ground\nT162 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: less(T159, T158)\n\nT158 is ground\nT159 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: delete(T158, T163, T162)\n\nT158 is ground\nT162 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: ','(less(T177, T178), delete(T177, T182, T181)) | delete(T177, T2, tree(T178, T181, T180)), SCOPE: 1, CLAUSE: 4\n\nT177 is ground\nT178 is ground\nT181 is ground\nT180 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T177, T2, tree(T178, T181, T180)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: delete(T10, T2, T11), SCOPE: 1, CLAUSE: 4\n\nT10 is ground\nT11 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX172 is free\nX173 is free\nX174 is free\nX175 is free\nX176 is free\ndelete(T10, T2, T11) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T10, T2, T11) !=? delete(X172, tree(X173, X174, X175), tree(X173, X176, X175))", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(less(T177, T178), delete(T177, T182, T181)), SCOPE: 5, CLAUSE: 7 | ','(less(T177, T178), delete(T177, T182, T181)), SCOPE: 5, CLAUSE: 8 | ?_5 | delete(T177, T2, tree(T178, T181, T180)), SCOPE: 1, CLAUSE: 4\n\nT177 is ground\nT178 is ground\nT181 is ground\nT180 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T177, T2, tree(T178, T181, T180)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: ','(less(T177, T178), delete(T177, T182, T181)), SCOPE: 5, CLAUSE: 7\n\nT177 is ground\nT178 is ground\nT181 is ground\nT180 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T177, T2, tree(T178, T181, T180)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: ','(less(T177, T178), delete(T177, T182, T181)), SCOPE: 5, CLAUSE: 8 | ?_5 | delete(T177, T2, tree(T178, T181, T180)), SCOPE: 1, CLAUSE: 4\n\nT177 is ground\nT178 is ground\nT181 is ground\nT180 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T177, T2, tree(T178, T181, T180)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: delete(0, T182, T181)\n\nT181 is ground\nT180 is ground\nT187 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(0, T2, tree(s(T187), T181, T180)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: ','(less(T177, T178), delete(T177, T182, T181)), SCOPE: 5, CLAUSE: 8\n\nT177 is ground\nT178 is ground\nT181 is ground\nT180 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T177, T2, tree(T178, T181, T180)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: ?_5 | delete(T177, T2, tree(T178, T181, T180)), SCOPE: 1, CLAUSE: 4\n\nT177 is ground\nT178 is ground\nT181 is ground\nT180 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T177, T2, tree(T178, T181, T180)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: ','(less(T198, T199), delete(s(T198), T182, T181))\n\nT181 is ground\nT180 is ground\nT198 is ground\nT199 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(s(T198), T2, tree(s(T199), T181, T180)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: less(T198, T199)\n\nT181 is ground\nT180 is ground\nT198 is ground\nT199 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(s(T198), T2, tree(s(T199), T181, T180)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: delete(s(T198), T182, T181)\n\nT181 is ground\nT180 is ground\nT198 is ground\nT199 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(s(T198), T2, tree(s(T199), T181, T180)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: delete(T177, T2, tree(T178, T181, T180)), SCOPE: 1, CLAUSE: 4\n\nT177 is ground\nT178 is ground\nT181 is ground\nT180 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T177, T2, tree(T178, T181, T180)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: ','(less(T219, T218), delete(T218, T223, T222))\n\nT218 is ground\nT219 is ground\nT220 is ground\nT222 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T218, T2, tree(T219, T220, T222)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: ','(less(T232, T231), delete(T231, T236, T235))\n\nT231 is ground\nT232 is ground\nT233 is ground\nT235 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX172 is free\nX173 is free\nX174 is free\nX175 is free\nX176 is free\ndelete(T231, T2, tree(T232, T233, T235)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T231, T2, tree(T232, T233, T235)) !=? delete(X172, tree(X173, X174, X175), tree(X173, X176, X175))", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: ','(less(T232, T231), delete(T231, T236, T235)), SCOPE: 6, CLAUSE: 7 | ','(less(T232, T231), delete(T231, T236, T235)), SCOPE: 6, CLAUSE: 8\n\nT231 is ground\nT232 is ground\nT233 is ground\nT235 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX172 is free\nX173 is free\nX174 is free\nX175 is free\nX176 is free\ndelete(T231, T2, tree(T232, T233, T235)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T231, T2, tree(T232, T233, T235)) !=? delete(X172, tree(X173, X174, X175), tree(X173, X176, X175))", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: ','(less(T232, T231), delete(T231, T236, T235)), SCOPE: 6, CLAUSE: 7\n\nT231 is ground\nT232 is ground\nT233 is ground\nT235 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX172 is free\nX173 is free\nX174 is free\nX175 is free\nX176 is free\ndelete(T231, T2, tree(T232, T233, T235)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T231, T2, tree(T232, T233, T235)) !=? delete(X172, tree(X173, X174, X175), tree(X173, X176, X175))", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: ','(less(T232, T231), delete(T231, T236, T235)), SCOPE: 6, CLAUSE: 8\n\nT231 is ground\nT232 is ground\nT233 is ground\nT235 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX172 is free\nX173 is free\nX174 is free\nX175 is free\nX176 is free\ndelete(T231, T2, tree(T232, T233, T235)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T231, T2, tree(T232, T233, T235)) !=? delete(X172, tree(X173, X174, X175), tree(X173, X176, X175))", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: delete(s(T241), T236, T235)\n\nT233 is ground\nT235 is ground\nT241 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX172 is free\nX173 is free\nX174 is free\nX175 is free\nX176 is free\ndelete(s(T241), T2, tree(0, T233, T235)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(s(T241), T2, tree(0, T233, T235)) !=? delete(X172, tree(X173, X174, X175), tree(X173, X176, X175))", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: ','(less(T250, T251), delete(s(T251), T236, T235))\n\nT233 is ground\nT235 is ground\nT250 is ground\nT251 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX172 is free\nX173 is free\nX174 is free\nX175 is free\nX176 is free\ndelete(s(T251), T2, tree(s(T250), T233, T235)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(s(T251), T2, tree(s(T250), T233, T235)) !=? delete(X172, tree(X173, X174, X175), tree(X173, X176, X175))", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: less(T250, T251)\n\nT233 is ground\nT235 is ground\nT250 is ground\nT251 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX172 is free\nX173 is free\nX174 is free\nX175 is free\nX176 is free\ndelete(s(T251), T2, tree(s(T250), T233, T235)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(s(T251), T2, tree(s(T250), T233, T235)) !=? delete(X172, tree(X173, X174, X175), tree(X173, X176, X175))", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: delete(s(T251), T236, T235)\n\nT233 is ground\nT235 is ground\nT250 is ground\nT251 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX172 is free\nX173 is free\nX174 is free\nX175 is free\nX176 is free\ndelete(s(T251), T2, tree(s(T250), T233, T235)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(s(T251), T2, tree(s(T250), T233, T235)) !=? delete(X172, tree(X173, X174, X175), tree(X173, X176, X175))", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: delmin(T270, T268, T269) | delete(T265, T2, tree(T268, T266, T269)), SCOPE: 1, CLAUSE: 3 | delete(T265, T2, tree(T268, T266, T269)), SCOPE: 1, CLAUSE: 4\n\nT265 is ground\nT268 is ground\nT266 is ground\nT269 is ground\nX10 is free\nX11 is free\ndelete(T265, T2, tree(T268, T266, T269)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: delete(T6, T2, T7), SCOPE: 1, CLAUSE: 3 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\nT7 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\ndelete(T6, T2, T7) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T6, T2, T7) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: delmin(T270, T268, T269), SCOPE: 7, CLAUSE: 5 | delmin(T270, T268, T269), SCOPE: 7, CLAUSE: 6 | ?_7 | delete(T265, T2, tree(T268, T266, T269)), SCOPE: 1, CLAUSE: 3 | delete(T265, T2, tree(T268, T266, T269)), SCOPE: 1, CLAUSE: 4\n\nT265 is ground\nT268 is ground\nT266 is ground\nT269 is ground\nX10 is free\nX11 is free\ndelete(T265, T2, tree(T268, T266, T269)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: delmin(T270, T268, T269), SCOPE: 7, CLAUSE: 5\n\nT265 is ground\nT268 is ground\nT266 is ground\nT269 is ground\nX10 is free\nX11 is free\ndelete(T265, T2, tree(T268, T266, T269)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: delmin(T270, T268, T269), SCOPE: 7, CLAUSE: 6 | ?_7 | delete(T265, T2, tree(T268, T266, T269)), SCOPE: 1, CLAUSE: 3 | delete(T265, T2, tree(T268, T266, T269)), SCOPE: 1, CLAUSE: 4\n\nT265 is ground\nT268 is ground\nT266 is ground\nT269 is ground\nX10 is free\nX11 is free\ndelete(T265, T2, tree(T268, T266, T269)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: delmin(T270, T268, T269), SCOPE: 7, CLAUSE: 6\n\nT265 is ground\nT268 is ground\nT266 is ground\nT269 is ground\nX10 is free\nX11 is free\ndelete(T265, T2, tree(T268, T266, T269)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: ?_7 | delete(T265, T2, tree(T268, T266, T269)), SCOPE: 1, CLAUSE: 3 | delete(T265, T2, tree(T268, T266, T269)), SCOPE: 1, CLAUSE: 4\n\nT265 is ground\nT268 is ground\nT266 is ground\nT269 is ground\nX10 is free\nX11 is free\ndelete(T265, T2, tree(T268, T266, T269)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: delmin(T311, T308, T309)\n\nT265 is ground\nT266 is ground\nT308 is ground\nT305 is ground\nT309 is ground\nT310 is ground\nX10 is free\nX11 is free\ndelete(T265, T2, tree(T308, T266, tree(T305, T309, T310))) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: delete(T265, T2, tree(T268, T266, T269)), SCOPE: 1, CLAUSE: 3 | delete(T265, T2, tree(T268, T266, T269)), SCOPE: 1, CLAUSE: 4\n\nT265 is ground\nT268 is ground\nT266 is ground\nT269 is ground\nX10 is free\nX11 is free\ndelete(T265, T2, tree(T268, T266, T269)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: delete(T265, T2, tree(T268, T266, T269)), SCOPE: 1, CLAUSE: 3\n\nT265 is ground\nT268 is ground\nT266 is ground\nT269 is ground\nX10 is free\nX11 is free\ndelete(T265, T2, tree(T268, T266, T269)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: delete(T265, T2, tree(T268, T266, T269)), SCOPE: 1, CLAUSE: 4\n\nT265 is ground\nT268 is ground\nT266 is ground\nT269 is ground\nX10 is free\nX11 is free\ndelete(T265, T2, tree(T268, T266, T269)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: ','(less(T336, T337), delete(T336, T341, T340))\n\nT336 is ground\nT337 is ground\nT340 is ground\nT339 is ground\nX10 is free\nX11 is free\ndelete(T336, T2, tree(T337, T340, T339)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: ','(less(T355, T354), delete(T354, T359, T358))\n\nT354 is ground\nT355 is ground\nT356 is ground\nT358 is ground\nX10 is free\nX11 is free\ndelete(T354, T2, tree(T355, T356, T358)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: ','(less(T367, T368), delete(T367, T372, T371)) | delete(T367, T2, tree(T368, T371, T370)), SCOPE: 1, CLAUSE: 4\n\nT367 is ground\nT368 is ground\nT371 is ground\nT370 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\ndelete(T367, T2, tree(T368, T371, T370)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T367, T2, tree(T368, T371, T370)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: delete(T6, T2, T7), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\nT7 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\nX357 is free\nX358 is free\nX359 is free\nX360 is free\nX361 is free\ndelete(T6, T2, T7) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T6, T2, T7) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))\ndelete(T6, T2, T7) !=? delete(X357, tree(X358, X359, X360), tree(X358, X361, X360))", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: ','(less(T367, T368), delete(T367, T372, T371)), SCOPE: 8, CLAUSE: 7 | ','(less(T367, T368), delete(T367, T372, T371)), SCOPE: 8, CLAUSE: 8 | ?_8 | delete(T367, T2, tree(T368, T371, T370)), SCOPE: 1, CLAUSE: 4\n\nT367 is ground\nT368 is ground\nT371 is ground\nT370 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\ndelete(T367, T2, tree(T368, T371, T370)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T367, T2, tree(T368, T371, T370)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: ','(less(T367, T368), delete(T367, T372, T371)), SCOPE: 8, CLAUSE: 7\n\nT367 is ground\nT368 is ground\nT371 is ground\nT370 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\ndelete(T367, T2, tree(T368, T371, T370)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T367, T2, tree(T368, T371, T370)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: ','(less(T367, T368), delete(T367, T372, T371)), SCOPE: 8, CLAUSE: 8 | ?_8 | delete(T367, T2, tree(T368, T371, T370)), SCOPE: 1, CLAUSE: 4\n\nT367 is ground\nT368 is ground\nT371 is ground\nT370 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\ndelete(T367, T2, tree(T368, T371, T370)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T367, T2, tree(T368, T371, T370)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: delete(0, T372, T371)\n\nT371 is ground\nT370 is ground\nT377 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\ndelete(0, T2, tree(s(T377), T371, T370)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(0, T2, tree(s(T377), T371, T370)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: ','(less(T367, T368), delete(T367, T372, T371)), SCOPE: 8, CLAUSE: 8\n\nT367 is ground\nT368 is ground\nT371 is ground\nT370 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\ndelete(T367, T2, tree(T368, T371, T370)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T367, T2, tree(T368, T371, T370)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: ?_8 | delete(T367, T2, tree(T368, T371, T370)), SCOPE: 1, CLAUSE: 4\n\nT367 is ground\nT368 is ground\nT371 is ground\nT370 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\ndelete(T367, T2, tree(T368, T371, T370)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T367, T2, tree(T368, T371, T370)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: ','(less(T388, T389), delete(s(T388), T372, T371))\n\nT371 is ground\nT370 is ground\nT388 is ground\nT389 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\ndelete(s(T388), T2, tree(s(T389), T371, T370)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(s(T388), T2, tree(s(T389), T371, T370)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: delete(T367, T2, tree(T368, T371, T370)), SCOPE: 1, CLAUSE: 4\n\nT367 is ground\nT368 is ground\nT371 is ground\nT370 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\ndelete(T367, T2, tree(T368, T371, T370)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T367, T2, tree(T368, T371, T370)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: ','(less(T403, T402), delete(T402, T407, T406))\n\nT402 is ground\nT403 is ground\nT404 is ground\nT406 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\ndelete(T402, T2, tree(T403, T404, T406)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T402, T2, tree(T403, T404, T406)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: ','(less(T416, T415), delete(T415, T420, T419))\n\nT415 is ground\nT416 is ground\nT417 is ground\nT419 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\nX357 is free\nX358 is free\nX359 is free\nX360 is free\nX361 is free\ndelete(T415, T2, tree(T416, T417, T419)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T415, T2, tree(T416, T417, T419)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))\ndelete(T415, T2, tree(T416, T417, T419)) !=? delete(X357, tree(X358, X359, X360), tree(X358, X361, X360))", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: ','(less(T416, T415), delete(T415, T420, T419)), SCOPE: 9, CLAUSE: 7 | ','(less(T416, T415), delete(T415, T420, T419)), SCOPE: 9, CLAUSE: 8\n\nT415 is ground\nT416 is ground\nT417 is ground\nT419 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\nX357 is free\nX358 is free\nX359 is free\nX360 is free\nX361 is free\ndelete(T415, T2, tree(T416, T417, T419)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T415, T2, tree(T416, T417, T419)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))\ndelete(T415, T2, tree(T416, T417, T419)) !=? delete(X357, tree(X358, X359, X360), tree(X358, X361, X360))", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ','(less(T416, T415), delete(T415, T420, T419)), SCOPE: 9, CLAUSE: 7\n\nT415 is ground\nT416 is ground\nT417 is ground\nT419 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\nX357 is free\nX358 is free\nX359 is free\nX360 is free\nX361 is free\ndelete(T415, T2, tree(T416, T417, T419)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T415, T2, tree(T416, T417, T419)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))\ndelete(T415, T2, tree(T416, T417, T419)) !=? delete(X357, tree(X358, X359, X360), tree(X358, X361, X360))", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: ','(less(T416, T415), delete(T415, T420, T419)), SCOPE: 9, CLAUSE: 8\n\nT415 is ground\nT416 is ground\nT417 is ground\nT419 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\nX357 is free\nX358 is free\nX359 is free\nX360 is free\nX361 is free\ndelete(T415, T2, tree(T416, T417, T419)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T415, T2, tree(T416, T417, T419)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))\ndelete(T415, T2, tree(T416, T417, T419)) !=? delete(X357, tree(X358, X359, X360), tree(X358, X361, X360))", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: delete(s(T425), T420, T419)\n\nT417 is ground\nT419 is ground\nT425 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\nX357 is free\nX358 is free\nX359 is free\nX360 is free\nX361 is free\ndelete(s(T425), T2, tree(0, T417, T419)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(s(T425), T2, tree(0, T417, T419)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))\ndelete(s(T425), T2, tree(0, T417, T419)) !=? delete(X357, tree(X358, X359, X360), tree(X358, X361, X360))", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: ','(less(T434, T435), delete(s(T435), T420, T419))\n\nT417 is ground\nT419 is ground\nT434 is ground\nT435 is ground\nX10 is free\nX11 is free\nX259 is free\nX260 is free\nX261 is free\nX262 is free\nX263 is free\nX357 is free\nX358 is free\nX359 is free\nX360 is free\nX361 is free\ndelete(s(T435), T2, tree(s(T434), T417, T419)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(s(T435), T2, tree(s(T434), T417, T419)) !=? delete(X259, tree(X259, X260, X261), tree(X262, X260, X263))\ndelete(s(T435), T2, tree(s(T434), T417, T419)) !=? delete(X357, tree(X358, X359, X360), tree(X358, X361, X360))", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: true | delete(T440, T2, T441), SCOPE: 1, CLAUSE: 2 | delete(T440, T2, T441), SCOPE: 1, CLAUSE: 3 | delete(T440, T2, T441), SCOPE: 1, CLAUSE: 4\n\nT440 is ground\nT441 is ground\nX6 is free\nX7 is free\ndelete(T440, T2, T441) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: 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\nT1 is ground\nT3 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X429, tree(X429, X430, void), X430)", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: delete(T440, T2, T441), SCOPE: 1, CLAUSE: 2 | delete(T440, T2, T441), SCOPE: 1, CLAUSE: 3 | delete(T440, T2, T441), SCOPE: 1, CLAUSE: 4\n\nT440 is ground\nT441 is ground\nX6 is free\nX7 is free\ndelete(T440, T2, T441) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: delmin(T452, T450, T451) | delete(T447, T2, tree(T450, T448, T451)), SCOPE: 1, CLAUSE: 3 | delete(T447, T2, tree(T450, T448, T451)), SCOPE: 1, CLAUSE: 4\n\nT447 is ground\nT450 is ground\nT448 is ground\nT451 is ground\nX6 is free\nX7 is free\ndelete(T447, T2, tree(T450, T448, T451)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: delete(T440, T2, T441), SCOPE: 1, CLAUSE: 3 | delete(T440, T2, T441), SCOPE: 1, CLAUSE: 4\n\nT440 is ground\nT441 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\ndelete(T440, T2, T441) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T440, T2, T441) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: delmin(T452, T450, T451), SCOPE: 10, CLAUSE: 5 | delmin(T452, T450, T451), SCOPE: 10, CLAUSE: 6 | ?_10 | delete(T447, T2, tree(T450, T448, T451)), SCOPE: 1, CLAUSE: 3 | delete(T447, T2, tree(T450, T448, T451)), SCOPE: 1, CLAUSE: 4\n\nT447 is ground\nT450 is ground\nT448 is ground\nT451 is ground\nX6 is free\nX7 is free\ndelete(T447, T2, tree(T450, T448, T451)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: delmin(T452, T450, T451), SCOPE: 10, CLAUSE: 5\n\nT447 is ground\nT450 is ground\nT448 is ground\nT451 is ground\nX6 is free\nX7 is free\ndelete(T447, T2, tree(T450, T448, T451)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: delmin(T452, T450, T451), SCOPE: 10, CLAUSE: 6 | ?_10 | delete(T447, T2, tree(T450, T448, T451)), SCOPE: 1, CLAUSE: 3 | delete(T447, T2, tree(T450, T448, T451)), SCOPE: 1, CLAUSE: 4\n\nT447 is ground\nT450 is ground\nT448 is ground\nT451 is ground\nX6 is free\nX7 is free\ndelete(T447, T2, tree(T450, T448, T451)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: delmin(T452, T450, T451), SCOPE: 10, CLAUSE: 6\n\nT447 is ground\nT450 is ground\nT448 is ground\nT451 is ground\nX6 is free\nX7 is free\ndelete(T447, T2, tree(T450, T448, T451)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: ?_10 | delete(T447, T2, tree(T450, T448, T451)), SCOPE: 1, CLAUSE: 3 | delete(T447, T2, tree(T450, T448, T451)), SCOPE: 1, CLAUSE: 4\n\nT447 is ground\nT450 is ground\nT448 is ground\nT451 is ground\nX6 is free\nX7 is free\ndelete(T447, T2, tree(T450, T448, T451)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: delmin(T493, T490, T491)\n\nT447 is ground\nT448 is ground\nT490 is ground\nT487 is ground\nT491 is ground\nT492 is ground\nX6 is free\nX7 is free\ndelete(T447, T2, tree(T490, T448, tree(T487, T491, T492))) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: delete(T447, T2, tree(T450, T448, T451)), SCOPE: 1, CLAUSE: 3 | delete(T447, T2, tree(T450, T448, T451)), SCOPE: 1, CLAUSE: 4\n\nT447 is ground\nT450 is ground\nT448 is ground\nT451 is ground\nX6 is free\nX7 is free\ndelete(T447, T2, tree(T450, T448, T451)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: delete(T447, T2, tree(T450, T448, T451)), SCOPE: 1, CLAUSE: 3\n\nT447 is ground\nT450 is ground\nT448 is ground\nT451 is ground\nX6 is free\nX7 is free\ndelete(T447, T2, tree(T450, T448, T451)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: delete(T447, T2, tree(T450, T448, T451)), SCOPE: 1, CLAUSE: 4\n\nT447 is ground\nT450 is ground\nT448 is ground\nT451 is ground\nX6 is free\nX7 is free\ndelete(T447, T2, tree(T450, T448, T451)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: ','(less(T518, T519), delete(T518, T523, T522))\n\nT518 is ground\nT519 is ground\nT522 is ground\nT521 is ground\nX6 is free\nX7 is free\ndelete(T518, T2, tree(T519, T522, T521)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: ','(less(T537, T536), delete(T536, T541, T540))\n\nT536 is ground\nT537 is ground\nT538 is ground\nT540 is ground\nX6 is free\nX7 is free\ndelete(T536, T2, tree(T537, T538, T540)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: ','(less(T549, T550), delete(T549, T554, T553)) | delete(T549, T2, tree(T550, T553, T552)), SCOPE: 1, CLAUSE: 4\n\nT549 is ground\nT550 is ground\nT553 is ground\nT552 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\ndelete(T549, T2, tree(T550, T553, T552)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T549, T2, tree(T550, T553, T552)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: delete(T440, T2, T441), SCOPE: 1, CLAUSE: 4\n\nT440 is ground\nT441 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\nX534 is free\nX535 is free\nX536 is free\nX537 is free\nX538 is free\ndelete(T440, T2, T441) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T440, T2, T441) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))\ndelete(T440, T2, T441) !=? delete(X534, tree(X535, X536, X537), tree(X535, X538, X537))", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: ','(less(T549, T550), delete(T549, T554, T553)), SCOPE: 11, CLAUSE: 7 | ','(less(T549, T550), delete(T549, T554, T553)), SCOPE: 11, CLAUSE: 8 | ?_11 | delete(T549, T2, tree(T550, T553, T552)), SCOPE: 1, CLAUSE: 4\n\nT549 is ground\nT550 is ground\nT553 is ground\nT552 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\ndelete(T549, T2, tree(T550, T553, T552)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T549, T2, tree(T550, T553, T552)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: ','(less(T549, T550), delete(T549, T554, T553)), SCOPE: 11, CLAUSE: 7\n\nT549 is ground\nT550 is ground\nT553 is ground\nT552 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\ndelete(T549, T2, tree(T550, T553, T552)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T549, T2, tree(T550, T553, T552)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: ','(less(T549, T550), delete(T549, T554, T553)), SCOPE: 11, CLAUSE: 8 | ?_11 | delete(T549, T2, tree(T550, T553, T552)), SCOPE: 1, CLAUSE: 4\n\nT549 is ground\nT550 is ground\nT553 is ground\nT552 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\ndelete(T549, T2, tree(T550, T553, T552)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T549, T2, tree(T550, T553, T552)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: delete(0, T554, T553)\n\nT553 is ground\nT552 is ground\nT559 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\ndelete(0, T2, tree(s(T559), T553, T552)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(0, T2, tree(s(T559), T553, T552)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: ','(less(T549, T550), delete(T549, T554, T553)), SCOPE: 11, CLAUSE: 8\n\nT549 is ground\nT550 is ground\nT553 is ground\nT552 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\ndelete(T549, T2, tree(T550, T553, T552)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T549, T2, tree(T550, T553, T552)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: ?_11 | delete(T549, T2, tree(T550, T553, T552)), SCOPE: 1, CLAUSE: 4\n\nT549 is ground\nT550 is ground\nT553 is ground\nT552 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\ndelete(T549, T2, tree(T550, T553, T552)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T549, T2, tree(T550, T553, T552)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: ','(less(T570, T571), delete(s(T570), T554, T553))\n\nT553 is ground\nT552 is ground\nT570 is ground\nT571 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\ndelete(s(T570), T2, tree(s(T571), T553, T552)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T570), T2, tree(s(T571), T553, T552)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: delete(T549, T2, tree(T550, T553, T552)), SCOPE: 1, CLAUSE: 4\n\nT549 is ground\nT550 is ground\nT553 is ground\nT552 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\ndelete(T549, T2, tree(T550, T553, T552)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T549, T2, tree(T550, T553, T552)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: ','(less(T585, T584), delete(T584, T589, T588))\n\nT584 is ground\nT585 is ground\nT586 is ground\nT588 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\ndelete(T584, T2, tree(T585, T586, T588)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T584, T2, tree(T585, T586, T588)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: ','(less(T598, T597), delete(T597, T602, T601))\n\nT597 is ground\nT598 is ground\nT599 is ground\nT601 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\nX534 is free\nX535 is free\nX536 is free\nX537 is free\nX538 is free\ndelete(T597, T2, tree(T598, T599, T601)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T597, T2, tree(T598, T599, T601)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))\ndelete(T597, T2, tree(T598, T599, T601)) !=? delete(X534, tree(X535, X536, X537), tree(X535, X538, X537))", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: ','(less(T598, T597), delete(T597, T602, T601)), SCOPE: 12, CLAUSE: 7 | ','(less(T598, T597), delete(T597, T602, T601)), SCOPE: 12, CLAUSE: 8\n\nT597 is ground\nT598 is ground\nT599 is ground\nT601 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\nX534 is free\nX535 is free\nX536 is free\nX537 is free\nX538 is free\ndelete(T597, T2, tree(T598, T599, T601)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T597, T2, tree(T598, T599, T601)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))\ndelete(T597, T2, tree(T598, T599, T601)) !=? delete(X534, tree(X535, X536, X537), tree(X535, X538, X537))", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: ','(less(T598, T597), delete(T597, T602, T601)), SCOPE: 12, CLAUSE: 7\n\nT597 is ground\nT598 is ground\nT599 is ground\nT601 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\nX534 is free\nX535 is free\nX536 is free\nX537 is free\nX538 is free\ndelete(T597, T2, tree(T598, T599, T601)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T597, T2, tree(T598, T599, T601)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))\ndelete(T597, T2, tree(T598, T599, T601)) !=? delete(X534, tree(X535, X536, X537), tree(X535, X538, X537))", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: ','(less(T598, T597), delete(T597, T602, T601)), SCOPE: 12, CLAUSE: 8\n\nT597 is ground\nT598 is ground\nT599 is ground\nT601 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\nX534 is free\nX535 is free\nX536 is free\nX537 is free\nX538 is free\ndelete(T597, T2, tree(T598, T599, T601)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T597, T2, tree(T598, T599, T601)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))\ndelete(T597, T2, tree(T598, T599, T601)) !=? delete(X534, tree(X535, X536, X537), tree(X535, X538, X537))", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: delete(s(T607), T602, T601)\n\nT599 is ground\nT601 is ground\nT607 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\nX534 is free\nX535 is free\nX536 is free\nX537 is free\nX538 is free\ndelete(s(T607), T2, tree(0, T599, T601)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T607), T2, tree(0, T599, T601)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))\ndelete(s(T607), T2, tree(0, T599, T601)) !=? delete(X534, tree(X535, X536, X537), tree(X535, X538, X537))", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: ','(less(T616, T617), delete(s(T617), T602, T601))\n\nT599 is ground\nT601 is ground\nT616 is ground\nT617 is ground\nX6 is free\nX7 is free\nX436 is free\nX437 is free\nX438 is free\nX439 is free\nX440 is free\nX534 is free\nX535 is free\nX536 is free\nX537 is free\nX538 is free\ndelete(s(T617), T2, tree(s(T616), T599, T601)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T617), T2, tree(s(T616), T599, T601)) !=? delete(X436, tree(X436, X437, X438), tree(X439, X437, X440))\ndelete(s(T617), T2, tree(s(T616), T599, T601)) !=? delete(X534, tree(X535, X536, X537), tree(X535, X538, X537))", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: delmin(T630, T628, T629) | delete(T625, T2, tree(T628, T626, T629)), SCOPE: 1, CLAUSE: 3 | delete(T625, T2, tree(T628, T626, T629)), SCOPE: 1, CLAUSE: 4\n\nT625 is ground\nT628 is ground\nT626 is ground\nT629 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X429, tree(X429, X430, void), X430)", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT3 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(T1, T2, T3) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: delmin(T630, T628, T629), SCOPE: 13, CLAUSE: 5 | delmin(T630, T628, T629), SCOPE: 13, CLAUSE: 6 | ?_13 | delete(T625, T2, tree(T628, T626, T629)), SCOPE: 1, CLAUSE: 3 | delete(T625, T2, tree(T628, T626, T629)), SCOPE: 1, CLAUSE: 4\n\nT625 is ground\nT628 is ground\nT626 is ground\nT629 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X429, tree(X429, X430, void), X430)", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: delmin(T630, T628, T629), SCOPE: 13, CLAUSE: 5\n\nT625 is ground\nT628 is ground\nT626 is ground\nT629 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X429, tree(X429, X430, void), X430)", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: delmin(T630, T628, T629), SCOPE: 13, CLAUSE: 6 | ?_13 | delete(T625, T2, tree(T628, T626, T629)), SCOPE: 1, CLAUSE: 3 | delete(T625, T2, tree(T628, T626, T629)), SCOPE: 1, CLAUSE: 4\n\nT625 is ground\nT628 is ground\nT626 is ground\nT629 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X429, tree(X429, X430, void), X430)", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: delmin(T630, T628, T629), SCOPE: 13, CLAUSE: 6\n\nT625 is ground\nT628 is ground\nT626 is ground\nT629 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X429, tree(X429, X430, void), X430)", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: ?_13 | delete(T625, T2, tree(T628, T626, T629)), SCOPE: 1, CLAUSE: 3 | delete(T625, T2, tree(T628, T626, T629)), SCOPE: 1, CLAUSE: 4\n\nT625 is ground\nT628 is ground\nT626 is ground\nT629 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X429, tree(X429, X430, void), X430)", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: delmin(T671, T668, T669)\n\nT625 is ground\nT626 is ground\nT668 is ground\nT665 is ground\nT669 is ground\nT670 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\ndelete(T625, T2, tree(T668, T626, tree(T665, T669, T670))) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T625, T2, tree(T668, T626, tree(T665, T669, T670))) !=? delete(X429, tree(X429, X430, void), X430)", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: delete(T625, T2, tree(T628, T626, T629)), SCOPE: 1, CLAUSE: 3 | delete(T625, T2, tree(T628, T626, T629)), SCOPE: 1, CLAUSE: 4\n\nT625 is ground\nT628 is ground\nT626 is ground\nT629 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X429, tree(X429, X430, void), X430)", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: delete(T625, T2, tree(T628, T626, T629)), SCOPE: 1, CLAUSE: 3\n\nT625 is ground\nT628 is ground\nT626 is ground\nT629 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X429, tree(X429, X430, void), X430)", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: delete(T625, T2, tree(T628, T626, T629)), SCOPE: 1, CLAUSE: 4\n\nT625 is ground\nT628 is ground\nT626 is ground\nT629 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T625, T2, tree(T628, T626, T629)) !=? delete(X429, tree(X429, X430, void), X430)", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: ','(less(T696, T697), delete(T696, T701, T700))\n\nT696 is ground\nT697 is ground\nT700 is ground\nT699 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\ndelete(T696, T2, tree(T697, T700, T699)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T696, T2, tree(T697, T700, T699)) !=? delete(X429, tree(X429, X430, void), X430)", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: ','(less(T715, T714), delete(T714, T719, T718))\n\nT714 is ground\nT715 is ground\nT716 is ground\nT718 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\ndelete(T714, T2, tree(T715, T716, T718)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T714, T2, tree(T715, T716, T718)) !=? delete(X429, tree(X429, X430, void), X430)", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: ','(less(T727, T728), delete(T727, T732, T731)) | delete(T727, T2, tree(T728, T731, T730)), SCOPE: 1, CLAUSE: 4\n\nT727 is ground\nT728 is ground\nT731 is ground\nT730 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT3 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\nX707 is free\nX708 is free\nX709 is free\nX710 is free\nX711 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(T1, T2, T3) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))\ndelete(T1, T2, T3) !=? delete(X707, tree(X708, X709, X710), tree(X708, X711, X710))", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: ','(less(T727, T728), delete(T727, T732, T731)), SCOPE: 14, CLAUSE: 7 | ','(less(T727, T728), delete(T727, T732, T731)), SCOPE: 14, CLAUSE: 8 | ?_14 | delete(T727, T2, tree(T728, T731, T730)), SCOPE: 1, CLAUSE: 4\n\nT727 is ground\nT728 is ground\nT731 is ground\nT730 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: ','(less(T727, T728), delete(T727, T732, T731)), SCOPE: 14, CLAUSE: 7\n\nT727 is ground\nT728 is ground\nT731 is ground\nT730 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: ','(less(T727, T728), delete(T727, T732, T731)), SCOPE: 14, CLAUSE: 8 | ?_14 | delete(T727, T2, tree(T728, T731, T730)), SCOPE: 1, CLAUSE: 4\n\nT727 is ground\nT728 is ground\nT731 is ground\nT730 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: delete(0, T732, T731)\n\nT731 is ground\nT730 is ground\nT737 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\ndelete(0, T2, tree(s(T737), T731, T730)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(0, T2, tree(s(T737), T731, T730)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(0, T2, tree(s(T737), T731, T730)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: ','(less(T727, T728), delete(T727, T732, T731)), SCOPE: 14, CLAUSE: 8\n\nT727 is ground\nT728 is ground\nT731 is ground\nT730 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: ?_14 | delete(T727, T2, tree(T728, T731, T730)), SCOPE: 1, CLAUSE: 4\n\nT727 is ground\nT728 is ground\nT731 is ground\nT730 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: ','(less(T748, T749), delete(s(T748), T732, T731))\n\nT731 is ground\nT730 is ground\nT748 is ground\nT749 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\ndelete(s(T748), T2, tree(s(T749), T731, T730)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T748), T2, tree(s(T749), T731, T730)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(s(T748), T2, tree(s(T749), T731, T730)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: delete(T727, T2, tree(T728, T731, T730)), SCOPE: 1, CLAUSE: 4\n\nT727 is ground\nT728 is ground\nT731 is ground\nT730 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(T727, T2, tree(T728, T731, T730)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: ','(less(T763, T762), delete(T762, T767, T766))\n\nT762 is ground\nT763 is ground\nT764 is ground\nT766 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\ndelete(T762, T2, tree(T763, T764, T766)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T762, T2, tree(T763, T764, T766)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(T762, T2, tree(T763, T764, T766)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: ','(less(T776, T775), delete(T775, T780, T779))\n\nT775 is ground\nT776 is ground\nT777 is ground\nT779 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\nX707 is free\nX708 is free\nX709 is free\nX710 is free\nX711 is free\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X707, tree(X708, X709, X710), tree(X708, X711, X710))", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: ','(less(T776, T775), delete(T775, T780, T779)), SCOPE: 15, CLAUSE: 7 | ','(less(T776, T775), delete(T775, T780, T779)), SCOPE: 15, CLAUSE: 8\n\nT775 is ground\nT776 is ground\nT777 is ground\nT779 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\nX707 is free\nX708 is free\nX709 is free\nX710 is free\nX711 is free\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X707, tree(X708, X709, X710), tree(X708, X711, X710))", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: ','(less(T776, T775), delete(T775, T780, T779)), SCOPE: 15, CLAUSE: 7\n\nT775 is ground\nT776 is ground\nT777 is ground\nT779 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\nX707 is free\nX708 is free\nX709 is free\nX710 is free\nX711 is free\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X707, tree(X708, X709, X710), tree(X708, X711, X710))", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: ','(less(T776, T775), delete(T775, T780, T779)), SCOPE: 15, CLAUSE: 8\n\nT775 is ground\nT776 is ground\nT777 is ground\nT779 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\nX707 is free\nX708 is free\nX709 is free\nX710 is free\nX711 is free\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))\ndelete(T775, T2, tree(T776, T777, T779)) !=? delete(X707, tree(X708, X709, X710), tree(X708, X711, X710))", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: delete(s(T785), T780, T779)\n\nT777 is ground\nT779 is ground\nT785 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\nX707 is free\nX708 is free\nX709 is free\nX710 is free\nX711 is free\ndelete(s(T785), T2, tree(0, T777, T779)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T785), T2, tree(0, T777, T779)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(s(T785), T2, tree(0, T777, T779)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))\ndelete(s(T785), T2, tree(0, T777, T779)) !=? delete(X707, tree(X708, X709, X710), tree(X708, X711, X710))", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: ','(less(T794, T795), delete(s(T795), T780, T779))\n\nT777 is ground\nT779 is ground\nT794 is ground\nT795 is ground\nX6 is free\nX7 is free\nX429 is free\nX430 is free\nX609 is free\nX610 is free\nX611 is free\nX612 is free\nX613 is free\nX707 is free\nX708 is free\nX709 is free\nX710 is free\nX711 is free\ndelete(s(T795), T2, tree(s(T794), T777, T779)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T795), T2, tree(s(T794), T777, T779)) !=? delete(X429, tree(X429, X430, void), X430)\ndelete(s(T795), T2, tree(s(T794), T777, T779)) !=? delete(X609, tree(X609, X610, X611), tree(X612, X610, X613))\ndelete(s(T795), T2, tree(s(T794), T777, T779)) !=? delete(X707, tree(X708, X709, X710), tree(X708, X711, X710))", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 204 [arrowhead = none ];
204 -> 2;

205 [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 -> 205 [arrowhead = none ];
205 -> 3;

206 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2 -> 206 [arrowhead = none ];
206 -> 4;

207 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 207 [arrowhead = none ];
207 -> 5;

208 [label="EVAL with clause\ndelete(X429, tree(X429, X430, void), X430).\nand substitutionT1 -> T440,\nX429 -> T440,\nX430 -> T441,\nT2 -> tree(T440, T441, void),\nT3 -> T441", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 208 [arrowhead = none ];
208 -> 117;

209 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 209 [arrowhead = none ];
209 -> 118;

210 [label="EVAL with clause\ndelete(X10, tree(X10, X11, void), X11).\nand substitutionT6 -> T10,\nX10 -> T10,\nX11 -> T11,\nT2 -> tree(T10, T11, void),\nT7 -> T11", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 210 [arrowhead = none ];
210 -> 6;

211 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 211 [arrowhead = none ];
211 -> 7;

212 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 212 [arrowhead = none ];
212 -> 8;

213 [label="EVAL with clause\ndelete(X259, tree(X259, X260, X261), tree(X262, X260, X263)) :- delmin(X261, X262, X263).\nand substitutionT6 -> T265,\nX259 -> T265,\nX260 -> T266,\nX261 -> T270,\nT2 -> tree(T265, T266, T270),\nX262 -> T268,\nX263 -> T269,\nT7 -> tree(T268, T266, T269),\nT267 -> T270", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 213 [arrowhead = none ];
213 -> 75;

214 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 214 [arrowhead = none ];
214 -> 76;

215 [label="EVAL with clause\ndelete(X17, tree(X17, X18, X19), tree(X20, X18, X21)) :- delmin(X19, X20, X21).\nand substitutionT10 -> 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 -> 215 [arrowhead = none ];
215 -> 9;

216 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 216 [arrowhead = none ];
216 -> 10;

217 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 217 [arrowhead = none ];
217 -> 11;

218 [label="EVAL with clause\ndelete(X172, tree(X173, X174, X175), tree(X173, X176, X175)) :- ','(less(X172, X173), delete(X172, X174, X176)).\nand substitutionT10 -> T177,\nX172 -> T177,\nX173 -> T178,\nX174 -> T182,\nX175 -> T180,\nT2 -> tree(T178, T182, T180),\nX176 -> T181,\nT11 -> tree(T178, T181, T180),\nT179 -> T182", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 218 [arrowhead = none ];
218 -> 48;

219 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
10 -> 219 [arrowhead = none ];
219 -> 49;

220 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 220 [arrowhead = none ];
220 -> 12;

221 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 221 [arrowhead = none ];
221 -> 13;

222 [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 -> 222 [arrowhead = none ];
222 -> 14;

223 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 223 [arrowhead = none ];
223 -> 15;

224 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 224 [arrowhead = none ];
224 -> 17;

225 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 225 [arrowhead = none ];
225 -> 18;

226 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
14 -> 226 [arrowhead = none ];
226 -> 16;

227 [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 -> 227 [arrowhead = none ];
227 -> 19;

228 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 228 [arrowhead = none ];
228 -> 20;

229 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
18 -> 229 [arrowhead = none ];
229 -> 29;

230 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
19 -> 230 [arrowhead = none ];
230 -> 21;

231 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 231 [arrowhead = none ];
231 -> 22;

232 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 232 [arrowhead = none ];
232 -> 23;

233 [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 -> 233 [arrowhead = none ];
233 -> 24;

234 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
22 -> 234 [arrowhead = none ];
234 -> 25;

235 [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 -> 235 [arrowhead = none ];
235 -> 27;

236 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
23 -> 236 [arrowhead = none ];
236 -> 28;

237 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
24 -> 237 [arrowhead = none ];
237 -> 26;

238 [label="INSTANCE with matching:\nT63 -> T96\nT60 -> T93\nT61 -> T94", fontsize=14, style = filled, fillcolor = lightgrey];
27 -> 238 [arrowhead = none , style=dashed];
238 -> 19[style=dashed];

239 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
29 -> 239 [arrowhead = none ];
239 -> 30;

240 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
29 -> 240 [arrowhead = none ];
240 -> 31;

241 [label="EVAL with clause\ndelete(X118, tree(X119, X120, X121), tree(X119, X122, X121)) :- ','(less(X118, X119), delete(X118, X120, X122)).\nand substitutionT17 -> T121,\nX118 -> T121,\nX119 -> T122,\nX120 -> T126,\nX121 -> T124,\nT2 -> tree(T122, T126, T124),\nT20 -> T122,\nT18 -> T125,\nX122 -> T125,\nT21 -> T124,\nT123 -> T126", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 241 [arrowhead = none ];
241 -> 32;

242 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 242 [arrowhead = none ];
242 -> 33;

243 [label="EVAL with clause\ndelete(X154, tree(X155, X156, X157), tree(X155, X156, X158)) :- ','(less(X155, X154), delete(X154, X157, X158)).\nand substitutionT17 -> T158,\nX154 -> T158,\nX155 -> T159,\nX156 -> T160,\nX157 -> T163,\nT2 -> tree(T159, T160, T163),\nT20 -> T159,\nT18 -> T160,\nT21 -> T162,\nX158 -> T162,\nT161 -> T163", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 243 [arrowhead = none ];
243 -> 44;

244 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
31 -> 244 [arrowhead = none ];
244 -> 45;

245 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
32 -> 245 [arrowhead = none ];
245 -> 34;

246 [label="SPLIT 2\nnew knowledge:\nT121 is ground\nT122 is ground", fontsize=14, style = filled, fillcolor = violet];
32 -> 246 [arrowhead = none ];
246 -> 35;

247 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
34 -> 247 [arrowhead = none ];
247 -> 36;

248 [label="INSTANCE with matching:\nT1 -> T121\nT2 -> T126\nT3 -> T125", fontsize=14, style = filled, fillcolor = lightgrey];
35 -> 248 [arrowhead = none , style=dashed];
248 -> 1[style=dashed];

249 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
36 -> 249 [arrowhead = none ];
249 -> 37;

250 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
36 -> 250 [arrowhead = none ];
250 -> 38;

251 [label="EVAL with clause\nless(0, s(X131)).\nand substitutionT121 -> 0,\nX131 -> T135,\nT122 -> s(T135)", fontsize=14, style = filled, fillcolor = lightblue];
37 -> 251 [arrowhead = none ];
251 -> 39;

252 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
37 -> 252 [arrowhead = none ];
252 -> 40;

253 [label="EVAL with clause\nless(s(X136), s(X137)) :- less(X136, X137).\nand substitutionX136 -> T140,\nT121 -> s(T140),\nX137 -> T141,\nT122 -> s(T141)", fontsize=14, style = filled, fillcolor = lightblue];
38 -> 253 [arrowhead = none ];
253 -> 42;

254 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
38 -> 254 [arrowhead = none ];
254 -> 43;

255 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
39 -> 255 [arrowhead = none ];
255 -> 41;

256 [label="INSTANCE with matching:\nT121 -> T140\nT122 -> T141", fontsize=14, style = filled, fillcolor = lightgrey];
42 -> 256 [arrowhead = none , style=dashed];
256 -> 34[style=dashed];

257 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
44 -> 257 [arrowhead = none ];
257 -> 46;

258 [label="SPLIT 2\nnew knowledge:\nT159 is ground\nT158 is ground", fontsize=14, style = filled, fillcolor = violet];
44 -> 258 [arrowhead = none ];
258 -> 47;

259 [label="INSTANCE with matching:\nT121 -> T159\nT122 -> T158", fontsize=14, style = filled, fillcolor = lightgrey];
46 -> 259 [arrowhead = none , style=dashed];
259 -> 34[style=dashed];

260 [label="INSTANCE with matching:\nT1 -> T158\nT2 -> T163\nT3 -> T162", fontsize=14, style = filled, fillcolor = lightgrey];
47 -> 260 [arrowhead = none , style=dashed];
260 -> 1[style=dashed];

261 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
48 -> 261 [arrowhead = none ];
261 -> 50;

262 [label="EVAL with clause\ndelete(X226, tree(X227, X228, X229), tree(X227, X228, X230)) :- ','(less(X227, X226), delete(X226, X229, X230)).\nand substitutionT10 -> T231,\nX226 -> T231,\nX227 -> T232,\nX228 -> T233,\nX229 -> T236,\nT2 -> tree(T232, T233, T236),\nX230 -> T235,\nT11 -> tree(T232, T233, T235),\nT234 -> T236", fontsize=14, style = filled, fillcolor = lightblue];
49 -> 262 [arrowhead = none ];
262 -> 64;

263 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
49 -> 263 [arrowhead = none ];
263 -> 65;

264 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
50 -> 264 [arrowhead = none ];
264 -> 51;

265 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
50 -> 265 [arrowhead = none ];
265 -> 52;

266 [label="EVAL with clause\nless(0, s(X181)).\nand substitutionT177 -> 0,\nX181 -> T187,\nT178 -> s(T187)", fontsize=14, style = filled, fillcolor = lightblue];
51 -> 266 [arrowhead = none ];
266 -> 53;

267 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
51 -> 267 [arrowhead = none ];
267 -> 54;

268 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
52 -> 268 [arrowhead = none ];
268 -> 55;

269 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
52 -> 269 [arrowhead = none ];
269 -> 56;

270 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T182\nT3 -> T181", fontsize=14, style = filled, fillcolor = lightgrey];
53 -> 270 [arrowhead = none , style=dashed];
270 -> 1[style=dashed];

271 [label="EVAL with clause\nless(s(X194), s(X195)) :- less(X194, X195).\nand substitutionX194 -> T198,\nT177 -> s(T198),\nX195 -> T199,\nT178 -> s(T199)", fontsize=14, style = filled, fillcolor = lightblue];
55 -> 271 [arrowhead = none ];
271 -> 57;

272 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
55 -> 272 [arrowhead = none ];
272 -> 58;

273 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
56 -> 273 [arrowhead = none ];
273 -> 61;

274 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
57 -> 274 [arrowhead = none ];
274 -> 59;

275 [label="SPLIT 2\nnew knowledge:\nT198 is ground\nT199 is ground", fontsize=14, style = filled, fillcolor = violet];
57 -> 275 [arrowhead = none ];
275 -> 60;

276 [label="INSTANCE with matching:\nT121 -> T198\nT122 -> T199", fontsize=14, style = filled, fillcolor = lightgrey];
59 -> 276 [arrowhead = none , style=dashed];
276 -> 34[style=dashed];

277 [label="INSTANCE with matching:\nT1 -> s(T198)\nT2 -> T182\nT3 -> T181", fontsize=14, style = filled, fillcolor = lightgrey];
60 -> 277 [arrowhead = none , style=dashed];
277 -> 1[style=dashed];

278 [label="EVAL with clause\ndelete(X214, tree(X215, X216, X217), tree(X215, X216, X218)) :- ','(less(X215, X214), delete(X214, X217, X218)).\nand substitutionT177 -> T218,\nX214 -> T218,\nX215 -> T219,\nX216 -> T220,\nX217 -> T223,\nT2 -> tree(T219, T220, T223),\nT178 -> T219,\nT181 -> T220,\nT180 -> T222,\nX218 -> T222,\nT221 -> T223", fontsize=14, style = filled, fillcolor = lightblue];
61 -> 278 [arrowhead = none ];
278 -> 62;

279 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
61 -> 279 [arrowhead = none ];
279 -> 63;

280 [label="INSTANCE with matching:\nT159 -> T219\nT158 -> T218\nT163 -> T223\nT162 -> T222", fontsize=14, style = filled, fillcolor = lightgrey];
62 -> 280 [arrowhead = none , style=dashed];
280 -> 44[style=dashed];

281 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
64 -> 281 [arrowhead = none ];
281 -> 66;

282 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
66 -> 282 [arrowhead = none ];
282 -> 67;

283 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
66 -> 283 [arrowhead = none ];
283 -> 68;

284 [label="EVAL with clause\nless(0, s(X235)).\nand substitutionT232 -> 0,\nX235 -> T241,\nT231 -> s(T241)", fontsize=14, style = filled, fillcolor = lightblue];
67 -> 284 [arrowhead = none ];
284 -> 69;

285 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
67 -> 285 [arrowhead = none ];
285 -> 70;

286 [label="EVAL with clause\nless(s(X244), s(X245)) :- less(X244, X245).\nand substitutionX244 -> T250,\nT232 -> s(T250),\nX245 -> T251,\nT231 -> s(T251)", fontsize=14, style = filled, fillcolor = lightblue];
68 -> 286 [arrowhead = none ];
286 -> 71;

287 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
68 -> 287 [arrowhead = none ];
287 -> 72;

288 [label="INSTANCE with matching:\nT1 -> s(T241)\nT2 -> T236\nT3 -> T235", fontsize=14, style = filled, fillcolor = lightgrey];
69 -> 288 [arrowhead = none , style=dashed];
288 -> 1[style=dashed];

289 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
71 -> 289 [arrowhead = none ];
289 -> 73;

290 [label="SPLIT 2\nnew knowledge:\nT250 is ground\nT251 is ground", fontsize=14, style = filled, fillcolor = violet];
71 -> 290 [arrowhead = none ];
290 -> 74;

291 [label="INSTANCE with matching:\nT121 -> T250\nT122 -> T251", fontsize=14, style = filled, fillcolor = lightgrey];
73 -> 291 [arrowhead = none , style=dashed];
291 -> 34[style=dashed];

292 [label="INSTANCE with matching:\nT1 -> s(T251)\nT2 -> T236\nT3 -> T235", fontsize=14, style = filled, fillcolor = lightgrey];
74 -> 292 [arrowhead = none , style=dashed];
292 -> 1[style=dashed];

293 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
75 -> 293 [arrowhead = none ];
293 -> 77;

294 [label="EVAL with clause\ndelete(X357, tree(X358, X359, X360), tree(X358, X361, X360)) :- ','(less(X357, X358), delete(X357, X359, X361)).\nand substitutionT6 -> T367,\nX357 -> T367,\nX358 -> T368,\nX359 -> T372,\nX360 -> T370,\nT2 -> tree(T368, T372, T370),\nX361 -> T371,\nT7 -> tree(T368, T371, T370),\nT369 -> T372", fontsize=14, style = filled, fillcolor = lightblue];
76 -> 294 [arrowhead = none ];
294 -> 94;

295 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
76 -> 295 [arrowhead = none ];
295 -> 95;

296 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
77 -> 296 [arrowhead = none ];
296 -> 78;

297 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
77 -> 297 [arrowhead = none ];
297 -> 79;

298 [label="EVAL with clause\ndelmin(tree(X272, void, X273), X272, X273).\nand substitutionX272 -> T279,\nX273 -> T280,\nT270 -> tree(T279, void, T280),\nT268 -> T279,\nT269 -> T280", fontsize=14, style = filled, fillcolor = lightblue];
78 -> 298 [arrowhead = none ];
298 -> 80;

299 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
78 -> 299 [arrowhead = none ];
299 -> 81;

300 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
79 -> 300 [arrowhead = none ];
300 -> 83;

301 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
79 -> 301 [arrowhead = none ];
301 -> 84;

302 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
80 -> 302 [arrowhead = none ];
302 -> 82;

303 [label="EVAL with clause\ndelmin(tree(X298, X299, X300), X301, tree(X298, X302, X303)) :- delmin(X299, X301, X302).\nand substitutionX298 -> T305,\nX299 -> T311,\nX300 -> T307,\nT270 -> tree(T305, T311, T307),\nT268 -> T308,\nX301 -> T308,\nX302 -> T309,\nX303 -> T310,\nT269 -> tree(T305, T309, T310),\nT306 -> T311", fontsize=14, style = filled, fillcolor = lightblue];
83 -> 303 [arrowhead = none ];
303 -> 85;

304 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
83 -> 304 [arrowhead = none ];
304 -> 86;

305 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
84 -> 305 [arrowhead = none ];
305 -> 87;

306 [label="INSTANCE with matching:\nT63 -> T311\nT60 -> T308\nT61 -> T309", fontsize=14, style = filled, fillcolor = lightgrey];
85 -> 306 [arrowhead = none , style=dashed];
306 -> 19[style=dashed];

307 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
87 -> 307 [arrowhead = none ];
307 -> 88;

308 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
87 -> 308 [arrowhead = none ];
308 -> 89;

309 [label="EVAL with clause\ndelete(X328, tree(X329, X330, X331), tree(X329, X332, X331)) :- ','(less(X328, X329), delete(X328, X330, X332)).\nand substitutionT265 -> T336,\nX328 -> T336,\nX329 -> T337,\nX330 -> T341,\nX331 -> T339,\nT2 -> tree(T337, T341, T339),\nT268 -> T337,\nT266 -> T340,\nX332 -> T340,\nT269 -> T339,\nT338 -> T341", fontsize=14, style = filled, fillcolor = lightblue];
88 -> 309 [arrowhead = none ];
309 -> 90;

310 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
88 -> 310 [arrowhead = none ];
310 -> 91;

311 [label="EVAL with clause\ndelete(X345, tree(X346, X347, X348), tree(X346, X347, X349)) :- ','(less(X346, X345), delete(X345, X348, X349)).\nand substitutionT265 -> T354,\nX345 -> T354,\nX346 -> T355,\nX347 -> T356,\nX348 -> T359,\nT2 -> tree(T355, T356, T359),\nT268 -> T355,\nT266 -> T356,\nT269 -> T358,\nX349 -> T358,\nT357 -> T359", fontsize=14, style = filled, fillcolor = lightblue];
89 -> 311 [arrowhead = none ];
311 -> 92;

312 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
89 -> 312 [arrowhead = none ];
312 -> 93;

313 [label="INSTANCE with matching:\nT121 -> T336\nT122 -> T337\nT126 -> T341\nT125 -> T340", fontsize=14, style = filled, fillcolor = lightgrey];
90 -> 313 [arrowhead = none , style=dashed];
313 -> 32[style=dashed];

314 [label="INSTANCE with matching:\nT159 -> T355\nT158 -> T354\nT163 -> T359\nT162 -> T358", fontsize=14, style = filled, fillcolor = lightgrey];
92 -> 314 [arrowhead = none , style=dashed];
314 -> 44[style=dashed];

315 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
94 -> 315 [arrowhead = none ];
315 -> 96;

316 [label="EVAL with clause\ndelete(X405, tree(X406, X407, X408), tree(X406, X407, X409)) :- ','(less(X406, X405), delete(X405, X408, X409)).\nand substitutionT6 -> T415,\nX405 -> T415,\nX406 -> T416,\nX407 -> T417,\nX408 -> T420,\nT2 -> tree(T416, T417, T420),\nX409 -> T419,\nT7 -> tree(T416, T417, T419),\nT418 -> T420", fontsize=14, style = filled, fillcolor = lightblue];
95 -> 316 [arrowhead = none ];
316 -> 108;

317 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
95 -> 317 [arrowhead = none ];
317 -> 109;

318 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
96 -> 318 [arrowhead = none ];
318 -> 97;

319 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
96 -> 319 [arrowhead = none ];
319 -> 98;

320 [label="EVAL with clause\nless(0, s(X366)).\nand substitutionT367 -> 0,\nX366 -> T377,\nT368 -> s(T377)", fontsize=14, style = filled, fillcolor = lightblue];
97 -> 320 [arrowhead = none ];
320 -> 99;

321 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
97 -> 321 [arrowhead = none ];
321 -> 100;

322 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
98 -> 322 [arrowhead = none ];
322 -> 101;

323 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
98 -> 323 [arrowhead = none ];
323 -> 102;

324 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T372\nT3 -> T371", fontsize=14, style = filled, fillcolor = lightgrey];
99 -> 324 [arrowhead = none , style=dashed];
324 -> 1[style=dashed];

325 [label="EVAL with clause\nless(s(X379), s(X380)) :- less(X379, X380).\nand substitutionX379 -> T388,\nT367 -> s(T388),\nX380 -> T389,\nT368 -> s(T389)", fontsize=14, style = filled, fillcolor = lightblue];
101 -> 325 [arrowhead = none ];
325 -> 103;

326 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
101 -> 326 [arrowhead = none ];
326 -> 104;

327 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
102 -> 327 [arrowhead = none ];
327 -> 105;

328 [label="INSTANCE with matching:\nT198 -> T388\nT199 -> T389\nT182 -> T372\nT181 -> T371\nT180 -> T370\nX17 -> X259\nX18 -> X260\nX19 -> X261\nX20 -> X262\nX21 -> X263", fontsize=14, style = filled, fillcolor = lightgrey];
103 -> 328 [arrowhead = none , style=dashed];
328 -> 57[style=dashed];

329 [label="EVAL with clause\ndelete(X393, tree(X394, X395, X396), tree(X394, X395, X397)) :- ','(less(X394, X393), delete(X393, X396, X397)).\nand substitutionT367 -> T402,\nX393 -> T402,\nX394 -> T403,\nX395 -> T404,\nX396 -> T407,\nT2 -> tree(T403, T404, T407),\nT368 -> T403,\nT371 -> T404,\nT370 -> T406,\nX397 -> T406,\nT405 -> T407", fontsize=14, style = filled, fillcolor = lightblue];
105 -> 329 [arrowhead = none ];
329 -> 106;

330 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
105 -> 330 [arrowhead = none ];
330 -> 107;

331 [label="INSTANCE with matching:\nT159 -> T403\nT158 -> T402\nT163 -> T407\nT162 -> T406", fontsize=14, style = filled, fillcolor = lightgrey];
106 -> 331 [arrowhead = none , style=dashed];
331 -> 44[style=dashed];

332 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
108 -> 332 [arrowhead = none ];
332 -> 110;

333 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
110 -> 333 [arrowhead = none ];
333 -> 111;

334 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
110 -> 334 [arrowhead = none ];
334 -> 112;

335 [label="EVAL with clause\nless(0, s(X414)).\nand substitutionT416 -> 0,\nX414 -> T425,\nT415 -> s(T425)", fontsize=14, style = filled, fillcolor = lightblue];
111 -> 335 [arrowhead = none ];
335 -> 113;

336 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
111 -> 336 [arrowhead = none ];
336 -> 114;

337 [label="EVAL with clause\nless(s(X423), s(X424)) :- less(X423, X424).\nand substitutionX423 -> T434,\nT416 -> s(T434),\nX424 -> T435,\nT415 -> s(T435)", fontsize=14, style = filled, fillcolor = lightblue];
112 -> 337 [arrowhead = none ];
337 -> 115;

338 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
112 -> 338 [arrowhead = none ];
338 -> 116;

339 [label="INSTANCE with matching:\nT1 -> s(T425)\nT2 -> T420\nT3 -> T419", fontsize=14, style = filled, fillcolor = lightgrey];
113 -> 339 [arrowhead = none , style=dashed];
339 -> 1[style=dashed];

340 [label="INSTANCE with matching:\nT250 -> T434\nT251 -> T435\nT236 -> T420\nT235 -> T419\nT233 -> T417\nX17 -> X259\nX18 -> X260\nX19 -> X261\nX20 -> X262\nX21 -> X263\nX172 -> X357\nX173 -> X358\nX174 -> X359\nX175 -> X360\nX176 -> X361", fontsize=14, style = filled, fillcolor = lightgrey];
115 -> 340 [arrowhead = none , style=dashed];
340 -> 71[style=dashed];

341 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
117 -> 341 [arrowhead = none ];
341 -> 119;

342 [label="EVAL with clause\ndelete(X609, tree(X609, X610, X611), tree(X612, X610, X613)) :- delmin(X611, X612, X613).\nand substitutionT1 -> T625,\nX609 -> T625,\nX610 -> T626,\nX611 -> T630,\nT2 -> tree(T625, T626, T630),\nX612 -> T628,\nX613 -> T629,\nT3 -> tree(T628, T626, T629),\nT627 -> T630", fontsize=14, style = filled, fillcolor = lightblue];
118 -> 342 [arrowhead = none ];
342 -> 162;

343 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
118 -> 343 [arrowhead = none ];
343 -> 163;

344 [label="EVAL with clause\ndelete(X436, tree(X436, X437, X438), tree(X439, X437, X440)) :- delmin(X438, X439, X440).\nand substitutionT440 -> T447,\nX436 -> T447,\nX437 -> T448,\nX438 -> T452,\nT2 -> tree(T447, T448, T452),\nX439 -> T450,\nX440 -> T451,\nT441 -> tree(T450, T448, T451),\nT449 -> T452", fontsize=14, style = filled, fillcolor = lightblue];
119 -> 344 [arrowhead = none ];
344 -> 120;

345 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
119 -> 345 [arrowhead = none ];
345 -> 121;

346 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
120 -> 346 [arrowhead = none ];
346 -> 122;

347 [label="EVAL with clause\ndelete(X534, tree(X535, X536, X537), tree(X535, X538, X537)) :- ','(less(X534, X535), delete(X534, X536, X538)).\nand substitutionT440 -> T549,\nX534 -> T549,\nX535 -> T550,\nX536 -> T554,\nX537 -> T552,\nT2 -> tree(T550, T554, T552),\nX538 -> T553,\nT441 -> tree(T550, T553, T552),\nT551 -> T554", fontsize=14, style = filled, fillcolor = lightblue];
121 -> 347 [arrowhead = none ];
347 -> 139;

348 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
121 -> 348 [arrowhead = none ];
348 -> 140;

349 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
122 -> 349 [arrowhead = none ];
349 -> 123;

350 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
122 -> 350 [arrowhead = none ];
350 -> 124;

351 [label="EVAL with clause\ndelmin(tree(X449, void, X450), X449, X450).\nand substitutionX449 -> T461,\nX450 -> T462,\nT452 -> tree(T461, void, T462),\nT450 -> T461,\nT451 -> T462", fontsize=14, style = filled, fillcolor = lightblue];
123 -> 351 [arrowhead = none ];
351 -> 125;

352 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
123 -> 352 [arrowhead = none ];
352 -> 126;

353 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
124 -> 353 [arrowhead = none ];
353 -> 128;

354 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
124 -> 354 [arrowhead = none ];
354 -> 129;

355 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
125 -> 355 [arrowhead = none ];
355 -> 127;

356 [label="EVAL with clause\ndelmin(tree(X475, X476, X477), X478, tree(X475, X479, X480)) :- delmin(X476, X478, X479).\nand substitutionX475 -> T487,\nX476 -> T493,\nX477 -> T489,\nT452 -> tree(T487, T493, T489),\nT450 -> T490,\nX478 -> T490,\nX479 -> T491,\nX480 -> T492,\nT451 -> tree(T487, T491, T492),\nT488 -> T493", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 356 [arrowhead = none ];
356 -> 130;

357 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
128 -> 357 [arrowhead = none ];
357 -> 131;

358 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 358 [arrowhead = none ];
358 -> 132;

359 [label="INSTANCE with matching:\nT63 -> T493\nT60 -> T490\nT61 -> T491", fontsize=14, style = filled, fillcolor = lightgrey];
130 -> 359 [arrowhead = none , style=dashed];
359 -> 19[style=dashed];

360 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
132 -> 360 [arrowhead = none ];
360 -> 133;

361 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
132 -> 361 [arrowhead = none ];
361 -> 134;

362 [label="EVAL with clause\ndelete(X505, tree(X506, X507, X508), tree(X506, X509, X508)) :- ','(less(X505, X506), delete(X505, X507, X509)).\nand substitutionT447 -> T518,\nX505 -> T518,\nX506 -> T519,\nX507 -> T523,\nX508 -> T521,\nT2 -> tree(T519, T523, T521),\nT450 -> T519,\nT448 -> T522,\nX509 -> T522,\nT451 -> T521,\nT520 -> T523", fontsize=14, style = filled, fillcolor = lightblue];
133 -> 362 [arrowhead = none ];
362 -> 135;

363 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
133 -> 363 [arrowhead = none ];
363 -> 136;

364 [label="EVAL with clause\ndelete(X522, tree(X523, X524, X525), tree(X523, X524, X526)) :- ','(less(X523, X522), delete(X522, X525, X526)).\nand substitutionT447 -> T536,\nX522 -> T536,\nX523 -> T537,\nX524 -> T538,\nX525 -> T541,\nT2 -> tree(T537, T538, T541),\nT450 -> T537,\nT448 -> T538,\nT451 -> T540,\nX526 -> T540,\nT539 -> T541", fontsize=14, style = filled, fillcolor = lightblue];
134 -> 364 [arrowhead = none ];
364 -> 137;

365 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
134 -> 365 [arrowhead = none ];
365 -> 138;

366 [label="INSTANCE with matching:\nT121 -> T518\nT122 -> T519\nT126 -> T523\nT125 -> T522", fontsize=14, style = filled, fillcolor = lightgrey];
135 -> 366 [arrowhead = none , style=dashed];
366 -> 32[style=dashed];

367 [label="INSTANCE with matching:\nT159 -> T537\nT158 -> T536\nT163 -> T541\nT162 -> T540", fontsize=14, style = filled, fillcolor = lightgrey];
137 -> 367 [arrowhead = none , style=dashed];
367 -> 44[style=dashed];

368 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
139 -> 368 [arrowhead = none ];
368 -> 141;

369 [label="EVAL with clause\ndelete(X582, tree(X583, X584, X585), tree(X583, X584, X586)) :- ','(less(X583, X582), delete(X582, X585, X586)).\nand substitutionT440 -> T597,\nX582 -> T597,\nX583 -> T598,\nX584 -> T599,\nX585 -> T602,\nT2 -> tree(T598, T599, T602),\nX586 -> T601,\nT441 -> tree(T598, T599, T601),\nT600 -> T602", fontsize=14, style = filled, fillcolor = lightblue];
140 -> 369 [arrowhead = none ];
369 -> 153;

370 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
140 -> 370 [arrowhead = none ];
370 -> 154;

371 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
141 -> 371 [arrowhead = none ];
371 -> 142;

372 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
141 -> 372 [arrowhead = none ];
372 -> 143;

373 [label="EVAL with clause\nless(0, s(X543)).\nand substitutionT549 -> 0,\nX543 -> T559,\nT550 -> s(T559)", fontsize=14, style = filled, fillcolor = lightblue];
142 -> 373 [arrowhead = none ];
373 -> 144;

374 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
142 -> 374 [arrowhead = none ];
374 -> 145;

375 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
143 -> 375 [arrowhead = none ];
375 -> 146;

376 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
143 -> 376 [arrowhead = none ];
376 -> 147;

377 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T554\nT3 -> T553", fontsize=14, style = filled, fillcolor = lightgrey];
144 -> 377 [arrowhead = none , style=dashed];
377 -> 1[style=dashed];

378 [label="EVAL with clause\nless(s(X556), s(X557)) :- less(X556, X557).\nand substitutionX556 -> T570,\nT549 -> s(T570),\nX557 -> T571,\nT550 -> s(T571)", fontsize=14, style = filled, fillcolor = lightblue];
146 -> 378 [arrowhead = none ];
378 -> 148;

379 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
146 -> 379 [arrowhead = none ];
379 -> 149;

380 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
147 -> 380 [arrowhead = none ];
380 -> 150;

381 [label="INSTANCE with matching:\nT198 -> T570\nT199 -> T571\nT182 -> T554\nT181 -> T553\nT180 -> T552\nX17 -> X436\nX18 -> X437\nX19 -> X438\nX20 -> X439\nX21 -> X440", fontsize=14, style = filled, fillcolor = lightgrey];
148 -> 381 [arrowhead = none , style=dashed];
381 -> 57[style=dashed];

382 [label="EVAL with clause\ndelete(X570, tree(X571, X572, X573), tree(X571, X572, X574)) :- ','(less(X571, X570), delete(X570, X573, X574)).\nand substitutionT549 -> T584,\nX570 -> T584,\nX571 -> T585,\nX572 -> T586,\nX573 -> T589,\nT2 -> tree(T585, T586, T589),\nT550 -> T585,\nT553 -> T586,\nT552 -> T588,\nX574 -> T588,\nT587 -> T589", fontsize=14, style = filled, fillcolor = lightblue];
150 -> 382 [arrowhead = none ];
382 -> 151;

383 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
150 -> 383 [arrowhead = none ];
383 -> 152;

384 [label="INSTANCE with matching:\nT159 -> T585\nT158 -> T584\nT163 -> T589\nT162 -> T588", fontsize=14, style = filled, fillcolor = lightgrey];
151 -> 384 [arrowhead = none , style=dashed];
384 -> 44[style=dashed];

385 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
153 -> 385 [arrowhead = none ];
385 -> 155;

386 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
155 -> 386 [arrowhead = none ];
386 -> 156;

387 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
155 -> 387 [arrowhead = none ];
387 -> 157;

388 [label="EVAL with clause\nless(0, s(X591)).\nand substitutionT598 -> 0,\nX591 -> T607,\nT597 -> s(T607)", fontsize=14, style = filled, fillcolor = lightblue];
156 -> 388 [arrowhead = none ];
388 -> 158;

389 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
156 -> 389 [arrowhead = none ];
389 -> 159;

390 [label="EVAL with clause\nless(s(X600), s(X601)) :- less(X600, X601).\nand substitutionX600 -> T616,\nT598 -> s(T616),\nX601 -> T617,\nT597 -> s(T617)", fontsize=14, style = filled, fillcolor = lightblue];
157 -> 390 [arrowhead = none ];
390 -> 160;

391 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
157 -> 391 [arrowhead = none ];
391 -> 161;

392 [label="INSTANCE with matching:\nT1 -> s(T607)\nT2 -> T602\nT3 -> T601", fontsize=14, style = filled, fillcolor = lightgrey];
158 -> 392 [arrowhead = none , style=dashed];
392 -> 1[style=dashed];

393 [label="INSTANCE with matching:\nT250 -> T616\nT251 -> T617\nT236 -> T602\nT235 -> T601\nT233 -> T599\nX17 -> X436\nX18 -> X437\nX19 -> X438\nX20 -> X439\nX21 -> X440\nX172 -> X534\nX173 -> X535\nX174 -> X536\nX175 -> X537\nX176 -> X538", fontsize=14, style = filled, fillcolor = lightgrey];
160 -> 393 [arrowhead = none , style=dashed];
393 -> 71[style=dashed];

394 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
162 -> 394 [arrowhead = none ];
394 -> 164;

395 [label="EVAL with clause\ndelete(X707, tree(X708, X709, X710), tree(X708, X711, X710)) :- ','(less(X707, X708), delete(X707, X709, X711)).\nand substitutionT1 -> T727,\nX707 -> T727,\nX708 -> T728,\nX709 -> T732,\nX710 -> T730,\nT2 -> tree(T728, T732, T730),\nX711 -> T731,\nT3 -> tree(T728, T731, T730),\nT729 -> T732", fontsize=14, style = filled, fillcolor = lightblue];
163 -> 395 [arrowhead = none ];
395 -> 181;

396 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
163 -> 396 [arrowhead = none ];
396 -> 182;

397 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
164 -> 397 [arrowhead = none ];
397 -> 165;

398 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
164 -> 398 [arrowhead = none ];
398 -> 166;

399 [label="EVAL with clause\ndelmin(tree(X622, void, X623), X622, X623).\nand substitutionX622 -> T639,\nX623 -> T640,\nT630 -> tree(T639, void, T640),\nT628 -> T639,\nT629 -> T640", fontsize=14, style = filled, fillcolor = lightblue];
165 -> 399 [arrowhead = none ];
399 -> 167;

400 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
165 -> 400 [arrowhead = none ];
400 -> 168;

401 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
166 -> 401 [arrowhead = none ];
401 -> 170;

402 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
166 -> 402 [arrowhead = none ];
402 -> 171;

403 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
167 -> 403 [arrowhead = none ];
403 -> 169;

404 [label="EVAL with clause\ndelmin(tree(X648, X649, X650), X651, tree(X648, X652, X653)) :- delmin(X649, X651, X652).\nand substitutionX648 -> T665,\nX649 -> T671,\nX650 -> T667,\nT630 -> tree(T665, T671, T667),\nT628 -> T668,\nX651 -> T668,\nX652 -> T669,\nX653 -> T670,\nT629 -> tree(T665, T669, T670),\nT666 -> T671", fontsize=14, style = filled, fillcolor = lightblue];
170 -> 404 [arrowhead = none ];
404 -> 172;

405 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
170 -> 405 [arrowhead = none ];
405 -> 173;

406 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
171 -> 406 [arrowhead = none ];
406 -> 174;

407 [label="INSTANCE with matching:\nT63 -> T671\nT60 -> T668\nT61 -> T669", fontsize=14, style = filled, fillcolor = lightgrey];
172 -> 407 [arrowhead = none , style=dashed];
407 -> 19[style=dashed];

408 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
174 -> 408 [arrowhead = none ];
408 -> 175;

409 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
174 -> 409 [arrowhead = none ];
409 -> 176;

410 [label="EVAL with clause\ndelete(X678, tree(X679, X680, X681), tree(X679, X682, X681)) :- ','(less(X678, X679), delete(X678, X680, X682)).\nand substitutionT625 -> T696,\nX678 -> T696,\nX679 -> T697,\nX680 -> T701,\nX681 -> T699,\nT2 -> tree(T697, T701, T699),\nT628 -> T697,\nT626 -> T700,\nX682 -> T700,\nT629 -> T699,\nT698 -> T701", fontsize=14, style = filled, fillcolor = lightblue];
175 -> 410 [arrowhead = none ];
410 -> 177;

411 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
175 -> 411 [arrowhead = none ];
411 -> 178;

412 [label="EVAL with clause\ndelete(X695, tree(X696, X697, X698), tree(X696, X697, X699)) :- ','(less(X696, X695), delete(X695, X698, X699)).\nand substitutionT625 -> T714,\nX695 -> T714,\nX696 -> T715,\nX697 -> T716,\nX698 -> T719,\nT2 -> tree(T715, T716, T719),\nT628 -> T715,\nT626 -> T716,\nT629 -> T718,\nX699 -> T718,\nT717 -> T719", fontsize=14, style = filled, fillcolor = lightblue];
176 -> 412 [arrowhead = none ];
412 -> 179;

413 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
176 -> 413 [arrowhead = none ];
413 -> 180;

414 [label="INSTANCE with matching:\nT121 -> T696\nT122 -> T697\nT126 -> T701\nT125 -> T700", fontsize=14, style = filled, fillcolor = lightgrey];
177 -> 414 [arrowhead = none , style=dashed];
414 -> 32[style=dashed];

415 [label="INSTANCE with matching:\nT159 -> T715\nT158 -> T714\nT163 -> T719\nT162 -> T718", fontsize=14, style = filled, fillcolor = lightgrey];
179 -> 415 [arrowhead = none , style=dashed];
415 -> 44[style=dashed];

416 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
181 -> 416 [arrowhead = none ];
416 -> 183;

417 [label="EVAL with clause\ndelete(X755, tree(X756, X757, X758), tree(X756, X757, X759)) :- ','(less(X756, X755), delete(X755, X758, X759)).\nand substitutionT1 -> T775,\nX755 -> T775,\nX756 -> T776,\nX757 -> T777,\nX758 -> T780,\nT2 -> tree(T776, T777, T780),\nX759 -> T779,\nT3 -> tree(T776, T777, T779),\nT778 -> T780", fontsize=14, style = filled, fillcolor = lightblue];
182 -> 417 [arrowhead = none ];
417 -> 195;

418 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
182 -> 418 [arrowhead = none ];
418 -> 196;

419 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
183 -> 419 [arrowhead = none ];
419 -> 184;

420 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
183 -> 420 [arrowhead = none ];
420 -> 185;

421 [label="EVAL with clause\nless(0, s(X716)).\nand substitutionT727 -> 0,\nX716 -> T737,\nT728 -> s(T737)", fontsize=14, style = filled, fillcolor = lightblue];
184 -> 421 [arrowhead = none ];
421 -> 186;

422 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
184 -> 422 [arrowhead = none ];
422 -> 187;

423 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
185 -> 423 [arrowhead = none ];
423 -> 188;

424 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
185 -> 424 [arrowhead = none ];
424 -> 189;

425 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T732\nT3 -> T731", fontsize=14, style = filled, fillcolor = lightgrey];
186 -> 425 [arrowhead = none , style=dashed];
425 -> 1[style=dashed];

426 [label="EVAL with clause\nless(s(X729), s(X730)) :- less(X729, X730).\nand substitutionX729 -> T748,\nT727 -> s(T748),\nX730 -> T749,\nT728 -> s(T749)", fontsize=14, style = filled, fillcolor = lightblue];
188 -> 426 [arrowhead = none ];
426 -> 190;

427 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
188 -> 427 [arrowhead = none ];
427 -> 191;

428 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
189 -> 428 [arrowhead = none ];
428 -> 192;

429 [label="INSTANCE with matching:\nT198 -> T748\nT199 -> T749\nT182 -> T732\nT181 -> T731\nT180 -> T730\nX17 -> X609\nX18 -> X610\nX19 -> X611\nX20 -> X612\nX21 -> X613", fontsize=14, style = filled, fillcolor = lightgrey];
190 -> 429 [arrowhead = none , style=dashed];
429 -> 57[style=dashed];

430 [label="EVAL with clause\ndelete(X743, tree(X744, X745, X746), tree(X744, X745, X747)) :- ','(less(X744, X743), delete(X743, X746, X747)).\nand substitutionT727 -> T762,\nX743 -> T762,\nX744 -> T763,\nX745 -> T764,\nX746 -> T767,\nT2 -> tree(T763, T764, T767),\nT728 -> T763,\nT731 -> T764,\nT730 -> T766,\nX747 -> T766,\nT765 -> T767", fontsize=14, style = filled, fillcolor = lightblue];
192 -> 430 [arrowhead = none ];
430 -> 193;

431 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
192 -> 431 [arrowhead = none ];
431 -> 194;

432 [label="INSTANCE with matching:\nT159 -> T763\nT158 -> T762\nT163 -> T767\nT162 -> T766", fontsize=14, style = filled, fillcolor = lightgrey];
193 -> 432 [arrowhead = none , style=dashed];
432 -> 44[style=dashed];

433 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
195 -> 433 [arrowhead = none ];
433 -> 197;

434 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
197 -> 434 [arrowhead = none ];
434 -> 198;

435 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
197 -> 435 [arrowhead = none ];
435 -> 199;

436 [label="EVAL with clause\nless(0, s(X764)).\nand substitutionT776 -> 0,\nX764 -> T785,\nT775 -> s(T785)", fontsize=14, style = filled, fillcolor = lightblue];
198 -> 436 [arrowhead = none ];
436 -> 200;

437 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
198 -> 437 [arrowhead = none ];
437 -> 201;

438 [label="EVAL with clause\nless(s(X773), s(X774)) :- less(X773, X774).\nand substitutionX773 -> T794,\nT776 -> s(T794),\nX774 -> T795,\nT775 -> s(T795)", fontsize=14, style = filled, fillcolor = lightblue];
199 -> 438 [arrowhead = none ];
438 -> 202;

439 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
199 -> 439 [arrowhead = none ];
439 -> 203;

440 [label="INSTANCE with matching:\nT1 -> s(T785)\nT2 -> T780\nT3 -> T779", fontsize=14, style = filled, fillcolor = lightgrey];
200 -> 440 [arrowhead = none , style=dashed];
440 -> 1[style=dashed];

441 [label="INSTANCE with matching:\nT250 -> T794\nT251 -> T795\nT236 -> T780\nT235 -> T779\nT233 -> T777\nX17 -> X609\nX18 -> X610\nX19 -> X611\nX20 -> X612\nX21 -> X613\nX172 -> X707\nX173 -> X708\nX174 -> X709\nX175 -> X710\nX176 -> X711", fontsize=14, style = filled, fillcolor = lightgrey];
202 -> 441 [arrowhead = none , style=dashed];
441 -> 71[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(T135)).
lessB(s(T140), s(T141)) :- lessB(T140, T141).
pC(T159, T158, T163, T162) :- lessB(T159, T158).
pC(T159, T158, T163, T162) :- ','(lessB(T159, T158), deleteD(T158, T163, T162)).
pE(T121, T122, T126, T125) :- lessB(T121, T122).
pE(T121, T122, T126, T125) :- ','(lessB(T121, T122), deleteD(T121, T126, T125)).
pF(T198, T199, T182, T181) :- lessB(T198, T199).
pF(T198, T199, T182, T181) :- ','(lessB(T198, T199), deleteD(s(T198), T182, T181)).
pG(T250, T251, T236, T235) :- lessB(T250, T251).
pG(T250, T251, T236, T235) :- ','(lessB(T250, T251), deleteD(s(T251), T236, T235)).
deleteD(T6, tree(T6, void, T7), T7).
deleteD(T10, tree(T10, T11, void), T11).
deleteD(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)).
deleteD(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) :- delminA(T63, T60, T61).
deleteD(T121, tree(T122, T126, T124), tree(T122, T125, T124)) :- pE(T121, T122, T126, T125).
deleteD(T158, tree(T159, T160, T163), tree(T159, T160, T162)) :- pC(T159, T158, T163, T162).
deleteD(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180)) :- deleteD(0, T182, T181).
deleteD(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180)) :- pF(T198, T199, T182, T181).
deleteD(T218, tree(T219, T220, T223), tree(T219, T220, T222)) :- pC(T219, T218, T223, T222).
deleteD(s(T241), tree(0, T233, T236), tree(0, T233, T235)) :- deleteD(s(T241), T236, T235).
deleteD(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235)) :- pG(T250, T251, T236, T235).
deleteD(T265, tree(T265, T266, tree(T279, void, T280)), tree(T279, T266, T280)).
deleteD(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310))) :- delminA(T311, T308, T309).
deleteD(T336, tree(T337, T341, T339), tree(T337, T340, T339)) :- pE(T336, T337, T341, T340).
deleteD(T354, tree(T355, T356, T359), tree(T355, T356, T358)) :- pC(T355, T354, T359, T358).
deleteD(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370)) :- deleteD(0, T372, T371).
deleteD(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370)) :- pF(T388, T389, T372, T371).
deleteD(T402, tree(T403, T404, T407), tree(T403, T404, T406)) :- pC(T403, T402, T407, T406).
deleteD(s(T425), tree(0, T417, T420), tree(0, T417, T419)) :- deleteD(s(T425), T420, T419).
deleteD(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419)) :- pG(T434, T435, T420, T419).
deleteD(T440, tree(T440, T441, void), T441).
deleteD(T447, tree(T447, T448, tree(T461, void, T462)), tree(T461, T448, T462)).
deleteD(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492))) :- delminA(T493, T490, T491).
deleteD(T518, tree(T519, T523, T521), tree(T519, T522, T521)) :- pE(T518, T519, T523, T522).
deleteD(T536, tree(T537, T538, T541), tree(T537, T538, T540)) :- pC(T537, T536, T541, T540).
deleteD(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552)) :- deleteD(0, T554, T553).
deleteD(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552)) :- pF(T570, T571, T554, T553).
deleteD(T584, tree(T585, T586, T589), tree(T585, T586, T588)) :- pC(T585, T584, T589, T588).
deleteD(s(T607), tree(0, T599, T602), tree(0, T599, T601)) :- deleteD(s(T607), T602, T601).
deleteD(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601)) :- pG(T616, T617, T602, T601).
deleteD(T625, tree(T625, T626, tree(T639, void, T640)), tree(T639, T626, T640)).
deleteD(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670))) :- delminA(T671, T668, T669).
deleteD(T696, tree(T697, T701, T699), tree(T697, T700, T699)) :- pE(T696, T697, T701, T700).
deleteD(T714, tree(T715, T716, T719), tree(T715, T716, T718)) :- pC(T715, T714, T719, T718).
deleteD(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730)) :- deleteD(0, T732, T731).
deleteD(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730)) :- pF(T748, T749, T732, T731).
deleteD(T762, tree(T763, T764, T767), tree(T763, T764, T766)) :- pC(T763, T762, T767, T766).
deleteD(s(T785), tree(0, T777, T780), tree(0, T777, T779)) :- deleteD(s(T785), T780, T779).
deleteD(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779)) :- pG(T794, T795, T780, T779).

Query: deleteD(g,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:
deleteD_in: (b,f,b)
delminA_in: (f,b,b)
pE_in: (b,b,f,b)
lessB_in: (b,b)
pC_in: (b,b,f,b)
pF_in: (b,b,f,b)
pG_in: (b,b,f,b)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

deleteD_in_gag(T6, tree(T6, void, T7), T7) → deleteD_out_gag(T6, tree(T6, void, T7), T7)
deleteD_in_gag(T10, tree(T10, T11, void), T11) → deleteD_out_gag(T10, tree(T10, T11, void), T11)
deleteD_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteD_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteD_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U11_gag(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))
U11_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteD_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteD_in_gag(T121, tree(T122, T126, T124), tree(T122, T125, T124)) → U12_gag(T121, T122, T126, T124, T125, pE_in_ggag(T121, T122, T126, T125))
pE_in_ggag(T121, T122, T126, T125) → U5_ggag(T121, T122, T126, T125, lessB_in_gg(T121, T122))
lessB_in_gg(0, s(T135)) → lessB_out_gg(0, s(T135))
lessB_in_gg(s(T140), s(T141)) → U2_gg(T140, T141, lessB_in_gg(T140, T141))
U2_gg(T140, T141, lessB_out_gg(T140, T141)) → lessB_out_gg(s(T140), s(T141))
U5_ggag(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → pE_out_ggag(T121, T122, T126, T125)
U5_ggag(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → U6_ggag(T121, T122, T126, T125, deleteD_in_gag(T121, T126, T125))
deleteD_in_gag(T158, tree(T159, T160, T163), tree(T159, T160, T162)) → U13_gag(T158, T159, T160, T163, T162, pC_in_ggag(T159, T158, T163, T162))
pC_in_ggag(T159, T158, T163, T162) → U3_ggag(T159, T158, T163, T162, lessB_in_gg(T159, T158))
U3_ggag(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → pC_out_ggag(T159, T158, T163, T162)
U3_ggag(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → U4_ggag(T159, T158, T163, T162, deleteD_in_gag(T158, T163, T162))
deleteD_in_gag(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180)) → U14_gag(T187, T182, T180, T181, deleteD_in_gag(0, T182, T181))
deleteD_in_gag(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180)) → U15_gag(T198, T199, T182, T180, T181, pF_in_ggag(T198, T199, T182, T181))
pF_in_ggag(T198, T199, T182, T181) → U7_ggag(T198, T199, T182, T181, lessB_in_gg(T198, T199))
U7_ggag(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → pF_out_ggag(T198, T199, T182, T181)
U7_ggag(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → U8_ggag(T198, T199, T182, T181, deleteD_in_gag(s(T198), T182, T181))
deleteD_in_gag(T218, tree(T219, T220, T223), tree(T219, T220, T222)) → U16_gag(T218, T219, T220, T223, T222, pC_in_ggag(T219, T218, T223, T222))
U16_gag(T218, T219, T220, T223, T222, pC_out_ggag(T219, T218, T223, T222)) → deleteD_out_gag(T218, tree(T219, T220, T223), tree(T219, T220, T222))
deleteD_in_gag(s(T241), tree(0, T233, T236), tree(0, T233, T235)) → U17_gag(T241, T233, T236, T235, deleteD_in_gag(s(T241), T236, T235))
deleteD_in_gag(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235)) → U18_gag(T251, T250, T233, T236, T235, pG_in_ggag(T250, T251, T236, T235))
pG_in_ggag(T250, T251, T236, T235) → U9_ggag(T250, T251, T236, T235, lessB_in_gg(T250, T251))
U9_ggag(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → pG_out_ggag(T250, T251, T236, T235)
U9_ggag(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → U10_ggag(T250, T251, T236, T235, deleteD_in_gag(s(T251), T236, T235))
deleteD_in_gag(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310))) → U19_gag(T265, T266, T305, T311, T307, T308, T309, T310, delminA_in_agg(T311, T308, T309))
U19_gag(T265, T266, T305, T311, T307, T308, T309, T310, delminA_out_agg(T311, T308, T309)) → deleteD_out_gag(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310)))
deleteD_in_gag(T336, tree(T337, T341, T339), tree(T337, T340, T339)) → U20_gag(T336, T337, T341, T339, T340, pE_in_ggag(T336, T337, T341, T340))
U20_gag(T336, T337, T341, T339, T340, pE_out_ggag(T336, T337, T341, T340)) → deleteD_out_gag(T336, tree(T337, T341, T339), tree(T337, T340, T339))
deleteD_in_gag(T354, tree(T355, T356, T359), tree(T355, T356, T358)) → U21_gag(T354, T355, T356, T359, T358, pC_in_ggag(T355, T354, T359, T358))
U21_gag(T354, T355, T356, T359, T358, pC_out_ggag(T355, T354, T359, T358)) → deleteD_out_gag(T354, tree(T355, T356, T359), tree(T355, T356, T358))
deleteD_in_gag(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370)) → U22_gag(T377, T372, T370, T371, deleteD_in_gag(0, T372, T371))
deleteD_in_gag(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370)) → U23_gag(T388, T389, T372, T370, T371, pF_in_ggag(T388, T389, T372, T371))
U23_gag(T388, T389, T372, T370, T371, pF_out_ggag(T388, T389, T372, T371)) → deleteD_out_gag(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370))
deleteD_in_gag(T402, tree(T403, T404, T407), tree(T403, T404, T406)) → U24_gag(T402, T403, T404, T407, T406, pC_in_ggag(T403, T402, T407, T406))
U24_gag(T402, T403, T404, T407, T406, pC_out_ggag(T403, T402, T407, T406)) → deleteD_out_gag(T402, tree(T403, T404, T407), tree(T403, T404, T406))
deleteD_in_gag(s(T425), tree(0, T417, T420), tree(0, T417, T419)) → U25_gag(T425, T417, T420, T419, deleteD_in_gag(s(T425), T420, T419))
deleteD_in_gag(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419)) → U26_gag(T435, T434, T417, T420, T419, pG_in_ggag(T434, T435, T420, T419))
U26_gag(T435, T434, T417, T420, T419, pG_out_ggag(T434, T435, T420, T419)) → deleteD_out_gag(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419))
deleteD_in_gag(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492))) → U27_gag(T447, T448, T487, T493, T489, T490, T491, T492, delminA_in_agg(T493, T490, T491))
U27_gag(T447, T448, T487, T493, T489, T490, T491, T492, delminA_out_agg(T493, T490, T491)) → deleteD_out_gag(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492)))
deleteD_in_gag(T518, tree(T519, T523, T521), tree(T519, T522, T521)) → U28_gag(T518, T519, T523, T521, T522, pE_in_ggag(T518, T519, T523, T522))
U28_gag(T518, T519, T523, T521, T522, pE_out_ggag(T518, T519, T523, T522)) → deleteD_out_gag(T518, tree(T519, T523, T521), tree(T519, T522, T521))
deleteD_in_gag(T536, tree(T537, T538, T541), tree(T537, T538, T540)) → U29_gag(T536, T537, T538, T541, T540, pC_in_ggag(T537, T536, T541, T540))
U29_gag(T536, T537, T538, T541, T540, pC_out_ggag(T537, T536, T541, T540)) → deleteD_out_gag(T536, tree(T537, T538, T541), tree(T537, T538, T540))
deleteD_in_gag(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552)) → U30_gag(T559, T554, T552, T553, deleteD_in_gag(0, T554, T553))
deleteD_in_gag(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552)) → U31_gag(T570, T571, T554, T552, T553, pF_in_ggag(T570, T571, T554, T553))
U31_gag(T570, T571, T554, T552, T553, pF_out_ggag(T570, T571, T554, T553)) → deleteD_out_gag(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552))
deleteD_in_gag(T584, tree(T585, T586, T589), tree(T585, T586, T588)) → U32_gag(T584, T585, T586, T589, T588, pC_in_ggag(T585, T584, T589, T588))
U32_gag(T584, T585, T586, T589, T588, pC_out_ggag(T585, T584, T589, T588)) → deleteD_out_gag(T584, tree(T585, T586, T589), tree(T585, T586, T588))
deleteD_in_gag(s(T607), tree(0, T599, T602), tree(0, T599, T601)) → U33_gag(T607, T599, T602, T601, deleteD_in_gag(s(T607), T602, T601))
deleteD_in_gag(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601)) → U34_gag(T617, T616, T599, T602, T601, pG_in_ggag(T616, T617, T602, T601))
U34_gag(T617, T616, T599, T602, T601, pG_out_ggag(T616, T617, T602, T601)) → deleteD_out_gag(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601))
deleteD_in_gag(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670))) → U35_gag(T625, T626, T665, T671, T667, T668, T669, T670, delminA_in_agg(T671, T668, T669))
U35_gag(T625, T626, T665, T671, T667, T668, T669, T670, delminA_out_agg(T671, T668, T669)) → deleteD_out_gag(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670)))
deleteD_in_gag(T696, tree(T697, T701, T699), tree(T697, T700, T699)) → U36_gag(T696, T697, T701, T699, T700, pE_in_ggag(T696, T697, T701, T700))
U36_gag(T696, T697, T701, T699, T700, pE_out_ggag(T696, T697, T701, T700)) → deleteD_out_gag(T696, tree(T697, T701, T699), tree(T697, T700, T699))
deleteD_in_gag(T714, tree(T715, T716, T719), tree(T715, T716, T718)) → U37_gag(T714, T715, T716, T719, T718, pC_in_ggag(T715, T714, T719, T718))
U37_gag(T714, T715, T716, T719, T718, pC_out_ggag(T715, T714, T719, T718)) → deleteD_out_gag(T714, tree(T715, T716, T719), tree(T715, T716, T718))
deleteD_in_gag(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730)) → U38_gag(T737, T732, T730, T731, deleteD_in_gag(0, T732, T731))
deleteD_in_gag(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730)) → U39_gag(T748, T749, T732, T730, T731, pF_in_ggag(T748, T749, T732, T731))
U39_gag(T748, T749, T732, T730, T731, pF_out_ggag(T748, T749, T732, T731)) → deleteD_out_gag(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730))
deleteD_in_gag(T762, tree(T763, T764, T767), tree(T763, T764, T766)) → U40_gag(T762, T763, T764, T767, T766, pC_in_ggag(T763, T762, T767, T766))
U40_gag(T762, T763, T764, T767, T766, pC_out_ggag(T763, T762, T767, T766)) → deleteD_out_gag(T762, tree(T763, T764, T767), tree(T763, T764, T766))
deleteD_in_gag(s(T785), tree(0, T777, T780), tree(0, T777, T779)) → U41_gag(T785, T777, T780, T779, deleteD_in_gag(s(T785), T780, T779))
deleteD_in_gag(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779)) → U42_gag(T795, T794, T777, T780, T779, pG_in_ggag(T794, T795, T780, T779))
U42_gag(T795, T794, T777, T780, T779, pG_out_ggag(T794, T795, T780, T779)) → deleteD_out_gag(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779))
U41_gag(T785, T777, T780, T779, deleteD_out_gag(s(T785), T780, T779)) → deleteD_out_gag(s(T785), tree(0, T777, T780), tree(0, T777, T779))
U38_gag(T737, T732, T730, T731, deleteD_out_gag(0, T732, T731)) → deleteD_out_gag(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730))
U33_gag(T607, T599, T602, T601, deleteD_out_gag(s(T607), T602, T601)) → deleteD_out_gag(s(T607), tree(0, T599, T602), tree(0, T599, T601))
U30_gag(T559, T554, T552, T553, deleteD_out_gag(0, T554, T553)) → deleteD_out_gag(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552))
U25_gag(T425, T417, T420, T419, deleteD_out_gag(s(T425), T420, T419)) → deleteD_out_gag(s(T425), tree(0, T417, T420), tree(0, T417, T419))
U22_gag(T377, T372, T370, T371, deleteD_out_gag(0, T372, T371)) → deleteD_out_gag(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370))
U10_ggag(T250, T251, T236, T235, deleteD_out_gag(s(T251), T236, T235)) → pG_out_ggag(T250, T251, T236, T235)
U18_gag(T251, T250, T233, T236, T235, pG_out_ggag(T250, T251, T236, T235)) → deleteD_out_gag(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235))
U17_gag(T241, T233, T236, T235, deleteD_out_gag(s(T241), T236, T235)) → deleteD_out_gag(s(T241), tree(0, T233, T236), tree(0, T233, T235))
U8_ggag(T198, T199, T182, T181, deleteD_out_gag(s(T198), T182, T181)) → pF_out_ggag(T198, T199, T182, T181)
U15_gag(T198, T199, T182, T180, T181, pF_out_ggag(T198, T199, T182, T181)) → deleteD_out_gag(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180))
U14_gag(T187, T182, T180, T181, deleteD_out_gag(0, T182, T181)) → deleteD_out_gag(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180))
U4_ggag(T159, T158, T163, T162, deleteD_out_gag(T158, T163, T162)) → pC_out_ggag(T159, T158, T163, T162)
U13_gag(T158, T159, T160, T163, T162, pC_out_ggag(T159, T158, T163, T162)) → deleteD_out_gag(T158, tree(T159, T160, T163), tree(T159, T160, T162))
U6_ggag(T121, T122, T126, T125, deleteD_out_gag(T121, T126, T125)) → pE_out_ggag(T121, T122, T126, T125)
U12_gag(T121, T122, T126, T124, T125, pE_out_ggag(T121, T122, T126, T125)) → deleteD_out_gag(T121, tree(T122, T126, T124), tree(T122, T125, T124))

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

deleteD_in_gag(T6, tree(T6, void, T7), T7) → deleteD_out_gag(T6, tree(T6, void, T7), T7)
deleteD_in_gag(T10, tree(T10, T11, void), T11) → deleteD_out_gag(T10, tree(T10, T11, void), T11)
deleteD_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteD_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteD_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U11_gag(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))
U11_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteD_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteD_in_gag(T121, tree(T122, T126, T124), tree(T122, T125, T124)) → U12_gag(T121, T122, T126, T124, T125, pE_in_ggag(T121, T122, T126, T125))
pE_in_ggag(T121, T122, T126, T125) → U5_ggag(T121, T122, T126, T125, lessB_in_gg(T121, T122))
lessB_in_gg(0, s(T135)) → lessB_out_gg(0, s(T135))
lessB_in_gg(s(T140), s(T141)) → U2_gg(T140, T141, lessB_in_gg(T140, T141))
U2_gg(T140, T141, lessB_out_gg(T140, T141)) → lessB_out_gg(s(T140), s(T141))
U5_ggag(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → pE_out_ggag(T121, T122, T126, T125)
U5_ggag(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → U6_ggag(T121, T122, T126, T125, deleteD_in_gag(T121, T126, T125))
deleteD_in_gag(T158, tree(T159, T160, T163), tree(T159, T160, T162)) → U13_gag(T158, T159, T160, T163, T162, pC_in_ggag(T159, T158, T163, T162))
pC_in_ggag(T159, T158, T163, T162) → U3_ggag(T159, T158, T163, T162, lessB_in_gg(T159, T158))
U3_ggag(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → pC_out_ggag(T159, T158, T163, T162)
U3_ggag(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → U4_ggag(T159, T158, T163, T162, deleteD_in_gag(T158, T163, T162))
deleteD_in_gag(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180)) → U14_gag(T187, T182, T180, T181, deleteD_in_gag(0, T182, T181))
deleteD_in_gag(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180)) → U15_gag(T198, T199, T182, T180, T181, pF_in_ggag(T198, T199, T182, T181))
pF_in_ggag(T198, T199, T182, T181) → U7_ggag(T198, T199, T182, T181, lessB_in_gg(T198, T199))
U7_ggag(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → pF_out_ggag(T198, T199, T182, T181)
U7_ggag(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → U8_ggag(T198, T199, T182, T181, deleteD_in_gag(s(T198), T182, T181))
deleteD_in_gag(T218, tree(T219, T220, T223), tree(T219, T220, T222)) → U16_gag(T218, T219, T220, T223, T222, pC_in_ggag(T219, T218, T223, T222))
U16_gag(T218, T219, T220, T223, T222, pC_out_ggag(T219, T218, T223, T222)) → deleteD_out_gag(T218, tree(T219, T220, T223), tree(T219, T220, T222))
deleteD_in_gag(s(T241), tree(0, T233, T236), tree(0, T233, T235)) → U17_gag(T241, T233, T236, T235, deleteD_in_gag(s(T241), T236, T235))
deleteD_in_gag(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235)) → U18_gag(T251, T250, T233, T236, T235, pG_in_ggag(T250, T251, T236, T235))
pG_in_ggag(T250, T251, T236, T235) → U9_ggag(T250, T251, T236, T235, lessB_in_gg(T250, T251))
U9_ggag(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → pG_out_ggag(T250, T251, T236, T235)
U9_ggag(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → U10_ggag(T250, T251, T236, T235, deleteD_in_gag(s(T251), T236, T235))
deleteD_in_gag(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310))) → U19_gag(T265, T266, T305, T311, T307, T308, T309, T310, delminA_in_agg(T311, T308, T309))
U19_gag(T265, T266, T305, T311, T307, T308, T309, T310, delminA_out_agg(T311, T308, T309)) → deleteD_out_gag(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310)))
deleteD_in_gag(T336, tree(T337, T341, T339), tree(T337, T340, T339)) → U20_gag(T336, T337, T341, T339, T340, pE_in_ggag(T336, T337, T341, T340))
U20_gag(T336, T337, T341, T339, T340, pE_out_ggag(T336, T337, T341, T340)) → deleteD_out_gag(T336, tree(T337, T341, T339), tree(T337, T340, T339))
deleteD_in_gag(T354, tree(T355, T356, T359), tree(T355, T356, T358)) → U21_gag(T354, T355, T356, T359, T358, pC_in_ggag(T355, T354, T359, T358))
U21_gag(T354, T355, T356, T359, T358, pC_out_ggag(T355, T354, T359, T358)) → deleteD_out_gag(T354, tree(T355, T356, T359), tree(T355, T356, T358))
deleteD_in_gag(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370)) → U22_gag(T377, T372, T370, T371, deleteD_in_gag(0, T372, T371))
deleteD_in_gag(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370)) → U23_gag(T388, T389, T372, T370, T371, pF_in_ggag(T388, T389, T372, T371))
U23_gag(T388, T389, T372, T370, T371, pF_out_ggag(T388, T389, T372, T371)) → deleteD_out_gag(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370))
deleteD_in_gag(T402, tree(T403, T404, T407), tree(T403, T404, T406)) → U24_gag(T402, T403, T404, T407, T406, pC_in_ggag(T403, T402, T407, T406))
U24_gag(T402, T403, T404, T407, T406, pC_out_ggag(T403, T402, T407, T406)) → deleteD_out_gag(T402, tree(T403, T404, T407), tree(T403, T404, T406))
deleteD_in_gag(s(T425), tree(0, T417, T420), tree(0, T417, T419)) → U25_gag(T425, T417, T420, T419, deleteD_in_gag(s(T425), T420, T419))
deleteD_in_gag(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419)) → U26_gag(T435, T434, T417, T420, T419, pG_in_ggag(T434, T435, T420, T419))
U26_gag(T435, T434, T417, T420, T419, pG_out_ggag(T434, T435, T420, T419)) → deleteD_out_gag(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419))
deleteD_in_gag(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492))) → U27_gag(T447, T448, T487, T493, T489, T490, T491, T492, delminA_in_agg(T493, T490, T491))
U27_gag(T447, T448, T487, T493, T489, T490, T491, T492, delminA_out_agg(T493, T490, T491)) → deleteD_out_gag(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492)))
deleteD_in_gag(T518, tree(T519, T523, T521), tree(T519, T522, T521)) → U28_gag(T518, T519, T523, T521, T522, pE_in_ggag(T518, T519, T523, T522))
U28_gag(T518, T519, T523, T521, T522, pE_out_ggag(T518, T519, T523, T522)) → deleteD_out_gag(T518, tree(T519, T523, T521), tree(T519, T522, T521))
deleteD_in_gag(T536, tree(T537, T538, T541), tree(T537, T538, T540)) → U29_gag(T536, T537, T538, T541, T540, pC_in_ggag(T537, T536, T541, T540))
U29_gag(T536, T537, T538, T541, T540, pC_out_ggag(T537, T536, T541, T540)) → deleteD_out_gag(T536, tree(T537, T538, T541), tree(T537, T538, T540))
deleteD_in_gag(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552)) → U30_gag(T559, T554, T552, T553, deleteD_in_gag(0, T554, T553))
deleteD_in_gag(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552)) → U31_gag(T570, T571, T554, T552, T553, pF_in_ggag(T570, T571, T554, T553))
U31_gag(T570, T571, T554, T552, T553, pF_out_ggag(T570, T571, T554, T553)) → deleteD_out_gag(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552))
deleteD_in_gag(T584, tree(T585, T586, T589), tree(T585, T586, T588)) → U32_gag(T584, T585, T586, T589, T588, pC_in_ggag(T585, T584, T589, T588))
U32_gag(T584, T585, T586, T589, T588, pC_out_ggag(T585, T584, T589, T588)) → deleteD_out_gag(T584, tree(T585, T586, T589), tree(T585, T586, T588))
deleteD_in_gag(s(T607), tree(0, T599, T602), tree(0, T599, T601)) → U33_gag(T607, T599, T602, T601, deleteD_in_gag(s(T607), T602, T601))
deleteD_in_gag(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601)) → U34_gag(T617, T616, T599, T602, T601, pG_in_ggag(T616, T617, T602, T601))
U34_gag(T617, T616, T599, T602, T601, pG_out_ggag(T616, T617, T602, T601)) → deleteD_out_gag(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601))
deleteD_in_gag(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670))) → U35_gag(T625, T626, T665, T671, T667, T668, T669, T670, delminA_in_agg(T671, T668, T669))
U35_gag(T625, T626, T665, T671, T667, T668, T669, T670, delminA_out_agg(T671, T668, T669)) → deleteD_out_gag(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670)))
deleteD_in_gag(T696, tree(T697, T701, T699), tree(T697, T700, T699)) → U36_gag(T696, T697, T701, T699, T700, pE_in_ggag(T696, T697, T701, T700))
U36_gag(T696, T697, T701, T699, T700, pE_out_ggag(T696, T697, T701, T700)) → deleteD_out_gag(T696, tree(T697, T701, T699), tree(T697, T700, T699))
deleteD_in_gag(T714, tree(T715, T716, T719), tree(T715, T716, T718)) → U37_gag(T714, T715, T716, T719, T718, pC_in_ggag(T715, T714, T719, T718))
U37_gag(T714, T715, T716, T719, T718, pC_out_ggag(T715, T714, T719, T718)) → deleteD_out_gag(T714, tree(T715, T716, T719), tree(T715, T716, T718))
deleteD_in_gag(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730)) → U38_gag(T737, T732, T730, T731, deleteD_in_gag(0, T732, T731))
deleteD_in_gag(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730)) → U39_gag(T748, T749, T732, T730, T731, pF_in_ggag(T748, T749, T732, T731))
U39_gag(T748, T749, T732, T730, T731, pF_out_ggag(T748, T749, T732, T731)) → deleteD_out_gag(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730))
deleteD_in_gag(T762, tree(T763, T764, T767), tree(T763, T764, T766)) → U40_gag(T762, T763, T764, T767, T766, pC_in_ggag(T763, T762, T767, T766))
U40_gag(T762, T763, T764, T767, T766, pC_out_ggag(T763, T762, T767, T766)) → deleteD_out_gag(T762, tree(T763, T764, T767), tree(T763, T764, T766))
deleteD_in_gag(s(T785), tree(0, T777, T780), tree(0, T777, T779)) → U41_gag(T785, T777, T780, T779, deleteD_in_gag(s(T785), T780, T779))
deleteD_in_gag(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779)) → U42_gag(T795, T794, T777, T780, T779, pG_in_ggag(T794, T795, T780, T779))
U42_gag(T795, T794, T777, T780, T779, pG_out_ggag(T794, T795, T780, T779)) → deleteD_out_gag(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779))
U41_gag(T785, T777, T780, T779, deleteD_out_gag(s(T785), T780, T779)) → deleteD_out_gag(s(T785), tree(0, T777, T780), tree(0, T777, T779))
U38_gag(T737, T732, T730, T731, deleteD_out_gag(0, T732, T731)) → deleteD_out_gag(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730))
U33_gag(T607, T599, T602, T601, deleteD_out_gag(s(T607), T602, T601)) → deleteD_out_gag(s(T607), tree(0, T599, T602), tree(0, T599, T601))
U30_gag(T559, T554, T552, T553, deleteD_out_gag(0, T554, T553)) → deleteD_out_gag(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552))
U25_gag(T425, T417, T420, T419, deleteD_out_gag(s(T425), T420, T419)) → deleteD_out_gag(s(T425), tree(0, T417, T420), tree(0, T417, T419))
U22_gag(T377, T372, T370, T371, deleteD_out_gag(0, T372, T371)) → deleteD_out_gag(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370))
U10_ggag(T250, T251, T236, T235, deleteD_out_gag(s(T251), T236, T235)) → pG_out_ggag(T250, T251, T236, T235)
U18_gag(T251, T250, T233, T236, T235, pG_out_ggag(T250, T251, T236, T235)) → deleteD_out_gag(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235))
U17_gag(T241, T233, T236, T235, deleteD_out_gag(s(T241), T236, T235)) → deleteD_out_gag(s(T241), tree(0, T233, T236), tree(0, T233, T235))
U8_ggag(T198, T199, T182, T181, deleteD_out_gag(s(T198), T182, T181)) → pF_out_ggag(T198, T199, T182, T181)
U15_gag(T198, T199, T182, T180, T181, pF_out_ggag(T198, T199, T182, T181)) → deleteD_out_gag(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180))
U14_gag(T187, T182, T180, T181, deleteD_out_gag(0, T182, T181)) → deleteD_out_gag(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180))
U4_ggag(T159, T158, T163, T162, deleteD_out_gag(T158, T163, T162)) → pC_out_ggag(T159, T158, T163, T162)
U13_gag(T158, T159, T160, T163, T162, pC_out_ggag(T159, T158, T163, T162)) → deleteD_out_gag(T158, tree(T159, T160, T163), tree(T159, T160, T162))
U6_ggag(T121, T122, T126, T125, deleteD_out_gag(T121, T126, T125)) → pE_out_ggag(T121, T122, T126, T125)
U12_gag(T121, T122, T126, T124, T125, pE_out_ggag(T121, T122, T126, T125)) → deleteD_out_gag(T121, tree(T122, T126, T124), tree(T122, T125, T124))

(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:

DELETED_IN_GAG(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U11_GAG(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
DELETED_IN_GAG(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)
DELETED_IN_GAG(T121, tree(T122, T126, T124), tree(T122, T125, T124)) → U12_GAG(T121, T122, T126, T124, T125, pE_in_ggag(T121, T122, T126, T125))
DELETED_IN_GAG(T121, tree(T122, T126, T124), tree(T122, T125, T124)) → PE_IN_GGAG(T121, T122, T126, T125)
PE_IN_GGAG(T121, T122, T126, T125) → U5_GGAG(T121, T122, T126, T125, lessB_in_gg(T121, T122))
PE_IN_GGAG(T121, T122, T126, T125) → LESSB_IN_GG(T121, T122)
LESSB_IN_GG(s(T140), s(T141)) → U2_GG(T140, T141, lessB_in_gg(T140, T141))
LESSB_IN_GG(s(T140), s(T141)) → LESSB_IN_GG(T140, T141)
U5_GGAG(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → U6_GGAG(T121, T122, T126, T125, deleteD_in_gag(T121, T126, T125))
U5_GGAG(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → DELETED_IN_GAG(T121, T126, T125)
DELETED_IN_GAG(T158, tree(T159, T160, T163), tree(T159, T160, T162)) → U13_GAG(T158, T159, T160, T163, T162, pC_in_ggag(T159, T158, T163, T162))
DELETED_IN_GAG(T158, tree(T159, T160, T163), tree(T159, T160, T162)) → PC_IN_GGAG(T159, T158, T163, T162)
PC_IN_GGAG(T159, T158, T163, T162) → U3_GGAG(T159, T158, T163, T162, lessB_in_gg(T159, T158))
PC_IN_GGAG(T159, T158, T163, T162) → LESSB_IN_GG(T159, T158)
U3_GGAG(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → U4_GGAG(T159, T158, T163, T162, deleteD_in_gag(T158, T163, T162))
U3_GGAG(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → DELETED_IN_GAG(T158, T163, T162)
DELETED_IN_GAG(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180)) → U14_GAG(T187, T182, T180, T181, deleteD_in_gag(0, T182, T181))
DELETED_IN_GAG(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180)) → DELETED_IN_GAG(0, T182, T181)
DELETED_IN_GAG(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180)) → U15_GAG(T198, T199, T182, T180, T181, pF_in_ggag(T198, T199, T182, T181))
DELETED_IN_GAG(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180)) → PF_IN_GGAG(T198, T199, T182, T181)
PF_IN_GGAG(T198, T199, T182, T181) → U7_GGAG(T198, T199, T182, T181, lessB_in_gg(T198, T199))
PF_IN_GGAG(T198, T199, T182, T181) → LESSB_IN_GG(T198, T199)
U7_GGAG(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → U8_GGAG(T198, T199, T182, T181, deleteD_in_gag(s(T198), T182, T181))
U7_GGAG(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → DELETED_IN_GAG(s(T198), T182, T181)
DELETED_IN_GAG(T218, tree(T219, T220, T223), tree(T219, T220, T222)) → U16_GAG(T218, T219, T220, T223, T222, pC_in_ggag(T219, T218, T223, T222))
DELETED_IN_GAG(s(T241), tree(0, T233, T236), tree(0, T233, T235)) → U17_GAG(T241, T233, T236, T235, deleteD_in_gag(s(T241), T236, T235))
DELETED_IN_GAG(s(T241), tree(0, T233, T236), tree(0, T233, T235)) → DELETED_IN_GAG(s(T241), T236, T235)
DELETED_IN_GAG(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235)) → U18_GAG(T251, T250, T233, T236, T235, pG_in_ggag(T250, T251, T236, T235))
DELETED_IN_GAG(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235)) → PG_IN_GGAG(T250, T251, T236, T235)
PG_IN_GGAG(T250, T251, T236, T235) → U9_GGAG(T250, T251, T236, T235, lessB_in_gg(T250, T251))
PG_IN_GGAG(T250, T251, T236, T235) → LESSB_IN_GG(T250, T251)
U9_GGAG(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → U10_GGAG(T250, T251, T236, T235, deleteD_in_gag(s(T251), T236, T235))
U9_GGAG(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → DELETED_IN_GAG(s(T251), T236, T235)
DELETED_IN_GAG(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310))) → U19_GAG(T265, T266, T305, T311, T307, T308, T309, T310, delminA_in_agg(T311, T308, T309))
DELETED_IN_GAG(T336, tree(T337, T341, T339), tree(T337, T340, T339)) → U20_GAG(T336, T337, T341, T339, T340, pE_in_ggag(T336, T337, T341, T340))
DELETED_IN_GAG(T354, tree(T355, T356, T359), tree(T355, T356, T358)) → U21_GAG(T354, T355, T356, T359, T358, pC_in_ggag(T355, T354, T359, T358))
DELETED_IN_GAG(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370)) → U22_GAG(T377, T372, T370, T371, deleteD_in_gag(0, T372, T371))
DELETED_IN_GAG(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370)) → U23_GAG(T388, T389, T372, T370, T371, pF_in_ggag(T388, T389, T372, T371))
DELETED_IN_GAG(T402, tree(T403, T404, T407), tree(T403, T404, T406)) → U24_GAG(T402, T403, T404, T407, T406, pC_in_ggag(T403, T402, T407, T406))
DELETED_IN_GAG(s(T425), tree(0, T417, T420), tree(0, T417, T419)) → U25_GAG(T425, T417, T420, T419, deleteD_in_gag(s(T425), T420, T419))
DELETED_IN_GAG(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419)) → U26_GAG(T435, T434, T417, T420, T419, pG_in_ggag(T434, T435, T420, T419))
DELETED_IN_GAG(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492))) → U27_GAG(T447, T448, T487, T493, T489, T490, T491, T492, delminA_in_agg(T493, T490, T491))
DELETED_IN_GAG(T518, tree(T519, T523, T521), tree(T519, T522, T521)) → U28_GAG(T518, T519, T523, T521, T522, pE_in_ggag(T518, T519, T523, T522))
DELETED_IN_GAG(T536, tree(T537, T538, T541), tree(T537, T538, T540)) → U29_GAG(T536, T537, T538, T541, T540, pC_in_ggag(T537, T536, T541, T540))
DELETED_IN_GAG(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552)) → U30_GAG(T559, T554, T552, T553, deleteD_in_gag(0, T554, T553))
DELETED_IN_GAG(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552)) → U31_GAG(T570, T571, T554, T552, T553, pF_in_ggag(T570, T571, T554, T553))
DELETED_IN_GAG(T584, tree(T585, T586, T589), tree(T585, T586, T588)) → U32_GAG(T584, T585, T586, T589, T588, pC_in_ggag(T585, T584, T589, T588))
DELETED_IN_GAG(s(T607), tree(0, T599, T602), tree(0, T599, T601)) → U33_GAG(T607, T599, T602, T601, deleteD_in_gag(s(T607), T602, T601))
DELETED_IN_GAG(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601)) → U34_GAG(T617, T616, T599, T602, T601, pG_in_ggag(T616, T617, T602, T601))
DELETED_IN_GAG(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670))) → U35_GAG(T625, T626, T665, T671, T667, T668, T669, T670, delminA_in_agg(T671, T668, T669))
DELETED_IN_GAG(T696, tree(T697, T701, T699), tree(T697, T700, T699)) → U36_GAG(T696, T697, T701, T699, T700, pE_in_ggag(T696, T697, T701, T700))
DELETED_IN_GAG(T714, tree(T715, T716, T719), tree(T715, T716, T718)) → U37_GAG(T714, T715, T716, T719, T718, pC_in_ggag(T715, T714, T719, T718))
DELETED_IN_GAG(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730)) → U38_GAG(T737, T732, T730, T731, deleteD_in_gag(0, T732, T731))
DELETED_IN_GAG(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730)) → U39_GAG(T748, T749, T732, T730, T731, pF_in_ggag(T748, T749, T732, T731))
DELETED_IN_GAG(T762, tree(T763, T764, T767), tree(T763, T764, T766)) → U40_GAG(T762, T763, T764, T767, T766, pC_in_ggag(T763, T762, T767, T766))
DELETED_IN_GAG(s(T785), tree(0, T777, T780), tree(0, T777, T779)) → U41_GAG(T785, T777, T780, T779, deleteD_in_gag(s(T785), T780, T779))
DELETED_IN_GAG(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779)) → U42_GAG(T795, T794, T777, T780, T779, pG_in_ggag(T794, T795, T780, T779))

The TRS R consists of the following rules:

deleteD_in_gag(T6, tree(T6, void, T7), T7) → deleteD_out_gag(T6, tree(T6, void, T7), T7)
deleteD_in_gag(T10, tree(T10, T11, void), T11) → deleteD_out_gag(T10, tree(T10, T11, void), T11)
deleteD_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteD_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteD_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U11_gag(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))
U11_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteD_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteD_in_gag(T121, tree(T122, T126, T124), tree(T122, T125, T124)) → U12_gag(T121, T122, T126, T124, T125, pE_in_ggag(T121, T122, T126, T125))
pE_in_ggag(T121, T122, T126, T125) → U5_ggag(T121, T122, T126, T125, lessB_in_gg(T121, T122))
lessB_in_gg(0, s(T135)) → lessB_out_gg(0, s(T135))
lessB_in_gg(s(T140), s(T141)) → U2_gg(T140, T141, lessB_in_gg(T140, T141))
U2_gg(T140, T141, lessB_out_gg(T140, T141)) → lessB_out_gg(s(T140), s(T141))
U5_ggag(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → pE_out_ggag(T121, T122, T126, T125)
U5_ggag(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → U6_ggag(T121, T122, T126, T125, deleteD_in_gag(T121, T126, T125))
deleteD_in_gag(T158, tree(T159, T160, T163), tree(T159, T160, T162)) → U13_gag(T158, T159, T160, T163, T162, pC_in_ggag(T159, T158, T163, T162))
pC_in_ggag(T159, T158, T163, T162) → U3_ggag(T159, T158, T163, T162, lessB_in_gg(T159, T158))
U3_ggag(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → pC_out_ggag(T159, T158, T163, T162)
U3_ggag(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → U4_ggag(T159, T158, T163, T162, deleteD_in_gag(T158, T163, T162))
deleteD_in_gag(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180)) → U14_gag(T187, T182, T180, T181, deleteD_in_gag(0, T182, T181))
deleteD_in_gag(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180)) → U15_gag(T198, T199, T182, T180, T181, pF_in_ggag(T198, T199, T182, T181))
pF_in_ggag(T198, T199, T182, T181) → U7_ggag(T198, T199, T182, T181, lessB_in_gg(T198, T199))
U7_ggag(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → pF_out_ggag(T198, T199, T182, T181)
U7_ggag(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → U8_ggag(T198, T199, T182, T181, deleteD_in_gag(s(T198), T182, T181))
deleteD_in_gag(T218, tree(T219, T220, T223), tree(T219, T220, T222)) → U16_gag(T218, T219, T220, T223, T222, pC_in_ggag(T219, T218, T223, T222))
U16_gag(T218, T219, T220, T223, T222, pC_out_ggag(T219, T218, T223, T222)) → deleteD_out_gag(T218, tree(T219, T220, T223), tree(T219, T220, T222))
deleteD_in_gag(s(T241), tree(0, T233, T236), tree(0, T233, T235)) → U17_gag(T241, T233, T236, T235, deleteD_in_gag(s(T241), T236, T235))
deleteD_in_gag(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235)) → U18_gag(T251, T250, T233, T236, T235, pG_in_ggag(T250, T251, T236, T235))
pG_in_ggag(T250, T251, T236, T235) → U9_ggag(T250, T251, T236, T235, lessB_in_gg(T250, T251))
U9_ggag(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → pG_out_ggag(T250, T251, T236, T235)
U9_ggag(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → U10_ggag(T250, T251, T236, T235, deleteD_in_gag(s(T251), T236, T235))
deleteD_in_gag(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310))) → U19_gag(T265, T266, T305, T311, T307, T308, T309, T310, delminA_in_agg(T311, T308, T309))
U19_gag(T265, T266, T305, T311, T307, T308, T309, T310, delminA_out_agg(T311, T308, T309)) → deleteD_out_gag(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310)))
deleteD_in_gag(T336, tree(T337, T341, T339), tree(T337, T340, T339)) → U20_gag(T336, T337, T341, T339, T340, pE_in_ggag(T336, T337, T341, T340))
U20_gag(T336, T337, T341, T339, T340, pE_out_ggag(T336, T337, T341, T340)) → deleteD_out_gag(T336, tree(T337, T341, T339), tree(T337, T340, T339))
deleteD_in_gag(T354, tree(T355, T356, T359), tree(T355, T356, T358)) → U21_gag(T354, T355, T356, T359, T358, pC_in_ggag(T355, T354, T359, T358))
U21_gag(T354, T355, T356, T359, T358, pC_out_ggag(T355, T354, T359, T358)) → deleteD_out_gag(T354, tree(T355, T356, T359), tree(T355, T356, T358))
deleteD_in_gag(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370)) → U22_gag(T377, T372, T370, T371, deleteD_in_gag(0, T372, T371))
deleteD_in_gag(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370)) → U23_gag(T388, T389, T372, T370, T371, pF_in_ggag(T388, T389, T372, T371))
U23_gag(T388, T389, T372, T370, T371, pF_out_ggag(T388, T389, T372, T371)) → deleteD_out_gag(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370))
deleteD_in_gag(T402, tree(T403, T404, T407), tree(T403, T404, T406)) → U24_gag(T402, T403, T404, T407, T406, pC_in_ggag(T403, T402, T407, T406))
U24_gag(T402, T403, T404, T407, T406, pC_out_ggag(T403, T402, T407, T406)) → deleteD_out_gag(T402, tree(T403, T404, T407), tree(T403, T404, T406))
deleteD_in_gag(s(T425), tree(0, T417, T420), tree(0, T417, T419)) → U25_gag(T425, T417, T420, T419, deleteD_in_gag(s(T425), T420, T419))
deleteD_in_gag(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419)) → U26_gag(T435, T434, T417, T420, T419, pG_in_ggag(T434, T435, T420, T419))
U26_gag(T435, T434, T417, T420, T419, pG_out_ggag(T434, T435, T420, T419)) → deleteD_out_gag(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419))
deleteD_in_gag(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492))) → U27_gag(T447, T448, T487, T493, T489, T490, T491, T492, delminA_in_agg(T493, T490, T491))
U27_gag(T447, T448, T487, T493, T489, T490, T491, T492, delminA_out_agg(T493, T490, T491)) → deleteD_out_gag(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492)))
deleteD_in_gag(T518, tree(T519, T523, T521), tree(T519, T522, T521)) → U28_gag(T518, T519, T523, T521, T522, pE_in_ggag(T518, T519, T523, T522))
U28_gag(T518, T519, T523, T521, T522, pE_out_ggag(T518, T519, T523, T522)) → deleteD_out_gag(T518, tree(T519, T523, T521), tree(T519, T522, T521))
deleteD_in_gag(T536, tree(T537, T538, T541), tree(T537, T538, T540)) → U29_gag(T536, T537, T538, T541, T540, pC_in_ggag(T537, T536, T541, T540))
U29_gag(T536, T537, T538, T541, T540, pC_out_ggag(T537, T536, T541, T540)) → deleteD_out_gag(T536, tree(T537, T538, T541), tree(T537, T538, T540))
deleteD_in_gag(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552)) → U30_gag(T559, T554, T552, T553, deleteD_in_gag(0, T554, T553))
deleteD_in_gag(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552)) → U31_gag(T570, T571, T554, T552, T553, pF_in_ggag(T570, T571, T554, T553))
U31_gag(T570, T571, T554, T552, T553, pF_out_ggag(T570, T571, T554, T553)) → deleteD_out_gag(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552))
deleteD_in_gag(T584, tree(T585, T586, T589), tree(T585, T586, T588)) → U32_gag(T584, T585, T586, T589, T588, pC_in_ggag(T585, T584, T589, T588))
U32_gag(T584, T585, T586, T589, T588, pC_out_ggag(T585, T584, T589, T588)) → deleteD_out_gag(T584, tree(T585, T586, T589), tree(T585, T586, T588))
deleteD_in_gag(s(T607), tree(0, T599, T602), tree(0, T599, T601)) → U33_gag(T607, T599, T602, T601, deleteD_in_gag(s(T607), T602, T601))
deleteD_in_gag(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601)) → U34_gag(T617, T616, T599, T602, T601, pG_in_ggag(T616, T617, T602, T601))
U34_gag(T617, T616, T599, T602, T601, pG_out_ggag(T616, T617, T602, T601)) → deleteD_out_gag(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601))
deleteD_in_gag(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670))) → U35_gag(T625, T626, T665, T671, T667, T668, T669, T670, delminA_in_agg(T671, T668, T669))
U35_gag(T625, T626, T665, T671, T667, T668, T669, T670, delminA_out_agg(T671, T668, T669)) → deleteD_out_gag(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670)))
deleteD_in_gag(T696, tree(T697, T701, T699), tree(T697, T700, T699)) → U36_gag(T696, T697, T701, T699, T700, pE_in_ggag(T696, T697, T701, T700))
U36_gag(T696, T697, T701, T699, T700, pE_out_ggag(T696, T697, T701, T700)) → deleteD_out_gag(T696, tree(T697, T701, T699), tree(T697, T700, T699))
deleteD_in_gag(T714, tree(T715, T716, T719), tree(T715, T716, T718)) → U37_gag(T714, T715, T716, T719, T718, pC_in_ggag(T715, T714, T719, T718))
U37_gag(T714, T715, T716, T719, T718, pC_out_ggag(T715, T714, T719, T718)) → deleteD_out_gag(T714, tree(T715, T716, T719), tree(T715, T716, T718))
deleteD_in_gag(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730)) → U38_gag(T737, T732, T730, T731, deleteD_in_gag(0, T732, T731))
deleteD_in_gag(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730)) → U39_gag(T748, T749, T732, T730, T731, pF_in_ggag(T748, T749, T732, T731))
U39_gag(T748, T749, T732, T730, T731, pF_out_ggag(T748, T749, T732, T731)) → deleteD_out_gag(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730))
deleteD_in_gag(T762, tree(T763, T764, T767), tree(T763, T764, T766)) → U40_gag(T762, T763, T764, T767, T766, pC_in_ggag(T763, T762, T767, T766))
U40_gag(T762, T763, T764, T767, T766, pC_out_ggag(T763, T762, T767, T766)) → deleteD_out_gag(T762, tree(T763, T764, T767), tree(T763, T764, T766))
deleteD_in_gag(s(T785), tree(0, T777, T780), tree(0, T777, T779)) → U41_gag(T785, T777, T780, T779, deleteD_in_gag(s(T785), T780, T779))
deleteD_in_gag(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779)) → U42_gag(T795, T794, T777, T780, T779, pG_in_ggag(T794, T795, T780, T779))
U42_gag(T795, T794, T777, T780, T779, pG_out_ggag(T794, T795, T780, T779)) → deleteD_out_gag(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779))
U41_gag(T785, T777, T780, T779, deleteD_out_gag(s(T785), T780, T779)) → deleteD_out_gag(s(T785), tree(0, T777, T780), tree(0, T777, T779))
U38_gag(T737, T732, T730, T731, deleteD_out_gag(0, T732, T731)) → deleteD_out_gag(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730))
U33_gag(T607, T599, T602, T601, deleteD_out_gag(s(T607), T602, T601)) → deleteD_out_gag(s(T607), tree(0, T599, T602), tree(0, T599, T601))
U30_gag(T559, T554, T552, T553, deleteD_out_gag(0, T554, T553)) → deleteD_out_gag(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552))
U25_gag(T425, T417, T420, T419, deleteD_out_gag(s(T425), T420, T419)) → deleteD_out_gag(s(T425), tree(0, T417, T420), tree(0, T417, T419))
U22_gag(T377, T372, T370, T371, deleteD_out_gag(0, T372, T371)) → deleteD_out_gag(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370))
U10_ggag(T250, T251, T236, T235, deleteD_out_gag(s(T251), T236, T235)) → pG_out_ggag(T250, T251, T236, T235)
U18_gag(T251, T250, T233, T236, T235, pG_out_ggag(T250, T251, T236, T235)) → deleteD_out_gag(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235))
U17_gag(T241, T233, T236, T235, deleteD_out_gag(s(T241), T236, T235)) → deleteD_out_gag(s(T241), tree(0, T233, T236), tree(0, T233, T235))
U8_ggag(T198, T199, T182, T181, deleteD_out_gag(s(T198), T182, T181)) → pF_out_ggag(T198, T199, T182, T181)
U15_gag(T198, T199, T182, T180, T181, pF_out_ggag(T198, T199, T182, T181)) → deleteD_out_gag(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180))
U14_gag(T187, T182, T180, T181, deleteD_out_gag(0, T182, T181)) → deleteD_out_gag(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180))
U4_ggag(T159, T158, T163, T162, deleteD_out_gag(T158, T163, T162)) → pC_out_ggag(T159, T158, T163, T162)
U13_gag(T158, T159, T160, T163, T162, pC_out_ggag(T159, T158, T163, T162)) → deleteD_out_gag(T158, tree(T159, T160, T163), tree(T159, T160, T162))
U6_ggag(T121, T122, T126, T125, deleteD_out_gag(T121, T126, T125)) → pE_out_ggag(T121, T122, T126, T125)
U12_gag(T121, T122, T126, T124, T125, pE_out_ggag(T121, T122, T126, T125)) → deleteD_out_gag(T121, tree(T122, T126, T124), tree(T122, T125, T124))

The argument filtering Pi contains the following mapping:
deleteD_in_gag(x1, x2, x3) = deleteD_in_gag(x1, x3)
deleteD_out_gag(x1, x2, x3) = deleteD_out_gag(x1, x3)
tree(x1, x2, x3) = tree(x1, x2, x3)
U11_gag(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U11_gag(x1, x2, x3, x6, x7, x8, x9)
delminA_in_agg(x1, x2, x3) = delminA_in_agg(x2, x3)
delminA_out_agg(x1, x2, x3) = delminA_out_agg(x2, x3)
U1_agg(x1, x2, x3, x4, x5, x6, x7) = U1_agg(x1, x4, x5, x6, x7)
U12_gag(x1, x2, x3, x4, x5, x6) = U12_gag(x1, x2, x4, x5, x6)
pE_in_ggag(x1, x2, x3, x4) = pE_in_ggag(x1, x2, x4)
U5_ggag(x1, x2, x3, x4, x5) = U5_ggag(x1, x2, x4, x5)
lessB_in_gg(x1, x2) = lessB_in_gg(x1, x2)
0 = 0
s(x1) = s(x1)
lessB_out_gg(x1, x2) = lessB_out_gg(x1, x2)
U2_gg(x1, x2, x3) = U2_gg(x1, x2, x3)
pE_out_ggag(x1, x2, x3, x4) = pE_out_ggag(x1, x2, x4)
U6_ggag(x1, x2, x3, x4, x5) = U6_ggag(x1, x2, x4, x5)
U13_gag(x1, x2, x3, x4, x5, x6) = U13_gag(x1, x2, x3, x5, x6)
pC_in_ggag(x1, x2, x3, x4) = pC_in_ggag(x1, x2, x4)
U3_ggag(x1, x2, x3, x4, x5) = U3_ggag(x1, x2, x4, x5)
pC_out_ggag(x1, x2, x3, x4) = pC_out_ggag(x1, x2, x4)
U4_ggag(x1, x2, x3, x4, x5) = U4_ggag(x1, x2, x4, x5)
U14_gag(x1, x2, x3, x4, x5) = U14_gag(x1, x3, x4, x5)
U15_gag(x1, x2, x3, x4, x5, x6) = U15_gag(x1, x2, x4, x5, x6)
pF_in_ggag(x1, x2, x3, x4) = pF_in_ggag(x1, x2, x4)
U7_ggag(x1, x2, x3, x4, x5) = U7_ggag(x1, x2, x4, x5)
pF_out_ggag(x1, x2, x3, x4) = pF_out_ggag(x1, x2, x4)
U8_ggag(x1, x2, x3, x4, x5) = U8_ggag(x1, x2, x4, x5)
U16_gag(x1, x2, x3, x4, x5, x6) = U16_gag(x1, x2, x3, x5, x6)
U17_gag(x1, x2, x3, x4, x5) = U17_gag(x1, x2, x4, x5)
U18_gag(x1, x2, x3, x4, x5, x6) = U18_gag(x1, x2, x3, x5, x6)
pG_in_ggag(x1, x2, x3, x4) = pG_in_ggag(x1, x2, x4)
U9_ggag(x1, x2, x3, x4, x5) = U9_ggag(x1, x2, x4, x5)
pG_out_ggag(x1, x2, x3, x4) = pG_out_ggag(x1, x2, x4)
U10_ggag(x1, x2, x3, x4, x5) = U10_ggag(x1, x2, x4, x5)
U19_gag(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U19_gag(x1, x2, x3, x6, x7, x8, x9)
U20_gag(x1, x2, x3, x4, x5, x6) = U20_gag(x1, x2, x4, x5, x6)
U21_gag(x1, x2, x3, x4, x5, x6) = U21_gag(x1, x2, x3, x5, x6)
U22_gag(x1, x2, x3, x4, x5) = U22_gag(x1, x3, x4, x5)
U23_gag(x1, x2, x3, x4, x5, x6) = U23_gag(x1, x2, x4, x5, x6)
U24_gag(x1, x2, x3, x4, x5, x6) = U24_gag(x1, x2, x3, x5, x6)
U25_gag(x1, x2, x3, x4, x5) = U25_gag(x1, x2, x4, x5)
U26_gag(x1, x2, x3, x4, x5, x6) = U26_gag(x1, x2, x3, x5, x6)
U27_gag(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U27_gag(x1, x2, x3, x6, x7, x8, x9)
U28_gag(x1, x2, x3, x4, x5, x6) = U28_gag(x1, x2, x4, x5, x6)
U29_gag(x1, x2, x3, x4, x5, x6) = U29_gag(x1, x2, x3, x5, x6)
U30_gag(x1, x2, x3, x4, x5) = U30_gag(x1, x3, x4, x5)
U31_gag(x1, x2, x3, x4, x5, x6) = U31_gag(x1, x2, x4, x5, x6)
U32_gag(x1, x2, x3, x4, x5, x6) = U32_gag(x1, x2, x3, x5, x6)
U33_gag(x1, x2, x3, x4, x5) = U33_gag(x1, x2, x4, x5)
U34_gag(x1, x2, x3, x4, x5, x6) = U34_gag(x1, x2, x3, x5, x6)
U35_gag(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U35_gag(x1, x2, x3, x6, x7, x8, x9)
U36_gag(x1, x2, x3, x4, x5, x6) = U36_gag(x1, x2, x4, x5, x6)
U37_gag(x1, x2, x3, x4, x5, x6) = U37_gag(x1, x2, x3, x5, x6)
U38_gag(x1, x2, x3, x4, x5) = U38_gag(x1, x3, x4, x5)
U39_gag(x1, x2, x3, x4, x5, x6) = U39_gag(x1, x2, x4, x5, x6)
U40_gag(x1, x2, x3, x4, x5, x6) = U40_gag(x1, x2, x3, x5, x6)
U41_gag(x1, x2, x3, x4, x5) = U41_gag(x1, x2, x4, x5)
U42_gag(x1, x2, x3, x4, x5, x6) = U42_gag(x1, x2, x3, x5, x6)
DELETED_IN_GAG(x1, x2, x3) = DELETED_IN_GAG(x1, x3)
U11_GAG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U11_GAG(x1, x2, x3, x6, x7, x8, x9)
DELMINA_IN_AGG(x1, x2, x3) = DELMINA_IN_AGG(x2, x3)
U1_AGG(x1, x2, x3, x4, x5, x6, x7) = U1_AGG(x1, x4, x5, x6, x7)
U12_GAG(x1, x2, x3, x4, x5, x6) = U12_GAG(x1, x2, x4, x5, x6)
PE_IN_GGAG(x1, x2, x3, x4) = PE_IN_GGAG(x1, x2, x4)
U5_GGAG(x1, x2, x3, x4, x5) = U5_GGAG(x1, x2, x4, x5)
LESSB_IN_GG(x1, x2) = LESSB_IN_GG(x1, x2)
U2_GG(x1, x2, x3) = U2_GG(x1, x2, x3)
U6_GGAG(x1, x2, x3, x4, x5) = U6_GGAG(x1, x2, x4, x5)
U13_GAG(x1, x2, x3, x4, x5, x6) = U13_GAG(x1, x2, x3, x5, x6)
PC_IN_GGAG(x1, x2, x3, x4) = PC_IN_GGAG(x1, x2, x4)
U3_GGAG(x1, x2, x3, x4, x5) = U3_GGAG(x1, x2, x4, x5)
U4_GGAG(x1, x2, x3, x4, x5) = U4_GGAG(x1, x2, x4, x5)
U14_GAG(x1, x2, x3, x4, x5) = U14_GAG(x1, x3, x4, x5)
U15_GAG(x1, x2, x3, x4, x5, x6) = U15_GAG(x1, x2, x4, x5, x6)
PF_IN_GGAG(x1, x2, x3, x4) = PF_IN_GGAG(x1, x2, x4)
U7_GGAG(x1, x2, x3, x4, x5) = U7_GGAG(x1, x2, x4, x5)
U8_GGAG(x1, x2, x3, x4, x5) = U8_GGAG(x1, x2, x4, x5)
U16_GAG(x1, x2, x3, x4, x5, x6) = U16_GAG(x1, x2, x3, x5, x6)
U17_GAG(x1, x2, x3, x4, x5) = U17_GAG(x1, x2, x4, x5)
U18_GAG(x1, x2, x3, x4, x5, x6) = U18_GAG(x1, x2, x3, x5, x6)
PG_IN_GGAG(x1, x2, x3, x4) = PG_IN_GGAG(x1, x2, x4)
U9_GGAG(x1, x2, x3, x4, x5) = U9_GGAG(x1, x2, x4, x5)
U10_GGAG(x1, x2, x3, x4, x5) = U10_GGAG(x1, x2, x4, x5)
U19_GAG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U19_GAG(x1, x2, x3, x6, x7, x8, x9)
U20_GAG(x1, x2, x3, x4, x5, x6) = U20_GAG(x1, x2, x4, x5, x6)
U21_GAG(x1, x2, x3, x4, x5, x6) = U21_GAG(x1, x2, x3, x5, x6)
U22_GAG(x1, x2, x3, x4, x5) = U22_GAG(x1, x3, x4, x5)
U23_GAG(x1, x2, x3, x4, x5, x6) = U23_GAG(x1, x2, x4, x5, x6)
U24_GAG(x1, x2, x3, x4, x5, x6) = U24_GAG(x1, x2, x3, x5, x6)
U25_GAG(x1, x2, x3, x4, x5) = U25_GAG(x1, x2, x4, x5)
U26_GAG(x1, x2, x3, x4, x5, x6) = U26_GAG(x1, x2, x3, x5, x6)
U27_GAG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U27_GAG(x1, x2, x3, x6, x7, x8, x9)
U28_GAG(x1, x2, x3, x4, x5, x6) = U28_GAG(x1, x2, x4, x5, x6)
U29_GAG(x1, x2, x3, x4, x5, x6) = U29_GAG(x1, x2, x3, x5, x6)
U30_GAG(x1, x2, x3, x4, x5) = U30_GAG(x1, x3, x4, x5)
U31_GAG(x1, x2, x3, x4, x5, x6) = U31_GAG(x1, x2, x4, x5, x6)
U32_GAG(x1, x2, x3, x4, x5, x6) = U32_GAG(x1, x2, x3, x5, x6)
U33_GAG(x1, x2, x3, x4, x5) = U33_GAG(x1, x2, x4, x5)
U34_GAG(x1, x2, x3, x4, x5, x6) = U34_GAG(x1, x2, x3, x5, x6)
U35_GAG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U35_GAG(x1, x2, x3, x6, x7, x8, x9)
U36_GAG(x1, x2, x3, x4, x5, x6) = U36_GAG(x1, x2, x4, x5, x6)
U37_GAG(x1, x2, x3, x4, x5, x6) = U37_GAG(x1, x2, x3, x5, x6)
U38_GAG(x1, x2, x3, x4, x5) = U38_GAG(x1, x3, x4, x5)
U39_GAG(x1, x2, x3, x4, x5, x6) = U39_GAG(x1, x2, x4, x5, x6)
U40_GAG(x1, x2, x3, x4, x5, x6) = U40_GAG(x1, x2, x3, x5, x6)
U41_GAG(x1, x2, x3, x4, x5) = U41_GAG(x1, x2, x4, x5)
U42_GAG(x1, x2, x3, x4, x5, x6) = U42_GAG(x1, x2, x3, x5, x6)

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

(6) Obligation:

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

DELETED_IN_GAG(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U11_GAG(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
DELETED_IN_GAG(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)
DELETED_IN_GAG(T121, tree(T122, T126, T124), tree(T122, T125, T124)) → U12_GAG(T121, T122, T126, T124, T125, pE_in_ggag(T121, T122, T126, T125))
DELETED_IN_GAG(T121, tree(T122, T126, T124), tree(T122, T125, T124)) → PE_IN_GGAG(T121, T122, T126, T125)
PE_IN_GGAG(T121, T122, T126, T125) → U5_GGAG(T121, T122, T126, T125, lessB_in_gg(T121, T122))
PE_IN_GGAG(T121, T122, T126, T125) → LESSB_IN_GG(T121, T122)
LESSB_IN_GG(s(T140), s(T141)) → U2_GG(T140, T141, lessB_in_gg(T140, T141))
LESSB_IN_GG(s(T140), s(T141)) → LESSB_IN_GG(T140, T141)
U5_GGAG(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → U6_GGAG(T121, T122, T126, T125, deleteD_in_gag(T121, T126, T125))
U5_GGAG(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → DELETED_IN_GAG(T121, T126, T125)
DELETED_IN_GAG(T158, tree(T159, T160, T163), tree(T159, T160, T162)) → U13_GAG(T158, T159, T160, T163, T162, pC_in_ggag(T159, T158, T163, T162))
DELETED_IN_GAG(T158, tree(T159, T160, T163), tree(T159, T160, T162)) → PC_IN_GGAG(T159, T158, T163, T162)
PC_IN_GGAG(T159, T158, T163, T162) → U3_GGAG(T159, T158, T163, T162, lessB_in_gg(T159, T158))
PC_IN_GGAG(T159, T158, T163, T162) → LESSB_IN_GG(T159, T158)
U3_GGAG(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → U4_GGAG(T159, T158, T163, T162, deleteD_in_gag(T158, T163, T162))
U3_GGAG(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → DELETED_IN_GAG(T158, T163, T162)
DELETED_IN_GAG(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180)) → U14_GAG(T187, T182, T180, T181, deleteD_in_gag(0, T182, T181))
DELETED_IN_GAG(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180)) → DELETED_IN_GAG(0, T182, T181)
DELETED_IN_GAG(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180)) → U15_GAG(T198, T199, T182, T180, T181, pF_in_ggag(T198, T199, T182, T181))
DELETED_IN_GAG(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180)) → PF_IN_GGAG(T198, T199, T182, T181)
PF_IN_GGAG(T198, T199, T182, T181) → U7_GGAG(T198, T199, T182, T181, lessB_in_gg(T198, T199))
PF_IN_GGAG(T198, T199, T182, T181) → LESSB_IN_GG(T198, T199)
U7_GGAG(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → U8_GGAG(T198, T199, T182, T181, deleteD_in_gag(s(T198), T182, T181))
U7_GGAG(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → DELETED_IN_GAG(s(T198), T182, T181)
DELETED_IN_GAG(T218, tree(T219, T220, T223), tree(T219, T220, T222)) → U16_GAG(T218, T219, T220, T223, T222, pC_in_ggag(T219, T218, T223, T222))
DELETED_IN_GAG(s(T241), tree(0, T233, T236), tree(0, T233, T235)) → U17_GAG(T241, T233, T236, T235, deleteD_in_gag(s(T241), T236, T235))
DELETED_IN_GAG(s(T241), tree(0, T233, T236), tree(0, T233, T235)) → DELETED_IN_GAG(s(T241), T236, T235)
DELETED_IN_GAG(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235)) → U18_GAG(T251, T250, T233, T236, T235, pG_in_ggag(T250, T251, T236, T235))
DELETED_IN_GAG(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235)) → PG_IN_GGAG(T250, T251, T236, T235)
PG_IN_GGAG(T250, T251, T236, T235) → U9_GGAG(T250, T251, T236, T235, lessB_in_gg(T250, T251))
PG_IN_GGAG(T250, T251, T236, T235) → LESSB_IN_GG(T250, T251)
U9_GGAG(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → U10_GGAG(T250, T251, T236, T235, deleteD_in_gag(s(T251), T236, T235))
U9_GGAG(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → DELETED_IN_GAG(s(T251), T236, T235)
DELETED_IN_GAG(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310))) → U19_GAG(T265, T266, T305, T311, T307, T308, T309, T310, delminA_in_agg(T311, T308, T309))
DELETED_IN_GAG(T336, tree(T337, T341, T339), tree(T337, T340, T339)) → U20_GAG(T336, T337, T341, T339, T340, pE_in_ggag(T336, T337, T341, T340))
DELETED_IN_GAG(T354, tree(T355, T356, T359), tree(T355, T356, T358)) → U21_GAG(T354, T355, T356, T359, T358, pC_in_ggag(T355, T354, T359, T358))
DELETED_IN_GAG(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370)) → U22_GAG(T377, T372, T370, T371, deleteD_in_gag(0, T372, T371))
DELETED_IN_GAG(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370)) → U23_GAG(T388, T389, T372, T370, T371, pF_in_ggag(T388, T389, T372, T371))
DELETED_IN_GAG(T402, tree(T403, T404, T407), tree(T403, T404, T406)) → U24_GAG(T402, T403, T404, T407, T406, pC_in_ggag(T403, T402, T407, T406))
DELETED_IN_GAG(s(T425), tree(0, T417, T420), tree(0, T417, T419)) → U25_GAG(T425, T417, T420, T419, deleteD_in_gag(s(T425), T420, T419))
DELETED_IN_GAG(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419)) → U26_GAG(T435, T434, T417, T420, T419, pG_in_ggag(T434, T435, T420, T419))
DELETED_IN_GAG(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492))) → U27_GAG(T447, T448, T487, T493, T489, T490, T491, T492, delminA_in_agg(T493, T490, T491))
DELETED_IN_GAG(T518, tree(T519, T523, T521), tree(T519, T522, T521)) → U28_GAG(T518, T519, T523, T521, T522, pE_in_ggag(T518, T519, T523, T522))
DELETED_IN_GAG(T536, tree(T537, T538, T541), tree(T537, T538, T540)) → U29_GAG(T536, T537, T538, T541, T540, pC_in_ggag(T537, T536, T541, T540))
DELETED_IN_GAG(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552)) → U30_GAG(T559, T554, T552, T553, deleteD_in_gag(0, T554, T553))
DELETED_IN_GAG(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552)) → U31_GAG(T570, T571, T554, T552, T553, pF_in_ggag(T570, T571, T554, T553))
DELETED_IN_GAG(T584, tree(T585, T586, T589), tree(T585, T586, T588)) → U32_GAG(T584, T585, T586, T589, T588, pC_in_ggag(T585, T584, T589, T588))
DELETED_IN_GAG(s(T607), tree(0, T599, T602), tree(0, T599, T601)) → U33_GAG(T607, T599, T602, T601, deleteD_in_gag(s(T607), T602, T601))
DELETED_IN_GAG(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601)) → U34_GAG(T617, T616, T599, T602, T601, pG_in_ggag(T616, T617, T602, T601))
DELETED_IN_GAG(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670))) → U35_GAG(T625, T626, T665, T671, T667, T668, T669, T670, delminA_in_agg(T671, T668, T669))
DELETED_IN_GAG(T696, tree(T697, T701, T699), tree(T697, T700, T699)) → U36_GAG(T696, T697, T701, T699, T700, pE_in_ggag(T696, T697, T701, T700))
DELETED_IN_GAG(T714, tree(T715, T716, T719), tree(T715, T716, T718)) → U37_GAG(T714, T715, T716, T719, T718, pC_in_ggag(T715, T714, T719, T718))
DELETED_IN_GAG(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730)) → U38_GAG(T737, T732, T730, T731, deleteD_in_gag(0, T732, T731))
DELETED_IN_GAG(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730)) → U39_GAG(T748, T749, T732, T730, T731, pF_in_ggag(T748, T749, T732, T731))
DELETED_IN_GAG(T762, tree(T763, T764, T767), tree(T763, T764, T766)) → U40_GAG(T762, T763, T764, T767, T766, pC_in_ggag(T763, T762, T767, T766))
DELETED_IN_GAG(s(T785), tree(0, T777, T780), tree(0, T777, T779)) → U41_GAG(T785, T777, T780, T779, deleteD_in_gag(s(T785), T780, T779))
DELETED_IN_GAG(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779)) → U42_GAG(T795, T794, T777, T780, T779, pG_in_ggag(T794, T795, T780, T779))

The TRS R consists of the following rules:

deleteD_in_gag(T6, tree(T6, void, T7), T7) → deleteD_out_gag(T6, tree(T6, void, T7), T7)
deleteD_in_gag(T10, tree(T10, T11, void), T11) → deleteD_out_gag(T10, tree(T10, T11, void), T11)
deleteD_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteD_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteD_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U11_gag(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))
U11_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteD_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteD_in_gag(T121, tree(T122, T126, T124), tree(T122, T125, T124)) → U12_gag(T121, T122, T126, T124, T125, pE_in_ggag(T121, T122, T126, T125))
pE_in_ggag(T121, T122, T126, T125) → U5_ggag(T121, T122, T126, T125, lessB_in_gg(T121, T122))
lessB_in_gg(0, s(T135)) → lessB_out_gg(0, s(T135))
lessB_in_gg(s(T140), s(T141)) → U2_gg(T140, T141, lessB_in_gg(T140, T141))
U2_gg(T140, T141, lessB_out_gg(T140, T141)) → lessB_out_gg(s(T140), s(T141))
U5_ggag(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → pE_out_ggag(T121, T122, T126, T125)
U5_ggag(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → U6_ggag(T121, T122, T126, T125, deleteD_in_gag(T121, T126, T125))
deleteD_in_gag(T158, tree(T159, T160, T163), tree(T159, T160, T162)) → U13_gag(T158, T159, T160, T163, T162, pC_in_ggag(T159, T158, T163, T162))
pC_in_ggag(T159, T158, T163, T162) → U3_ggag(T159, T158, T163, T162, lessB_in_gg(T159, T158))
U3_ggag(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → pC_out_ggag(T159, T158, T163, T162)
U3_ggag(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → U4_ggag(T159, T158, T163, T162, deleteD_in_gag(T158, T163, T162))
deleteD_in_gag(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180)) → U14_gag(T187, T182, T180, T181, deleteD_in_gag(0, T182, T181))
deleteD_in_gag(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180)) → U15_gag(T198, T199, T182, T180, T181, pF_in_ggag(T198, T199, T182, T181))
pF_in_ggag(T198, T199, T182, T181) → U7_ggag(T198, T199, T182, T181, lessB_in_gg(T198, T199))
U7_ggag(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → pF_out_ggag(T198, T199, T182, T181)
U7_ggag(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → U8_ggag(T198, T199, T182, T181, deleteD_in_gag(s(T198), T182, T181))
deleteD_in_gag(T218, tree(T219, T220, T223), tree(T219, T220, T222)) → U16_gag(T218, T219, T220, T223, T222, pC_in_ggag(T219, T218, T223, T222))
U16_gag(T218, T219, T220, T223, T222, pC_out_ggag(T219, T218, T223, T222)) → deleteD_out_gag(T218, tree(T219, T220, T223), tree(T219, T220, T222))
deleteD_in_gag(s(T241), tree(0, T233, T236), tree(0, T233, T235)) → U17_gag(T241, T233, T236, T235, deleteD_in_gag(s(T241), T236, T235))
deleteD_in_gag(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235)) → U18_gag(T251, T250, T233, T236, T235, pG_in_ggag(T250, T251, T236, T235))
pG_in_ggag(T250, T251, T236, T235) → U9_ggag(T250, T251, T236, T235, lessB_in_gg(T250, T251))
U9_ggag(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → pG_out_ggag(T250, T251, T236, T235)
U9_ggag(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → U10_ggag(T250, T251, T236, T235, deleteD_in_gag(s(T251), T236, T235))
deleteD_in_gag(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310))) → U19_gag(T265, T266, T305, T311, T307, T308, T309, T310, delminA_in_agg(T311, T308, T309))
U19_gag(T265, T266, T305, T311, T307, T308, T309, T310, delminA_out_agg(T311, T308, T309)) → deleteD_out_gag(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310)))
deleteD_in_gag(T336, tree(T337, T341, T339), tree(T337, T340, T339)) → U20_gag(T336, T337, T341, T339, T340, pE_in_ggag(T336, T337, T341, T340))
U20_gag(T336, T337, T341, T339, T340, pE_out_ggag(T336, T337, T341, T340)) → deleteD_out_gag(T336, tree(T337, T341, T339), tree(T337, T340, T339))
deleteD_in_gag(T354, tree(T355, T356, T359), tree(T355, T356, T358)) → U21_gag(T354, T355, T356, T359, T358, pC_in_ggag(T355, T354, T359, T358))
U21_gag(T354, T355, T356, T359, T358, pC_out_ggag(T355, T354, T359, T358)) → deleteD_out_gag(T354, tree(T355, T356, T359), tree(T355, T356, T358))
deleteD_in_gag(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370)) → U22_gag(T377, T372, T370, T371, deleteD_in_gag(0, T372, T371))
deleteD_in_gag(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370)) → U23_gag(T388, T389, T372, T370, T371, pF_in_ggag(T388, T389, T372, T371))
U23_gag(T388, T389, T372, T370, T371, pF_out_ggag(T388, T389, T372, T371)) → deleteD_out_gag(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370))
deleteD_in_gag(T402, tree(T403, T404, T407), tree(T403, T404, T406)) → U24_gag(T402, T403, T404, T407, T406, pC_in_ggag(T403, T402, T407, T406))
U24_gag(T402, T403, T404, T407, T406, pC_out_ggag(T403, T402, T407, T406)) → deleteD_out_gag(T402, tree(T403, T404, T407), tree(T403, T404, T406))
deleteD_in_gag(s(T425), tree(0, T417, T420), tree(0, T417, T419)) → U25_gag(T425, T417, T420, T419, deleteD_in_gag(s(T425), T420, T419))
deleteD_in_gag(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419)) → U26_gag(T435, T434, T417, T420, T419, pG_in_ggag(T434, T435, T420, T419))
U26_gag(T435, T434, T417, T420, T419, pG_out_ggag(T434, T435, T420, T419)) → deleteD_out_gag(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419))
deleteD_in_gag(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492))) → U27_gag(T447, T448, T487, T493, T489, T490, T491, T492, delminA_in_agg(T493, T490, T491))
U27_gag(T447, T448, T487, T493, T489, T490, T491, T492, delminA_out_agg(T493, T490, T491)) → deleteD_out_gag(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492)))
deleteD_in_gag(T518, tree(T519, T523, T521), tree(T519, T522, T521)) → U28_gag(T518, T519, T523, T521, T522, pE_in_ggag(T518, T519, T523, T522))
U28_gag(T518, T519, T523, T521, T522, pE_out_ggag(T518, T519, T523, T522)) → deleteD_out_gag(T518, tree(T519, T523, T521), tree(T519, T522, T521))
deleteD_in_gag(T536, tree(T537, T538, T541), tree(T537, T538, T540)) → U29_gag(T536, T537, T538, T541, T540, pC_in_ggag(T537, T536, T541, T540))
U29_gag(T536, T537, T538, T541, T540, pC_out_ggag(T537, T536, T541, T540)) → deleteD_out_gag(T536, tree(T537, T538, T541), tree(T537, T538, T540))
deleteD_in_gag(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552)) → U30_gag(T559, T554, T552, T553, deleteD_in_gag(0, T554, T553))
deleteD_in_gag(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552)) → U31_gag(T570, T571, T554, T552, T553, pF_in_ggag(T570, T571, T554, T553))
U31_gag(T570, T571, T554, T552, T553, pF_out_ggag(T570, T571, T554, T553)) → deleteD_out_gag(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552))
deleteD_in_gag(T584, tree(T585, T586, T589), tree(T585, T586, T588)) → U32_gag(T584, T585, T586, T589, T588, pC_in_ggag(T585, T584, T589, T588))
U32_gag(T584, T585, T586, T589, T588, pC_out_ggag(T585, T584, T589, T588)) → deleteD_out_gag(T584, tree(T585, T586, T589), tree(T585, T586, T588))
deleteD_in_gag(s(T607), tree(0, T599, T602), tree(0, T599, T601)) → U33_gag(T607, T599, T602, T601, deleteD_in_gag(s(T607), T602, T601))
deleteD_in_gag(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601)) → U34_gag(T617, T616, T599, T602, T601, pG_in_ggag(T616, T617, T602, T601))
U34_gag(T617, T616, T599, T602, T601, pG_out_ggag(T616, T617, T602, T601)) → deleteD_out_gag(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601))
deleteD_in_gag(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670))) → U35_gag(T625, T626, T665, T671, T667, T668, T669, T670, delminA_in_agg(T671, T668, T669))
U35_gag(T625, T626, T665, T671, T667, T668, T669, T670, delminA_out_agg(T671, T668, T669)) → deleteD_out_gag(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670)))
deleteD_in_gag(T696, tree(T697, T701, T699), tree(T697, T700, T699)) → U36_gag(T696, T697, T701, T699, T700, pE_in_ggag(T696, T697, T701, T700))
U36_gag(T696, T697, T701, T699, T700, pE_out_ggag(T696, T697, T701, T700)) → deleteD_out_gag(T696, tree(T697, T701, T699), tree(T697, T700, T699))
deleteD_in_gag(T714, tree(T715, T716, T719), tree(T715, T716, T718)) → U37_gag(T714, T715, T716, T719, T718, pC_in_ggag(T715, T714, T719, T718))
U37_gag(T714, T715, T716, T719, T718, pC_out_ggag(T715, T714, T719, T718)) → deleteD_out_gag(T714, tree(T715, T716, T719), tree(T715, T716, T718))
deleteD_in_gag(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730)) → U38_gag(T737, T732, T730, T731, deleteD_in_gag(0, T732, T731))
deleteD_in_gag(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730)) → U39_gag(T748, T749, T732, T730, T731, pF_in_ggag(T748, T749, T732, T731))
U39_gag(T748, T749, T732, T730, T731, pF_out_ggag(T748, T749, T732, T731)) → deleteD_out_gag(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730))
deleteD_in_gag(T762, tree(T763, T764, T767), tree(T763, T764, T766)) → U40_gag(T762, T763, T764, T767, T766, pC_in_ggag(T763, T762, T767, T766))
U40_gag(T762, T763, T764, T767, T766, pC_out_ggag(T763, T762, T767, T766)) → deleteD_out_gag(T762, tree(T763, T764, T767), tree(T763, T764, T766))
deleteD_in_gag(s(T785), tree(0, T777, T780), tree(0, T777, T779)) → U41_gag(T785, T777, T780, T779, deleteD_in_gag(s(T785), T780, T779))
deleteD_in_gag(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779)) → U42_gag(T795, T794, T777, T780, T779, pG_in_ggag(T794, T795, T780, T779))
U42_gag(T795, T794, T777, T780, T779, pG_out_ggag(T794, T795, T780, T779)) → deleteD_out_gag(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779))
U41_gag(T785, T777, T780, T779, deleteD_out_gag(s(T785), T780, T779)) → deleteD_out_gag(s(T785), tree(0, T777, T780), tree(0, T777, T779))
U38_gag(T737, T732, T730, T731, deleteD_out_gag(0, T732, T731)) → deleteD_out_gag(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730))
U33_gag(T607, T599, T602, T601, deleteD_out_gag(s(T607), T602, T601)) → deleteD_out_gag(s(T607), tree(0, T599, T602), tree(0, T599, T601))
U30_gag(T559, T554, T552, T553, deleteD_out_gag(0, T554, T553)) → deleteD_out_gag(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552))
U25_gag(T425, T417, T420, T419, deleteD_out_gag(s(T425), T420, T419)) → deleteD_out_gag(s(T425), tree(0, T417, T420), tree(0, T417, T419))
U22_gag(T377, T372, T370, T371, deleteD_out_gag(0, T372, T371)) → deleteD_out_gag(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370))
U10_ggag(T250, T251, T236, T235, deleteD_out_gag(s(T251), T236, T235)) → pG_out_ggag(T250, T251, T236, T235)
U18_gag(T251, T250, T233, T236, T235, pG_out_ggag(T250, T251, T236, T235)) → deleteD_out_gag(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235))
U17_gag(T241, T233, T236, T235, deleteD_out_gag(s(T241), T236, T235)) → deleteD_out_gag(s(T241), tree(0, T233, T236), tree(0, T233, T235))
U8_ggag(T198, T199, T182, T181, deleteD_out_gag(s(T198), T182, T181)) → pF_out_ggag(T198, T199, T182, T181)
U15_gag(T198, T199, T182, T180, T181, pF_out_ggag(T198, T199, T182, T181)) → deleteD_out_gag(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180))
U14_gag(T187, T182, T180, T181, deleteD_out_gag(0, T182, T181)) → deleteD_out_gag(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180))
U4_ggag(T159, T158, T163, T162, deleteD_out_gag(T158, T163, T162)) → pC_out_ggag(T159, T158, T163, T162)
U13_gag(T158, T159, T160, T163, T162, pC_out_ggag(T159, T158, T163, T162)) → deleteD_out_gag(T158, tree(T159, T160, T163), tree(T159, T160, T162))
U6_ggag(T121, T122, T126, T125, deleteD_out_gag(T121, T126, T125)) → pE_out_ggag(T121, T122, T126, T125)
U12_gag(T121, T122, T126, T124, T125, pE_out_ggag(T121, T122, T126, T125)) → deleteD_out_gag(T121, tree(T122, T126, T124), tree(T122, T125, T124))

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 3 SCCs with 43 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

LESSB_IN_GG(s(T140), s(T141)) → LESSB_IN_GG(T140, T141)

The TRS R consists of the following rules:

deleteD_in_gag(T6, tree(T6, void, T7), T7) → deleteD_out_gag(T6, tree(T6, void, T7), T7)
deleteD_in_gag(T10, tree(T10, T11, void), T11) → deleteD_out_gag(T10, tree(T10, T11, void), T11)
deleteD_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteD_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteD_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U11_gag(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))
U11_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteD_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteD_in_gag(T121, tree(T122, T126, T124), tree(T122, T125, T124)) → U12_gag(T121, T122, T126, T124, T125, pE_in_ggag(T121, T122, T126, T125))
pE_in_ggag(T121, T122, T126, T125) → U5_ggag(T121, T122, T126, T125, lessB_in_gg(T121, T122))
lessB_in_gg(0, s(T135)) → lessB_out_gg(0, s(T135))
lessB_in_gg(s(T140), s(T141)) → U2_gg(T140, T141, lessB_in_gg(T140, T141))
U2_gg(T140, T141, lessB_out_gg(T140, T141)) → lessB_out_gg(s(T140), s(T141))
U5_ggag(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → pE_out_ggag(T121, T122, T126, T125)
U5_ggag(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → U6_ggag(T121, T122, T126, T125, deleteD_in_gag(T121, T126, T125))
deleteD_in_gag(T158, tree(T159, T160, T163), tree(T159, T160, T162)) → U13_gag(T158, T159, T160, T163, T162, pC_in_ggag(T159, T158, T163, T162))
pC_in_ggag(T159, T158, T163, T162) → U3_ggag(T159, T158, T163, T162, lessB_in_gg(T159, T158))
U3_ggag(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → pC_out_ggag(T159, T158, T163, T162)
U3_ggag(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → U4_ggag(T159, T158, T163, T162, deleteD_in_gag(T158, T163, T162))
deleteD_in_gag(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180)) → U14_gag(T187, T182, T180, T181, deleteD_in_gag(0, T182, T181))
deleteD_in_gag(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180)) → U15_gag(T198, T199, T182, T180, T181, pF_in_ggag(T198, T199, T182, T181))
pF_in_ggag(T198, T199, T182, T181) → U7_ggag(T198, T199, T182, T181, lessB_in_gg(T198, T199))
U7_ggag(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → pF_out_ggag(T198, T199, T182, T181)
U7_ggag(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → U8_ggag(T198, T199, T182, T181, deleteD_in_gag(s(T198), T182, T181))
deleteD_in_gag(T218, tree(T219, T220, T223), tree(T219, T220, T222)) → U16_gag(T218, T219, T220, T223, T222, pC_in_ggag(T219, T218, T223, T222))
U16_gag(T218, T219, T220, T223, T222, pC_out_ggag(T219, T218, T223, T222)) → deleteD_out_gag(T218, tree(T219, T220, T223), tree(T219, T220, T222))
deleteD_in_gag(s(T241), tree(0, T233, T236), tree(0, T233, T235)) → U17_gag(T241, T233, T236, T235, deleteD_in_gag(s(T241), T236, T235))
deleteD_in_gag(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235)) → U18_gag(T251, T250, T233, T236, T235, pG_in_ggag(T250, T251, T236, T235))
pG_in_ggag(T250, T251, T236, T235) → U9_ggag(T250, T251, T236, T235, lessB_in_gg(T250, T251))
U9_ggag(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → pG_out_ggag(T250, T251, T236, T235)
U9_ggag(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → U10_ggag(T250, T251, T236, T235, deleteD_in_gag(s(T251), T236, T235))
deleteD_in_gag(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310))) → U19_gag(T265, T266, T305, T311, T307, T308, T309, T310, delminA_in_agg(T311, T308, T309))
U19_gag(T265, T266, T305, T311, T307, T308, T309, T310, delminA_out_agg(T311, T308, T309)) → deleteD_out_gag(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310)))
deleteD_in_gag(T336, tree(T337, T341, T339), tree(T337, T340, T339)) → U20_gag(T336, T337, T341, T339, T340, pE_in_ggag(T336, T337, T341, T340))
U20_gag(T336, T337, T341, T339, T340, pE_out_ggag(T336, T337, T341, T340)) → deleteD_out_gag(T336, tree(T337, T341, T339), tree(T337, T340, T339))
deleteD_in_gag(T354, tree(T355, T356, T359), tree(T355, T356, T358)) → U21_gag(T354, T355, T356, T359, T358, pC_in_ggag(T355, T354, T359, T358))
U21_gag(T354, T355, T356, T359, T358, pC_out_ggag(T355, T354, T359, T358)) → deleteD_out_gag(T354, tree(T355, T356, T359), tree(T355, T356, T358))
deleteD_in_gag(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370)) → U22_gag(T377, T372, T370, T371, deleteD_in_gag(0, T372, T371))
deleteD_in_gag(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370)) → U23_gag(T388, T389, T372, T370, T371, pF_in_ggag(T388, T389, T372, T371))
U23_gag(T388, T389, T372, T370, T371, pF_out_ggag(T388, T389, T372, T371)) → deleteD_out_gag(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370))
deleteD_in_gag(T402, tree(T403, T404, T407), tree(T403, T404, T406)) → U24_gag(T402, T403, T404, T407, T406, pC_in_ggag(T403, T402, T407, T406))
U24_gag(T402, T403, T404, T407, T406, pC_out_ggag(T403, T402, T407, T406)) → deleteD_out_gag(T402, tree(T403, T404, T407), tree(T403, T404, T406))
deleteD_in_gag(s(T425), tree(0, T417, T420), tree(0, T417, T419)) → U25_gag(T425, T417, T420, T419, deleteD_in_gag(s(T425), T420, T419))
deleteD_in_gag(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419)) → U26_gag(T435, T434, T417, T420, T419, pG_in_ggag(T434, T435, T420, T419))
U26_gag(T435, T434, T417, T420, T419, pG_out_ggag(T434, T435, T420, T419)) → deleteD_out_gag(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419))
deleteD_in_gag(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492))) → U27_gag(T447, T448, T487, T493, T489, T490, T491, T492, delminA_in_agg(T493, T490, T491))
U27_gag(T447, T448, T487, T493, T489, T490, T491, T492, delminA_out_agg(T493, T490, T491)) → deleteD_out_gag(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492)))
deleteD_in_gag(T518, tree(T519, T523, T521), tree(T519, T522, T521)) → U28_gag(T518, T519, T523, T521, T522, pE_in_ggag(T518, T519, T523, T522))
U28_gag(T518, T519, T523, T521, T522, pE_out_ggag(T518, T519, T523, T522)) → deleteD_out_gag(T518, tree(T519, T523, T521), tree(T519, T522, T521))
deleteD_in_gag(T536, tree(T537, T538, T541), tree(T537, T538, T540)) → U29_gag(T536, T537, T538, T541, T540, pC_in_ggag(T537, T536, T541, T540))
U29_gag(T536, T537, T538, T541, T540, pC_out_ggag(T537, T536, T541, T540)) → deleteD_out_gag(T536, tree(T537, T538, T541), tree(T537, T538, T540))
deleteD_in_gag(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552)) → U30_gag(T559, T554, T552, T553, deleteD_in_gag(0, T554, T553))
deleteD_in_gag(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552)) → U31_gag(T570, T571, T554, T552, T553, pF_in_ggag(T570, T571, T554, T553))
U31_gag(T570, T571, T554, T552, T553, pF_out_ggag(T570, T571, T554, T553)) → deleteD_out_gag(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552))
deleteD_in_gag(T584, tree(T585, T586, T589), tree(T585, T586, T588)) → U32_gag(T584, T585, T586, T589, T588, pC_in_ggag(T585, T584, T589, T588))
U32_gag(T584, T585, T586, T589, T588, pC_out_ggag(T585, T584, T589, T588)) → deleteD_out_gag(T584, tree(T585, T586, T589), tree(T585, T586, T588))
deleteD_in_gag(s(T607), tree(0, T599, T602), tree(0, T599, T601)) → U33_gag(T607, T599, T602, T601, deleteD_in_gag(s(T607), T602, T601))
deleteD_in_gag(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601)) → U34_gag(T617, T616, T599, T602, T601, pG_in_ggag(T616, T617, T602, T601))
U34_gag(T617, T616, T599, T602, T601, pG_out_ggag(T616, T617, T602, T601)) → deleteD_out_gag(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601))
deleteD_in_gag(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670))) → U35_gag(T625, T626, T665, T671, T667, T668, T669, T670, delminA_in_agg(T671, T668, T669))
U35_gag(T625, T626, T665, T671, T667, T668, T669, T670, delminA_out_agg(T671, T668, T669)) → deleteD_out_gag(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670)))
deleteD_in_gag(T696, tree(T697, T701, T699), tree(T697, T700, T699)) → U36_gag(T696, T697, T701, T699, T700, pE_in_ggag(T696, T697, T701, T700))
U36_gag(T696, T697, T701, T699, T700, pE_out_ggag(T696, T697, T701, T700)) → deleteD_out_gag(T696, tree(T697, T701, T699), tree(T697, T700, T699))
deleteD_in_gag(T714, tree(T715, T716, T719), tree(T715, T716, T718)) → U37_gag(T714, T715, T716, T719, T718, pC_in_ggag(T715, T714, T719, T718))
U37_gag(T714, T715, T716, T719, T718, pC_out_ggag(T715, T714, T719, T718)) → deleteD_out_gag(T714, tree(T715, T716, T719), tree(T715, T716, T718))
deleteD_in_gag(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730)) → U38_gag(T737, T732, T730, T731, deleteD_in_gag(0, T732, T731))
deleteD_in_gag(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730)) → U39_gag(T748, T749, T732, T730, T731, pF_in_ggag(T748, T749, T732, T731))
U39_gag(T748, T749, T732, T730, T731, pF_out_ggag(T748, T749, T732, T731)) → deleteD_out_gag(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730))
deleteD_in_gag(T762, tree(T763, T764, T767), tree(T763, T764, T766)) → U40_gag(T762, T763, T764, T767, T766, pC_in_ggag(T763, T762, T767, T766))
U40_gag(T762, T763, T764, T767, T766, pC_out_ggag(T763, T762, T767, T766)) → deleteD_out_gag(T762, tree(T763, T764, T767), tree(T763, T764, T766))
deleteD_in_gag(s(T785), tree(0, T777, T780), tree(0, T777, T779)) → U41_gag(T785, T777, T780, T779, deleteD_in_gag(s(T785), T780, T779))
deleteD_in_gag(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779)) → U42_gag(T795, T794, T777, T780, T779, pG_in_ggag(T794, T795, T780, T779))
U42_gag(T795, T794, T777, T780, T779, pG_out_ggag(T794, T795, T780, T779)) → deleteD_out_gag(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779))
U41_gag(T785, T777, T780, T779, deleteD_out_gag(s(T785), T780, T779)) → deleteD_out_gag(s(T785), tree(0, T777, T780), tree(0, T777, T779))
U38_gag(T737, T732, T730, T731, deleteD_out_gag(0, T732, T731)) → deleteD_out_gag(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730))
U33_gag(T607, T599, T602, T601, deleteD_out_gag(s(T607), T602, T601)) → deleteD_out_gag(s(T607), tree(0, T599, T602), tree(0, T599, T601))
U30_gag(T559, T554, T552, T553, deleteD_out_gag(0, T554, T553)) → deleteD_out_gag(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552))
U25_gag(T425, T417, T420, T419, deleteD_out_gag(s(T425), T420, T419)) → deleteD_out_gag(s(T425), tree(0, T417, T420), tree(0, T417, T419))
U22_gag(T377, T372, T370, T371, deleteD_out_gag(0, T372, T371)) → deleteD_out_gag(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370))
U10_ggag(T250, T251, T236, T235, deleteD_out_gag(s(T251), T236, T235)) → pG_out_ggag(T250, T251, T236, T235)
U18_gag(T251, T250, T233, T236, T235, pG_out_ggag(T250, T251, T236, T235)) → deleteD_out_gag(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235))
U17_gag(T241, T233, T236, T235, deleteD_out_gag(s(T241), T236, T235)) → deleteD_out_gag(s(T241), tree(0, T233, T236), tree(0, T233, T235))
U8_ggag(T198, T199, T182, T181, deleteD_out_gag(s(T198), T182, T181)) → pF_out_ggag(T198, T199, T182, T181)
U15_gag(T198, T199, T182, T180, T181, pF_out_ggag(T198, T199, T182, T181)) → deleteD_out_gag(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180))
U14_gag(T187, T182, T180, T181, deleteD_out_gag(0, T182, T181)) → deleteD_out_gag(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180))
U4_ggag(T159, T158, T163, T162, deleteD_out_gag(T158, T163, T162)) → pC_out_ggag(T159, T158, T163, T162)
U13_gag(T158, T159, T160, T163, T162, pC_out_ggag(T159, T158, T163, T162)) → deleteD_out_gag(T158, tree(T159, T160, T163), tree(T159, T160, T162))
U6_ggag(T121, T122, T126, T125, deleteD_out_gag(T121, T126, T125)) → pE_out_ggag(T121, T122, T126, T125)
U12_gag(T121, T122, T126, T124, T125, pE_out_ggag(T121, T122, T126, T125)) → deleteD_out_gag(T121, tree(T122, T126, T124), tree(T122, T125, T124))

(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:

LESSB_IN_GG(s(T140), s(T141)) → LESSB_IN_GG(T140, T141)

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

(12) PiDPToQDPProof (EQUIVALENT 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:

LESSB_IN_GG(s(T140), s(T141)) → LESSB_IN_GG(T140, T141)

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:

LESSB_IN_GG(s(T140), s(T141)) → LESSB_IN_GG(T140, T141)
The graph contains the following edges 1 > 1, 2 > 2

(15) YES

(16) 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:

deleteD_in_gag(T6, tree(T6, void, T7), T7) → deleteD_out_gag(T6, tree(T6, void, T7), T7)
deleteD_in_gag(T10, tree(T10, T11, void), T11) → deleteD_out_gag(T10, tree(T10, T11, void), T11)
deleteD_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteD_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteD_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U11_gag(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))
U11_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteD_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteD_in_gag(T121, tree(T122, T126, T124), tree(T122, T125, T124)) → U12_gag(T121, T122, T126, T124, T125, pE_in_ggag(T121, T122, T126, T125))
pE_in_ggag(T121, T122, T126, T125) → U5_ggag(T121, T122, T126, T125, lessB_in_gg(T121, T122))
lessB_in_gg(0, s(T135)) → lessB_out_gg(0, s(T135))
lessB_in_gg(s(T140), s(T141)) → U2_gg(T140, T141, lessB_in_gg(T140, T141))
U2_gg(T140, T141, lessB_out_gg(T140, T141)) → lessB_out_gg(s(T140), s(T141))
U5_ggag(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → pE_out_ggag(T121, T122, T126, T125)
U5_ggag(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → U6_ggag(T121, T122, T126, T125, deleteD_in_gag(T121, T126, T125))
deleteD_in_gag(T158, tree(T159, T160, T163), tree(T159, T160, T162)) → U13_gag(T158, T159, T160, T163, T162, pC_in_ggag(T159, T158, T163, T162))
pC_in_ggag(T159, T158, T163, T162) → U3_ggag(T159, T158, T163, T162, lessB_in_gg(T159, T158))
U3_ggag(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → pC_out_ggag(T159, T158, T163, T162)
U3_ggag(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → U4_ggag(T159, T158, T163, T162, deleteD_in_gag(T158, T163, T162))
deleteD_in_gag(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180)) → U14_gag(T187, T182, T180, T181, deleteD_in_gag(0, T182, T181))
deleteD_in_gag(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180)) → U15_gag(T198, T199, T182, T180, T181, pF_in_ggag(T198, T199, T182, T181))
pF_in_ggag(T198, T199, T182, T181) → U7_ggag(T198, T199, T182, T181, lessB_in_gg(T198, T199))
U7_ggag(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → pF_out_ggag(T198, T199, T182, T181)
U7_ggag(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → U8_ggag(T198, T199, T182, T181, deleteD_in_gag(s(T198), T182, T181))
deleteD_in_gag(T218, tree(T219, T220, T223), tree(T219, T220, T222)) → U16_gag(T218, T219, T220, T223, T222, pC_in_ggag(T219, T218, T223, T222))
U16_gag(T218, T219, T220, T223, T222, pC_out_ggag(T219, T218, T223, T222)) → deleteD_out_gag(T218, tree(T219, T220, T223), tree(T219, T220, T222))
deleteD_in_gag(s(T241), tree(0, T233, T236), tree(0, T233, T235)) → U17_gag(T241, T233, T236, T235, deleteD_in_gag(s(T241), T236, T235))
deleteD_in_gag(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235)) → U18_gag(T251, T250, T233, T236, T235, pG_in_ggag(T250, T251, T236, T235))
pG_in_ggag(T250, T251, T236, T235) → U9_ggag(T250, T251, T236, T235, lessB_in_gg(T250, T251))
U9_ggag(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → pG_out_ggag(T250, T251, T236, T235)
U9_ggag(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → U10_ggag(T250, T251, T236, T235, deleteD_in_gag(s(T251), T236, T235))
deleteD_in_gag(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310))) → U19_gag(T265, T266, T305, T311, T307, T308, T309, T310, delminA_in_agg(T311, T308, T309))
U19_gag(T265, T266, T305, T311, T307, T308, T309, T310, delminA_out_agg(T311, T308, T309)) → deleteD_out_gag(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310)))
deleteD_in_gag(T336, tree(T337, T341, T339), tree(T337, T340, T339)) → U20_gag(T336, T337, T341, T339, T340, pE_in_ggag(T336, T337, T341, T340))
U20_gag(T336, T337, T341, T339, T340, pE_out_ggag(T336, T337, T341, T340)) → deleteD_out_gag(T336, tree(T337, T341, T339), tree(T337, T340, T339))
deleteD_in_gag(T354, tree(T355, T356, T359), tree(T355, T356, T358)) → U21_gag(T354, T355, T356, T359, T358, pC_in_ggag(T355, T354, T359, T358))
U21_gag(T354, T355, T356, T359, T358, pC_out_ggag(T355, T354, T359, T358)) → deleteD_out_gag(T354, tree(T355, T356, T359), tree(T355, T356, T358))
deleteD_in_gag(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370)) → U22_gag(T377, T372, T370, T371, deleteD_in_gag(0, T372, T371))
deleteD_in_gag(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370)) → U23_gag(T388, T389, T372, T370, T371, pF_in_ggag(T388, T389, T372, T371))
U23_gag(T388, T389, T372, T370, T371, pF_out_ggag(T388, T389, T372, T371)) → deleteD_out_gag(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370))
deleteD_in_gag(T402, tree(T403, T404, T407), tree(T403, T404, T406)) → U24_gag(T402, T403, T404, T407, T406, pC_in_ggag(T403, T402, T407, T406))
U24_gag(T402, T403, T404, T407, T406, pC_out_ggag(T403, T402, T407, T406)) → deleteD_out_gag(T402, tree(T403, T404, T407), tree(T403, T404, T406))
deleteD_in_gag(s(T425), tree(0, T417, T420), tree(0, T417, T419)) → U25_gag(T425, T417, T420, T419, deleteD_in_gag(s(T425), T420, T419))
deleteD_in_gag(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419)) → U26_gag(T435, T434, T417, T420, T419, pG_in_ggag(T434, T435, T420, T419))
U26_gag(T435, T434, T417, T420, T419, pG_out_ggag(T434, T435, T420, T419)) → deleteD_out_gag(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419))
deleteD_in_gag(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492))) → U27_gag(T447, T448, T487, T493, T489, T490, T491, T492, delminA_in_agg(T493, T490, T491))
U27_gag(T447, T448, T487, T493, T489, T490, T491, T492, delminA_out_agg(T493, T490, T491)) → deleteD_out_gag(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492)))
deleteD_in_gag(T518, tree(T519, T523, T521), tree(T519, T522, T521)) → U28_gag(T518, T519, T523, T521, T522, pE_in_ggag(T518, T519, T523, T522))
U28_gag(T518, T519, T523, T521, T522, pE_out_ggag(T518, T519, T523, T522)) → deleteD_out_gag(T518, tree(T519, T523, T521), tree(T519, T522, T521))
deleteD_in_gag(T536, tree(T537, T538, T541), tree(T537, T538, T540)) → U29_gag(T536, T537, T538, T541, T540, pC_in_ggag(T537, T536, T541, T540))
U29_gag(T536, T537, T538, T541, T540, pC_out_ggag(T537, T536, T541, T540)) → deleteD_out_gag(T536, tree(T537, T538, T541), tree(T537, T538, T540))
deleteD_in_gag(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552)) → U30_gag(T559, T554, T552, T553, deleteD_in_gag(0, T554, T553))
deleteD_in_gag(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552)) → U31_gag(T570, T571, T554, T552, T553, pF_in_ggag(T570, T571, T554, T553))
U31_gag(T570, T571, T554, T552, T553, pF_out_ggag(T570, T571, T554, T553)) → deleteD_out_gag(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552))
deleteD_in_gag(T584, tree(T585, T586, T589), tree(T585, T586, T588)) → U32_gag(T584, T585, T586, T589, T588, pC_in_ggag(T585, T584, T589, T588))
U32_gag(T584, T585, T586, T589, T588, pC_out_ggag(T585, T584, T589, T588)) → deleteD_out_gag(T584, tree(T585, T586, T589), tree(T585, T586, T588))
deleteD_in_gag(s(T607), tree(0, T599, T602), tree(0, T599, T601)) → U33_gag(T607, T599, T602, T601, deleteD_in_gag(s(T607), T602, T601))
deleteD_in_gag(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601)) → U34_gag(T617, T616, T599, T602, T601, pG_in_ggag(T616, T617, T602, T601))
U34_gag(T617, T616, T599, T602, T601, pG_out_ggag(T616, T617, T602, T601)) → deleteD_out_gag(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601))
deleteD_in_gag(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670))) → U35_gag(T625, T626, T665, T671, T667, T668, T669, T670, delminA_in_agg(T671, T668, T669))
U35_gag(T625, T626, T665, T671, T667, T668, T669, T670, delminA_out_agg(T671, T668, T669)) → deleteD_out_gag(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670)))
deleteD_in_gag(T696, tree(T697, T701, T699), tree(T697, T700, T699)) → U36_gag(T696, T697, T701, T699, T700, pE_in_ggag(T696, T697, T701, T700))
U36_gag(T696, T697, T701, T699, T700, pE_out_ggag(T696, T697, T701, T700)) → deleteD_out_gag(T696, tree(T697, T701, T699), tree(T697, T700, T699))
deleteD_in_gag(T714, tree(T715, T716, T719), tree(T715, T716, T718)) → U37_gag(T714, T715, T716, T719, T718, pC_in_ggag(T715, T714, T719, T718))
U37_gag(T714, T715, T716, T719, T718, pC_out_ggag(T715, T714, T719, T718)) → deleteD_out_gag(T714, tree(T715, T716, T719), tree(T715, T716, T718))
deleteD_in_gag(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730)) → U38_gag(T737, T732, T730, T731, deleteD_in_gag(0, T732, T731))
deleteD_in_gag(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730)) → U39_gag(T748, T749, T732, T730, T731, pF_in_ggag(T748, T749, T732, T731))
U39_gag(T748, T749, T732, T730, T731, pF_out_ggag(T748, T749, T732, T731)) → deleteD_out_gag(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730))
deleteD_in_gag(T762, tree(T763, T764, T767), tree(T763, T764, T766)) → U40_gag(T762, T763, T764, T767, T766, pC_in_ggag(T763, T762, T767, T766))
U40_gag(T762, T763, T764, T767, T766, pC_out_ggag(T763, T762, T767, T766)) → deleteD_out_gag(T762, tree(T763, T764, T767), tree(T763, T764, T766))
deleteD_in_gag(s(T785), tree(0, T777, T780), tree(0, T777, T779)) → U41_gag(T785, T777, T780, T779, deleteD_in_gag(s(T785), T780, T779))
deleteD_in_gag(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779)) → U42_gag(T795, T794, T777, T780, T779, pG_in_ggag(T794, T795, T780, T779))
U42_gag(T795, T794, T777, T780, T779, pG_out_ggag(T794, T795, T780, T779)) → deleteD_out_gag(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779))
U41_gag(T785, T777, T780, T779, deleteD_out_gag(s(T785), T780, T779)) → deleteD_out_gag(s(T785), tree(0, T777, T780), tree(0, T777, T779))
U38_gag(T737, T732, T730, T731, deleteD_out_gag(0, T732, T731)) → deleteD_out_gag(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730))
U33_gag(T607, T599, T602, T601, deleteD_out_gag(s(T607), T602, T601)) → deleteD_out_gag(s(T607), tree(0, T599, T602), tree(0, T599, T601))
U30_gag(T559, T554, T552, T553, deleteD_out_gag(0, T554, T553)) → deleteD_out_gag(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552))
U25_gag(T425, T417, T420, T419, deleteD_out_gag(s(T425), T420, T419)) → deleteD_out_gag(s(T425), tree(0, T417, T420), tree(0, T417, T419))
U22_gag(T377, T372, T370, T371, deleteD_out_gag(0, T372, T371)) → deleteD_out_gag(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370))
U10_ggag(T250, T251, T236, T235, deleteD_out_gag(s(T251), T236, T235)) → pG_out_ggag(T250, T251, T236, T235)
U18_gag(T251, T250, T233, T236, T235, pG_out_ggag(T250, T251, T236, T235)) → deleteD_out_gag(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235))
U17_gag(T241, T233, T236, T235, deleteD_out_gag(s(T241), T236, T235)) → deleteD_out_gag(s(T241), tree(0, T233, T236), tree(0, T233, T235))
U8_ggag(T198, T199, T182, T181, deleteD_out_gag(s(T198), T182, T181)) → pF_out_ggag(T198, T199, T182, T181)
U15_gag(T198, T199, T182, T180, T181, pF_out_ggag(T198, T199, T182, T181)) → deleteD_out_gag(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180))
U14_gag(T187, T182, T180, T181, deleteD_out_gag(0, T182, T181)) → deleteD_out_gag(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180))
U4_ggag(T159, T158, T163, T162, deleteD_out_gag(T158, T163, T162)) → pC_out_ggag(T159, T158, T163, T162)
U13_gag(T158, T159, T160, T163, T162, pC_out_ggag(T159, T158, T163, T162)) → deleteD_out_gag(T158, tree(T159, T160, T163), tree(T159, T160, T162))
U6_ggag(T121, T122, T126, T125, deleteD_out_gag(T121, T126, T125)) → pE_out_ggag(T121, T122, T126, T125)
U12_gag(T121, T122, T126, T124, T125, pE_out_ggag(T121, T122, T126, T125)) → deleteD_out_gag(T121, tree(T122, T126, T124), tree(T122, T125, T124))

(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:

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

(19) PiDPToQDPProof (SOUND 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:

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.

(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:

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

DELETED_IN_GAG(T121, tree(T122, T126, T124), tree(T122, T125, T124)) → PE_IN_GGAG(T121, T122, T126, T125)
PE_IN_GGAG(T121, T122, T126, T125) → U5_GGAG(T121, T122, T126, T125, lessB_in_gg(T121, T122))
U5_GGAG(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → DELETED_IN_GAG(T121, T126, T125)
DELETED_IN_GAG(T158, tree(T159, T160, T163), tree(T159, T160, T162)) → PC_IN_GGAG(T159, T158, T163, T162)
PC_IN_GGAG(T159, T158, T163, T162) → U3_GGAG(T159, T158, T163, T162, lessB_in_gg(T159, T158))
U3_GGAG(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → DELETED_IN_GAG(T158, T163, T162)
DELETED_IN_GAG(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180)) → DELETED_IN_GAG(0, T182, T181)
DELETED_IN_GAG(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180)) → PF_IN_GGAG(T198, T199, T182, T181)
PF_IN_GGAG(T198, T199, T182, T181) → U7_GGAG(T198, T199, T182, T181, lessB_in_gg(T198, T199))
U7_GGAG(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → DELETED_IN_GAG(s(T198), T182, T181)
DELETED_IN_GAG(s(T241), tree(0, T233, T236), tree(0, T233, T235)) → DELETED_IN_GAG(s(T241), T236, T235)
DELETED_IN_GAG(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235)) → PG_IN_GGAG(T250, T251, T236, T235)
PG_IN_GGAG(T250, T251, T236, T235) → U9_GGAG(T250, T251, T236, T235, lessB_in_gg(T250, T251))
U9_GGAG(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → DELETED_IN_GAG(s(T251), T236, T235)

The TRS R consists of the following rules:

deleteD_in_gag(T6, tree(T6, void, T7), T7) → deleteD_out_gag(T6, tree(T6, void, T7), T7)
deleteD_in_gag(T10, tree(T10, T11, void), T11) → deleteD_out_gag(T10, tree(T10, T11, void), T11)
deleteD_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteD_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteD_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U11_gag(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))
U11_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteD_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteD_in_gag(T121, tree(T122, T126, T124), tree(T122, T125, T124)) → U12_gag(T121, T122, T126, T124, T125, pE_in_ggag(T121, T122, T126, T125))
pE_in_ggag(T121, T122, T126, T125) → U5_ggag(T121, T122, T126, T125, lessB_in_gg(T121, T122))
lessB_in_gg(0, s(T135)) → lessB_out_gg(0, s(T135))
lessB_in_gg(s(T140), s(T141)) → U2_gg(T140, T141, lessB_in_gg(T140, T141))
U2_gg(T140, T141, lessB_out_gg(T140, T141)) → lessB_out_gg(s(T140), s(T141))
U5_ggag(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → pE_out_ggag(T121, T122, T126, T125)
U5_ggag(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → U6_ggag(T121, T122, T126, T125, deleteD_in_gag(T121, T126, T125))
deleteD_in_gag(T158, tree(T159, T160, T163), tree(T159, T160, T162)) → U13_gag(T158, T159, T160, T163, T162, pC_in_ggag(T159, T158, T163, T162))
pC_in_ggag(T159, T158, T163, T162) → U3_ggag(T159, T158, T163, T162, lessB_in_gg(T159, T158))
U3_ggag(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → pC_out_ggag(T159, T158, T163, T162)
U3_ggag(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → U4_ggag(T159, T158, T163, T162, deleteD_in_gag(T158, T163, T162))
deleteD_in_gag(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180)) → U14_gag(T187, T182, T180, T181, deleteD_in_gag(0, T182, T181))
deleteD_in_gag(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180)) → U15_gag(T198, T199, T182, T180, T181, pF_in_ggag(T198, T199, T182, T181))
pF_in_ggag(T198, T199, T182, T181) → U7_ggag(T198, T199, T182, T181, lessB_in_gg(T198, T199))
U7_ggag(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → pF_out_ggag(T198, T199, T182, T181)
U7_ggag(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → U8_ggag(T198, T199, T182, T181, deleteD_in_gag(s(T198), T182, T181))
deleteD_in_gag(T218, tree(T219, T220, T223), tree(T219, T220, T222)) → U16_gag(T218, T219, T220, T223, T222, pC_in_ggag(T219, T218, T223, T222))
U16_gag(T218, T219, T220, T223, T222, pC_out_ggag(T219, T218, T223, T222)) → deleteD_out_gag(T218, tree(T219, T220, T223), tree(T219, T220, T222))
deleteD_in_gag(s(T241), tree(0, T233, T236), tree(0, T233, T235)) → U17_gag(T241, T233, T236, T235, deleteD_in_gag(s(T241), T236, T235))
deleteD_in_gag(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235)) → U18_gag(T251, T250, T233, T236, T235, pG_in_ggag(T250, T251, T236, T235))
pG_in_ggag(T250, T251, T236, T235) → U9_ggag(T250, T251, T236, T235, lessB_in_gg(T250, T251))
U9_ggag(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → pG_out_ggag(T250, T251, T236, T235)
U9_ggag(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → U10_ggag(T250, T251, T236, T235, deleteD_in_gag(s(T251), T236, T235))
deleteD_in_gag(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310))) → U19_gag(T265, T266, T305, T311, T307, T308, T309, T310, delminA_in_agg(T311, T308, T309))
U19_gag(T265, T266, T305, T311, T307, T308, T309, T310, delminA_out_agg(T311, T308, T309)) → deleteD_out_gag(T265, tree(T265, T266, tree(T305, T311, T307)), tree(T308, T266, tree(T305, T309, T310)))
deleteD_in_gag(T336, tree(T337, T341, T339), tree(T337, T340, T339)) → U20_gag(T336, T337, T341, T339, T340, pE_in_ggag(T336, T337, T341, T340))
U20_gag(T336, T337, T341, T339, T340, pE_out_ggag(T336, T337, T341, T340)) → deleteD_out_gag(T336, tree(T337, T341, T339), tree(T337, T340, T339))
deleteD_in_gag(T354, tree(T355, T356, T359), tree(T355, T356, T358)) → U21_gag(T354, T355, T356, T359, T358, pC_in_ggag(T355, T354, T359, T358))
U21_gag(T354, T355, T356, T359, T358, pC_out_ggag(T355, T354, T359, T358)) → deleteD_out_gag(T354, tree(T355, T356, T359), tree(T355, T356, T358))
deleteD_in_gag(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370)) → U22_gag(T377, T372, T370, T371, deleteD_in_gag(0, T372, T371))
deleteD_in_gag(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370)) → U23_gag(T388, T389, T372, T370, T371, pF_in_ggag(T388, T389, T372, T371))
U23_gag(T388, T389, T372, T370, T371, pF_out_ggag(T388, T389, T372, T371)) → deleteD_out_gag(s(T388), tree(s(T389), T372, T370), tree(s(T389), T371, T370))
deleteD_in_gag(T402, tree(T403, T404, T407), tree(T403, T404, T406)) → U24_gag(T402, T403, T404, T407, T406, pC_in_ggag(T403, T402, T407, T406))
U24_gag(T402, T403, T404, T407, T406, pC_out_ggag(T403, T402, T407, T406)) → deleteD_out_gag(T402, tree(T403, T404, T407), tree(T403, T404, T406))
deleteD_in_gag(s(T425), tree(0, T417, T420), tree(0, T417, T419)) → U25_gag(T425, T417, T420, T419, deleteD_in_gag(s(T425), T420, T419))
deleteD_in_gag(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419)) → U26_gag(T435, T434, T417, T420, T419, pG_in_ggag(T434, T435, T420, T419))
U26_gag(T435, T434, T417, T420, T419, pG_out_ggag(T434, T435, T420, T419)) → deleteD_out_gag(s(T435), tree(s(T434), T417, T420), tree(s(T434), T417, T419))
deleteD_in_gag(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492))) → U27_gag(T447, T448, T487, T493, T489, T490, T491, T492, delminA_in_agg(T493, T490, T491))
U27_gag(T447, T448, T487, T493, T489, T490, T491, T492, delminA_out_agg(T493, T490, T491)) → deleteD_out_gag(T447, tree(T447, T448, tree(T487, T493, T489)), tree(T490, T448, tree(T487, T491, T492)))
deleteD_in_gag(T518, tree(T519, T523, T521), tree(T519, T522, T521)) → U28_gag(T518, T519, T523, T521, T522, pE_in_ggag(T518, T519, T523, T522))
U28_gag(T518, T519, T523, T521, T522, pE_out_ggag(T518, T519, T523, T522)) → deleteD_out_gag(T518, tree(T519, T523, T521), tree(T519, T522, T521))
deleteD_in_gag(T536, tree(T537, T538, T541), tree(T537, T538, T540)) → U29_gag(T536, T537, T538, T541, T540, pC_in_ggag(T537, T536, T541, T540))
U29_gag(T536, T537, T538, T541, T540, pC_out_ggag(T537, T536, T541, T540)) → deleteD_out_gag(T536, tree(T537, T538, T541), tree(T537, T538, T540))
deleteD_in_gag(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552)) → U30_gag(T559, T554, T552, T553, deleteD_in_gag(0, T554, T553))
deleteD_in_gag(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552)) → U31_gag(T570, T571, T554, T552, T553, pF_in_ggag(T570, T571, T554, T553))
U31_gag(T570, T571, T554, T552, T553, pF_out_ggag(T570, T571, T554, T553)) → deleteD_out_gag(s(T570), tree(s(T571), T554, T552), tree(s(T571), T553, T552))
deleteD_in_gag(T584, tree(T585, T586, T589), tree(T585, T586, T588)) → U32_gag(T584, T585, T586, T589, T588, pC_in_ggag(T585, T584, T589, T588))
U32_gag(T584, T585, T586, T589, T588, pC_out_ggag(T585, T584, T589, T588)) → deleteD_out_gag(T584, tree(T585, T586, T589), tree(T585, T586, T588))
deleteD_in_gag(s(T607), tree(0, T599, T602), tree(0, T599, T601)) → U33_gag(T607, T599, T602, T601, deleteD_in_gag(s(T607), T602, T601))
deleteD_in_gag(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601)) → U34_gag(T617, T616, T599, T602, T601, pG_in_ggag(T616, T617, T602, T601))
U34_gag(T617, T616, T599, T602, T601, pG_out_ggag(T616, T617, T602, T601)) → deleteD_out_gag(s(T617), tree(s(T616), T599, T602), tree(s(T616), T599, T601))
deleteD_in_gag(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670))) → U35_gag(T625, T626, T665, T671, T667, T668, T669, T670, delminA_in_agg(T671, T668, T669))
U35_gag(T625, T626, T665, T671, T667, T668, T669, T670, delminA_out_agg(T671, T668, T669)) → deleteD_out_gag(T625, tree(T625, T626, tree(T665, T671, T667)), tree(T668, T626, tree(T665, T669, T670)))
deleteD_in_gag(T696, tree(T697, T701, T699), tree(T697, T700, T699)) → U36_gag(T696, T697, T701, T699, T700, pE_in_ggag(T696, T697, T701, T700))
U36_gag(T696, T697, T701, T699, T700, pE_out_ggag(T696, T697, T701, T700)) → deleteD_out_gag(T696, tree(T697, T701, T699), tree(T697, T700, T699))
deleteD_in_gag(T714, tree(T715, T716, T719), tree(T715, T716, T718)) → U37_gag(T714, T715, T716, T719, T718, pC_in_ggag(T715, T714, T719, T718))
U37_gag(T714, T715, T716, T719, T718, pC_out_ggag(T715, T714, T719, T718)) → deleteD_out_gag(T714, tree(T715, T716, T719), tree(T715, T716, T718))
deleteD_in_gag(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730)) → U38_gag(T737, T732, T730, T731, deleteD_in_gag(0, T732, T731))
deleteD_in_gag(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730)) → U39_gag(T748, T749, T732, T730, T731, pF_in_ggag(T748, T749, T732, T731))
U39_gag(T748, T749, T732, T730, T731, pF_out_ggag(T748, T749, T732, T731)) → deleteD_out_gag(s(T748), tree(s(T749), T732, T730), tree(s(T749), T731, T730))
deleteD_in_gag(T762, tree(T763, T764, T767), tree(T763, T764, T766)) → U40_gag(T762, T763, T764, T767, T766, pC_in_ggag(T763, T762, T767, T766))
U40_gag(T762, T763, T764, T767, T766, pC_out_ggag(T763, T762, T767, T766)) → deleteD_out_gag(T762, tree(T763, T764, T767), tree(T763, T764, T766))
deleteD_in_gag(s(T785), tree(0, T777, T780), tree(0, T777, T779)) → U41_gag(T785, T777, T780, T779, deleteD_in_gag(s(T785), T780, T779))
deleteD_in_gag(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779)) → U42_gag(T795, T794, T777, T780, T779, pG_in_ggag(T794, T795, T780, T779))
U42_gag(T795, T794, T777, T780, T779, pG_out_ggag(T794, T795, T780, T779)) → deleteD_out_gag(s(T795), tree(s(T794), T777, T780), tree(s(T794), T777, T779))
U41_gag(T785, T777, T780, T779, deleteD_out_gag(s(T785), T780, T779)) → deleteD_out_gag(s(T785), tree(0, T777, T780), tree(0, T777, T779))
U38_gag(T737, T732, T730, T731, deleteD_out_gag(0, T732, T731)) → deleteD_out_gag(0, tree(s(T737), T732, T730), tree(s(T737), T731, T730))
U33_gag(T607, T599, T602, T601, deleteD_out_gag(s(T607), T602, T601)) → deleteD_out_gag(s(T607), tree(0, T599, T602), tree(0, T599, T601))
U30_gag(T559, T554, T552, T553, deleteD_out_gag(0, T554, T553)) → deleteD_out_gag(0, tree(s(T559), T554, T552), tree(s(T559), T553, T552))
U25_gag(T425, T417, T420, T419, deleteD_out_gag(s(T425), T420, T419)) → deleteD_out_gag(s(T425), tree(0, T417, T420), tree(0, T417, T419))
U22_gag(T377, T372, T370, T371, deleteD_out_gag(0, T372, T371)) → deleteD_out_gag(0, tree(s(T377), T372, T370), tree(s(T377), T371, T370))
U10_ggag(T250, T251, T236, T235, deleteD_out_gag(s(T251), T236, T235)) → pG_out_ggag(T250, T251, T236, T235)
U18_gag(T251, T250, T233, T236, T235, pG_out_ggag(T250, T251, T236, T235)) → deleteD_out_gag(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235))
U17_gag(T241, T233, T236, T235, deleteD_out_gag(s(T241), T236, T235)) → deleteD_out_gag(s(T241), tree(0, T233, T236), tree(0, T233, T235))
U8_ggag(T198, T199, T182, T181, deleteD_out_gag(s(T198), T182, T181)) → pF_out_ggag(T198, T199, T182, T181)
U15_gag(T198, T199, T182, T180, T181, pF_out_ggag(T198, T199, T182, T181)) → deleteD_out_gag(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180))
U14_gag(T187, T182, T180, T181, deleteD_out_gag(0, T182, T181)) → deleteD_out_gag(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180))
U4_ggag(T159, T158, T163, T162, deleteD_out_gag(T158, T163, T162)) → pC_out_ggag(T159, T158, T163, T162)
U13_gag(T158, T159, T160, T163, T162, pC_out_ggag(T159, T158, T163, T162)) → deleteD_out_gag(T158, tree(T159, T160, T163), tree(T159, T160, T162))
U6_ggag(T121, T122, T126, T125, deleteD_out_gag(T121, T126, T125)) → pE_out_ggag(T121, T122, T126, T125)
U12_gag(T121, T122, T126, T124, T125, pE_out_ggag(T121, T122, T126, T125)) → deleteD_out_gag(T121, tree(T122, T126, T124), tree(T122, T125, T124))

(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:

DELETED_IN_GAG(T121, tree(T122, T126, T124), tree(T122, T125, T124)) → PE_IN_GGAG(T121, T122, T126, T125)
PE_IN_GGAG(T121, T122, T126, T125) → U5_GGAG(T121, T122, T126, T125, lessB_in_gg(T121, T122))
U5_GGAG(T121, T122, T126, T125, lessB_out_gg(T121, T122)) → DELETED_IN_GAG(T121, T126, T125)
DELETED_IN_GAG(T158, tree(T159, T160, T163), tree(T159, T160, T162)) → PC_IN_GGAG(T159, T158, T163, T162)
PC_IN_GGAG(T159, T158, T163, T162) → U3_GGAG(T159, T158, T163, T162, lessB_in_gg(T159, T158))
U3_GGAG(T159, T158, T163, T162, lessB_out_gg(T159, T158)) → DELETED_IN_GAG(T158, T163, T162)
DELETED_IN_GAG(0, tree(s(T187), T182, T180), tree(s(T187), T181, T180)) → DELETED_IN_GAG(0, T182, T181)
DELETED_IN_GAG(s(T198), tree(s(T199), T182, T180), tree(s(T199), T181, T180)) → PF_IN_GGAG(T198, T199, T182, T181)
PF_IN_GGAG(T198, T199, T182, T181) → U7_GGAG(T198, T199, T182, T181, lessB_in_gg(T198, T199))
U7_GGAG(T198, T199, T182, T181, lessB_out_gg(T198, T199)) → DELETED_IN_GAG(s(T198), T182, T181)
DELETED_IN_GAG(s(T241), tree(0, T233, T236), tree(0, T233, T235)) → DELETED_IN_GAG(s(T241), T236, T235)
DELETED_IN_GAG(s(T251), tree(s(T250), T233, T236), tree(s(T250), T233, T235)) → PG_IN_GGAG(T250, T251, T236, T235)
PG_IN_GGAG(T250, T251, T236, T235) → U9_GGAG(T250, T251, T236, T235, lessB_in_gg(T250, T251))
U9_GGAG(T250, T251, T236, T235, lessB_out_gg(T250, T251)) → DELETED_IN_GAG(s(T251), T236, T235)

The TRS R consists of the following rules:

lessB_in_gg(0, s(T135)) → lessB_out_gg(0, s(T135))
lessB_in_gg(s(T140), s(T141)) → U2_gg(T140, T141, lessB_in_gg(T140, T141))
U2_gg(T140, T141, lessB_out_gg(T140, T141)) → lessB_out_gg(s(T140), s(T141))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
lessB_in_gg(x1, x2) = lessB_in_gg(x1, x2)
0 = 0
s(x1) = s(x1)
lessB_out_gg(x1, x2) = lessB_out_gg(x1, x2)
U2_gg(x1, x2, x3) = U2_gg(x1, x2, x3)
DELETED_IN_GAG(x1, x2, x3) = DELETED_IN_GAG(x1, x3)
PE_IN_GGAG(x1, x2, x3, x4) = PE_IN_GGAG(x1, x2, x4)
U5_GGAG(x1, x2, x3, x4, x5) = U5_GGAG(x1, x2, x4, x5)
PC_IN_GGAG(x1, x2, x3, x4) = PC_IN_GGAG(x1, x2, x4)
U3_GGAG(x1, x2, x3, x4, x5) = U3_GGAG(x1, x2, x4, x5)
PF_IN_GGAG(x1, x2, x3, x4) = PF_IN_GGAG(x1, x2, x4)
U7_GGAG(x1, x2, x3, x4, x5) = U7_GGAG(x1, x2, x4, x5)
PG_IN_GGAG(x1, x2, x3, x4) = PG_IN_GGAG(x1, x2, x4)
U9_GGAG(x1, x2, x3, x4, x5) = U9_GGAG(x1, x2, x4, x5)

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

(26) PiDPToQDPProof (SOUND 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:

DELETED_IN_GAG(T121, tree(T122, T125, T124)) → PE_IN_GGAG(T121, T122, T125)
PE_IN_GGAG(T121, T122, T125) → U5_GGAG(T121, T122, T125, lessB_in_gg(T121, T122))
U5_GGAG(T121, T122, T125, lessB_out_gg(T121, T122)) → DELETED_IN_GAG(T121, T125)
DELETED_IN_GAG(T158, tree(T159, T160, T162)) → PC_IN_GGAG(T159, T158, T162)
PC_IN_GGAG(T159, T158, T162) → U3_GGAG(T159, T158, T162, lessB_in_gg(T159, T158))
U3_GGAG(T159, T158, T162, lessB_out_gg(T159, T158)) → DELETED_IN_GAG(T158, T162)
DELETED_IN_GAG(0, tree(s(T187), T181, T180)) → DELETED_IN_GAG(0, T181)
DELETED_IN_GAG(s(T198), tree(s(T199), T181, T180)) → PF_IN_GGAG(T198, T199, T181)
PF_IN_GGAG(T198, T199, T181) → U7_GGAG(T198, T199, T181, lessB_in_gg(T198, T199))
U7_GGAG(T198, T199, T181, lessB_out_gg(T198, T199)) → DELETED_IN_GAG(s(T198), T181)
DELETED_IN_GAG(s(T241), tree(0, T233, T235)) → DELETED_IN_GAG(s(T241), T235)
DELETED_IN_GAG(s(T251), tree(s(T250), T233, T235)) → PG_IN_GGAG(T250, T251, T235)
PG_IN_GGAG(T250, T251, T235) → U9_GGAG(T250, T251, T235, lessB_in_gg(T250, T251))
U9_GGAG(T250, T251, T235, lessB_out_gg(T250, T251)) → DELETED_IN_GAG(s(T251), T235)

The TRS R consists of the following rules:

lessB_in_gg(0, s(T135)) → lessB_out_gg(0, s(T135))
lessB_in_gg(s(T140), s(T141)) → U2_gg(T140, T141, lessB_in_gg(T140, T141))
U2_gg(T140, T141, lessB_out_gg(T140, T141)) → lessB_out_gg(s(T140), s(T141))

The set Q consists of the following terms:

lessB_in_gg(x0, x1)
U2_gg(x0, x1, x2)

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:

PE_IN_GGAG(T121, T122, T125) → U5_GGAG(T121, T122, T125, lessB_in_gg(T121, T122))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
U5_GGAG(T121, T122, T125, lessB_out_gg(T121, T122)) → DELETED_IN_GAG(T121, T125)
The graph contains the following edges 1 >= 1, 4 > 1, 3 >= 2
DELETED_IN_GAG(T121, tree(T122, T125, T124)) → PE_IN_GGAG(T121, T122, T125)
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
PC_IN_GGAG(T159, T158, T162) → U3_GGAG(T159, T158, T162, lessB_in_gg(T159, T158))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
U3_GGAG(T159, T158, T162, lessB_out_gg(T159, T158)) → DELETED_IN_GAG(T158, T162)
The graph contains the following edges 2 >= 1, 4 > 1, 3 >= 2
DELETED_IN_GAG(T158, tree(T159, T160, T162)) → PC_IN_GGAG(T159, T158, T162)
The graph contains the following edges 2 > 1, 1 >= 2, 2 > 3
DELETED_IN_GAG(0, tree(s(T187), T181, T180)) → DELETED_IN_GAG(0, T181)
The graph contains the following edges 1 >= 1, 2 > 2
DELETED_IN_GAG(s(T241), tree(0, T233, T235)) → DELETED_IN_GAG(s(T241), T235)
The graph contains the following edges 1 >= 1, 2 > 2
PF_IN_GGAG(T198, T199, T181) → U7_GGAG(T198, T199, T181, lessB_in_gg(T198, T199))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
PG_IN_GGAG(T250, T251, T235) → U9_GGAG(T250, T251, T235, lessB_in_gg(T250, T251))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
U7_GGAG(T198, T199, T181, lessB_out_gg(T198, T199)) → DELETED_IN_GAG(s(T198), T181)
The graph contains the following edges 3 >= 2
U9_GGAG(T250, T251, T235, lessB_out_gg(T250, T251)) → DELETED_IN_GAG(s(T251), T235)
The graph contains the following edges 3 >= 2
DELETED_IN_GAG(s(T198), tree(s(T199), T181, T180)) → PF_IN_GGAG(T198, T199, T181)
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3
DELETED_IN_GAG(s(T251), tree(s(T250), T233, T235)) → PG_IN_GGAG(T250, T251, T235)
The graph contains the following edges 2 > 1, 1 > 2, 2 > 3

(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 (EQUIVALENT transformation)

(13) Obligation:

(14) QDPSizeChangeProof (EQUIVALENT transformation)

(15) YES

(16) Obligation:

(17) UsableRulesProof (EQUIVALENT transformation)

(18) Obligation:

(19) PiDPToQDPProof (SOUND transformation)

(20) Obligation:

(21) QDPSizeChangeProof (EQUIVALENT transformation)

(22) YES

(23) Obligation:

(24) UsableRulesProof (EQUIVALENT transformation)

(25) Obligation:

(26) PiDPToQDPProof (SOUND transformation)

(27) Obligation:

(28) QDPSizeChangeProof (EQUIVALENT transformation)

(29) YES