Left Termination proof of /tmp/tmpHkpcZV/delete-fbf.pl

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

0 Prolog

↳1 PrologToPrologProblemTransformerProof (⇒, 683 ms)

↳2 Prolog

↳3 PrologToPiTRSProof (⇒, 503 ms)

↳4 PiTRS

↳5 DependencyPairsProof (⇔, 4241 ms)

↳6 PiDP

↳7 DependencyGraphProof (⇔, 22 ms)

↳8 AND

    ↳9 PiDP

        ↳10 UsableRulesProof (⇔, 0 ms)

        ↳11 PiDP

        ↳12 PiDPToQDPProof (⇒, 23 ms)

        ↳13 QDP

        ↳14 QDPSizeChangeProof (⇔, 0 ms)

        ↳15 YES

    ↳16 PiDP

        ↳17 UsableRulesProof (⇔, 0 ms)

        ↳18 PiDP

        ↳19 PiDPToQDPProof (⇒, 0 ms)

        ↳20 QDP

        ↳21 QDPSizeChangeProof (⇔, 0 ms)

        ↳22 YES

    ↳23 PiDP

        ↳24 UsableRulesProof (⇔, 0 ms)

        ↳25 PiDP

        ↳26 PiDPToQDPProof (⇔, 0 ms)

        ↳27 QDP

        ↳28 QDPSizeChangeProof (⇔, 0 ms)

        ↳29 YES

    ↳30 PiDP

        ↳31 UsableRulesProof (⇔, 0 ms)

        ↳32 PiDP

        ↳33 PiDPToQDPProof (⇔, 0 ms)

        ↳34 QDP

        ↳35 QDPSizeChangeProof (⇔, 0 ms)

        ↳36 YES

    ↳37 PiDP

        ↳38 UsableRulesProof (⇔, 0 ms)

        ↳39 PiDP

        ↳40 PiDPToQDPProof (⇒, 62 ms)

        ↳41 QDP

        ↳42 QDPSizeChangeProof (⇔, 76 ms)

        ↳43 YES

    ↳44 PiDP

        ↳45 UsableRulesProof (⇔, 0 ms)

        ↳46 PiDP

        ↳47 PiDPToQDPProof (⇒, 0 ms)

        ↳48 QDP

        ↳49 QDPSizeChangeProof (⇔, 0 ms)

        ↳50 YES

    ↳51 PiDP

        ↳52 UsableRulesProof (⇔, 0 ms)

        ↳53 PiDP

        ↳54 PiDPToQDPProof (⇒, 0 ms)

        ↳55 QDP

        ↳56 QDPSizeChangeProof (⇔, 0 ms)

        ↳57 YES

(0) Obligation:

Clauses:

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

Query: delete(a,g,a)

(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\nT2 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\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: true | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 1 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T6, void, T7), T3), 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\nT2 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 1 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: true | delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\nT7 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: delmin(void, T16, T17) | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT9 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T9, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: delmin(void, T16, T17), SCOPE: 2, CLAUSE: 5 | delmin(void, T16, T17), SCOPE: 2, CLAUSE: 6 | ?_2 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: delmin(void, T16, T17), SCOPE: 2, CLAUSE: 6 | ?_2 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ?_2 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 3\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: ','(less(T33, T31), delete(T33, void, T34))\n\nT31 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: less(T33, T31)\n\nT31 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: delete(T37, void, T38)\n\nT37 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: less(T33, T31), SCOPE: 3, CLAUSE: 7 | less(T33, T31), SCOPE: 3, CLAUSE: 8\n\nT31 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: less(T33, T31), SCOPE: 3, CLAUSE: 7\n\nT31 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: less(T33, T31), SCOPE: 3, CLAUSE: 8\n\nT31 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: less(T52, T51)\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: ','(less(T64, T66), delete(T66, void, T67))\n\nT64 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: less(T64, T66)\n\nT64 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: delete(T70, void, T71)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: less(T64, T66), SCOPE: 4, CLAUSE: 7 | less(T64, T66), SCOPE: 4, CLAUSE: 8\n\nT64 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: less(T64, T66), SCOPE: 4, CLAUSE: 7\n\nT64 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: less(T64, T66), SCOPE: 4, CLAUSE: 8\n\nT64 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: less(T83, T85)\n\nT83 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: ','(less(T96, T94), delete(T96, void, T97)) | delete(T1, tree(T94, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT94 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T94, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT9 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX117 is free\nX118 is free\nX119 is free\nX120 is free\nX121 is free\ndelete(T1, tree(T9, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, tree(T9, void, void), T3) !=? delete(X117, tree(X118, X119, X120), tree(X118, X121, X120))", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: ','(less(T96, T94), delete(T96, void, T97)), SCOPE: 5, CLAUSE: 7 | ','(less(T96, T94), delete(T96, void, T97)), SCOPE: 5, CLAUSE: 8 | ?_5 | delete(T1, tree(T94, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT94 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T94, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: ','(less(T96, T94), delete(T96, void, T97)), SCOPE: 5, CLAUSE: 7\n\nT94 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T94, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(less(T96, T94), delete(T96, void, T97)), SCOPE: 5, CLAUSE: 8 | ?_5 | delete(T1, tree(T94, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT94 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T94, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: delete(0, void, T103)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: ','(less(T96, T94), delete(T96, void, T97)), SCOPE: 5, CLAUSE: 8\n\nT94 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T94, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: ?_5 | delete(T1, tree(T94, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT94 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T94, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(less(T114, T113), delete(s(T114), void, T115))\n\nT113 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(s(T113), void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: less(T114, T113)\n\nT113 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(s(T113), void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: delete(s(T118), void, T119)\n\nT118 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: delete(T1, tree(T94, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT94 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T94, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: ','(less(T133, T135), delete(T135, void, T136))\n\nT133 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T133, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: ','(less(T143, T145), delete(T145, void, T146))\n\nT143 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX117 is free\nX118 is free\nX119 is free\nX120 is free\nX121 is free\ndelete(T1, tree(T143, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, tree(T143, void, void), T3) !=? delete(X117, tree(X118, X119, X120), tree(X118, X121, X120))", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ','(less(T143, T145), delete(T145, void, T146)), SCOPE: 6, CLAUSE: 7 | ','(less(T143, T145), delete(T145, void, T146)), SCOPE: 6, CLAUSE: 8\n\nT143 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX117 is free\nX118 is free\nX119 is free\nX120 is free\nX121 is free\ndelete(T1, tree(T143, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, tree(T143, void, void), T3) !=? delete(X117, tree(X118, X119, X120), tree(X118, X121, X120))", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: ','(less(T143, T145), delete(T145, void, T146)), SCOPE: 6, CLAUSE: 7\n\nT143 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX117 is free\nX118 is free\nX119 is free\nX120 is free\nX121 is free\ndelete(T1, tree(T143, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, tree(T143, void, void), T3) !=? delete(X117, tree(X118, X119, X120), tree(X118, X121, X120))", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(less(T143, T145), delete(T145, void, T146)), SCOPE: 6, CLAUSE: 8\n\nT143 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX117 is free\nX118 is free\nX119 is free\nX120 is free\nX121 is free\ndelete(T1, tree(T143, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, tree(T143, void, void), T3) !=? delete(X117, tree(X118, X119, X120), tree(X118, X121, X120))", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: delete(s(T153), void, T152)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: ','(less(T160, T162), delete(s(T162), void, T163))\n\nT160 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX117 is free\nX118 is free\nX119 is free\nX120 is free\nX121 is free\ndelete(T1, tree(s(T160), void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, tree(s(T160), void, void), T3) !=? delete(X117, tree(X118, X119, X120), tree(X118, X121, X120))", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: less(T160, T162)\n\nT160 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX117 is free\nX118 is free\nX119 is free\nX120 is free\nX121 is free\ndelete(T1, tree(s(T160), void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, tree(s(T160), void, void), T3) !=? delete(X117, tree(X118, X119, X120), tree(X118, X121, X120))", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: delete(s(T166), void, T167)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: delmin(T179, T182, T183) | delete(T1, tree(T178, void, T179), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T178, void, T179), T3), SCOPE: 1, CLAUSE: 4\n\nT178 is ground\nT179 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T178, void, T179), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\nT7 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: delmin(T179, T182, T183), SCOPE: 7, CLAUSE: 5 | delmin(T179, T182, T183), SCOPE: 7, CLAUSE: 6 | ?_7 | delete(T1, tree(T178, void, T179), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T178, void, T179), T3), SCOPE: 1, CLAUSE: 4\n\nT178 is ground\nT179 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T178, void, T179), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: delmin(T179, T182, T183), SCOPE: 7, CLAUSE: 5\n\nT178 is ground\nT179 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T178, void, T179), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: delmin(T179, T182, T183), SCOPE: 7, CLAUSE: 6 | ?_7 | delete(T1, tree(T178, void, T179), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T178, void, T179), T3), SCOPE: 1, CLAUSE: 4\n\nT178 is ground\nT179 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T178, void, T179), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: delmin(T179, T182, T183), SCOPE: 7, CLAUSE: 6\n\nT178 is ground\nT179 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T178, void, T179), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: ?_7 | delete(T1, tree(T178, void, T179), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T178, void, T179), T3), SCOPE: 1, CLAUSE: 4\n\nT178 is ground\nT179 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T178, void, T179), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: delmin(T219, T224, T225)\n\nT219 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: delmin(T219, T224, T225), SCOPE: 8, CLAUSE: 5 | delmin(T219, T224, T225), SCOPE: 8, CLAUSE: 6\n\nT219 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: delmin(T219, T224, T225), SCOPE: 8, CLAUSE: 5\n\nT219 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: delmin(T219, T224, T225), SCOPE: 8, CLAUSE: 6\n\nT219 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: delmin(T253, T258, T259)\n\nT253 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: delete(T1, tree(T178, void, T179), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T178, void, T179), T3), SCOPE: 1, CLAUSE: 4\n\nT178 is ground\nT179 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T178, void, T179), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: delete(T1, tree(T178, void, T179), T3), SCOPE: 1, CLAUSE: 3\n\nT178 is ground\nT179 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T178, void, T179), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: delete(T1, tree(T178, void, T179), T3), SCOPE: 1, CLAUSE: 4\n\nT178 is ground\nT179 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T178, void, T179), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: ','(less(T284, T281), delete(T284, void, T285))\n\nT281 is ground\nT282 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T281, void, T282), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: ','(less(T297, T300), delete(T300, T298, T301))\n\nT297 is ground\nT298 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T297, void, T298), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: less(T297, T300)\n\nT297 is ground\nT298 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T297, void, T298), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: delete(T304, T298, T305)\n\nT297 is ground\nT298 is ground\nX10 is free\nX11 is free\ndelete(T306, tree(T297, void, T298), T307) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: ','(less(T322, T319), delete(T322, void, T323)) | delete(T1, tree(T319, void, T320), T3), SCOPE: 1, CLAUSE: 4\n\nT319 is ground\nT320 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\ndelete(T1, tree(T319, void, T320), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T319, void, T320), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\nT7 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX340 is free\nX341 is free\nX342 is free\nX343 is free\nX344 is free\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X340, tree(X341, X342, X343), tree(X341, X344, X343))", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: ','(less(T322, T319), delete(T322, void, T323)), SCOPE: 9, CLAUSE: 7 | ','(less(T322, T319), delete(T322, void, T323)), SCOPE: 9, CLAUSE: 8 | ?_9 | delete(T1, tree(T319, void, T320), T3), SCOPE: 1, CLAUSE: 4\n\nT319 is ground\nT320 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\ndelete(T1, tree(T319, void, T320), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T319, void, T320), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: ','(less(T322, T319), delete(T322, void, T323)), SCOPE: 9, CLAUSE: 7\n\nT319 is ground\nT320 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\ndelete(T1, tree(T319, void, T320), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T319, void, T320), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: ','(less(T322, T319), delete(T322, void, T323)), SCOPE: 9, CLAUSE: 8 | ?_9 | delete(T1, tree(T319, void, T320), T3), SCOPE: 1, CLAUSE: 4\n\nT319 is ground\nT320 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\ndelete(T1, tree(T319, void, T320), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T319, void, T320), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: delete(0, void, T329)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: ','(less(T322, T319), delete(T322, void, T323)), SCOPE: 9, CLAUSE: 8\n\nT319 is ground\nT320 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\ndelete(T1, tree(T319, void, T320), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T319, void, T320), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: ?_9 | delete(T1, tree(T319, void, T320), T3), SCOPE: 1, CLAUSE: 4\n\nT319 is ground\nT320 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\ndelete(T1, tree(T319, void, T320), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T319, void, T320), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: ','(less(T340, T339), delete(s(T340), void, T341))\n\nT320 is ground\nT339 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\ndelete(T1, tree(s(T339), void, T320), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(s(T339), void, T320), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: less(T340, T339)\n\nT320 is ground\nT339 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\ndelete(T1, tree(s(T339), void, T320), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(s(T339), void, T320), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: delete(s(T344), void, T345)\n\nT344 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: delete(T1, tree(T319, void, T320), T3), SCOPE: 1, CLAUSE: 4\n\nT319 is ground\nT320 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\ndelete(T1, tree(T319, void, T320), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T319, void, T320), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ','(less(T361, T364), delete(T364, T362, T365))\n\nT361 is ground\nT362 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\ndelete(T1, tree(T361, void, T362), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T361, void, T362), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: ','(less(T373, T376), delete(T376, T374, T377))\n\nT373 is ground\nT374 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX340 is free\nX341 is free\nX342 is free\nX343 is free\nX344 is free\ndelete(T1, tree(T373, void, T374), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T373, void, T374), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))\ndelete(T1, tree(T373, void, T374), T3) !=? delete(X340, tree(X341, X342, X343), tree(X341, X344, X343))", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: ','(less(T373, T376), delete(T376, T374, T377)), SCOPE: 10, CLAUSE: 7 | ','(less(T373, T376), delete(T376, T374, T377)), SCOPE: 10, CLAUSE: 8\n\nT373 is ground\nT374 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX340 is free\nX341 is free\nX342 is free\nX343 is free\nX344 is free\ndelete(T1, tree(T373, void, T374), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T373, void, T374), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))\ndelete(T1, tree(T373, void, T374), T3) !=? delete(X340, tree(X341, X342, X343), tree(X341, X344, X343))", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: ','(less(T373, T376), delete(T376, T374, T377)), SCOPE: 10, CLAUSE: 7\n\nT373 is ground\nT374 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX340 is free\nX341 is free\nX342 is free\nX343 is free\nX344 is free\ndelete(T1, tree(T373, void, T374), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T373, void, T374), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))\ndelete(T1, tree(T373, void, T374), T3) !=? delete(X340, tree(X341, X342, X343), tree(X341, X344, X343))", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: ','(less(T373, T376), delete(T376, T374, T377)), SCOPE: 10, CLAUSE: 8\n\nT373 is ground\nT374 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX340 is free\nX341 is free\nX342 is free\nX343 is free\nX344 is free\ndelete(T1, tree(T373, void, T374), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T373, void, T374), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))\ndelete(T1, tree(T373, void, T374), T3) !=? delete(X340, tree(X341, X342, X343), tree(X341, X344, X343))", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: delete(s(T384), T374, T383)\n\nT374 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX340 is free\nX341 is free\nX342 is free\nX343 is free\nX344 is free\ndelete(T1, tree(0, void, T374), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(0, void, T374), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))\ndelete(T1, tree(0, void, T374), T3) !=? delete(X340, tree(X341, X342, X343), tree(X341, X344, X343))", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: ','(less(T393, T395), delete(s(T395), T374, T396))\n\nT374 is ground\nT393 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX340 is free\nX341 is free\nX342 is free\nX343 is free\nX344 is free\ndelete(T1, tree(s(T393), void, T374), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(s(T393), void, T374), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))\ndelete(T1, tree(s(T393), void, T374), T3) !=? delete(X340, tree(X341, X342, X343), tree(X341, X344, X343))", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: less(T393, T395)\n\nT374 is ground\nT393 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX340 is free\nX341 is free\nX342 is free\nX343 is free\nX344 is free\ndelete(T1, tree(s(T393), void, T374), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(s(T393), void, T374), T3) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))\ndelete(T1, tree(s(T393), void, T374), T3) !=? delete(X340, tree(X341, X342, X343), tree(X341, X344, X343))", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: delete(s(T399), T374, T400)\n\nT374 is ground\nT393 is ground\nX10 is free\nX11 is free\nX204 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX340 is free\nX341 is free\nX342 is free\nX343 is free\nX344 is free\ndelete(T401, tree(s(T393), void, T374), T402) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T401, tree(s(T393), void, T374), T402) !=? delete(X204, tree(X204, X205, X206), tree(X207, X205, X208))\ndelete(T401, tree(s(T393), void, T374), T402) !=? delete(X340, tree(X341, X342, X343), tree(X341, X344, X343))", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: true | delete(T1, tree(T411, T412, void), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T411, T412, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T411, T412, void), T3), SCOPE: 1, CLAUSE: 4\n\nT411 is ground\nT412 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T411, T412, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: 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\nT2 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: delete(T1, tree(T411, T412, void), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T411, T412, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T411, T412, void), T3), SCOPE: 1, CLAUSE: 4\n\nT411 is ground\nT412 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T411, T412, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: delmin(void, T421, T422) | delete(T1, tree(T417, T418, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T417, T418, void), T3), SCOPE: 1, CLAUSE: 4\n\nT417 is ground\nT418 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T417, T418, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: delete(T1, tree(T411, T412, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T411, T412, void), T3), SCOPE: 1, CLAUSE: 4\n\nT411 is ground\nT412 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\ndelete(T1, tree(T411, T412, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T411, T412, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: delmin(void, T421, T422), SCOPE: 11, CLAUSE: 5 | delmin(void, T421, T422), SCOPE: 11, CLAUSE: 6 | ?_11 | delete(T1, tree(T417, T418, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T417, T418, void), T3), SCOPE: 1, CLAUSE: 4\n\nT417 is ground\nT418 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T417, T418, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: delmin(void, T421, T422), SCOPE: 11, CLAUSE: 6 | ?_11 | delete(T1, tree(T417, T418, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T417, T418, void), T3), SCOPE: 1, CLAUSE: 4\n\nT417 is ground\nT418 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T417, T418, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: ?_11 | delete(T1, tree(T417, T418, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T417, T418, void), T3), SCOPE: 1, CLAUSE: 4\n\nT417 is ground\nT418 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T417, T418, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: delete(T1, tree(T417, T418, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T417, T418, void), T3), SCOPE: 1, CLAUSE: 4\n\nT417 is ground\nT418 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T417, T418, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: delete(T1, tree(T417, T418, void), T3), SCOPE: 1, CLAUSE: 3\n\nT417 is ground\nT418 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T417, T418, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: delete(T1, tree(T417, T418, void), T3), SCOPE: 1, CLAUSE: 4\n\nT417 is ground\nT418 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T417, T418, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: ','(less(T443, T440), delete(T443, T441, T444))\n\nT440 is ground\nT441 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T440, T441, void), T3) !=? 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(T443, T440)\n\nT440 is ground\nT441 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T440, T441, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: delete(T447, T441, T448)\n\nT440 is ground\nT441 is ground\nT447 is ground\nX6 is free\nX7 is free\ndelete(T449, tree(T440, T441, void), T450) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: ','(less(T466, T469), delete(T469, void, T470))\n\nT466 is ground\nT467 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T466, T467, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: ','(less(T481, T478), delete(T481, T479, T482)) | delete(T1, tree(T478, T479, void), T3), SCOPE: 1, CLAUSE: 4\n\nT478 is ground\nT479 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\ndelete(T1, tree(T478, T479, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T478, T479, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: delete(T1, tree(T411, T412, void), T3), SCOPE: 1, CLAUSE: 4\n\nT411 is ground\nT412 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\nX499 is free\nX500 is free\nX501 is free\nX502 is free\nX503 is free\ndelete(T1, tree(T411, T412, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T411, T412, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))\ndelete(T1, tree(T411, T412, void), T3) !=? delete(X499, tree(X500, X501, X502), tree(X500, X503, X502))", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: ','(less(T481, T478), delete(T481, T479, T482)), SCOPE: 12, CLAUSE: 7 | ','(less(T481, T478), delete(T481, T479, T482)), SCOPE: 12, CLAUSE: 8 | ?_12 | delete(T1, tree(T478, T479, void), T3), SCOPE: 1, CLAUSE: 4\n\nT478 is ground\nT479 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\ndelete(T1, tree(T478, T479, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T478, T479, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: ','(less(T481, T478), delete(T481, T479, T482)), SCOPE: 12, CLAUSE: 7\n\nT478 is ground\nT479 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\ndelete(T1, tree(T478, T479, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T478, T479, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: ','(less(T481, T478), delete(T481, T479, T482)), SCOPE: 12, CLAUSE: 8 | ?_12 | delete(T1, tree(T478, T479, void), T3), SCOPE: 1, CLAUSE: 4\n\nT478 is ground\nT479 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\ndelete(T1, tree(T478, T479, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T478, T479, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: delete(0, T479, T488)\n\nT479 is ground\nT487 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\ndelete(T1, tree(s(T487), T479, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T487), T479, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: ','(less(T481, T478), delete(T481, T479, T482)), SCOPE: 12, CLAUSE: 8\n\nT478 is ground\nT479 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\ndelete(T1, tree(T478, T479, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T478, T479, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: ?_12 | delete(T1, tree(T478, T479, void), T3), SCOPE: 1, CLAUSE: 4\n\nT478 is ground\nT479 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\ndelete(T1, tree(T478, T479, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T478, T479, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: ','(less(T501, T500), delete(s(T501), T479, T502))\n\nT479 is ground\nT500 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\ndelete(T1, tree(s(T500), T479, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T500), T479, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: less(T501, T500)\n\nT479 is ground\nT500 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\ndelete(T1, tree(s(T500), T479, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T500), T479, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: delete(s(T505), T479, T506)\n\nT479 is ground\nT500 is ground\nT505 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\ndelete(T507, tree(s(T500), T479, void), T508) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T507, tree(s(T500), T479, void), T508) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: delete(T1, tree(T478, T479, void), T3), SCOPE: 1, CLAUSE: 4\n\nT478 is ground\nT479 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\ndelete(T1, tree(T478, T479, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T478, T479, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: ','(less(T524, T527), delete(T527, void, T528))\n\nT524 is ground\nT525 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\ndelete(T1, tree(T524, T525, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T524, T525, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: ','(less(T536, T539), delete(T539, void, T540))\n\nT536 is ground\nT537 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\nX499 is free\nX500 is free\nX501 is free\nX502 is free\nX503 is free\ndelete(T1, tree(T536, T537, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T536, T537, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))\ndelete(T1, tree(T536, T537, void), T3) !=? delete(X499, tree(X500, X501, X502), tree(X500, X503, X502))", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: ','(less(T536, T539), delete(T539, void, T540)), SCOPE: 13, CLAUSE: 7 | ','(less(T536, T539), delete(T539, void, T540)), SCOPE: 13, CLAUSE: 8\n\nT536 is ground\nT537 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\nX499 is free\nX500 is free\nX501 is free\nX502 is free\nX503 is free\ndelete(T1, tree(T536, T537, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T536, T537, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))\ndelete(T1, tree(T536, T537, void), T3) !=? delete(X499, tree(X500, X501, X502), tree(X500, X503, X502))", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: ','(less(T536, T539), delete(T539, void, T540)), SCOPE: 13, CLAUSE: 7\n\nT536 is ground\nT537 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\nX499 is free\nX500 is free\nX501 is free\nX502 is free\nX503 is free\ndelete(T1, tree(T536, T537, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T536, T537, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))\ndelete(T1, tree(T536, T537, void), T3) !=? delete(X499, tree(X500, X501, X502), tree(X500, X503, X502))", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: ','(less(T536, T539), delete(T539, void, T540)), SCOPE: 13, CLAUSE: 8\n\nT536 is ground\nT537 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\nX499 is free\nX500 is free\nX501 is free\nX502 is free\nX503 is free\ndelete(T1, tree(T536, T537, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T536, T537, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))\ndelete(T1, tree(T536, T537, void), T3) !=? delete(X499, tree(X500, X501, X502), tree(X500, X503, X502))", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: delete(s(T547), void, T546)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: ','(less(T554, T556), delete(s(T556), void, T557))\n\nT537 is ground\nT554 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\nX499 is free\nX500 is free\nX501 is free\nX502 is free\nX503 is free\ndelete(T1, tree(s(T554), T537, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T554), T537, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))\ndelete(T1, tree(s(T554), T537, void), T3) !=? delete(X499, tree(X500, X501, X502), tree(X500, X503, X502))", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: less(T554, T556)\n\nT537 is ground\nT554 is ground\nX6 is free\nX7 is free\nX431 is free\nX432 is free\nX433 is free\nX434 is free\nX435 is free\nX499 is free\nX500 is free\nX501 is free\nX502 is free\nX503 is free\ndelete(T1, tree(s(T554), T537, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T554), T537, void), T3) !=? delete(X431, tree(X431, X432, X433), tree(X434, X432, X435))\ndelete(T1, tree(s(T554), T537, void), T3) !=? delete(X499, tree(X500, X501, X502), tree(X500, X503, X502))", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: delete(s(T560), void, T561)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: delmin(T575, T578, T579) | delete(T1, tree(T573, T574, T575), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T573, T574, T575), T3), SCOPE: 1, CLAUSE: 4\n\nT573 is ground\nT574 is ground\nT575 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT2 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, T2, T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: delmin(T575, T578, T579), SCOPE: 14, CLAUSE: 5 | delmin(T575, T578, T579), SCOPE: 14, CLAUSE: 6 | ?_14 | delete(T1, tree(T573, T574, T575), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T573, T574, T575), T3), SCOPE: 1, CLAUSE: 4\n\nT573 is ground\nT574 is ground\nT575 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: delmin(T575, T578, T579), SCOPE: 14, CLAUSE: 5\n\nT573 is ground\nT574 is ground\nT575 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: delmin(T575, T578, T579), SCOPE: 14, CLAUSE: 6 | ?_14 | delete(T1, tree(T573, T574, T575), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T573, T574, T575), T3), SCOPE: 1, CLAUSE: 4\n\nT573 is ground\nT574 is ground\nT575 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: delmin(T575, T578, T579), SCOPE: 14, CLAUSE: 6\n\nT573 is ground\nT574 is ground\nT575 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: ?_14 | delete(T1, tree(T573, T574, T575), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T573, T574, T575), T3), SCOPE: 1, CLAUSE: 4\n\nT573 is ground\nT574 is ground\nT575 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: delmin(T615, T620, T621)\n\nT573 is ground\nT574 is ground\nT614 is ground\nT615 is ground\nT616 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T573, T574, tree(T614, T615, T616)), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: delete(T1, tree(T573, T574, T575), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T573, T574, T575), T3), SCOPE: 1, CLAUSE: 4\n\nT573 is ground\nT574 is ground\nT575 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: delete(T1, tree(T573, T574, T575), T3), SCOPE: 1, CLAUSE: 3\n\nT573 is ground\nT574 is ground\nT575 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: delete(T1, tree(T573, T574, T575), T3), SCOPE: 1, CLAUSE: 4\n\nT573 is ground\nT574 is ground\nT575 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T573, T574, T575), T3) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: ','(less(T651, T647), delete(T651, T648, T652))\n\nT647 is ground\nT648 is ground\nT649 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T1, tree(T647, T648, T649), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T647, T648, T649), T3) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: less(T651, T647)\n\nT647 is ground\nT648 is ground\nT649 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T1, tree(T647, T648, T649), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T647, T648, T649), T3) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: delete(T655, T648, T656)\n\nT647 is ground\nT648 is ground\nT649 is ground\nT655 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T657, tree(T647, T648, T649), T658) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T657, tree(T647, T648, T649), T658) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: ','(less(T676, T680), delete(T680, T678, T681))\n\nT676 is ground\nT677 is ground\nT678 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T1, tree(T676, T677, T678), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T676, T677, T678), T3) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: less(T676, T680)\n\nT676 is ground\nT677 is ground\nT678 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T1, tree(T676, T677, T678), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T676, T677, T678), T3) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: delete(T684, T678, T685)\n\nT676 is ground\nT677 is ground\nT678 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\ndelete(T686, tree(T676, T677, T678), T687) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T686, tree(T676, T677, T678), T687) !=? delete(X424, tree(X424, X425, void), X425)", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: ','(less(T704, T700), delete(T704, T701, T705)) | delete(T1, tree(T700, T701, T702), T3), SCOPE: 1, CLAUSE: 4\n\nT700 is ground\nT701 is ground\nT702 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT2 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\nX696 is free\nX697 is free\nX698 is free\nX699 is free\nX700 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, T2, T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))\ndelete(T1, T2, T3) !=? delete(X696, tree(X697, X698, X699), tree(X697, X700, X699))", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: ','(less(T704, T700), delete(T704, T701, T705)), SCOPE: 15, CLAUSE: 7 | ','(less(T704, T700), delete(T704, T701, T705)), SCOPE: 15, CLAUSE: 8 | ?_15 | delete(T1, tree(T700, T701, T702), T3), SCOPE: 1, CLAUSE: 4\n\nT700 is ground\nT701 is ground\nT702 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: ','(less(T704, T700), delete(T704, T701, T705)), SCOPE: 15, CLAUSE: 7\n\nT700 is ground\nT701 is ground\nT702 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: ','(less(T704, T700), delete(T704, T701, T705)), SCOPE: 15, CLAUSE: 8 | ?_15 | delete(T1, tree(T700, T701, T702), T3), SCOPE: 1, CLAUSE: 4\n\nT700 is ground\nT701 is ground\nT702 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: delete(0, T701, T711)\n\nT701 is ground\nT702 is ground\nT710 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\ndelete(T1, tree(s(T710), T701, T702), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T710), T701, T702), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(s(T710), T701, T702), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: ','(less(T704, T700), delete(T704, T701, T705)), SCOPE: 15, CLAUSE: 8\n\nT700 is ground\nT701 is ground\nT702 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: ?_15 | delete(T1, tree(T700, T701, T702), T3), SCOPE: 1, CLAUSE: 4\n\nT700 is ground\nT701 is ground\nT702 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: ','(less(T724, T723), delete(s(T724), T701, T725))\n\nT701 is ground\nT702 is ground\nT723 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\ndelete(T1, tree(s(T723), T701, T702), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T723), T701, T702), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(s(T723), T701, T702), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: less(T724, T723)\n\nT701 is ground\nT702 is ground\nT723 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\ndelete(T1, tree(s(T723), T701, T702), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T723), T701, T702), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(s(T723), T701, T702), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: delete(s(T728), T701, T729)\n\nT701 is ground\nT702 is ground\nT723 is ground\nT728 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\ndelete(T730, tree(s(T723), T701, T702), T731) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T730, tree(s(T723), T701, T702), T731) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T730, tree(s(T723), T701, T702), T731) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: delete(T1, tree(T700, T701, T702), T3), SCOPE: 1, CLAUSE: 4\n\nT700 is ground\nT701 is ground\nT702 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(T700, T701, T702), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: ','(less(T749, T753), delete(T753, T751, T754))\n\nT749 is ground\nT750 is ground\nT751 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\ndelete(T1, tree(T749, T750, T751), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T749, T750, T751), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(T749, T750, T751), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: ','(less(T763, T767), delete(T767, T765, T768))\n\nT763 is ground\nT764 is ground\nT765 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\nX696 is free\nX697 is free\nX698 is free\nX699 is free\nX700 is free\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X696, tree(X697, X698, X699), tree(X697, X700, X699))", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: ','(less(T763, T767), delete(T767, T765, T768)), SCOPE: 16, CLAUSE: 7 | ','(less(T763, T767), delete(T767, T765, T768)), SCOPE: 16, CLAUSE: 8\n\nT763 is ground\nT764 is ground\nT765 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\nX696 is free\nX697 is free\nX698 is free\nX699 is free\nX700 is free\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X696, tree(X697, X698, X699), tree(X697, X700, X699))", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: ','(less(T763, T767), delete(T767, T765, T768)), SCOPE: 16, CLAUSE: 7\n\nT763 is ground\nT764 is ground\nT765 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\nX696 is free\nX697 is free\nX698 is free\nX699 is free\nX700 is free\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X696, tree(X697, X698, X699), tree(X697, X700, X699))", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: ','(less(T763, T767), delete(T767, T765, T768)), SCOPE: 16, CLAUSE: 8\n\nT763 is ground\nT764 is ground\nT765 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\nX696 is free\nX697 is free\nX698 is free\nX699 is free\nX700 is free\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))\ndelete(T1, tree(T763, T764, T765), T3) !=? delete(X696, tree(X697, X698, X699), tree(X697, X700, X699))", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: delete(s(T775), T765, T774)\n\nT764 is ground\nT765 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\nX696 is free\nX697 is free\nX698 is free\nX699 is free\nX700 is free\ndelete(T1, tree(0, T764, T765), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(0, T764, T765), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(0, T764, T765), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))\ndelete(T1, tree(0, T764, T765), T3) !=? delete(X696, tree(X697, X698, X699), tree(X697, X700, X699))", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: ','(less(T784, T786), delete(s(T786), T765, T787))\n\nT764 is ground\nT765 is ground\nT784 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\nX696 is free\nX697 is free\nX698 is free\nX699 is free\nX700 is free\ndelete(T1, tree(s(T784), T764, T765), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T784), T764, T765), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(s(T784), T764, T765), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))\ndelete(T1, tree(s(T784), T764, T765), T3) !=? delete(X696, tree(X697, X698, X699), tree(X697, X700, X699))", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: less(T784, T786)\n\nT764 is ground\nT765 is ground\nT784 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\nX696 is free\nX697 is free\nX698 is free\nX699 is free\nX700 is free\ndelete(T1, tree(s(T784), T764, T765), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T784), T764, T765), T3) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T1, tree(s(T784), T764, T765), T3) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))\ndelete(T1, tree(s(T784), T764, T765), T3) !=? delete(X696, tree(X697, X698, X699), tree(X697, X700, X699))", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: delete(s(T790), T765, T791)\n\nT764 is ground\nT765 is ground\nT784 is ground\nX6 is free\nX7 is free\nX424 is free\nX425 is free\nX586 is free\nX587 is free\nX588 is free\nX589 is free\nX590 is free\nX696 is free\nX697 is free\nX698 is free\nX699 is free\nX700 is free\ndelete(T792, tree(s(T784), T764, T765), T793) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T792, tree(s(T784), T764, T765), T793) !=? delete(X424, tree(X424, X425, void), X425)\ndelete(T792, tree(s(T784), T764, T765), T793) !=? delete(X586, tree(X586, X587, X588), tree(X589, X587, X590))\ndelete(T792, tree(s(T784), T764, T765), T793) !=? delete(X696, tree(X697, X698, X699), tree(X697, X700, X699))", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 218 [arrowhead = none ];
218 -> 2;

219 [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 -> 219 [arrowhead = none ];
219 -> 3;

220 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2 -> 220 [arrowhead = none ];
220 -> 4;

221 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 221 [arrowhead = none ];
221 -> 5;

222 [label="EVAL with clause\ndelete(X424, tree(X424, X425, void), X425).\nand substitutionT1 -> T411,\nX424 -> T411,\nX425 -> T412,\nT2 -> tree(T411, T412, void),\nT3 -> T412", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 222 [arrowhead = none ];
222 -> 124;

223 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 223 [arrowhead = none ];
223 -> 125;

224 [label="EVAL with clause\ndelete(X10, tree(X10, X11, void), X11).\nand substitutionT1 -> T9,\nX10 -> T9,\nT6 -> T9,\nX11 -> void,\nT7 -> void,\nT3 -> void", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 224 [arrowhead = none ];
224 -> 6;

225 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 225 [arrowhead = none ];
225 -> 7;

226 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 226 [arrowhead = none ];
226 -> 8;

227 [label="EVAL with clause\ndelete(X204, tree(X204, X205, X206), tree(X207, X205, X208)) :- delmin(X206, X207, X208).\nand substitutionT1 -> T178,\nX204 -> T178,\nT6 -> T178,\nX205 -> void,\nT7 -> T179,\nX206 -> T179,\nX207 -> T182,\nX208 -> T183,\nT3 -> tree(T182, void, T183),\nT180 -> T182,\nT181 -> T183", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 227 [arrowhead = none ];
227 -> 68;

228 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 228 [arrowhead = none ];
228 -> 69;

229 [label="EVAL with clause\ndelete(X17, tree(X17, X18, X19), tree(X20, X18, X21)) :- delmin(X19, X20, X21).\nand substitutionT1 -> T13,\nX17 -> T13,\nT9 -> T13,\nX18 -> void,\nX19 -> void,\nX20 -> T16,\nX21 -> T17,\nT3 -> tree(T16, void, T17),\nT14 -> T16,\nT15 -> T17", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 229 [arrowhead = none ];
229 -> 9;

230 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 230 [arrowhead = none ];
230 -> 10;

231 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 231 [arrowhead = none ];
231 -> 11;

232 [label="EVAL with clause\ndelete(X117, tree(X118, X119, X120), tree(X118, X121, X120)) :- ','(less(X117, X118), delete(X117, X119, X121)).\nand substitutionT1 -> T96,\nX117 -> T96,\nT9 -> T94,\nX118 -> T94,\nX119 -> void,\nX120 -> void,\nX121 -> T97,\nT3 -> tree(T94, T97, void),\nT93 -> T96,\nT95 -> T97", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 232 [arrowhead = none ];
232 -> 41;

233 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
10 -> 233 [arrowhead = none ];
233 -> 42;

234 [label="BACKTRACK\nfor clause: delmin(tree(Y, void, Right), Y, Right)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 234 [arrowhead = none ];
234 -> 12;

235 [label="BACKTRACK\nfor clause: delmin(tree(X, Left, X1), Y, tree(X, Left1, X2)) :- delmin(Left, Y, Left1)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 235 [arrowhead = none ];
235 -> 13;

236 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
13 -> 236 [arrowhead = none ];
236 -> 14;

237 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 237 [arrowhead = none ];
237 -> 15;

238 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 238 [arrowhead = none ];
238 -> 16;

239 [label="EVAL with clause\ndelete(X50, tree(X51, X52, X53), tree(X51, X54, X53)) :- ','(less(X50, X51), delete(X50, X52, X54)).\nand substitutionT1 -> T33,\nX50 -> T33,\nT13 -> T31,\nX51 -> T31,\nX52 -> void,\nX53 -> void,\nX54 -> T34,\nT3 -> tree(T31, T34, void),\nT30 -> T33,\nT32 -> T34", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 239 [arrowhead = none ];
239 -> 17;

240 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
15 -> 240 [arrowhead = none ];
240 -> 18;

241 [label="EVAL with clause\ndelete(X86, tree(X87, X88, X89), tree(X87, X88, X90)) :- ','(less(X87, X86), delete(X86, X89, X90)).\nand substitutionT1 -> T66,\nX86 -> T66,\nT13 -> T64,\nX87 -> T64,\nX88 -> void,\nX89 -> void,\nX90 -> T67,\nT3 -> tree(T64, void, T67),\nT63 -> T66,\nT65 -> T67", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 241 [arrowhead = none ];
241 -> 29;

242 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 242 [arrowhead = none ];
242 -> 30;

243 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
17 -> 243 [arrowhead = none ];
243 -> 19;

244 [label="SPLIT 2\nnew knowledge:\nT37 is ground\nT31 is ground\nreplacements:T33 -> T37,\nT34 -> T38", fontsize=14, style = filled, fillcolor = violet];
17 -> 244 [arrowhead = none ];
244 -> 20;

245 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
19 -> 245 [arrowhead = none ];
245 -> 21;

246 [label="INSTANCE with matching:\nT1 -> T37\nT2 -> void\nT3 -> T38", fontsize=14, style = filled, fillcolor = lightgrey];
20 -> 246 [arrowhead = none , style=dashed];
246 -> 1[style=dashed];

247 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 247 [arrowhead = none ];
247 -> 22;

248 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 248 [arrowhead = none ];
248 -> 23;

249 [label="EVAL with clause\nless(0, s(X63)).\nand substitutionT33 -> 0,\nX63 -> T45,\nT31 -> s(T45)", fontsize=14, style = filled, fillcolor = lightblue];
22 -> 249 [arrowhead = none ];
249 -> 24;

250 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
22 -> 250 [arrowhead = none ];
250 -> 25;

251 [label="EVAL with clause\nless(s(X68), s(X69)) :- less(X68, X69).\nand substitutionX68 -> T52,\nT33 -> s(T52),\nX69 -> T51,\nT31 -> s(T51),\nT50 -> T52", fontsize=14, style = filled, fillcolor = lightblue];
23 -> 251 [arrowhead = none ];
251 -> 27;

252 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
23 -> 252 [arrowhead = none ];
252 -> 28;

253 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
24 -> 253 [arrowhead = none ];
253 -> 26;

254 [label="INSTANCE with matching:\nT33 -> T52\nT31 -> T51", fontsize=14, style = filled, fillcolor = lightgrey];
27 -> 254 [arrowhead = none , style=dashed];
254 -> 19[style=dashed];

255 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
29 -> 255 [arrowhead = none ];
255 -> 31;

256 [label="SPLIT 2\nnew knowledge:\nT64 is ground\nreplacements:T66 -> T70,\nT67 -> T71", fontsize=14, style = filled, fillcolor = violet];
29 -> 256 [arrowhead = none ];
256 -> 32;

257 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
31 -> 257 [arrowhead = none ];
257 -> 33;

258 [label="INSTANCE with matching:\nT1 -> T70\nT2 -> void\nT3 -> T71", fontsize=14, style = filled, fillcolor = lightgrey];
32 -> 258 [arrowhead = none , style=dashed];
258 -> 1[style=dashed];

259 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
33 -> 259 [arrowhead = none ];
259 -> 34;

260 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
33 -> 260 [arrowhead = none ];
260 -> 35;

261 [label="EVAL with clause\nless(0, s(X99)).\nand substitutionT64 -> 0,\nX99 -> T78,\nT66 -> s(T78)", fontsize=14, style = filled, fillcolor = lightblue];
34 -> 261 [arrowhead = none ];
261 -> 36;

262 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
34 -> 262 [arrowhead = none ];
262 -> 37;

263 [label="EVAL with clause\nless(s(X104), s(X105)) :- less(X104, X105).\nand substitutionX104 -> T83,\nT64 -> s(T83),\nX105 -> T85,\nT66 -> s(T85),\nT84 -> T85", fontsize=14, style = filled, fillcolor = lightblue];
35 -> 263 [arrowhead = none ];
263 -> 39;

264 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
35 -> 264 [arrowhead = none ];
264 -> 40;

265 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
36 -> 265 [arrowhead = none ];
265 -> 38;

266 [label="INSTANCE with matching:\nT64 -> T83\nT66 -> T85", fontsize=14, style = filled, fillcolor = lightgrey];
39 -> 266 [arrowhead = none , style=dashed];
266 -> 31[style=dashed];

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

268 [label="EVAL with clause\ndelete(X171, tree(X172, X173, X174), tree(X172, X173, X175)) :- ','(less(X172, X171), delete(X171, X174, X175)).\nand substitutionT1 -> T145,\nX171 -> T145,\nT9 -> T143,\nX172 -> T143,\nX173 -> void,\nX174 -> void,\nX175 -> T146,\nT3 -> tree(T143, void, T146),\nT142 -> T145,\nT144 -> T146", fontsize=14, style = filled, fillcolor = lightblue];
42 -> 268 [arrowhead = none ];
268 -> 57;

269 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
42 -> 269 [arrowhead = none ];
269 -> 58;

270 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
43 -> 270 [arrowhead = none ];
270 -> 44;

271 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
43 -> 271 [arrowhead = none ];
271 -> 45;

272 [label="EVAL with clause\nless(0, s(X126)).\nand substitutionT96 -> 0,\nX126 -> T102,\nT94 -> s(T102),\nT97 -> T103", fontsize=14, style = filled, fillcolor = lightblue];
44 -> 272 [arrowhead = none ];
272 -> 46;

273 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
44 -> 273 [arrowhead = none ];
273 -> 47;

274 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
45 -> 274 [arrowhead = none ];
274 -> 48;

275 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
45 -> 275 [arrowhead = none ];
275 -> 49;

276 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> void\nT3 -> T103", fontsize=14, style = filled, fillcolor = lightgrey];
46 -> 276 [arrowhead = none , style=dashed];
276 -> 1[style=dashed];

277 [label="EVAL with clause\nless(s(X139), s(X140)) :- less(X139, X140).\nand substitutionX139 -> T114,\nT96 -> s(T114),\nX140 -> T113,\nT94 -> s(T113),\nT112 -> T114,\nT97 -> T115", fontsize=14, style = filled, fillcolor = lightblue];
48 -> 277 [arrowhead = none ];
277 -> 50;

278 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
48 -> 278 [arrowhead = none ];
278 -> 51;

279 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
49 -> 279 [arrowhead = none ];
279 -> 54;

280 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
50 -> 280 [arrowhead = none ];
280 -> 52;

281 [label="SPLIT 2\nnew knowledge:\nT118 is ground\nT113 is ground\nreplacements:T114 -> T118,\nT115 -> T119,\nT1 -> T120,\nT3 -> T121", fontsize=14, style = filled, fillcolor = violet];
50 -> 281 [arrowhead = none ];
281 -> 53;

282 [label="INSTANCE with matching:\nT33 -> T114\nT31 -> T113", fontsize=14, style = filled, fillcolor = lightgrey];
52 -> 282 [arrowhead = none , style=dashed];
282 -> 19[style=dashed];

283 [label="INSTANCE with matching:\nT1 -> s(T118)\nT2 -> void\nT3 -> T119", fontsize=14, style = filled, fillcolor = lightgrey];
53 -> 283 [arrowhead = none , style=dashed];
283 -> 1[style=dashed];

284 [label="EVAL with clause\ndelete(X159, tree(X160, X161, X162), tree(X160, X161, X163)) :- ','(less(X160, X159), delete(X159, X162, X163)).\nand substitutionT1 -> T135,\nX159 -> T135,\nT94 -> T133,\nX160 -> T133,\nX161 -> void,\nX162 -> void,\nX163 -> T136,\nT3 -> tree(T133, void, T136),\nT132 -> T135,\nT134 -> T136", fontsize=14, style = filled, fillcolor = lightblue];
54 -> 284 [arrowhead = none ];
284 -> 55;

285 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
54 -> 285 [arrowhead = none ];
285 -> 56;

286 [label="INSTANCE with matching:\nT64 -> T133\nT66 -> T135\nT67 -> T136", fontsize=14, style = filled, fillcolor = lightgrey];
55 -> 286 [arrowhead = none , style=dashed];
286 -> 29[style=dashed];

287 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
57 -> 287 [arrowhead = none ];
287 -> 59;

288 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
59 -> 288 [arrowhead = none ];
288 -> 60;

289 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
59 -> 289 [arrowhead = none ];
289 -> 61;

290 [label="EVAL with clause\nless(0, s(X180)).\nand substitutionT143 -> 0,\nX180 -> T153,\nT145 -> s(T153),\nT146 -> T152,\nT151 -> T153", fontsize=14, style = filled, fillcolor = lightblue];
60 -> 290 [arrowhead = none ];
290 -> 62;

291 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
60 -> 291 [arrowhead = none ];
291 -> 63;

292 [label="EVAL with clause\nless(s(X189), s(X190)) :- less(X189, X190).\nand substitutionX189 -> T160,\nT143 -> s(T160),\nX190 -> T162,\nT145 -> s(T162),\nT161 -> T162,\nT146 -> T163", fontsize=14, style = filled, fillcolor = lightblue];
61 -> 292 [arrowhead = none ];
292 -> 64;

293 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
61 -> 293 [arrowhead = none ];
293 -> 65;

294 [label="INSTANCE with matching:\nT1 -> s(T153)\nT2 -> void\nT3 -> T152", fontsize=14, style = filled, fillcolor = lightgrey];
62 -> 294 [arrowhead = none , style=dashed];
294 -> 1[style=dashed];

295 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
64 -> 295 [arrowhead = none ];
295 -> 66;

296 [label="SPLIT 2\nnew knowledge:\nT160 is ground\nreplacements:T162 -> T166,\nT163 -> T167,\nT1 -> T168,\nT3 -> T169", fontsize=14, style = filled, fillcolor = violet];
64 -> 296 [arrowhead = none ];
296 -> 67;

297 [label="INSTANCE with matching:\nT64 -> T160\nT66 -> T162", fontsize=14, style = filled, fillcolor = lightgrey];
66 -> 297 [arrowhead = none , style=dashed];
297 -> 31[style=dashed];

298 [label="INSTANCE with matching:\nT1 -> s(T166)\nT2 -> void\nT3 -> T167", fontsize=14, style = filled, fillcolor = lightgrey];
67 -> 298 [arrowhead = none , style=dashed];
298 -> 1[style=dashed];

299 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
68 -> 299 [arrowhead = none ];
299 -> 70;

300 [label="EVAL with clause\ndelete(X340, tree(X341, X342, X343), tree(X341, X344, X343)) :- ','(less(X340, X341), delete(X340, X342, X344)).\nand substitutionT1 -> T322,\nX340 -> T322,\nT6 -> T319,\nX341 -> T319,\nX342 -> void,\nT7 -> T320,\nX343 -> T320,\nX344 -> T323,\nT3 -> tree(T319, T323, T320),\nT318 -> T322,\nT321 -> T323", fontsize=14, style = filled, fillcolor = lightblue];
69 -> 300 [arrowhead = none ];
300 -> 97;

301 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
69 -> 301 [arrowhead = none ];
301 -> 98;

302 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
70 -> 302 [arrowhead = none ];
302 -> 71;

303 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
70 -> 303 [arrowhead = none ];
303 -> 72;

304 [label="EVAL with clause\ndelmin(tree(X217, void, X218), X217, X218).\nand substitutionX217 -> T192,\nX218 -> T193,\nT179 -> tree(T192, void, T193),\nT182 -> T192,\nT183 -> T193", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 304 [arrowhead = none ];
304 -> 73;

305 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
71 -> 305 [arrowhead = none ];
305 -> 74;

306 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
72 -> 306 [arrowhead = none ];
306 -> 76;

307 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
72 -> 307 [arrowhead = none ];
307 -> 77;

308 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
73 -> 308 [arrowhead = none ];
308 -> 75;

309 [label="EVAL with clause\ndelmin(tree(X243, X244, X245), X246, tree(X243, X247, X248)) :- delmin(X244, X246, X247).\nand substitutionX243 -> T218,\nX244 -> T219,\nX245 -> T220,\nT179 -> tree(T218, T219, T220),\nT182 -> T224,\nX246 -> T224,\nX247 -> T225,\nX248 -> T223,\nT183 -> tree(T218, T225, T223),\nT221 -> T224,\nT222 -> T225", fontsize=14, style = filled, fillcolor = lightblue];
76 -> 309 [arrowhead = none ];
309 -> 78;

310 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
76 -> 310 [arrowhead = none ];
310 -> 79;

311 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
77 -> 311 [arrowhead = none ];
311 -> 88;

312 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
78 -> 312 [arrowhead = none ];
312 -> 80;

313 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
80 -> 313 [arrowhead = none ];
313 -> 81;

314 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
80 -> 314 [arrowhead = none ];
314 -> 82;

315 [label="EVAL with clause\ndelmin(tree(X261, void, X262), X261, X262).\nand substitutionX261 -> T238,\nX262 -> T239,\nT219 -> tree(T238, void, T239),\nT224 -> T238,\nT225 -> T239", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 315 [arrowhead = none ];
315 -> 83;

316 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
81 -> 316 [arrowhead = none ];
316 -> 84;

317 [label="EVAL with clause\ndelmin(tree(X275, X276, X277), X278, tree(X275, X279, X280)) :- delmin(X276, X278, X279).\nand substitutionX275 -> T252,\nX276 -> T253,\nX277 -> T254,\nT219 -> tree(T252, T253, T254),\nT224 -> T258,\nX278 -> T258,\nX279 -> T259,\nX280 -> T257,\nT225 -> tree(T252, T259, T257),\nT255 -> T258,\nT256 -> T259", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 317 [arrowhead = none ];
317 -> 86;

318 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
82 -> 318 [arrowhead = none ];
318 -> 87;

319 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
83 -> 319 [arrowhead = none ];
319 -> 85;

320 [label="INSTANCE with matching:\nT219 -> T253\nT224 -> T258\nT225 -> T259", fontsize=14, style = filled, fillcolor = lightgrey];
86 -> 320 [arrowhead = none , style=dashed];
320 -> 78[style=dashed];

321 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
88 -> 321 [arrowhead = none ];
321 -> 89;

322 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
88 -> 322 [arrowhead = none ];
322 -> 90;

323 [label="EVAL with clause\ndelete(X305, tree(X306, X307, X308), tree(X306, X309, X308)) :- ','(less(X305, X306), delete(X305, X307, X309)).\nand substitutionT1 -> T284,\nX305 -> T284,\nT178 -> T281,\nX306 -> T281,\nX307 -> void,\nT179 -> T282,\nX308 -> T282,\nX309 -> T285,\nT3 -> tree(T281, T285, T282),\nT280 -> T284,\nT283 -> T285", fontsize=14, style = filled, fillcolor = lightblue];
89 -> 323 [arrowhead = none ];
323 -> 91;

324 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
89 -> 324 [arrowhead = none ];
324 -> 92;

325 [label="EVAL with clause\ndelete(X322, tree(X323, X324, X325), tree(X323, X324, X326)) :- ','(less(X323, X322), delete(X322, X325, X326)).\nand substitutionT1 -> T300,\nX322 -> T300,\nT178 -> T297,\nX323 -> T297,\nX324 -> void,\nT179 -> T298,\nX325 -> T298,\nX326 -> T301,\nT3 -> tree(T297, void, T301),\nT296 -> T300,\nT299 -> T301", fontsize=14, style = filled, fillcolor = lightblue];
90 -> 325 [arrowhead = none ];
325 -> 93;

326 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
90 -> 326 [arrowhead = none ];
326 -> 94;

327 [label="INSTANCE with matching:\nT33 -> T284\nT31 -> T281\nT34 -> T285", fontsize=14, style = filled, fillcolor = lightgrey];
91 -> 327 [arrowhead = none , style=dashed];
327 -> 17[style=dashed];

328 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
93 -> 328 [arrowhead = none ];
328 -> 95;

329 [label="SPLIT 2\nnew knowledge:\nT297 is ground\nreplacements:T300 -> T304,\nT301 -> T305,\nT1 -> T306,\nT3 -> T307", fontsize=14, style = filled, fillcolor = violet];
93 -> 329 [arrowhead = none ];
329 -> 96;

330 [label="INSTANCE with matching:\nT64 -> T297\nT66 -> T300", fontsize=14, style = filled, fillcolor = lightgrey];
95 -> 330 [arrowhead = none , style=dashed];
330 -> 31[style=dashed];

331 [label="INSTANCE with matching:\nT1 -> T304\nT2 -> T298\nT3 -> T305", fontsize=14, style = filled, fillcolor = lightgrey];
96 -> 331 [arrowhead = none , style=dashed];
331 -> 1[style=dashed];

332 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
97 -> 332 [arrowhead = none ];
332 -> 99;

333 [label="EVAL with clause\ndelete(X394, tree(X395, X396, X397), tree(X395, X396, X398)) :- ','(less(X395, X394), delete(X394, X397, X398)).\nand substitutionT1 -> T376,\nX394 -> T376,\nT6 -> T373,\nX395 -> T373,\nX396 -> void,\nT7 -> T374,\nX397 -> T374,\nX398 -> T377,\nT3 -> tree(T373, void, T377),\nT372 -> T376,\nT375 -> T377", fontsize=14, style = filled, fillcolor = lightblue];
98 -> 333 [arrowhead = none ];
333 -> 113;

334 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
98 -> 334 [arrowhead = none ];
334 -> 114;

335 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
99 -> 335 [arrowhead = none ];
335 -> 100;

336 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
99 -> 336 [arrowhead = none ];
336 -> 101;

337 [label="EVAL with clause\nless(0, s(X349)).\nand substitutionT322 -> 0,\nX349 -> T328,\nT319 -> s(T328),\nT323 -> T329", fontsize=14, style = filled, fillcolor = lightblue];
100 -> 337 [arrowhead = none ];
337 -> 102;

338 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
100 -> 338 [arrowhead = none ];
338 -> 103;

339 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
101 -> 339 [arrowhead = none ];
339 -> 104;

340 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
101 -> 340 [arrowhead = none ];
340 -> 105;

341 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> void\nT3 -> T329", fontsize=14, style = filled, fillcolor = lightgrey];
102 -> 341 [arrowhead = none , style=dashed];
341 -> 1[style=dashed];

342 [label="EVAL with clause\nless(s(X362), s(X363)) :- less(X362, X363).\nand substitutionX362 -> T340,\nT322 -> s(T340),\nX363 -> T339,\nT319 -> s(T339),\nT338 -> T340,\nT323 -> T341", fontsize=14, style = filled, fillcolor = lightblue];
104 -> 342 [arrowhead = none ];
342 -> 106;

343 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
104 -> 343 [arrowhead = none ];
343 -> 107;

344 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
105 -> 344 [arrowhead = none ];
344 -> 110;

345 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
106 -> 345 [arrowhead = none ];
345 -> 108;

346 [label="SPLIT 2\nnew knowledge:\nT344 is ground\nT339 is ground\nreplacements:T340 -> T344,\nT341 -> T345,\nT1 -> T346,\nT3 -> T347", fontsize=14, style = filled, fillcolor = violet];
106 -> 346 [arrowhead = none ];
346 -> 109;

347 [label="INSTANCE with matching:\nT33 -> T340\nT31 -> T339", fontsize=14, style = filled, fillcolor = lightgrey];
108 -> 347 [arrowhead = none , style=dashed];
347 -> 19[style=dashed];

348 [label="INSTANCE with matching:\nT1 -> s(T344)\nT2 -> void\nT3 -> T345", fontsize=14, style = filled, fillcolor = lightgrey];
109 -> 348 [arrowhead = none , style=dashed];
348 -> 1[style=dashed];

349 [label="EVAL with clause\ndelete(X382, tree(X383, X384, X385), tree(X383, X384, X386)) :- ','(less(X383, X382), delete(X382, X385, X386)).\nand substitutionT1 -> T364,\nX382 -> T364,\nT319 -> T361,\nX383 -> T361,\nX384 -> void,\nT320 -> T362,\nX385 -> T362,\nX386 -> T365,\nT3 -> tree(T361, void, T365),\nT360 -> T364,\nT363 -> T365", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 349 [arrowhead = none ];
349 -> 111;

350 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
110 -> 350 [arrowhead = none ];
350 -> 112;

351 [label="INSTANCE with matching:\nT297 -> T361\nT300 -> T364\nT298 -> T362\nT301 -> T365", fontsize=14, style = filled, fillcolor = lightgrey];
111 -> 351 [arrowhead = none , style=dashed];
351 -> 93[style=dashed];

352 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
113 -> 352 [arrowhead = none ];
352 -> 115;

353 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
115 -> 353 [arrowhead = none ];
353 -> 116;

354 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
115 -> 354 [arrowhead = none ];
354 -> 117;

355 [label="EVAL with clause\nless(0, s(X403)).\nand substitutionT373 -> 0,\nX403 -> T384,\nT376 -> s(T384),\nT377 -> T383,\nT382 -> T384", fontsize=14, style = filled, fillcolor = lightblue];
116 -> 355 [arrowhead = none ];
355 -> 118;

356 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
116 -> 356 [arrowhead = none ];
356 -> 119;

357 [label="EVAL with clause\nless(s(X412), s(X413)) :- less(X412, X413).\nand substitutionX412 -> T393,\nT373 -> s(T393),\nX413 -> T395,\nT376 -> s(T395),\nT394 -> T395,\nT377 -> T396", fontsize=14, style = filled, fillcolor = lightblue];
117 -> 357 [arrowhead = none ];
357 -> 120;

358 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
117 -> 358 [arrowhead = none ];
358 -> 121;

359 [label="INSTANCE with matching:\nT1 -> s(T384)\nT2 -> T374\nT3 -> T383", fontsize=14, style = filled, fillcolor = lightgrey];
118 -> 359 [arrowhead = none , style=dashed];
359 -> 1[style=dashed];

360 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
120 -> 360 [arrowhead = none ];
360 -> 122;

361 [label="SPLIT 2\nnew knowledge:\nT393 is ground\nreplacements:T395 -> T399,\nT396 -> T400,\nT1 -> T401,\nT3 -> T402", fontsize=14, style = filled, fillcolor = violet];
120 -> 361 [arrowhead = none ];
361 -> 123;

362 [label="INSTANCE with matching:\nT64 -> T393\nT66 -> T395", fontsize=14, style = filled, fillcolor = lightgrey];
122 -> 362 [arrowhead = none , style=dashed];
362 -> 31[style=dashed];

363 [label="INSTANCE with matching:\nT1 -> s(T399)\nT2 -> T374\nT3 -> T400", fontsize=14, style = filled, fillcolor = lightgrey];
123 -> 363 [arrowhead = none , style=dashed];
363 -> 1[style=dashed];

364 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
124 -> 364 [arrowhead = none ];
364 -> 126;

365 [label="EVAL with clause\ndelete(X586, tree(X586, X587, X588), tree(X589, X587, X590)) :- delmin(X588, X589, X590).\nand substitutionT1 -> T573,\nX586 -> T573,\nX587 -> T574,\nX588 -> T575,\nT2 -> tree(T573, T574, T575),\nX589 -> T578,\nX590 -> T579,\nT3 -> tree(T578, T574, T579),\nT576 -> T578,\nT577 -> T579", fontsize=14, style = filled, fillcolor = lightblue];
125 -> 365 [arrowhead = none ];
365 -> 168;

366 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
125 -> 366 [arrowhead = none ];
366 -> 169;

367 [label="EVAL with clause\ndelete(X431, tree(X431, X432, X433), tree(X434, X432, X435)) :- delmin(X433, X434, X435).\nand substitutionT1 -> T417,\nX431 -> T417,\nT411 -> T417,\nT412 -> T418,\nX432 -> T418,\nX433 -> void,\nX434 -> T421,\nX435 -> T422,\nT3 -> tree(T421, T418, T422),\nT419 -> T421,\nT420 -> T422", fontsize=14, style = filled, fillcolor = lightblue];
126 -> 367 [arrowhead = none ];
367 -> 127;

368 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
126 -> 368 [arrowhead = none ];
368 -> 128;

369 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
127 -> 369 [arrowhead = none ];
369 -> 129;

370 [label="EVAL with clause\ndelete(X499, tree(X500, X501, X502), tree(X500, X503, X502)) :- ','(less(X499, X500), delete(X499, X501, X503)).\nand substitutionT1 -> T481,\nX499 -> T481,\nT411 -> T478,\nX500 -> T478,\nT412 -> T479,\nX501 -> T479,\nX502 -> void,\nX503 -> T482,\nT3 -> tree(T478, T482, void),\nT477 -> T481,\nT480 -> T482", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 370 [arrowhead = none ];
370 -> 141;

371 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
128 -> 371 [arrowhead = none ];
371 -> 142;

372 [label="BACKTRACK\nfor clause: delmin(tree(Y, void, Right), Y, Right)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 372 [arrowhead = none ];
372 -> 130;

373 [label="BACKTRACK\nfor clause: delmin(tree(X, Left, X1), Y, tree(X, Left1, X2)) :- delmin(Left, Y, Left1)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
130 -> 373 [arrowhead = none ];
373 -> 131;

374 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
131 -> 374 [arrowhead = none ];
374 -> 132;

375 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
132 -> 375 [arrowhead = none ];
375 -> 133;

376 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
132 -> 376 [arrowhead = none ];
376 -> 134;

377 [label="EVAL with clause\ndelete(X464, tree(X465, X466, X467), tree(X465, X468, X467)) :- ','(less(X464, X465), delete(X464, X466, X468)).\nand substitutionT1 -> T443,\nX464 -> T443,\nT417 -> T440,\nX465 -> T440,\nT418 -> T441,\nX466 -> T441,\nX467 -> void,\nX468 -> T444,\nT3 -> tree(T440, T444, void),\nT439 -> T443,\nT442 -> T444", fontsize=14, style = filled, fillcolor = lightblue];
133 -> 377 [arrowhead = none ];
377 -> 135;

378 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
133 -> 378 [arrowhead = none ];
378 -> 136;

379 [label="EVAL with clause\ndelete(X487, tree(X488, X489, X490), tree(X488, X489, X491)) :- ','(less(X488, X487), delete(X487, X490, X491)).\nand substitutionT1 -> T469,\nX487 -> T469,\nT417 -> T466,\nX488 -> T466,\nT418 -> T467,\nX489 -> T467,\nX490 -> void,\nX491 -> T470,\nT3 -> tree(T466, T467, T470),\nT465 -> T469,\nT468 -> T470", fontsize=14, style = filled, fillcolor = lightblue];
134 -> 379 [arrowhead = none ];
379 -> 139;

380 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
134 -> 380 [arrowhead = none ];
380 -> 140;

381 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
135 -> 381 [arrowhead = none ];
381 -> 137;

382 [label="SPLIT 2\nnew knowledge:\nT447 is ground\nT440 is ground\nreplacements:T443 -> T447,\nT444 -> T448,\nT1 -> T449,\nT3 -> T450", fontsize=14, style = filled, fillcolor = violet];
135 -> 382 [arrowhead = none ];
382 -> 138;

383 [label="INSTANCE with matching:\nT33 -> T443\nT31 -> T440", fontsize=14, style = filled, fillcolor = lightgrey];
137 -> 383 [arrowhead = none , style=dashed];
383 -> 19[style=dashed];

384 [label="INSTANCE with matching:\nT1 -> T447\nT2 -> T441\nT3 -> T448", fontsize=14, style = filled, fillcolor = lightgrey];
138 -> 384 [arrowhead = none , style=dashed];
384 -> 1[style=dashed];

385 [label="INSTANCE with matching:\nT64 -> T466\nT66 -> T469\nT67 -> T470", fontsize=14, style = filled, fillcolor = lightgrey];
139 -> 385 [arrowhead = none , style=dashed];
385 -> 29[style=dashed];

386 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
141 -> 386 [arrowhead = none ];
386 -> 143;

387 [label="EVAL with clause\ndelete(X553, tree(X554, X555, X556), tree(X554, X555, X557)) :- ','(less(X554, X553), delete(X553, X556, X557)).\nand substitutionT1 -> T539,\nX553 -> T539,\nT411 -> T536,\nX554 -> T536,\nT412 -> T537,\nX555 -> T537,\nX556 -> void,\nX557 -> T540,\nT3 -> tree(T536, T537, T540),\nT535 -> T539,\nT538 -> T540", fontsize=14, style = filled, fillcolor = lightblue];
142 -> 387 [arrowhead = none ];
387 -> 157;

388 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
142 -> 388 [arrowhead = none ];
388 -> 158;

389 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
143 -> 389 [arrowhead = none ];
389 -> 144;

390 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
143 -> 390 [arrowhead = none ];
390 -> 145;

391 [label="EVAL with clause\nless(0, s(X508)).\nand substitutionT481 -> 0,\nX508 -> T487,\nT478 -> s(T487),\nT482 -> T488", fontsize=14, style = filled, fillcolor = lightblue];
144 -> 391 [arrowhead = none ];
391 -> 146;

392 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
144 -> 392 [arrowhead = none ];
392 -> 147;

393 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
145 -> 393 [arrowhead = none ];
393 -> 148;

394 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
145 -> 394 [arrowhead = none ];
394 -> 149;

395 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T479\nT3 -> T488", fontsize=14, style = filled, fillcolor = lightgrey];
146 -> 395 [arrowhead = none , style=dashed];
395 -> 1[style=dashed];

396 [label="EVAL with clause\nless(s(X521), s(X522)) :- less(X521, X522).\nand substitutionX521 -> T501,\nT481 -> s(T501),\nX522 -> T500,\nT478 -> s(T500),\nT499 -> T501,\nT482 -> T502", fontsize=14, style = filled, fillcolor = lightblue];
148 -> 396 [arrowhead = none ];
396 -> 150;

397 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
148 -> 397 [arrowhead = none ];
397 -> 151;

398 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
149 -> 398 [arrowhead = none ];
398 -> 154;

399 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
150 -> 399 [arrowhead = none ];
399 -> 152;

400 [label="SPLIT 2\nnew knowledge:\nT505 is ground\nT500 is ground\nreplacements:T501 -> T505,\nT502 -> T506,\nT1 -> T507,\nT3 -> T508", fontsize=14, style = filled, fillcolor = violet];
150 -> 400 [arrowhead = none ];
400 -> 153;

401 [label="INSTANCE with matching:\nT33 -> T501\nT31 -> T500", fontsize=14, style = filled, fillcolor = lightgrey];
152 -> 401 [arrowhead = none , style=dashed];
401 -> 19[style=dashed];

402 [label="INSTANCE with matching:\nT1 -> s(T505)\nT2 -> T479\nT3 -> T506", fontsize=14, style = filled, fillcolor = lightgrey];
153 -> 402 [arrowhead = none , style=dashed];
402 -> 1[style=dashed];

403 [label="EVAL with clause\ndelete(X541, tree(X542, X543, X544), tree(X542, X543, X545)) :- ','(less(X542, X541), delete(X541, X544, X545)).\nand substitutionT1 -> T527,\nX541 -> T527,\nT478 -> T524,\nX542 -> T524,\nT479 -> T525,\nX543 -> T525,\nX544 -> void,\nX545 -> T528,\nT3 -> tree(T524, T525, T528),\nT523 -> T527,\nT526 -> T528", fontsize=14, style = filled, fillcolor = lightblue];
154 -> 403 [arrowhead = none ];
403 -> 155;

404 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
154 -> 404 [arrowhead = none ];
404 -> 156;

405 [label="INSTANCE with matching:\nT64 -> T524\nT66 -> T527\nT67 -> T528", fontsize=14, style = filled, fillcolor = lightgrey];
155 -> 405 [arrowhead = none , style=dashed];
405 -> 29[style=dashed];

406 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
157 -> 406 [arrowhead = none ];
406 -> 159;

407 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
159 -> 407 [arrowhead = none ];
407 -> 160;

408 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
159 -> 408 [arrowhead = none ];
408 -> 161;

409 [label="EVAL with clause\nless(0, s(X562)).\nand substitutionT536 -> 0,\nX562 -> T547,\nT539 -> s(T547),\nT540 -> T546,\nT545 -> T547", fontsize=14, style = filled, fillcolor = lightblue];
160 -> 409 [arrowhead = none ];
409 -> 162;

410 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
160 -> 410 [arrowhead = none ];
410 -> 163;

411 [label="EVAL with clause\nless(s(X571), s(X572)) :- less(X571, X572).\nand substitutionX571 -> T554,\nT536 -> s(T554),\nX572 -> T556,\nT539 -> s(T556),\nT555 -> T556,\nT540 -> T557", fontsize=14, style = filled, fillcolor = lightblue];
161 -> 411 [arrowhead = none ];
411 -> 164;

412 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
161 -> 412 [arrowhead = none ];
412 -> 165;

413 [label="INSTANCE with matching:\nT1 -> s(T547)\nT2 -> void\nT3 -> T546", fontsize=14, style = filled, fillcolor = lightgrey];
162 -> 413 [arrowhead = none , style=dashed];
413 -> 1[style=dashed];

414 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
164 -> 414 [arrowhead = none ];
414 -> 166;

415 [label="SPLIT 2\nnew knowledge:\nT554 is ground\nreplacements:T556 -> T560,\nT557 -> T561,\nT1 -> T562,\nT3 -> T563", fontsize=14, style = filled, fillcolor = violet];
164 -> 415 [arrowhead = none ];
415 -> 167;

416 [label="INSTANCE with matching:\nT64 -> T554\nT66 -> T556", fontsize=14, style = filled, fillcolor = lightgrey];
166 -> 416 [arrowhead = none , style=dashed];
416 -> 31[style=dashed];

417 [label="INSTANCE with matching:\nT1 -> s(T560)\nT2 -> void\nT3 -> T561", fontsize=14, style = filled, fillcolor = lightgrey];
167 -> 417 [arrowhead = none , style=dashed];
417 -> 1[style=dashed];

418 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
168 -> 418 [arrowhead = none ];
418 -> 170;

419 [label="EVAL with clause\ndelete(X696, tree(X697, X698, X699), tree(X697, X700, X699)) :- ','(less(X696, X697), delete(X696, X698, X700)).\nand substitutionT1 -> T704,\nX696 -> T704,\nX697 -> T700,\nX698 -> T701,\nX699 -> T702,\nT2 -> tree(T700, T701, T702),\nX700 -> T705,\nT3 -> tree(T700, T705, T702),\nT699 -> T704,\nT703 -> T705", fontsize=14, style = filled, fillcolor = lightblue];
169 -> 419 [arrowhead = none ];
419 -> 191;

420 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
169 -> 420 [arrowhead = none ];
420 -> 192;

421 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
170 -> 421 [arrowhead = none ];
421 -> 171;

422 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
170 -> 422 [arrowhead = none ];
422 -> 172;

423 [label="EVAL with clause\ndelmin(tree(X599, void, X600), X599, X600).\nand substitutionX599 -> T588,\nX600 -> T589,\nT575 -> tree(T588, void, T589),\nT578 -> T588,\nT579 -> T589", fontsize=14, style = filled, fillcolor = lightblue];
171 -> 423 [arrowhead = none ];
423 -> 173;

424 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
171 -> 424 [arrowhead = none ];
424 -> 174;

425 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
172 -> 425 [arrowhead = none ];
425 -> 176;

426 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
172 -> 426 [arrowhead = none ];
426 -> 177;

427 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
173 -> 427 [arrowhead = none ];
427 -> 175;

428 [label="EVAL with clause\ndelmin(tree(X625, X626, X627), X628, tree(X625, X629, X630)) :- delmin(X626, X628, X629).\nand substitutionX625 -> T614,\nX626 -> T615,\nX627 -> T616,\nT575 -> tree(T614, T615, T616),\nT578 -> T620,\nX628 -> T620,\nX629 -> T621,\nX630 -> T619,\nT579 -> tree(T614, T621, T619),\nT617 -> T620,\nT618 -> T621", fontsize=14, style = filled, fillcolor = lightblue];
176 -> 428 [arrowhead = none ];
428 -> 178;

429 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
176 -> 429 [arrowhead = none ];
429 -> 179;

430 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
177 -> 430 [arrowhead = none ];
430 -> 180;

431 [label="INSTANCE with matching:\nT219 -> T615\nT224 -> T620\nT225 -> T621", fontsize=14, style = filled, fillcolor = lightgrey];
178 -> 431 [arrowhead = none , style=dashed];
431 -> 78[style=dashed];

432 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
180 -> 432 [arrowhead = none ];
432 -> 181;

433 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
180 -> 433 [arrowhead = none ];
433 -> 182;

434 [label="EVAL with clause\ndelete(X655, tree(X656, X657, X658), tree(X656, X659, X658)) :- ','(less(X655, X656), delete(X655, X657, X659)).\nand substitutionT1 -> T651,\nX655 -> T651,\nT573 -> T647,\nX656 -> T647,\nT574 -> T648,\nX657 -> T648,\nT575 -> T649,\nX658 -> T649,\nX659 -> T652,\nT3 -> tree(T647, T652, T649),\nT646 -> T651,\nT650 -> T652", fontsize=14, style = filled, fillcolor = lightblue];
181 -> 434 [arrowhead = none ];
434 -> 183;

435 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
181 -> 435 [arrowhead = none ];
435 -> 184;

436 [label="EVAL with clause\ndelete(X678, tree(X679, X680, X681), tree(X679, X680, X682)) :- ','(less(X679, X678), delete(X678, X681, X682)).\nand substitutionT1 -> T680,\nX678 -> T680,\nT573 -> T676,\nX679 -> T676,\nT574 -> T677,\nX680 -> T677,\nT575 -> T678,\nX681 -> T678,\nX682 -> T681,\nT3 -> tree(T676, T677, T681),\nT675 -> T680,\nT679 -> T681", fontsize=14, style = filled, fillcolor = lightblue];
182 -> 436 [arrowhead = none ];
436 -> 187;

437 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
182 -> 437 [arrowhead = none ];
437 -> 188;

438 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
183 -> 438 [arrowhead = none ];
438 -> 185;

439 [label="SPLIT 2\nnew knowledge:\nT655 is ground\nT647 is ground\nreplacements:T651 -> T655,\nT652 -> T656,\nT1 -> T657,\nT3 -> T658", fontsize=14, style = filled, fillcolor = violet];
183 -> 439 [arrowhead = none ];
439 -> 186;

440 [label="INSTANCE with matching:\nT33 -> T651\nT31 -> T647", fontsize=14, style = filled, fillcolor = lightgrey];
185 -> 440 [arrowhead = none , style=dashed];
440 -> 19[style=dashed];

441 [label="INSTANCE with matching:\nT1 -> T655\nT2 -> T648\nT3 -> T656", fontsize=14, style = filled, fillcolor = lightgrey];
186 -> 441 [arrowhead = none , style=dashed];
441 -> 1[style=dashed];

442 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
187 -> 442 [arrowhead = none ];
442 -> 189;

443 [label="SPLIT 2\nnew knowledge:\nT676 is ground\nreplacements:T680 -> T684,\nT681 -> T685,\nT1 -> T686,\nT3 -> T687", fontsize=14, style = filled, fillcolor = violet];
187 -> 443 [arrowhead = none ];
443 -> 190;

444 [label="INSTANCE with matching:\nT64 -> T676\nT66 -> T680", fontsize=14, style = filled, fillcolor = lightgrey];
189 -> 444 [arrowhead = none , style=dashed];
444 -> 31[style=dashed];

445 [label="INSTANCE with matching:\nT1 -> T684\nT2 -> T678\nT3 -> T685", fontsize=14, style = filled, fillcolor = lightgrey];
190 -> 445 [arrowhead = none , style=dashed];
445 -> 1[style=dashed];

446 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
191 -> 446 [arrowhead = none ];
446 -> 193;

447 [label="EVAL with clause\ndelete(X750, tree(X751, X752, X753), tree(X751, X752, X754)) :- ','(less(X751, X750), delete(X750, X753, X754)).\nand substitutionT1 -> T767,\nX750 -> T767,\nX751 -> T763,\nX752 -> T764,\nX753 -> T765,\nT2 -> tree(T763, T764, T765),\nX754 -> T768,\nT3 -> tree(T763, T764, T768),\nT762 -> T767,\nT766 -> T768", fontsize=14, style = filled, fillcolor = lightblue];
192 -> 447 [arrowhead = none ];
447 -> 207;

448 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
192 -> 448 [arrowhead = none ];
448 -> 208;

449 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
193 -> 449 [arrowhead = none ];
449 -> 194;

450 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
193 -> 450 [arrowhead = none ];
450 -> 195;

451 [label="EVAL with clause\nless(0, s(X705)).\nand substitutionT704 -> 0,\nX705 -> T710,\nT700 -> s(T710),\nT705 -> T711", fontsize=14, style = filled, fillcolor = lightblue];
194 -> 451 [arrowhead = none ];
451 -> 196;

452 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
194 -> 452 [arrowhead = none ];
452 -> 197;

453 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
195 -> 453 [arrowhead = none ];
453 -> 198;

454 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
195 -> 454 [arrowhead = none ];
454 -> 199;

455 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T701\nT3 -> T711", fontsize=14, style = filled, fillcolor = lightgrey];
196 -> 455 [arrowhead = none , style=dashed];
455 -> 1[style=dashed];

456 [label="EVAL with clause\nless(s(X718), s(X719)) :- less(X718, X719).\nand substitutionX718 -> T724,\nT704 -> s(T724),\nX719 -> T723,\nT700 -> s(T723),\nT722 -> T724,\nT705 -> T725", fontsize=14, style = filled, fillcolor = lightblue];
198 -> 456 [arrowhead = none ];
456 -> 200;

457 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
198 -> 457 [arrowhead = none ];
457 -> 201;

458 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
199 -> 458 [arrowhead = none ];
458 -> 204;

459 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
200 -> 459 [arrowhead = none ];
459 -> 202;

460 [label="SPLIT 2\nnew knowledge:\nT728 is ground\nT723 is ground\nreplacements:T724 -> T728,\nT725 -> T729,\nT1 -> T730,\nT3 -> T731", fontsize=14, style = filled, fillcolor = violet];
200 -> 460 [arrowhead = none ];
460 -> 203;

461 [label="INSTANCE with matching:\nT33 -> T724\nT31 -> T723", fontsize=14, style = filled, fillcolor = lightgrey];
202 -> 461 [arrowhead = none , style=dashed];
461 -> 19[style=dashed];

462 [label="INSTANCE with matching:\nT1 -> s(T728)\nT2 -> T701\nT3 -> T729", fontsize=14, style = filled, fillcolor = lightgrey];
203 -> 462 [arrowhead = none , style=dashed];
462 -> 1[style=dashed];

463 [label="EVAL with clause\ndelete(X738, tree(X739, X740, X741), tree(X739, X740, X742)) :- ','(less(X739, X738), delete(X738, X741, X742)).\nand substitutionT1 -> T753,\nX738 -> T753,\nT700 -> T749,\nX739 -> T749,\nT701 -> T750,\nX740 -> T750,\nT702 -> T751,\nX741 -> T751,\nX742 -> T754,\nT3 -> tree(T749, T750, T754),\nT748 -> T753,\nT752 -> T754", fontsize=14, style = filled, fillcolor = lightblue];
204 -> 463 [arrowhead = none ];
463 -> 205;

464 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
204 -> 464 [arrowhead = none ];
464 -> 206;

465 [label="INSTANCE with matching:\nT676 -> T749\nT680 -> T753\nT678 -> T751\nT681 -> T754\nT677 -> T750", fontsize=14, style = filled, fillcolor = lightgrey];
205 -> 465 [arrowhead = none , style=dashed];
465 -> 187[style=dashed];

466 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
207 -> 466 [arrowhead = none ];
466 -> 209;

467 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
209 -> 467 [arrowhead = none ];
467 -> 210;

468 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
209 -> 468 [arrowhead = none ];
468 -> 211;

469 [label="EVAL with clause\nless(0, s(X759)).\nand substitutionT763 -> 0,\nX759 -> T775,\nT767 -> s(T775),\nT768 -> T774,\nT773 -> T775", fontsize=14, style = filled, fillcolor = lightblue];
210 -> 469 [arrowhead = none ];
469 -> 212;

470 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
210 -> 470 [arrowhead = none ];
470 -> 213;

471 [label="EVAL with clause\nless(s(X768), s(X769)) :- less(X768, X769).\nand substitutionX768 -> T784,\nT763 -> s(T784),\nX769 -> T786,\nT767 -> s(T786),\nT785 -> T786,\nT768 -> T787", fontsize=14, style = filled, fillcolor = lightblue];
211 -> 471 [arrowhead = none ];
471 -> 214;

472 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
211 -> 472 [arrowhead = none ];
472 -> 215;

473 [label="INSTANCE with matching:\nT1 -> s(T775)\nT2 -> T765\nT3 -> T774", fontsize=14, style = filled, fillcolor = lightgrey];
212 -> 473 [arrowhead = none , style=dashed];
473 -> 1[style=dashed];

474 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
214 -> 474 [arrowhead = none ];
474 -> 216;

475 [label="SPLIT 2\nnew knowledge:\nT784 is ground\nreplacements:T786 -> T790,\nT787 -> T791,\nT1 -> T792,\nT3 -> T793", fontsize=14, style = filled, fillcolor = violet];
214 -> 475 [arrowhead = none ];
475 -> 217;

476 [label="INSTANCE with matching:\nT64 -> T784\nT66 -> T786", fontsize=14, style = filled, fillcolor = lightgrey];
216 -> 476 [arrowhead = none , style=dashed];
476 -> 31[style=dashed];

477 [label="INSTANCE with matching:\nT1 -> s(T790)\nT2 -> T765\nT3 -> T791", fontsize=14, style = filled, fillcolor = lightgrey];
217 -> 477 [arrowhead = none , style=dashed];
477 -> 1[style=dashed];

}

(2) Obligation:

Clauses:

lessA(0, s(T45)).
lessA(s(T52), s(T51)) :- lessA(T52, T51).
lessB(0, s(T78)).
lessB(s(T83), s(T85)) :- lessB(T83, T85).
pC(T64, T66, T67) :- lessB(T64, T66).
pC(T64, T70, T71) :- ','(lessB(T64, T70), deleteD(T70, void, T71)).
delminE(tree(T238, void, T239), T238, T239).
delminE(tree(T252, T253, T254), T258, tree(T252, T259, T257)) :- delminE(T253, T258, T259).
pF(T33, T31, T34) :- lessA(T33, T31).
pF(T37, T31, T38) :- ','(lessA(T37, T31), deleteD(T37, void, T38)).
pG(T297, T300, T298, T301) :- lessB(T297, T300).
pG(T297, T304, T298, T305) :- ','(lessB(T297, T304), deleteD(T304, T298, T305)).
pH(T676, T680, T678, T681) :- lessB(T676, T680).
pH(T676, T684, T678, T685) :- ','(lessB(T676, T684), deleteD(T684, T678, T685)).
deleteD(T6, tree(T6, void, T7), T7).
deleteD(T9, tree(T9, void, void), void).
deleteD(T33, tree(T31, void, void), tree(T31, T34, void)) :- pF(T33, T31, T34).
deleteD(T66, tree(T64, void, void), tree(T64, void, T67)) :- pC(T64, T66, T67).
deleteD(0, tree(s(T102), void, void), tree(s(T102), T103, void)) :- deleteD(0, void, T103).
deleteD(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) :- lessA(T114, T113).
deleteD(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) :- ','(lessA(T118, T113), deleteD(s(T118), void, T119)).
deleteD(T135, tree(T133, void, void), tree(T133, void, T136)) :- pC(T133, T135, T136).
deleteD(s(T153), tree(0, void, void), tree(0, void, T152)) :- deleteD(s(T153), void, T152).
deleteD(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) :- lessB(T160, T162).
deleteD(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) :- ','(lessB(T160, T166), deleteD(s(T166), void, T167)).
deleteD(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)).
deleteD(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) :- delminE(T219, T224, T225).
deleteD(T284, tree(T281, void, T282), tree(T281, T285, T282)) :- pF(T284, T281, T285).
deleteD(T300, tree(T297, void, T298), tree(T297, void, T301)) :- pG(T297, T300, T298, T301).
deleteD(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) :- deleteD(0, void, T329).
deleteD(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) :- lessA(T340, T339).
deleteD(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) :- ','(lessA(T344, T339), deleteD(s(T344), void, T345)).
deleteD(T364, tree(T361, void, T362), tree(T361, void, T365)) :- pG(T361, T364, T362, T365).
deleteD(s(T384), tree(0, void, T374), tree(0, void, T383)) :- deleteD(s(T384), T374, T383).
deleteD(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) :- lessB(T393, T395).
deleteD(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) :- ','(lessB(T393, T399), deleteD(s(T399), T374, T400)).
deleteD(T411, tree(T411, T412, void), T412).
deleteD(T443, tree(T440, T441, void), tree(T440, T444, void)) :- lessA(T443, T440).
deleteD(T447, tree(T440, T441, void), tree(T440, T448, void)) :- ','(lessA(T447, T440), deleteD(T447, T441, T448)).
deleteD(T469, tree(T466, T467, void), tree(T466, T467, T470)) :- pC(T466, T469, T470).
deleteD(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) :- deleteD(0, T479, T488).
deleteD(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) :- lessA(T501, T500).
deleteD(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) :- ','(lessA(T505, T500), deleteD(s(T505), T479, T506)).
deleteD(T527, tree(T524, T525, void), tree(T524, T525, T528)) :- pC(T524, T527, T528).
deleteD(s(T547), tree(0, T537, void), tree(0, T537, T546)) :- deleteD(s(T547), void, T546).
deleteD(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) :- lessB(T554, T556).
deleteD(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) :- ','(lessB(T554, T560), deleteD(s(T560), void, T561)).
deleteD(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)).
deleteD(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) :- delminE(T615, T620, T621).
deleteD(T651, tree(T647, T648, T649), tree(T647, T652, T649)) :- lessA(T651, T647).
deleteD(T655, tree(T647, T648, T649), tree(T647, T656, T649)) :- ','(lessA(T655, T647), deleteD(T655, T648, T656)).
deleteD(T680, tree(T676, T677, T678), tree(T676, T677, T681)) :- pH(T676, T680, T678, T681).
deleteD(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) :- deleteD(0, T701, T711).
deleteD(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) :- lessA(T724, T723).
deleteD(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) :- ','(lessA(T728, T723), deleteD(s(T728), T701, T729)).
deleteD(T753, tree(T749, T750, T751), tree(T749, T750, T754)) :- pH(T749, T753, T751, T754).
deleteD(s(T775), tree(0, T764, T765), tree(0, T764, T774)) :- deleteD(s(T775), T765, T774).
deleteD(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) :- lessB(T784, T786).
deleteD(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) :- ','(lessB(T784, T790), deleteD(s(T790), T765, T791)).

Query: deleteD(a,g,a)

(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: (f,b,f) (b,b,f)
pF_in: (f,b,f) (b,b,f)
lessA_in: (f,b) (b,b)
pC_in: (b,b,f) (b,f,f)
lessB_in: (b,b) (b,f)
delminE_in: (b,f,f)
pG_in: (b,b,b,f) (b,f,b,f)
pH_in: (b,b,b,f) (b,f,b,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

deleteD_in_aga(T6, tree(T6, void, T7), T7) → deleteD_out_aga(T6, tree(T6, void, T7), T7)
deleteD_in_aga(T9, tree(T9, void, void), void) → deleteD_out_aga(T9, tree(T9, void, void), void)
deleteD_in_aga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_aga(T33, T31, T34, pF_in_aga(T33, T31, T34))
pF_in_aga(T33, T31, T34) → U7_aga(T33, T31, T34, lessA_in_ag(T33, T31))
lessA_in_ag(0, s(T45)) → lessA_out_ag(0, s(T45))
lessA_in_ag(s(T52), s(T51)) → U1_ag(T52, T51, lessA_in_ag(T52, T51))
U1_ag(T52, T51, lessA_out_ag(T52, T51)) → lessA_out_ag(s(T52), s(T51))
U7_aga(T33, T31, T34, lessA_out_ag(T33, T31)) → pF_out_aga(T33, T31, T34)
pF_in_aga(T37, T31, T38) → U8_aga(T37, T31, T38, lessA_in_ag(T37, T31))
U8_aga(T37, T31, T38, lessA_out_ag(T37, T31)) → U9_aga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T6, tree(T6, void, T7), T7) → deleteD_out_gga(T6, tree(T6, void, T7), T7)
deleteD_in_gga(T9, tree(T9, void, void), void) → deleteD_out_gga(T9, tree(T9, void, void), void)
deleteD_in_gga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_gga(T33, T31, T34, pF_in_gga(T33, T31, T34))
pF_in_gga(T33, T31, T34) → U7_gga(T33, T31, T34, lessA_in_gg(T33, T31))
lessA_in_gg(0, s(T45)) → lessA_out_gg(0, s(T45))
lessA_in_gg(s(T52), s(T51)) → U1_gg(T52, T51, lessA_in_gg(T52, T51))
U1_gg(T52, T51, lessA_out_gg(T52, T51)) → lessA_out_gg(s(T52), s(T51))
U7_gga(T33, T31, T34, lessA_out_gg(T33, T31)) → pF_out_gga(T33, T31, T34)
pF_in_gga(T37, T31, T38) → U8_gga(T37, T31, T38, lessA_in_gg(T37, T31))
U8_gga(T37, T31, T38, lessA_out_gg(T37, T31)) → U9_gga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_gga(T66, T64, T67, pC_in_gga(T64, T66, T67))
pC_in_gga(T64, T66, T67) → U3_gga(T64, T66, T67, lessB_in_gg(T64, T66))
lessB_in_gg(0, s(T78)) → lessB_out_gg(0, s(T78))
lessB_in_gg(s(T83), s(T85)) → U2_gg(T83, T85, lessB_in_gg(T83, T85))
U2_gg(T83, T85, lessB_out_gg(T83, T85)) → lessB_out_gg(s(T83), s(T85))
U3_gga(T64, T66, T67, lessB_out_gg(T64, T66)) → pC_out_gga(T64, T66, T67)
pC_in_gga(T64, T70, T71) → U4_gga(T64, T70, T71, lessB_in_gg(T64, T70))
U4_gga(T64, T70, T71, lessB_out_gg(T64, T70)) → U5_gga(T64, T70, T71, deleteD_in_gga(T70, void, T71))
deleteD_in_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_gga(T102, T103, deleteD_in_gga(0, void, T103))
deleteD_in_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_gga(T114, T113, T115, lessA_in_gg(T114, T113))
U19_gga(T114, T113, T115, lessA_out_gg(T114, T113)) → deleteD_out_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_gga(T118, T113, T119, lessA_in_gg(T118, T113))
U20_gga(T118, T113, T119, lessA_out_gg(T118, T113)) → U21_gga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
deleteD_in_gga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_gga(T135, T133, T136, pC_in_gga(T133, T135, T136))
U22_gga(T135, T133, T136, pC_out_gga(T133, T135, T136)) → deleteD_out_gga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_gga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_gga(T153, T152, deleteD_in_gga(s(T153), void, T152))
deleteD_in_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_gga(T162, T160, T163, lessB_in_gg(T160, T162))
U24_gga(T162, T160, T163, lessB_out_gg(T160, T162)) → deleteD_out_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_gga(T166, T160, T167, lessB_in_gg(T160, T166))
U25_gga(T166, T160, T167, lessB_out_gg(T160, T166)) → U26_gga(T166, T160, T167, deleteD_in_gga(s(T166), void, T167))
deleteD_in_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
delminE_in_gaa(tree(T238, void, T239), T238, T239) → delminE_out_gaa(tree(T238, void, T239), T238, T239)
delminE_in_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → U6_gaa(T252, T253, T254, T258, T259, T257, delminE_in_gaa(T253, T258, T259))
U6_gaa(T252, T253, T254, T258, T259, T257, delminE_out_gaa(T253, T258, T259)) → delminE_out_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257))
U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_gga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_gga(T284, T281, T282, T285, pF_in_gga(T284, T281, T285))
U28_gga(T284, T281, T282, T285, pF_out_gga(T284, T281, T285)) → deleteD_out_gga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_gga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_gga(T300, T297, T298, T301, pG_in_ggga(T297, T300, T298, T301))
pG_in_ggga(T297, T300, T298, T301) → U10_ggga(T297, T300, T298, T301, lessB_in_gg(T297, T300))
U10_ggga(T297, T300, T298, T301, lessB_out_gg(T297, T300)) → pG_out_ggga(T297, T300, T298, T301)
pG_in_ggga(T297, T304, T298, T305) → U11_ggga(T297, T304, T298, T305, lessB_in_gg(T297, T304))
U11_ggga(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → U12_ggga(T297, T304, T298, T305, deleteD_in_gga(T304, T298, T305))
deleteD_in_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_gga(T328, T320, T329, deleteD_in_gga(0, void, T329))
deleteD_in_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_gga(T340, T339, T320, T341, lessA_in_gg(T340, T339))
U31_gga(T340, T339, T320, T341, lessA_out_gg(T340, T339)) → deleteD_out_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_gga(T344, T339, T320, T345, lessA_in_gg(T344, T339))
U32_gga(T344, T339, T320, T345, lessA_out_gg(T344, T339)) → U33_gga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
deleteD_in_gga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_gga(T364, T361, T362, T365, pG_in_ggga(T361, T364, T362, T365))
U34_gga(T364, T361, T362, T365, pG_out_ggga(T361, T364, T362, T365)) → deleteD_out_gga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_gga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_gga(T384, T374, T383, deleteD_in_gga(s(T384), T374, T383))
deleteD_in_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_gga(T395, T393, T374, T396, lessB_in_gg(T393, T395))
U36_gga(T395, T393, T374, T396, lessB_out_gg(T393, T395)) → deleteD_out_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_gga(T399, T393, T374, T400, lessB_in_gg(T393, T399))
U37_gga(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → U38_gga(T399, T393, T374, T400, deleteD_in_gga(s(T399), T374, T400))
deleteD_in_gga(T411, tree(T411, T412, void), T412) → deleteD_out_gga(T411, tree(T411, T412, void), T412)
deleteD_in_gga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_gga(T443, T440, T441, T444, lessA_in_gg(T443, T440))
U39_gga(T443, T440, T441, T444, lessA_out_gg(T443, T440)) → deleteD_out_gga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_gga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_gga(T447, T440, T441, T448, lessA_in_gg(T447, T440))
U40_gga(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → U41_gga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
deleteD_in_gga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_gga(T469, T466, T467, T470, pC_in_gga(T466, T469, T470))
U42_gga(T469, T466, T467, T470, pC_out_gga(T466, T469, T470)) → deleteD_out_gga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_gga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
deleteD_in_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_gga(T501, T500, T479, T502, lessA_in_gg(T501, T500))
U44_gga(T501, T500, T479, T502, lessA_out_gg(T501, T500)) → deleteD_out_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_gga(T505, T500, T479, T506, lessA_in_gg(T505, T500))
U45_gga(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → U46_gga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
deleteD_in_gga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_gga(T527, T524, T525, T528, pC_in_gga(T524, T527, T528))
U47_gga(T527, T524, T525, T528, pC_out_gga(T524, T527, T528)) → deleteD_out_gga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_gga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_gga(T547, T537, T546, deleteD_in_gga(s(T547), void, T546))
deleteD_in_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_gga(T556, T554, T537, T557, lessB_in_gg(T554, T556))
U49_gga(T556, T554, T537, T557, lessB_out_gg(T554, T556)) → deleteD_out_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_gga(T560, T554, T537, T561, lessB_in_gg(T554, T560))
U50_gga(T560, T554, T537, T561, lessB_out_gg(T554, T560)) → U51_gga(T560, T554, T537, T561, deleteD_in_gga(s(T560), void, T561))
deleteD_in_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_gga(T651, T647, T648, T649, T652, lessA_in_gg(T651, T647))
U53_gga(T651, T647, T648, T649, T652, lessA_out_gg(T651, T647)) → deleteD_out_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_gga(T655, T647, T648, T649, T656, lessA_in_gg(T655, T647))
U54_gga(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → U55_gga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
deleteD_in_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_gga(T680, T676, T677, T678, T681, pH_in_ggga(T676, T680, T678, T681))
pH_in_ggga(T676, T680, T678, T681) → U13_ggga(T676, T680, T678, T681, lessB_in_gg(T676, T680))
U13_ggga(T676, T680, T678, T681, lessB_out_gg(T676, T680)) → pH_out_ggga(T676, T680, T678, T681)
pH_in_ggga(T676, T684, T678, T685) → U14_ggga(T676, T684, T678, T685, lessB_in_gg(T676, T684))
U14_ggga(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → U15_ggga(T676, T684, T678, T685, deleteD_in_gga(T684, T678, T685))
deleteD_in_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_gga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
deleteD_in_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_gga(T724, T723, T701, T702, T725, lessA_in_gg(T724, T723))
U58_gga(T724, T723, T701, T702, T725, lessA_out_gg(T724, T723)) → deleteD_out_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_gga(T728, T723, T701, T702, T729, lessA_in_gg(T728, T723))
U59_gga(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → U60_gga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
deleteD_in_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_gga(T753, T749, T750, T751, T754, pH_in_ggga(T749, T753, T751, T754))
U61_gga(T753, T749, T750, T751, T754, pH_out_ggga(T749, T753, T751, T754)) → deleteD_out_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_gga(T775, T764, T765, T774, deleteD_in_gga(s(T775), T765, T774))
deleteD_in_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_gga(T786, T784, T764, T765, T787, lessB_in_gg(T784, T786))
U63_gga(T786, T784, T764, T765, T787, lessB_out_gg(T784, T786)) → deleteD_out_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_gga(T790, T784, T764, T765, T791, lessB_in_gg(T784, T790))
U64_gga(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → U65_gga(T790, T784, T764, T765, T791, deleteD_in_gga(s(T790), T765, T791))
U65_gga(T790, T784, T764, T765, T791, deleteD_out_gga(s(T790), T765, T791)) → deleteD_out_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_gga(T775, T764, T765, T774, deleteD_out_gga(s(T775), T765, T774)) → deleteD_out_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U60_gga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
U57_gga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
U15_ggga(T676, T684, T678, T685, deleteD_out_gga(T684, T678, T685)) → pH_out_ggga(T676, T684, T678, T685)
U56_gga(T680, T676, T677, T678, T681, pH_out_ggga(T676, T680, T678, T681)) → deleteD_out_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U55_gga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
U51_gga(T560, T554, T537, T561, deleteD_out_gga(s(T560), void, T561)) → deleteD_out_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_gga(T547, T537, T546, deleteD_out_gga(s(T547), void, T546)) → deleteD_out_gga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U46_gga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
U43_gga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
U41_gga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_gga(T447, tree(T440, T441, void), tree(T440, T448, void))
U38_gga(T399, T393, T374, T400, deleteD_out_gga(s(T399), T374, T400)) → deleteD_out_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_gga(T384, T374, T383, deleteD_out_gga(s(T384), T374, T383)) → deleteD_out_gga(s(T384), tree(0, void, T374), tree(0, void, T383))
U33_gga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
U30_gga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
U12_ggga(T297, T304, T298, T305, deleteD_out_gga(T304, T298, T305)) → pG_out_ggga(T297, T304, T298, T305)
U29_gga(T300, T297, T298, T301, pG_out_ggga(T297, T300, T298, T301)) → deleteD_out_gga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_gga(T166, T160, T167, deleteD_out_gga(s(T166), void, T167)) → deleteD_out_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_gga(T153, T152, deleteD_out_gga(s(T153), void, T152)) → deleteD_out_gga(s(T153), tree(0, void, void), tree(0, void, T152))
U21_gga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
U18_gga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
U5_gga(T64, T70, T71, deleteD_out_gga(T70, void, T71)) → pC_out_gga(T64, T70, T71)
U17_gga(T66, T64, T67, pC_out_gga(T64, T66, T67)) → deleteD_out_gga(T66, tree(T64, void, void), tree(T64, void, T67))
U9_gga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_gga(T37, T31, T38)
U16_gga(T33, T31, T34, pF_out_gga(T33, T31, T34)) → deleteD_out_gga(T33, tree(T31, void, void), tree(T31, T34, void))
U9_aga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_aga(T37, T31, T38)
U16_aga(T33, T31, T34, pF_out_aga(T33, T31, T34)) → deleteD_out_aga(T33, tree(T31, void, void), tree(T31, T34, void))
deleteD_in_aga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_aga(T66, T64, T67, pC_in_gaa(T64, T66, T67))
pC_in_gaa(T64, T66, T67) → U3_gaa(T64, T66, T67, lessB_in_ga(T64, T66))
lessB_in_ga(0, s(T78)) → lessB_out_ga(0, s(T78))
lessB_in_ga(s(T83), s(T85)) → U2_ga(T83, T85, lessB_in_ga(T83, T85))
U2_ga(T83, T85, lessB_out_ga(T83, T85)) → lessB_out_ga(s(T83), s(T85))
U3_gaa(T64, T66, T67, lessB_out_ga(T64, T66)) → pC_out_gaa(T64, T66, T67)
pC_in_gaa(T64, T70, T71) → U4_gaa(T64, T70, T71, lessB_in_ga(T64, T70))
U4_gaa(T64, T70, T71, lessB_out_ga(T64, T70)) → U5_gaa(T64, T70, T71, deleteD_in_aga(T70, void, T71))
deleteD_in_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_aga(T102, T103, deleteD_in_gga(0, void, T103))
U18_aga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
deleteD_in_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_aga(T114, T113, T115, lessA_in_ag(T114, T113))
U19_aga(T114, T113, T115, lessA_out_ag(T114, T113)) → deleteD_out_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_aga(T118, T113, T119, lessA_in_ag(T118, T113))
U20_aga(T118, T113, T119, lessA_out_ag(T118, T113)) → U21_aga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
U21_aga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
deleteD_in_aga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_aga(T135, T133, T136, pC_in_gaa(T133, T135, T136))
U22_aga(T135, T133, T136, pC_out_gaa(T133, T135, T136)) → deleteD_out_aga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_aga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_aga(T153, T152, deleteD_in_aga(s(T153), void, T152))
deleteD_in_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_aga(T162, T160, T163, lessB_in_ga(T160, T162))
U24_aga(T162, T160, T163, lessB_out_ga(T160, T162)) → deleteD_out_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_aga(T166, T160, T167, lessB_in_ga(T160, T166))
U25_aga(T166, T160, T167, lessB_out_ga(T160, T166)) → U26_aga(T166, T160, T167, deleteD_in_aga(s(T166), void, T167))
deleteD_in_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_aga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_aga(T284, T281, T282, T285, pF_in_aga(T284, T281, T285))
U28_aga(T284, T281, T282, T285, pF_out_aga(T284, T281, T285)) → deleteD_out_aga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_aga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_aga(T300, T297, T298, T301, pG_in_gaga(T297, T300, T298, T301))
pG_in_gaga(T297, T300, T298, T301) → U10_gaga(T297, T300, T298, T301, lessB_in_ga(T297, T300))
U10_gaga(T297, T300, T298, T301, lessB_out_ga(T297, T300)) → pG_out_gaga(T297, T300, T298, T301)
pG_in_gaga(T297, T304, T298, T305) → U11_gaga(T297, T304, T298, T305, lessB_in_ga(T297, T304))
U11_gaga(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → U12_gaga(T297, T304, T298, T305, deleteD_in_aga(T304, T298, T305))
deleteD_in_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_aga(T328, T320, T329, deleteD_in_gga(0, void, T329))
U30_aga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
deleteD_in_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_aga(T340, T339, T320, T341, lessA_in_ag(T340, T339))
U31_aga(T340, T339, T320, T341, lessA_out_ag(T340, T339)) → deleteD_out_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_aga(T344, T339, T320, T345, lessA_in_ag(T344, T339))
U32_aga(T344, T339, T320, T345, lessA_out_ag(T344, T339)) → U33_aga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
U33_aga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
deleteD_in_aga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_aga(T364, T361, T362, T365, pG_in_gaga(T361, T364, T362, T365))
U34_aga(T364, T361, T362, T365, pG_out_gaga(T361, T364, T362, T365)) → deleteD_out_aga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_aga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_aga(T384, T374, T383, deleteD_in_aga(s(T384), T374, T383))
deleteD_in_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_aga(T395, T393, T374, T396, lessB_in_ga(T393, T395))
U36_aga(T395, T393, T374, T396, lessB_out_ga(T393, T395)) → deleteD_out_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_aga(T399, T393, T374, T400, lessB_in_ga(T393, T399))
U37_aga(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → U38_aga(T399, T393, T374, T400, deleteD_in_aga(s(T399), T374, T400))
deleteD_in_aga(T411, tree(T411, T412, void), T412) → deleteD_out_aga(T411, tree(T411, T412, void), T412)
deleteD_in_aga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_aga(T443, T440, T441, T444, lessA_in_ag(T443, T440))
U39_aga(T443, T440, T441, T444, lessA_out_ag(T443, T440)) → deleteD_out_aga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_aga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_aga(T447, T440, T441, T448, lessA_in_ag(T447, T440))
U40_aga(T447, T440, T441, T448, lessA_out_ag(T447, T440)) → U41_aga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
U41_aga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_aga(T447, tree(T440, T441, void), tree(T440, T448, void))
deleteD_in_aga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_aga(T469, T466, T467, T470, pC_in_gaa(T466, T469, T470))
U42_aga(T469, T466, T467, T470, pC_out_gaa(T466, T469, T470)) → deleteD_out_aga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_aga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
U43_aga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
deleteD_in_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_aga(T501, T500, T479, T502, lessA_in_ag(T501, T500))
U44_aga(T501, T500, T479, T502, lessA_out_ag(T501, T500)) → deleteD_out_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_aga(T505, T500, T479, T506, lessA_in_ag(T505, T500))
U45_aga(T505, T500, T479, T506, lessA_out_ag(T505, T500)) → U46_aga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
U46_aga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
deleteD_in_aga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_aga(T527, T524, T525, T528, pC_in_gaa(T524, T527, T528))
U47_aga(T527, T524, T525, T528, pC_out_gaa(T524, T527, T528)) → deleteD_out_aga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_aga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_aga(T547, T537, T546, deleteD_in_aga(s(T547), void, T546))
deleteD_in_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_aga(T556, T554, T537, T557, lessB_in_ga(T554, T556))
U49_aga(T556, T554, T537, T557, lessB_out_ga(T554, T556)) → deleteD_out_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_aga(T560, T554, T537, T561, lessB_in_ga(T554, T560))
U50_aga(T560, T554, T537, T561, lessB_out_ga(T554, T560)) → U51_aga(T560, T554, T537, T561, deleteD_in_aga(s(T560), void, T561))
deleteD_in_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_aga(T651, T647, T648, T649, T652, lessA_in_ag(T651, T647))
U53_aga(T651, T647, T648, T649, T652, lessA_out_ag(T651, T647)) → deleteD_out_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_aga(T655, T647, T648, T649, T656, lessA_in_ag(T655, T647))
U54_aga(T655, T647, T648, T649, T656, lessA_out_ag(T655, T647)) → U55_aga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
U55_aga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
deleteD_in_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_aga(T680, T676, T677, T678, T681, pH_in_gaga(T676, T680, T678, T681))
pH_in_gaga(T676, T680, T678, T681) → U13_gaga(T676, T680, T678, T681, lessB_in_ga(T676, T680))
U13_gaga(T676, T680, T678, T681, lessB_out_ga(T676, T680)) → pH_out_gaga(T676, T680, T678, T681)
pH_in_gaga(T676, T684, T678, T685) → U14_gaga(T676, T684, T678, T685, lessB_in_ga(T676, T684))
U14_gaga(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → U15_gaga(T676, T684, T678, T685, deleteD_in_aga(T684, T678, T685))
deleteD_in_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_aga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
U57_aga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
deleteD_in_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_aga(T724, T723, T701, T702, T725, lessA_in_ag(T724, T723))
U58_aga(T724, T723, T701, T702, T725, lessA_out_ag(T724, T723)) → deleteD_out_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_aga(T728, T723, T701, T702, T729, lessA_in_ag(T728, T723))
U59_aga(T728, T723, T701, T702, T729, lessA_out_ag(T728, T723)) → U60_aga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
U60_aga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
deleteD_in_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_aga(T753, T749, T750, T751, T754, pH_in_gaga(T749, T753, T751, T754))
U61_aga(T753, T749, T750, T751, T754, pH_out_gaga(T749, T753, T751, T754)) → deleteD_out_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_aga(T775, T764, T765, T774, deleteD_in_aga(s(T775), T765, T774))
deleteD_in_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_aga(T786, T784, T764, T765, T787, lessB_in_ga(T784, T786))
U63_aga(T786, T784, T764, T765, T787, lessB_out_ga(T784, T786)) → deleteD_out_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_aga(T790, T784, T764, T765, T791, lessB_in_ga(T784, T790))
U64_aga(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → U65_aga(T790, T784, T764, T765, T791, deleteD_in_aga(s(T790), T765, T791))
U65_aga(T790, T784, T764, T765, T791, deleteD_out_aga(s(T790), T765, T791)) → deleteD_out_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_aga(T775, T764, T765, T774, deleteD_out_aga(s(T775), T765, T774)) → deleteD_out_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U15_gaga(T676, T684, T678, T685, deleteD_out_aga(T684, T678, T685)) → pH_out_gaga(T676, T684, T678, T685)
U56_aga(T680, T676, T677, T678, T681, pH_out_gaga(T676, T680, T678, T681)) → deleteD_out_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U51_aga(T560, T554, T537, T561, deleteD_out_aga(s(T560), void, T561)) → deleteD_out_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_aga(T547, T537, T546, deleteD_out_aga(s(T547), void, T546)) → deleteD_out_aga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U38_aga(T399, T393, T374, T400, deleteD_out_aga(s(T399), T374, T400)) → deleteD_out_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_aga(T384, T374, T383, deleteD_out_aga(s(T384), T374, T383)) → deleteD_out_aga(s(T384), tree(0, void, T374), tree(0, void, T383))
U12_gaga(T297, T304, T298, T305, deleteD_out_aga(T304, T298, T305)) → pG_out_gaga(T297, T304, T298, T305)
U29_aga(T300, T297, T298, T301, pG_out_gaga(T297, T300, T298, T301)) → deleteD_out_aga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_aga(T166, T160, T167, deleteD_out_aga(s(T166), void, T167)) → deleteD_out_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_aga(T153, T152, deleteD_out_aga(s(T153), void, T152)) → deleteD_out_aga(s(T153), tree(0, void, void), tree(0, void, T152))
U5_gaa(T64, T70, T71, deleteD_out_aga(T70, void, T71)) → pC_out_gaa(T64, T70, T71)
U17_aga(T66, T64, T67, pC_out_gaa(T64, T66, T67)) → deleteD_out_aga(T66, tree(T64, void, void), tree(T64, void, T67))

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_aga(T6, tree(T6, void, T7), T7) → deleteD_out_aga(T6, tree(T6, void, T7), T7)
deleteD_in_aga(T9, tree(T9, void, void), void) → deleteD_out_aga(T9, tree(T9, void, void), void)
deleteD_in_aga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_aga(T33, T31, T34, pF_in_aga(T33, T31, T34))
pF_in_aga(T33, T31, T34) → U7_aga(T33, T31, T34, lessA_in_ag(T33, T31))
lessA_in_ag(0, s(T45)) → lessA_out_ag(0, s(T45))
lessA_in_ag(s(T52), s(T51)) → U1_ag(T52, T51, lessA_in_ag(T52, T51))
U1_ag(T52, T51, lessA_out_ag(T52, T51)) → lessA_out_ag(s(T52), s(T51))
U7_aga(T33, T31, T34, lessA_out_ag(T33, T31)) → pF_out_aga(T33, T31, T34)
pF_in_aga(T37, T31, T38) → U8_aga(T37, T31, T38, lessA_in_ag(T37, T31))
U8_aga(T37, T31, T38, lessA_out_ag(T37, T31)) → U9_aga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T6, tree(T6, void, T7), T7) → deleteD_out_gga(T6, tree(T6, void, T7), T7)
deleteD_in_gga(T9, tree(T9, void, void), void) → deleteD_out_gga(T9, tree(T9, void, void), void)
deleteD_in_gga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_gga(T33, T31, T34, pF_in_gga(T33, T31, T34))
pF_in_gga(T33, T31, T34) → U7_gga(T33, T31, T34, lessA_in_gg(T33, T31))
lessA_in_gg(0, s(T45)) → lessA_out_gg(0, s(T45))
lessA_in_gg(s(T52), s(T51)) → U1_gg(T52, T51, lessA_in_gg(T52, T51))
U1_gg(T52, T51, lessA_out_gg(T52, T51)) → lessA_out_gg(s(T52), s(T51))
U7_gga(T33, T31, T34, lessA_out_gg(T33, T31)) → pF_out_gga(T33, T31, T34)
pF_in_gga(T37, T31, T38) → U8_gga(T37, T31, T38, lessA_in_gg(T37, T31))
U8_gga(T37, T31, T38, lessA_out_gg(T37, T31)) → U9_gga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_gga(T66, T64, T67, pC_in_gga(T64, T66, T67))
pC_in_gga(T64, T66, T67) → U3_gga(T64, T66, T67, lessB_in_gg(T64, T66))
lessB_in_gg(0, s(T78)) → lessB_out_gg(0, s(T78))
lessB_in_gg(s(T83), s(T85)) → U2_gg(T83, T85, lessB_in_gg(T83, T85))
U2_gg(T83, T85, lessB_out_gg(T83, T85)) → lessB_out_gg(s(T83), s(T85))
U3_gga(T64, T66, T67, lessB_out_gg(T64, T66)) → pC_out_gga(T64, T66, T67)
pC_in_gga(T64, T70, T71) → U4_gga(T64, T70, T71, lessB_in_gg(T64, T70))
U4_gga(T64, T70, T71, lessB_out_gg(T64, T70)) → U5_gga(T64, T70, T71, deleteD_in_gga(T70, void, T71))
deleteD_in_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_gga(T102, T103, deleteD_in_gga(0, void, T103))
deleteD_in_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_gga(T114, T113, T115, lessA_in_gg(T114, T113))
U19_gga(T114, T113, T115, lessA_out_gg(T114, T113)) → deleteD_out_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_gga(T118, T113, T119, lessA_in_gg(T118, T113))
U20_gga(T118, T113, T119, lessA_out_gg(T118, T113)) → U21_gga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
deleteD_in_gga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_gga(T135, T133, T136, pC_in_gga(T133, T135, T136))
U22_gga(T135, T133, T136, pC_out_gga(T133, T135, T136)) → deleteD_out_gga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_gga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_gga(T153, T152, deleteD_in_gga(s(T153), void, T152))
deleteD_in_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_gga(T162, T160, T163, lessB_in_gg(T160, T162))
U24_gga(T162, T160, T163, lessB_out_gg(T160, T162)) → deleteD_out_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_gga(T166, T160, T167, lessB_in_gg(T160, T166))
U25_gga(T166, T160, T167, lessB_out_gg(T160, T166)) → U26_gga(T166, T160, T167, deleteD_in_gga(s(T166), void, T167))
deleteD_in_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
delminE_in_gaa(tree(T238, void, T239), T238, T239) → delminE_out_gaa(tree(T238, void, T239), T238, T239)
delminE_in_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → U6_gaa(T252, T253, T254, T258, T259, T257, delminE_in_gaa(T253, T258, T259))
U6_gaa(T252, T253, T254, T258, T259, T257, delminE_out_gaa(T253, T258, T259)) → delminE_out_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257))
U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_gga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_gga(T284, T281, T282, T285, pF_in_gga(T284, T281, T285))
U28_gga(T284, T281, T282, T285, pF_out_gga(T284, T281, T285)) → deleteD_out_gga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_gga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_gga(T300, T297, T298, T301, pG_in_ggga(T297, T300, T298, T301))
pG_in_ggga(T297, T300, T298, T301) → U10_ggga(T297, T300, T298, T301, lessB_in_gg(T297, T300))
U10_ggga(T297, T300, T298, T301, lessB_out_gg(T297, T300)) → pG_out_ggga(T297, T300, T298, T301)
pG_in_ggga(T297, T304, T298, T305) → U11_ggga(T297, T304, T298, T305, lessB_in_gg(T297, T304))
U11_ggga(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → U12_ggga(T297, T304, T298, T305, deleteD_in_gga(T304, T298, T305))
deleteD_in_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_gga(T328, T320, T329, deleteD_in_gga(0, void, T329))
deleteD_in_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_gga(T340, T339, T320, T341, lessA_in_gg(T340, T339))
U31_gga(T340, T339, T320, T341, lessA_out_gg(T340, T339)) → deleteD_out_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_gga(T344, T339, T320, T345, lessA_in_gg(T344, T339))
U32_gga(T344, T339, T320, T345, lessA_out_gg(T344, T339)) → U33_gga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
deleteD_in_gga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_gga(T364, T361, T362, T365, pG_in_ggga(T361, T364, T362, T365))
U34_gga(T364, T361, T362, T365, pG_out_ggga(T361, T364, T362, T365)) → deleteD_out_gga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_gga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_gga(T384, T374, T383, deleteD_in_gga(s(T384), T374, T383))
deleteD_in_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_gga(T395, T393, T374, T396, lessB_in_gg(T393, T395))
U36_gga(T395, T393, T374, T396, lessB_out_gg(T393, T395)) → deleteD_out_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_gga(T399, T393, T374, T400, lessB_in_gg(T393, T399))
U37_gga(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → U38_gga(T399, T393, T374, T400, deleteD_in_gga(s(T399), T374, T400))
deleteD_in_gga(T411, tree(T411, T412, void), T412) → deleteD_out_gga(T411, tree(T411, T412, void), T412)
deleteD_in_gga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_gga(T443, T440, T441, T444, lessA_in_gg(T443, T440))
U39_gga(T443, T440, T441, T444, lessA_out_gg(T443, T440)) → deleteD_out_gga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_gga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_gga(T447, T440, T441, T448, lessA_in_gg(T447, T440))
U40_gga(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → U41_gga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
deleteD_in_gga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_gga(T469, T466, T467, T470, pC_in_gga(T466, T469, T470))
U42_gga(T469, T466, T467, T470, pC_out_gga(T466, T469, T470)) → deleteD_out_gga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_gga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
deleteD_in_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_gga(T501, T500, T479, T502, lessA_in_gg(T501, T500))
U44_gga(T501, T500, T479, T502, lessA_out_gg(T501, T500)) → deleteD_out_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_gga(T505, T500, T479, T506, lessA_in_gg(T505, T500))
U45_gga(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → U46_gga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
deleteD_in_gga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_gga(T527, T524, T525, T528, pC_in_gga(T524, T527, T528))
U47_gga(T527, T524, T525, T528, pC_out_gga(T524, T527, T528)) → deleteD_out_gga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_gga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_gga(T547, T537, T546, deleteD_in_gga(s(T547), void, T546))
deleteD_in_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_gga(T556, T554, T537, T557, lessB_in_gg(T554, T556))
U49_gga(T556, T554, T537, T557, lessB_out_gg(T554, T556)) → deleteD_out_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_gga(T560, T554, T537, T561, lessB_in_gg(T554, T560))
U50_gga(T560, T554, T537, T561, lessB_out_gg(T554, T560)) → U51_gga(T560, T554, T537, T561, deleteD_in_gga(s(T560), void, T561))
deleteD_in_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_gga(T651, T647, T648, T649, T652, lessA_in_gg(T651, T647))
U53_gga(T651, T647, T648, T649, T652, lessA_out_gg(T651, T647)) → deleteD_out_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_gga(T655, T647, T648, T649, T656, lessA_in_gg(T655, T647))
U54_gga(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → U55_gga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
deleteD_in_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_gga(T680, T676, T677, T678, T681, pH_in_ggga(T676, T680, T678, T681))
pH_in_ggga(T676, T680, T678, T681) → U13_ggga(T676, T680, T678, T681, lessB_in_gg(T676, T680))
U13_ggga(T676, T680, T678, T681, lessB_out_gg(T676, T680)) → pH_out_ggga(T676, T680, T678, T681)
pH_in_ggga(T676, T684, T678, T685) → U14_ggga(T676, T684, T678, T685, lessB_in_gg(T676, T684))
U14_ggga(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → U15_ggga(T676, T684, T678, T685, deleteD_in_gga(T684, T678, T685))
deleteD_in_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_gga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
deleteD_in_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_gga(T724, T723, T701, T702, T725, lessA_in_gg(T724, T723))
U58_gga(T724, T723, T701, T702, T725, lessA_out_gg(T724, T723)) → deleteD_out_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_gga(T728, T723, T701, T702, T729, lessA_in_gg(T728, T723))
U59_gga(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → U60_gga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
deleteD_in_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_gga(T753, T749, T750, T751, T754, pH_in_ggga(T749, T753, T751, T754))
U61_gga(T753, T749, T750, T751, T754, pH_out_ggga(T749, T753, T751, T754)) → deleteD_out_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_gga(T775, T764, T765, T774, deleteD_in_gga(s(T775), T765, T774))
deleteD_in_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_gga(T786, T784, T764, T765, T787, lessB_in_gg(T784, T786))
U63_gga(T786, T784, T764, T765, T787, lessB_out_gg(T784, T786)) → deleteD_out_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_gga(T790, T784, T764, T765, T791, lessB_in_gg(T784, T790))
U64_gga(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → U65_gga(T790, T784, T764, T765, T791, deleteD_in_gga(s(T790), T765, T791))
U65_gga(T790, T784, T764, T765, T791, deleteD_out_gga(s(T790), T765, T791)) → deleteD_out_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_gga(T775, T764, T765, T774, deleteD_out_gga(s(T775), T765, T774)) → deleteD_out_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U60_gga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
U57_gga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
U15_ggga(T676, T684, T678, T685, deleteD_out_gga(T684, T678, T685)) → pH_out_ggga(T676, T684, T678, T685)
U56_gga(T680, T676, T677, T678, T681, pH_out_ggga(T676, T680, T678, T681)) → deleteD_out_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U55_gga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
U51_gga(T560, T554, T537, T561, deleteD_out_gga(s(T560), void, T561)) → deleteD_out_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_gga(T547, T537, T546, deleteD_out_gga(s(T547), void, T546)) → deleteD_out_gga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U46_gga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
U43_gga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
U41_gga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_gga(T447, tree(T440, T441, void), tree(T440, T448, void))
U38_gga(T399, T393, T374, T400, deleteD_out_gga(s(T399), T374, T400)) → deleteD_out_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_gga(T384, T374, T383, deleteD_out_gga(s(T384), T374, T383)) → deleteD_out_gga(s(T384), tree(0, void, T374), tree(0, void, T383))
U33_gga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
U30_gga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
U12_ggga(T297, T304, T298, T305, deleteD_out_gga(T304, T298, T305)) → pG_out_ggga(T297, T304, T298, T305)
U29_gga(T300, T297, T298, T301, pG_out_ggga(T297, T300, T298, T301)) → deleteD_out_gga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_gga(T166, T160, T167, deleteD_out_gga(s(T166), void, T167)) → deleteD_out_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_gga(T153, T152, deleteD_out_gga(s(T153), void, T152)) → deleteD_out_gga(s(T153), tree(0, void, void), tree(0, void, T152))
U21_gga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
U18_gga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
U5_gga(T64, T70, T71, deleteD_out_gga(T70, void, T71)) → pC_out_gga(T64, T70, T71)
U17_gga(T66, T64, T67, pC_out_gga(T64, T66, T67)) → deleteD_out_gga(T66, tree(T64, void, void), tree(T64, void, T67))
U9_gga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_gga(T37, T31, T38)
U16_gga(T33, T31, T34, pF_out_gga(T33, T31, T34)) → deleteD_out_gga(T33, tree(T31, void, void), tree(T31, T34, void))
U9_aga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_aga(T37, T31, T38)
U16_aga(T33, T31, T34, pF_out_aga(T33, T31, T34)) → deleteD_out_aga(T33, tree(T31, void, void), tree(T31, T34, void))
deleteD_in_aga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_aga(T66, T64, T67, pC_in_gaa(T64, T66, T67))
pC_in_gaa(T64, T66, T67) → U3_gaa(T64, T66, T67, lessB_in_ga(T64, T66))
lessB_in_ga(0, s(T78)) → lessB_out_ga(0, s(T78))
lessB_in_ga(s(T83), s(T85)) → U2_ga(T83, T85, lessB_in_ga(T83, T85))
U2_ga(T83, T85, lessB_out_ga(T83, T85)) → lessB_out_ga(s(T83), s(T85))
U3_gaa(T64, T66, T67, lessB_out_ga(T64, T66)) → pC_out_gaa(T64, T66, T67)
pC_in_gaa(T64, T70, T71) → U4_gaa(T64, T70, T71, lessB_in_ga(T64, T70))
U4_gaa(T64, T70, T71, lessB_out_ga(T64, T70)) → U5_gaa(T64, T70, T71, deleteD_in_aga(T70, void, T71))
deleteD_in_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_aga(T102, T103, deleteD_in_gga(0, void, T103))
U18_aga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
deleteD_in_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_aga(T114, T113, T115, lessA_in_ag(T114, T113))
U19_aga(T114, T113, T115, lessA_out_ag(T114, T113)) → deleteD_out_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_aga(T118, T113, T119, lessA_in_ag(T118, T113))
U20_aga(T118, T113, T119, lessA_out_ag(T118, T113)) → U21_aga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
U21_aga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
deleteD_in_aga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_aga(T135, T133, T136, pC_in_gaa(T133, T135, T136))
U22_aga(T135, T133, T136, pC_out_gaa(T133, T135, T136)) → deleteD_out_aga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_aga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_aga(T153, T152, deleteD_in_aga(s(T153), void, T152))
deleteD_in_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_aga(T162, T160, T163, lessB_in_ga(T160, T162))
U24_aga(T162, T160, T163, lessB_out_ga(T160, T162)) → deleteD_out_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_aga(T166, T160, T167, lessB_in_ga(T160, T166))
U25_aga(T166, T160, T167, lessB_out_ga(T160, T166)) → U26_aga(T166, T160, T167, deleteD_in_aga(s(T166), void, T167))
deleteD_in_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_aga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_aga(T284, T281, T282, T285, pF_in_aga(T284, T281, T285))
U28_aga(T284, T281, T282, T285, pF_out_aga(T284, T281, T285)) → deleteD_out_aga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_aga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_aga(T300, T297, T298, T301, pG_in_gaga(T297, T300, T298, T301))
pG_in_gaga(T297, T300, T298, T301) → U10_gaga(T297, T300, T298, T301, lessB_in_ga(T297, T300))
U10_gaga(T297, T300, T298, T301, lessB_out_ga(T297, T300)) → pG_out_gaga(T297, T300, T298, T301)
pG_in_gaga(T297, T304, T298, T305) → U11_gaga(T297, T304, T298, T305, lessB_in_ga(T297, T304))
U11_gaga(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → U12_gaga(T297, T304, T298, T305, deleteD_in_aga(T304, T298, T305))
deleteD_in_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_aga(T328, T320, T329, deleteD_in_gga(0, void, T329))
U30_aga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
deleteD_in_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_aga(T340, T339, T320, T341, lessA_in_ag(T340, T339))
U31_aga(T340, T339, T320, T341, lessA_out_ag(T340, T339)) → deleteD_out_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_aga(T344, T339, T320, T345, lessA_in_ag(T344, T339))
U32_aga(T344, T339, T320, T345, lessA_out_ag(T344, T339)) → U33_aga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
U33_aga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
deleteD_in_aga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_aga(T364, T361, T362, T365, pG_in_gaga(T361, T364, T362, T365))
U34_aga(T364, T361, T362, T365, pG_out_gaga(T361, T364, T362, T365)) → deleteD_out_aga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_aga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_aga(T384, T374, T383, deleteD_in_aga(s(T384), T374, T383))
deleteD_in_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_aga(T395, T393, T374, T396, lessB_in_ga(T393, T395))
U36_aga(T395, T393, T374, T396, lessB_out_ga(T393, T395)) → deleteD_out_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_aga(T399, T393, T374, T400, lessB_in_ga(T393, T399))
U37_aga(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → U38_aga(T399, T393, T374, T400, deleteD_in_aga(s(T399), T374, T400))
deleteD_in_aga(T411, tree(T411, T412, void), T412) → deleteD_out_aga(T411, tree(T411, T412, void), T412)
deleteD_in_aga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_aga(T443, T440, T441, T444, lessA_in_ag(T443, T440))
U39_aga(T443, T440, T441, T444, lessA_out_ag(T443, T440)) → deleteD_out_aga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_aga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_aga(T447, T440, T441, T448, lessA_in_ag(T447, T440))
U40_aga(T447, T440, T441, T448, lessA_out_ag(T447, T440)) → U41_aga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
U41_aga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_aga(T447, tree(T440, T441, void), tree(T440, T448, void))
deleteD_in_aga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_aga(T469, T466, T467, T470, pC_in_gaa(T466, T469, T470))
U42_aga(T469, T466, T467, T470, pC_out_gaa(T466, T469, T470)) → deleteD_out_aga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_aga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
U43_aga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
deleteD_in_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_aga(T501, T500, T479, T502, lessA_in_ag(T501, T500))
U44_aga(T501, T500, T479, T502, lessA_out_ag(T501, T500)) → deleteD_out_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_aga(T505, T500, T479, T506, lessA_in_ag(T505, T500))
U45_aga(T505, T500, T479, T506, lessA_out_ag(T505, T500)) → U46_aga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
U46_aga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
deleteD_in_aga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_aga(T527, T524, T525, T528, pC_in_gaa(T524, T527, T528))
U47_aga(T527, T524, T525, T528, pC_out_gaa(T524, T527, T528)) → deleteD_out_aga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_aga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_aga(T547, T537, T546, deleteD_in_aga(s(T547), void, T546))
deleteD_in_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_aga(T556, T554, T537, T557, lessB_in_ga(T554, T556))
U49_aga(T556, T554, T537, T557, lessB_out_ga(T554, T556)) → deleteD_out_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_aga(T560, T554, T537, T561, lessB_in_ga(T554, T560))
U50_aga(T560, T554, T537, T561, lessB_out_ga(T554, T560)) → U51_aga(T560, T554, T537, T561, deleteD_in_aga(s(T560), void, T561))
deleteD_in_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_aga(T651, T647, T648, T649, T652, lessA_in_ag(T651, T647))
U53_aga(T651, T647, T648, T649, T652, lessA_out_ag(T651, T647)) → deleteD_out_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_aga(T655, T647, T648, T649, T656, lessA_in_ag(T655, T647))
U54_aga(T655, T647, T648, T649, T656, lessA_out_ag(T655, T647)) → U55_aga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
U55_aga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
deleteD_in_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_aga(T680, T676, T677, T678, T681, pH_in_gaga(T676, T680, T678, T681))
pH_in_gaga(T676, T680, T678, T681) → U13_gaga(T676, T680, T678, T681, lessB_in_ga(T676, T680))
U13_gaga(T676, T680, T678, T681, lessB_out_ga(T676, T680)) → pH_out_gaga(T676, T680, T678, T681)
pH_in_gaga(T676, T684, T678, T685) → U14_gaga(T676, T684, T678, T685, lessB_in_ga(T676, T684))
U14_gaga(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → U15_gaga(T676, T684, T678, T685, deleteD_in_aga(T684, T678, T685))
deleteD_in_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_aga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
U57_aga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
deleteD_in_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_aga(T724, T723, T701, T702, T725, lessA_in_ag(T724, T723))
U58_aga(T724, T723, T701, T702, T725, lessA_out_ag(T724, T723)) → deleteD_out_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_aga(T728, T723, T701, T702, T729, lessA_in_ag(T728, T723))
U59_aga(T728, T723, T701, T702, T729, lessA_out_ag(T728, T723)) → U60_aga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
U60_aga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
deleteD_in_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_aga(T753, T749, T750, T751, T754, pH_in_gaga(T749, T753, T751, T754))
U61_aga(T753, T749, T750, T751, T754, pH_out_gaga(T749, T753, T751, T754)) → deleteD_out_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_aga(T775, T764, T765, T774, deleteD_in_aga(s(T775), T765, T774))
deleteD_in_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_aga(T786, T784, T764, T765, T787, lessB_in_ga(T784, T786))
U63_aga(T786, T784, T764, T765, T787, lessB_out_ga(T784, T786)) → deleteD_out_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_aga(T790, T784, T764, T765, T791, lessB_in_ga(T784, T790))
U64_aga(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → U65_aga(T790, T784, T764, T765, T791, deleteD_in_aga(s(T790), T765, T791))
U65_aga(T790, T784, T764, T765, T791, deleteD_out_aga(s(T790), T765, T791)) → deleteD_out_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_aga(T775, T764, T765, T774, deleteD_out_aga(s(T775), T765, T774)) → deleteD_out_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U15_gaga(T676, T684, T678, T685, deleteD_out_aga(T684, T678, T685)) → pH_out_gaga(T676, T684, T678, T685)
U56_aga(T680, T676, T677, T678, T681, pH_out_gaga(T676, T680, T678, T681)) → deleteD_out_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U51_aga(T560, T554, T537, T561, deleteD_out_aga(s(T560), void, T561)) → deleteD_out_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_aga(T547, T537, T546, deleteD_out_aga(s(T547), void, T546)) → deleteD_out_aga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U38_aga(T399, T393, T374, T400, deleteD_out_aga(s(T399), T374, T400)) → deleteD_out_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_aga(T384, T374, T383, deleteD_out_aga(s(T384), T374, T383)) → deleteD_out_aga(s(T384), tree(0, void, T374), tree(0, void, T383))
U12_gaga(T297, T304, T298, T305, deleteD_out_aga(T304, T298, T305)) → pG_out_gaga(T297, T304, T298, T305)
U29_aga(T300, T297, T298, T301, pG_out_gaga(T297, T300, T298, T301)) → deleteD_out_aga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_aga(T166, T160, T167, deleteD_out_aga(s(T166), void, T167)) → deleteD_out_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_aga(T153, T152, deleteD_out_aga(s(T153), void, T152)) → deleteD_out_aga(s(T153), tree(0, void, void), tree(0, void, T152))
U5_gaa(T64, T70, T71, deleteD_out_aga(T70, void, T71)) → pC_out_gaa(T64, T70, T71)
U17_aga(T66, T64, T67, pC_out_gaa(T64, T66, T67)) → deleteD_out_aga(T66, tree(T64, void, void), tree(T64, void, T67))

(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_AGA(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_AGA(T33, T31, T34, pF_in_aga(T33, T31, T34))
DELETED_IN_AGA(T33, tree(T31, void, void), tree(T31, T34, void)) → PF_IN_AGA(T33, T31, T34)
PF_IN_AGA(T33, T31, T34) → U7_AGA(T33, T31, T34, lessA_in_ag(T33, T31))
PF_IN_AGA(T33, T31, T34) → LESSA_IN_AG(T33, T31)
LESSA_IN_AG(s(T52), s(T51)) → U1_AG(T52, T51, lessA_in_ag(T52, T51))
LESSA_IN_AG(s(T52), s(T51)) → LESSA_IN_AG(T52, T51)
PF_IN_AGA(T37, T31, T38) → U8_AGA(T37, T31, T38, lessA_in_ag(T37, T31))
U8_AGA(T37, T31, T38, lessA_out_ag(T37, T31)) → U9_AGA(T37, T31, T38, deleteD_in_gga(T37, void, T38))
U8_AGA(T37, T31, T38, lessA_out_ag(T37, T31)) → DELETED_IN_GGA(T37, void, T38)
DELETED_IN_GGA(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_GGA(T33, T31, T34, pF_in_gga(T33, T31, T34))
DELETED_IN_GGA(T33, tree(T31, void, void), tree(T31, T34, void)) → PF_IN_GGA(T33, T31, T34)
PF_IN_GGA(T33, T31, T34) → U7_GGA(T33, T31, T34, lessA_in_gg(T33, T31))
PF_IN_GGA(T33, T31, T34) → LESSA_IN_GG(T33, T31)
LESSA_IN_GG(s(T52), s(T51)) → U1_GG(T52, T51, lessA_in_gg(T52, T51))
LESSA_IN_GG(s(T52), s(T51)) → LESSA_IN_GG(T52, T51)
PF_IN_GGA(T37, T31, T38) → U8_GGA(T37, T31, T38, lessA_in_gg(T37, T31))
U8_GGA(T37, T31, T38, lessA_out_gg(T37, T31)) → U9_GGA(T37, T31, T38, deleteD_in_gga(T37, void, T38))
U8_GGA(T37, T31, T38, lessA_out_gg(T37, T31)) → DELETED_IN_GGA(T37, void, T38)
DELETED_IN_GGA(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_GGA(T66, T64, T67, pC_in_gga(T64, T66, T67))
DELETED_IN_GGA(T66, tree(T64, void, void), tree(T64, void, T67)) → PC_IN_GGA(T64, T66, T67)
PC_IN_GGA(T64, T66, T67) → U3_GGA(T64, T66, T67, lessB_in_gg(T64, T66))
PC_IN_GGA(T64, T66, T67) → LESSB_IN_GG(T64, T66)
LESSB_IN_GG(s(T83), s(T85)) → U2_GG(T83, T85, lessB_in_gg(T83, T85))
LESSB_IN_GG(s(T83), s(T85)) → LESSB_IN_GG(T83, T85)
PC_IN_GGA(T64, T70, T71) → U4_GGA(T64, T70, T71, lessB_in_gg(T64, T70))
U4_GGA(T64, T70, T71, lessB_out_gg(T64, T70)) → U5_GGA(T64, T70, T71, deleteD_in_gga(T70, void, T71))
U4_GGA(T64, T70, T71, lessB_out_gg(T64, T70)) → DELETED_IN_GGA(T70, void, T71)
DELETED_IN_GGA(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_GGA(T102, T103, deleteD_in_gga(0, void, T103))
DELETED_IN_GGA(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → DELETED_IN_GGA(0, void, T103)
DELETED_IN_GGA(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_GGA(T114, T113, T115, lessA_in_gg(T114, T113))
DELETED_IN_GGA(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → LESSA_IN_GG(T114, T113)
DELETED_IN_GGA(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_GGA(T118, T113, T119, lessA_in_gg(T118, T113))
U20_GGA(T118, T113, T119, lessA_out_gg(T118, T113)) → U21_GGA(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
U20_GGA(T118, T113, T119, lessA_out_gg(T118, T113)) → DELETED_IN_GGA(s(T118), void, T119)
DELETED_IN_GGA(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_GGA(T135, T133, T136, pC_in_gga(T133, T135, T136))
DELETED_IN_GGA(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_GGA(T153, T152, deleteD_in_gga(s(T153), void, T152))
DELETED_IN_GGA(s(T153), tree(0, void, void), tree(0, void, T152)) → DELETED_IN_GGA(s(T153), void, T152)
DELETED_IN_GGA(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_GGA(T162, T160, T163, lessB_in_gg(T160, T162))
DELETED_IN_GGA(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → LESSB_IN_GG(T160, T162)
DELETED_IN_GGA(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_GGA(T166, T160, T167, lessB_in_gg(T160, T166))
U25_GGA(T166, T160, T167, lessB_out_gg(T160, T166)) → U26_GGA(T166, T160, T167, deleteD_in_gga(s(T166), void, T167))
U25_GGA(T166, T160, T167, lessB_out_gg(T160, T166)) → DELETED_IN_GGA(s(T166), void, T167)
DELETED_IN_GGA(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_GGA(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
DELETED_IN_GGA(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → DELMINE_IN_GAA(T219, T224, T225)
DELMINE_IN_GAA(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → U6_GAA(T252, T253, T254, T258, T259, T257, delminE_in_gaa(T253, T258, T259))
DELMINE_IN_GAA(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → DELMINE_IN_GAA(T253, T258, T259)
DELETED_IN_GGA(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_GGA(T284, T281, T282, T285, pF_in_gga(T284, T281, T285))
DELETED_IN_GGA(T284, tree(T281, void, T282), tree(T281, T285, T282)) → PF_IN_GGA(T284, T281, T285)
DELETED_IN_GGA(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_GGA(T300, T297, T298, T301, pG_in_ggga(T297, T300, T298, T301))
DELETED_IN_GGA(T300, tree(T297, void, T298), tree(T297, void, T301)) → PG_IN_GGGA(T297, T300, T298, T301)
PG_IN_GGGA(T297, T300, T298, T301) → U10_GGGA(T297, T300, T298, T301, lessB_in_gg(T297, T300))
PG_IN_GGGA(T297, T300, T298, T301) → LESSB_IN_GG(T297, T300)
PG_IN_GGGA(T297, T304, T298, T305) → U11_GGGA(T297, T304, T298, T305, lessB_in_gg(T297, T304))
U11_GGGA(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → U12_GGGA(T297, T304, T298, T305, deleteD_in_gga(T304, T298, T305))
U11_GGGA(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → DELETED_IN_GGA(T304, T298, T305)
DELETED_IN_GGA(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_GGA(T328, T320, T329, deleteD_in_gga(0, void, T329))
DELETED_IN_GGA(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → DELETED_IN_GGA(0, void, T329)
DELETED_IN_GGA(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_GGA(T340, T339, T320, T341, lessA_in_gg(T340, T339))
DELETED_IN_GGA(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → LESSA_IN_GG(T340, T339)
DELETED_IN_GGA(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_GGA(T344, T339, T320, T345, lessA_in_gg(T344, T339))
U32_GGA(T344, T339, T320, T345, lessA_out_gg(T344, T339)) → U33_GGA(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
U32_GGA(T344, T339, T320, T345, lessA_out_gg(T344, T339)) → DELETED_IN_GGA(s(T344), void, T345)
DELETED_IN_GGA(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_GGA(T364, T361, T362, T365, pG_in_ggga(T361, T364, T362, T365))
DELETED_IN_GGA(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_GGA(T384, T374, T383, deleteD_in_gga(s(T384), T374, T383))
DELETED_IN_GGA(s(T384), tree(0, void, T374), tree(0, void, T383)) → DELETED_IN_GGA(s(T384), T374, T383)
DELETED_IN_GGA(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_GGA(T395, T393, T374, T396, lessB_in_gg(T393, T395))
DELETED_IN_GGA(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → LESSB_IN_GG(T393, T395)
DELETED_IN_GGA(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_GGA(T399, T393, T374, T400, lessB_in_gg(T393, T399))
U37_GGA(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → U38_GGA(T399, T393, T374, T400, deleteD_in_gga(s(T399), T374, T400))
U37_GGA(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → DELETED_IN_GGA(s(T399), T374, T400)
DELETED_IN_GGA(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_GGA(T443, T440, T441, T444, lessA_in_gg(T443, T440))
DELETED_IN_GGA(T443, tree(T440, T441, void), tree(T440, T444, void)) → LESSA_IN_GG(T443, T440)
DELETED_IN_GGA(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_GGA(T447, T440, T441, T448, lessA_in_gg(T447, T440))
U40_GGA(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → U41_GGA(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
U40_GGA(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → DELETED_IN_GGA(T447, T441, T448)
DELETED_IN_GGA(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_GGA(T469, T466, T467, T470, pC_in_gga(T466, T469, T470))
DELETED_IN_GGA(T469, tree(T466, T467, void), tree(T466, T467, T470)) → PC_IN_GGA(T466, T469, T470)
DELETED_IN_GGA(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_GGA(T487, T479, T488, deleteD_in_gga(0, T479, T488))
DELETED_IN_GGA(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → DELETED_IN_GGA(0, T479, T488)
DELETED_IN_GGA(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_GGA(T501, T500, T479, T502, lessA_in_gg(T501, T500))
DELETED_IN_GGA(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → LESSA_IN_GG(T501, T500)
DELETED_IN_GGA(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_GGA(T505, T500, T479, T506, lessA_in_gg(T505, T500))
U45_GGA(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → U46_GGA(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
U45_GGA(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → DELETED_IN_GGA(s(T505), T479, T506)
DELETED_IN_GGA(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_GGA(T527, T524, T525, T528, pC_in_gga(T524, T527, T528))
DELETED_IN_GGA(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_GGA(T547, T537, T546, deleteD_in_gga(s(T547), void, T546))
DELETED_IN_GGA(s(T547), tree(0, T537, void), tree(0, T537, T546)) → DELETED_IN_GGA(s(T547), void, T546)
DELETED_IN_GGA(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_GGA(T556, T554, T537, T557, lessB_in_gg(T554, T556))
DELETED_IN_GGA(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → LESSB_IN_GG(T554, T556)
DELETED_IN_GGA(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_GGA(T560, T554, T537, T561, lessB_in_gg(T554, T560))
U50_GGA(T560, T554, T537, T561, lessB_out_gg(T554, T560)) → U51_GGA(T560, T554, T537, T561, deleteD_in_gga(s(T560), void, T561))
U50_GGA(T560, T554, T537, T561, lessB_out_gg(T554, T560)) → DELETED_IN_GGA(s(T560), void, T561)
DELETED_IN_GGA(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_GGA(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
DELETED_IN_GGA(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → DELMINE_IN_GAA(T615, T620, T621)
DELETED_IN_GGA(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_GGA(T651, T647, T648, T649, T652, lessA_in_gg(T651, T647))
DELETED_IN_GGA(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → LESSA_IN_GG(T651, T647)
DELETED_IN_GGA(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_GGA(T655, T647, T648, T649, T656, lessA_in_gg(T655, T647))
U54_GGA(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → U55_GGA(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
U54_GGA(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → DELETED_IN_GGA(T655, T648, T656)
DELETED_IN_GGA(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_GGA(T680, T676, T677, T678, T681, pH_in_ggga(T676, T680, T678, T681))
DELETED_IN_GGA(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → PH_IN_GGGA(T676, T680, T678, T681)
PH_IN_GGGA(T676, T680, T678, T681) → U13_GGGA(T676, T680, T678, T681, lessB_in_gg(T676, T680))
PH_IN_GGGA(T676, T680, T678, T681) → LESSB_IN_GG(T676, T680)
PH_IN_GGGA(T676, T684, T678, T685) → U14_GGGA(T676, T684, T678, T685, lessB_in_gg(T676, T684))
U14_GGGA(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → U15_GGGA(T676, T684, T678, T685, deleteD_in_gga(T684, T678, T685))
U14_GGGA(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → DELETED_IN_GGA(T684, T678, T685)
DELETED_IN_GGA(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_GGA(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
DELETED_IN_GGA(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → DELETED_IN_GGA(0, T701, T711)
DELETED_IN_GGA(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_GGA(T724, T723, T701, T702, T725, lessA_in_gg(T724, T723))
DELETED_IN_GGA(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → LESSA_IN_GG(T724, T723)
DELETED_IN_GGA(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_GGA(T728, T723, T701, T702, T729, lessA_in_gg(T728, T723))
U59_GGA(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → U60_GGA(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
U59_GGA(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → DELETED_IN_GGA(s(T728), T701, T729)
DELETED_IN_GGA(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_GGA(T753, T749, T750, T751, T754, pH_in_ggga(T749, T753, T751, T754))
DELETED_IN_GGA(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_GGA(T775, T764, T765, T774, deleteD_in_gga(s(T775), T765, T774))
DELETED_IN_GGA(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → DELETED_IN_GGA(s(T775), T765, T774)
DELETED_IN_GGA(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_GGA(T786, T784, T764, T765, T787, lessB_in_gg(T784, T786))
DELETED_IN_GGA(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → LESSB_IN_GG(T784, T786)
DELETED_IN_GGA(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_GGA(T790, T784, T764, T765, T791, lessB_in_gg(T784, T790))
U64_GGA(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → U65_GGA(T790, T784, T764, T765, T791, deleteD_in_gga(s(T790), T765, T791))
U64_GGA(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → DELETED_IN_GGA(s(T790), T765, T791)
DELETED_IN_AGA(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_AGA(T66, T64, T67, pC_in_gaa(T64, T66, T67))
DELETED_IN_AGA(T66, tree(T64, void, void), tree(T64, void, T67)) → PC_IN_GAA(T64, T66, T67)
PC_IN_GAA(T64, T66, T67) → U3_GAA(T64, T66, T67, lessB_in_ga(T64, T66))
PC_IN_GAA(T64, T66, T67) → LESSB_IN_GA(T64, T66)
LESSB_IN_GA(s(T83), s(T85)) → U2_GA(T83, T85, lessB_in_ga(T83, T85))
LESSB_IN_GA(s(T83), s(T85)) → LESSB_IN_GA(T83, T85)
PC_IN_GAA(T64, T70, T71) → U4_GAA(T64, T70, T71, lessB_in_ga(T64, T70))
U4_GAA(T64, T70, T71, lessB_out_ga(T64, T70)) → U5_GAA(T64, T70, T71, deleteD_in_aga(T70, void, T71))
U4_GAA(T64, T70, T71, lessB_out_ga(T64, T70)) → DELETED_IN_AGA(T70, void, T71)
DELETED_IN_AGA(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_AGA(T102, T103, deleteD_in_gga(0, void, T103))
DELETED_IN_AGA(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → DELETED_IN_GGA(0, void, T103)
DELETED_IN_AGA(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_AGA(T114, T113, T115, lessA_in_ag(T114, T113))
DELETED_IN_AGA(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → LESSA_IN_AG(T114, T113)
DELETED_IN_AGA(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_AGA(T118, T113, T119, lessA_in_ag(T118, T113))
U20_AGA(T118, T113, T119, lessA_out_ag(T118, T113)) → U21_AGA(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
U20_AGA(T118, T113, T119, lessA_out_ag(T118, T113)) → DELETED_IN_GGA(s(T118), void, T119)
DELETED_IN_AGA(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_AGA(T135, T133, T136, pC_in_gaa(T133, T135, T136))
DELETED_IN_AGA(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_AGA(T153, T152, deleteD_in_aga(s(T153), void, T152))
DELETED_IN_AGA(s(T153), tree(0, void, void), tree(0, void, T152)) → DELETED_IN_AGA(s(T153), void, T152)
DELETED_IN_AGA(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_AGA(T162, T160, T163, lessB_in_ga(T160, T162))
DELETED_IN_AGA(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → LESSB_IN_GA(T160, T162)
DELETED_IN_AGA(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_AGA(T166, T160, T167, lessB_in_ga(T160, T166))
U25_AGA(T166, T160, T167, lessB_out_ga(T160, T166)) → U26_AGA(T166, T160, T167, deleteD_in_aga(s(T166), void, T167))
U25_AGA(T166, T160, T167, lessB_out_ga(T160, T166)) → DELETED_IN_AGA(s(T166), void, T167)
DELETED_IN_AGA(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_AGA(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
DELETED_IN_AGA(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → DELMINE_IN_GAA(T219, T224, T225)
DELETED_IN_AGA(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_AGA(T284, T281, T282, T285, pF_in_aga(T284, T281, T285))
DELETED_IN_AGA(T284, tree(T281, void, T282), tree(T281, T285, T282)) → PF_IN_AGA(T284, T281, T285)
DELETED_IN_AGA(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_AGA(T300, T297, T298, T301, pG_in_gaga(T297, T300, T298, T301))
DELETED_IN_AGA(T300, tree(T297, void, T298), tree(T297, void, T301)) → PG_IN_GAGA(T297, T300, T298, T301)
PG_IN_GAGA(T297, T300, T298, T301) → U10_GAGA(T297, T300, T298, T301, lessB_in_ga(T297, T300))
PG_IN_GAGA(T297, T300, T298, T301) → LESSB_IN_GA(T297, T300)
PG_IN_GAGA(T297, T304, T298, T305) → U11_GAGA(T297, T304, T298, T305, lessB_in_ga(T297, T304))
U11_GAGA(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → U12_GAGA(T297, T304, T298, T305, deleteD_in_aga(T304, T298, T305))
U11_GAGA(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → DELETED_IN_AGA(T304, T298, T305)
DELETED_IN_AGA(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_AGA(T328, T320, T329, deleteD_in_gga(0, void, T329))
DELETED_IN_AGA(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → DELETED_IN_GGA(0, void, T329)
DELETED_IN_AGA(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_AGA(T340, T339, T320, T341, lessA_in_ag(T340, T339))
DELETED_IN_AGA(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → LESSA_IN_AG(T340, T339)
DELETED_IN_AGA(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_AGA(T344, T339, T320, T345, lessA_in_ag(T344, T339))
U32_AGA(T344, T339, T320, T345, lessA_out_ag(T344, T339)) → U33_AGA(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
U32_AGA(T344, T339, T320, T345, lessA_out_ag(T344, T339)) → DELETED_IN_GGA(s(T344), void, T345)
DELETED_IN_AGA(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_AGA(T364, T361, T362, T365, pG_in_gaga(T361, T364, T362, T365))
DELETED_IN_AGA(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_AGA(T384, T374, T383, deleteD_in_aga(s(T384), T374, T383))
DELETED_IN_AGA(s(T384), tree(0, void, T374), tree(0, void, T383)) → DELETED_IN_AGA(s(T384), T374, T383)
DELETED_IN_AGA(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_AGA(T395, T393, T374, T396, lessB_in_ga(T393, T395))
DELETED_IN_AGA(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → LESSB_IN_GA(T393, T395)
DELETED_IN_AGA(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_AGA(T399, T393, T374, T400, lessB_in_ga(T393, T399))
U37_AGA(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → U38_AGA(T399, T393, T374, T400, deleteD_in_aga(s(T399), T374, T400))
U37_AGA(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → DELETED_IN_AGA(s(T399), T374, T400)
DELETED_IN_AGA(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_AGA(T443, T440, T441, T444, lessA_in_ag(T443, T440))
DELETED_IN_AGA(T443, tree(T440, T441, void), tree(T440, T444, void)) → LESSA_IN_AG(T443, T440)
DELETED_IN_AGA(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_AGA(T447, T440, T441, T448, lessA_in_ag(T447, T440))
U40_AGA(T447, T440, T441, T448, lessA_out_ag(T447, T440)) → U41_AGA(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
U40_AGA(T447, T440, T441, T448, lessA_out_ag(T447, T440)) → DELETED_IN_GGA(T447, T441, T448)
DELETED_IN_AGA(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_AGA(T469, T466, T467, T470, pC_in_gaa(T466, T469, T470))
DELETED_IN_AGA(T469, tree(T466, T467, void), tree(T466, T467, T470)) → PC_IN_GAA(T466, T469, T470)
DELETED_IN_AGA(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_AGA(T487, T479, T488, deleteD_in_gga(0, T479, T488))
DELETED_IN_AGA(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → DELETED_IN_GGA(0, T479, T488)
DELETED_IN_AGA(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_AGA(T501, T500, T479, T502, lessA_in_ag(T501, T500))
DELETED_IN_AGA(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → LESSA_IN_AG(T501, T500)
DELETED_IN_AGA(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_AGA(T505, T500, T479, T506, lessA_in_ag(T505, T500))
U45_AGA(T505, T500, T479, T506, lessA_out_ag(T505, T500)) → U46_AGA(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
U45_AGA(T505, T500, T479, T506, lessA_out_ag(T505, T500)) → DELETED_IN_GGA(s(T505), T479, T506)
DELETED_IN_AGA(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_AGA(T527, T524, T525, T528, pC_in_gaa(T524, T527, T528))
DELETED_IN_AGA(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_AGA(T547, T537, T546, deleteD_in_aga(s(T547), void, T546))
DELETED_IN_AGA(s(T547), tree(0, T537, void), tree(0, T537, T546)) → DELETED_IN_AGA(s(T547), void, T546)
DELETED_IN_AGA(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_AGA(T556, T554, T537, T557, lessB_in_ga(T554, T556))
DELETED_IN_AGA(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → LESSB_IN_GA(T554, T556)
DELETED_IN_AGA(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_AGA(T560, T554, T537, T561, lessB_in_ga(T554, T560))
U50_AGA(T560, T554, T537, T561, lessB_out_ga(T554, T560)) → U51_AGA(T560, T554, T537, T561, deleteD_in_aga(s(T560), void, T561))
U50_AGA(T560, T554, T537, T561, lessB_out_ga(T554, T560)) → DELETED_IN_AGA(s(T560), void, T561)
DELETED_IN_AGA(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_AGA(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
DELETED_IN_AGA(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → DELMINE_IN_GAA(T615, T620, T621)
DELETED_IN_AGA(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_AGA(T651, T647, T648, T649, T652, lessA_in_ag(T651, T647))
DELETED_IN_AGA(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → LESSA_IN_AG(T651, T647)
DELETED_IN_AGA(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_AGA(T655, T647, T648, T649, T656, lessA_in_ag(T655, T647))
U54_AGA(T655, T647, T648, T649, T656, lessA_out_ag(T655, T647)) → U55_AGA(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
U54_AGA(T655, T647, T648, T649, T656, lessA_out_ag(T655, T647)) → DELETED_IN_GGA(T655, T648, T656)
DELETED_IN_AGA(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_AGA(T680, T676, T677, T678, T681, pH_in_gaga(T676, T680, T678, T681))
DELETED_IN_AGA(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → PH_IN_GAGA(T676, T680, T678, T681)
PH_IN_GAGA(T676, T680, T678, T681) → U13_GAGA(T676, T680, T678, T681, lessB_in_ga(T676, T680))
PH_IN_GAGA(T676, T680, T678, T681) → LESSB_IN_GA(T676, T680)
PH_IN_GAGA(T676, T684, T678, T685) → U14_GAGA(T676, T684, T678, T685, lessB_in_ga(T676, T684))
U14_GAGA(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → U15_GAGA(T676, T684, T678, T685, deleteD_in_aga(T684, T678, T685))
U14_GAGA(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → DELETED_IN_AGA(T684, T678, T685)
DELETED_IN_AGA(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_AGA(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
DELETED_IN_AGA(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → DELETED_IN_GGA(0, T701, T711)
DELETED_IN_AGA(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_AGA(T724, T723, T701, T702, T725, lessA_in_ag(T724, T723))
DELETED_IN_AGA(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → LESSA_IN_AG(T724, T723)
DELETED_IN_AGA(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_AGA(T728, T723, T701, T702, T729, lessA_in_ag(T728, T723))
U59_AGA(T728, T723, T701, T702, T729, lessA_out_ag(T728, T723)) → U60_AGA(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
U59_AGA(T728, T723, T701, T702, T729, lessA_out_ag(T728, T723)) → DELETED_IN_GGA(s(T728), T701, T729)
DELETED_IN_AGA(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_AGA(T753, T749, T750, T751, T754, pH_in_gaga(T749, T753, T751, T754))
DELETED_IN_AGA(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_AGA(T775, T764, T765, T774, deleteD_in_aga(s(T775), T765, T774))
DELETED_IN_AGA(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → DELETED_IN_AGA(s(T775), T765, T774)
DELETED_IN_AGA(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_AGA(T786, T784, T764, T765, T787, lessB_in_ga(T784, T786))
DELETED_IN_AGA(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → LESSB_IN_GA(T784, T786)
DELETED_IN_AGA(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_AGA(T790, T784, T764, T765, T791, lessB_in_ga(T784, T790))
U64_AGA(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → U65_AGA(T790, T784, T764, T765, T791, deleteD_in_aga(s(T790), T765, T791))
U64_AGA(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → DELETED_IN_AGA(s(T790), T765, T791)

The TRS R consists of the following rules:

deleteD_in_aga(T6, tree(T6, void, T7), T7) → deleteD_out_aga(T6, tree(T6, void, T7), T7)
deleteD_in_aga(T9, tree(T9, void, void), void) → deleteD_out_aga(T9, tree(T9, void, void), void)
deleteD_in_aga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_aga(T33, T31, T34, pF_in_aga(T33, T31, T34))
pF_in_aga(T33, T31, T34) → U7_aga(T33, T31, T34, lessA_in_ag(T33, T31))
lessA_in_ag(0, s(T45)) → lessA_out_ag(0, s(T45))
lessA_in_ag(s(T52), s(T51)) → U1_ag(T52, T51, lessA_in_ag(T52, T51))
U1_ag(T52, T51, lessA_out_ag(T52, T51)) → lessA_out_ag(s(T52), s(T51))
U7_aga(T33, T31, T34, lessA_out_ag(T33, T31)) → pF_out_aga(T33, T31, T34)
pF_in_aga(T37, T31, T38) → U8_aga(T37, T31, T38, lessA_in_ag(T37, T31))
U8_aga(T37, T31, T38, lessA_out_ag(T37, T31)) → U9_aga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T6, tree(T6, void, T7), T7) → deleteD_out_gga(T6, tree(T6, void, T7), T7)
deleteD_in_gga(T9, tree(T9, void, void), void) → deleteD_out_gga(T9, tree(T9, void, void), void)
deleteD_in_gga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_gga(T33, T31, T34, pF_in_gga(T33, T31, T34))
pF_in_gga(T33, T31, T34) → U7_gga(T33, T31, T34, lessA_in_gg(T33, T31))
lessA_in_gg(0, s(T45)) → lessA_out_gg(0, s(T45))
lessA_in_gg(s(T52), s(T51)) → U1_gg(T52, T51, lessA_in_gg(T52, T51))
U1_gg(T52, T51, lessA_out_gg(T52, T51)) → lessA_out_gg(s(T52), s(T51))
U7_gga(T33, T31, T34, lessA_out_gg(T33, T31)) → pF_out_gga(T33, T31, T34)
pF_in_gga(T37, T31, T38) → U8_gga(T37, T31, T38, lessA_in_gg(T37, T31))
U8_gga(T37, T31, T38, lessA_out_gg(T37, T31)) → U9_gga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_gga(T66, T64, T67, pC_in_gga(T64, T66, T67))
pC_in_gga(T64, T66, T67) → U3_gga(T64, T66, T67, lessB_in_gg(T64, T66))
lessB_in_gg(0, s(T78)) → lessB_out_gg(0, s(T78))
lessB_in_gg(s(T83), s(T85)) → U2_gg(T83, T85, lessB_in_gg(T83, T85))
U2_gg(T83, T85, lessB_out_gg(T83, T85)) → lessB_out_gg(s(T83), s(T85))
U3_gga(T64, T66, T67, lessB_out_gg(T64, T66)) → pC_out_gga(T64, T66, T67)
pC_in_gga(T64, T70, T71) → U4_gga(T64, T70, T71, lessB_in_gg(T64, T70))
U4_gga(T64, T70, T71, lessB_out_gg(T64, T70)) → U5_gga(T64, T70, T71, deleteD_in_gga(T70, void, T71))
deleteD_in_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_gga(T102, T103, deleteD_in_gga(0, void, T103))
deleteD_in_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_gga(T114, T113, T115, lessA_in_gg(T114, T113))
U19_gga(T114, T113, T115, lessA_out_gg(T114, T113)) → deleteD_out_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_gga(T118, T113, T119, lessA_in_gg(T118, T113))
U20_gga(T118, T113, T119, lessA_out_gg(T118, T113)) → U21_gga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
deleteD_in_gga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_gga(T135, T133, T136, pC_in_gga(T133, T135, T136))
U22_gga(T135, T133, T136, pC_out_gga(T133, T135, T136)) → deleteD_out_gga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_gga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_gga(T153, T152, deleteD_in_gga(s(T153), void, T152))
deleteD_in_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_gga(T162, T160, T163, lessB_in_gg(T160, T162))
U24_gga(T162, T160, T163, lessB_out_gg(T160, T162)) → deleteD_out_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_gga(T166, T160, T167, lessB_in_gg(T160, T166))
U25_gga(T166, T160, T167, lessB_out_gg(T160, T166)) → U26_gga(T166, T160, T167, deleteD_in_gga(s(T166), void, T167))
deleteD_in_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
delminE_in_gaa(tree(T238, void, T239), T238, T239) → delminE_out_gaa(tree(T238, void, T239), T238, T239)
delminE_in_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → U6_gaa(T252, T253, T254, T258, T259, T257, delminE_in_gaa(T253, T258, T259))
U6_gaa(T252, T253, T254, T258, T259, T257, delminE_out_gaa(T253, T258, T259)) → delminE_out_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257))
U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_gga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_gga(T284, T281, T282, T285, pF_in_gga(T284, T281, T285))
U28_gga(T284, T281, T282, T285, pF_out_gga(T284, T281, T285)) → deleteD_out_gga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_gga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_gga(T300, T297, T298, T301, pG_in_ggga(T297, T300, T298, T301))
pG_in_ggga(T297, T300, T298, T301) → U10_ggga(T297, T300, T298, T301, lessB_in_gg(T297, T300))
U10_ggga(T297, T300, T298, T301, lessB_out_gg(T297, T300)) → pG_out_ggga(T297, T300, T298, T301)
pG_in_ggga(T297, T304, T298, T305) → U11_ggga(T297, T304, T298, T305, lessB_in_gg(T297, T304))
U11_ggga(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → U12_ggga(T297, T304, T298, T305, deleteD_in_gga(T304, T298, T305))
deleteD_in_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_gga(T328, T320, T329, deleteD_in_gga(0, void, T329))
deleteD_in_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_gga(T340, T339, T320, T341, lessA_in_gg(T340, T339))
U31_gga(T340, T339, T320, T341, lessA_out_gg(T340, T339)) → deleteD_out_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_gga(T344, T339, T320, T345, lessA_in_gg(T344, T339))
U32_gga(T344, T339, T320, T345, lessA_out_gg(T344, T339)) → U33_gga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
deleteD_in_gga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_gga(T364, T361, T362, T365, pG_in_ggga(T361, T364, T362, T365))
U34_gga(T364, T361, T362, T365, pG_out_ggga(T361, T364, T362, T365)) → deleteD_out_gga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_gga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_gga(T384, T374, T383, deleteD_in_gga(s(T384), T374, T383))
deleteD_in_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_gga(T395, T393, T374, T396, lessB_in_gg(T393, T395))
U36_gga(T395, T393, T374, T396, lessB_out_gg(T393, T395)) → deleteD_out_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_gga(T399, T393, T374, T400, lessB_in_gg(T393, T399))
U37_gga(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → U38_gga(T399, T393, T374, T400, deleteD_in_gga(s(T399), T374, T400))
deleteD_in_gga(T411, tree(T411, T412, void), T412) → deleteD_out_gga(T411, tree(T411, T412, void), T412)
deleteD_in_gga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_gga(T443, T440, T441, T444, lessA_in_gg(T443, T440))
U39_gga(T443, T440, T441, T444, lessA_out_gg(T443, T440)) → deleteD_out_gga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_gga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_gga(T447, T440, T441, T448, lessA_in_gg(T447, T440))
U40_gga(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → U41_gga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
deleteD_in_gga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_gga(T469, T466, T467, T470, pC_in_gga(T466, T469, T470))
U42_gga(T469, T466, T467, T470, pC_out_gga(T466, T469, T470)) → deleteD_out_gga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_gga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
deleteD_in_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_gga(T501, T500, T479, T502, lessA_in_gg(T501, T500))
U44_gga(T501, T500, T479, T502, lessA_out_gg(T501, T500)) → deleteD_out_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_gga(T505, T500, T479, T506, lessA_in_gg(T505, T500))
U45_gga(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → U46_gga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
deleteD_in_gga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_gga(T527, T524, T525, T528, pC_in_gga(T524, T527, T528))
U47_gga(T527, T524, T525, T528, pC_out_gga(T524, T527, T528)) → deleteD_out_gga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_gga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_gga(T547, T537, T546, deleteD_in_gga(s(T547), void, T546))
deleteD_in_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_gga(T556, T554, T537, T557, lessB_in_gg(T554, T556))
U49_gga(T556, T554, T537, T557, lessB_out_gg(T554, T556)) → deleteD_out_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_gga(T560, T554, T537, T561, lessB_in_gg(T554, T560))
U50_gga(T560, T554, T537, T561, lessB_out_gg(T554, T560)) → U51_gga(T560, T554, T537, T561, deleteD_in_gga(s(T560), void, T561))
deleteD_in_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_gga(T651, T647, T648, T649, T652, lessA_in_gg(T651, T647))
U53_gga(T651, T647, T648, T649, T652, lessA_out_gg(T651, T647)) → deleteD_out_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_gga(T655, T647, T648, T649, T656, lessA_in_gg(T655, T647))
U54_gga(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → U55_gga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
deleteD_in_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_gga(T680, T676, T677, T678, T681, pH_in_ggga(T676, T680, T678, T681))
pH_in_ggga(T676, T680, T678, T681) → U13_ggga(T676, T680, T678, T681, lessB_in_gg(T676, T680))
U13_ggga(T676, T680, T678, T681, lessB_out_gg(T676, T680)) → pH_out_ggga(T676, T680, T678, T681)
pH_in_ggga(T676, T684, T678, T685) → U14_ggga(T676, T684, T678, T685, lessB_in_gg(T676, T684))
U14_ggga(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → U15_ggga(T676, T684, T678, T685, deleteD_in_gga(T684, T678, T685))
deleteD_in_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_gga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
deleteD_in_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_gga(T724, T723, T701, T702, T725, lessA_in_gg(T724, T723))
U58_gga(T724, T723, T701, T702, T725, lessA_out_gg(T724, T723)) → deleteD_out_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_gga(T728, T723, T701, T702, T729, lessA_in_gg(T728, T723))
U59_gga(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → U60_gga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
deleteD_in_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_gga(T753, T749, T750, T751, T754, pH_in_ggga(T749, T753, T751, T754))
U61_gga(T753, T749, T750, T751, T754, pH_out_ggga(T749, T753, T751, T754)) → deleteD_out_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_gga(T775, T764, T765, T774, deleteD_in_gga(s(T775), T765, T774))
deleteD_in_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_gga(T786, T784, T764, T765, T787, lessB_in_gg(T784, T786))
U63_gga(T786, T784, T764, T765, T787, lessB_out_gg(T784, T786)) → deleteD_out_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_gga(T790, T784, T764, T765, T791, lessB_in_gg(T784, T790))
U64_gga(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → U65_gga(T790, T784, T764, T765, T791, deleteD_in_gga(s(T790), T765, T791))
U65_gga(T790, T784, T764, T765, T791, deleteD_out_gga(s(T790), T765, T791)) → deleteD_out_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_gga(T775, T764, T765, T774, deleteD_out_gga(s(T775), T765, T774)) → deleteD_out_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U60_gga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
U57_gga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
U15_ggga(T676, T684, T678, T685, deleteD_out_gga(T684, T678, T685)) → pH_out_ggga(T676, T684, T678, T685)
U56_gga(T680, T676, T677, T678, T681, pH_out_ggga(T676, T680, T678, T681)) → deleteD_out_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U55_gga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
U51_gga(T560, T554, T537, T561, deleteD_out_gga(s(T560), void, T561)) → deleteD_out_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_gga(T547, T537, T546, deleteD_out_gga(s(T547), void, T546)) → deleteD_out_gga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U46_gga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
U43_gga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
U41_gga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_gga(T447, tree(T440, T441, void), tree(T440, T448, void))
U38_gga(T399, T393, T374, T400, deleteD_out_gga(s(T399), T374, T400)) → deleteD_out_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_gga(T384, T374, T383, deleteD_out_gga(s(T384), T374, T383)) → deleteD_out_gga(s(T384), tree(0, void, T374), tree(0, void, T383))
U33_gga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
U30_gga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
U12_ggga(T297, T304, T298, T305, deleteD_out_gga(T304, T298, T305)) → pG_out_ggga(T297, T304, T298, T305)
U29_gga(T300, T297, T298, T301, pG_out_ggga(T297, T300, T298, T301)) → deleteD_out_gga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_gga(T166, T160, T167, deleteD_out_gga(s(T166), void, T167)) → deleteD_out_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_gga(T153, T152, deleteD_out_gga(s(T153), void, T152)) → deleteD_out_gga(s(T153), tree(0, void, void), tree(0, void, T152))
U21_gga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
U18_gga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
U5_gga(T64, T70, T71, deleteD_out_gga(T70, void, T71)) → pC_out_gga(T64, T70, T71)
U17_gga(T66, T64, T67, pC_out_gga(T64, T66, T67)) → deleteD_out_gga(T66, tree(T64, void, void), tree(T64, void, T67))
U9_gga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_gga(T37, T31, T38)
U16_gga(T33, T31, T34, pF_out_gga(T33, T31, T34)) → deleteD_out_gga(T33, tree(T31, void, void), tree(T31, T34, void))
U9_aga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_aga(T37, T31, T38)
U16_aga(T33, T31, T34, pF_out_aga(T33, T31, T34)) → deleteD_out_aga(T33, tree(T31, void, void), tree(T31, T34, void))
deleteD_in_aga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_aga(T66, T64, T67, pC_in_gaa(T64, T66, T67))
pC_in_gaa(T64, T66, T67) → U3_gaa(T64, T66, T67, lessB_in_ga(T64, T66))
lessB_in_ga(0, s(T78)) → lessB_out_ga(0, s(T78))
lessB_in_ga(s(T83), s(T85)) → U2_ga(T83, T85, lessB_in_ga(T83, T85))
U2_ga(T83, T85, lessB_out_ga(T83, T85)) → lessB_out_ga(s(T83), s(T85))
U3_gaa(T64, T66, T67, lessB_out_ga(T64, T66)) → pC_out_gaa(T64, T66, T67)
pC_in_gaa(T64, T70, T71) → U4_gaa(T64, T70, T71, lessB_in_ga(T64, T70))
U4_gaa(T64, T70, T71, lessB_out_ga(T64, T70)) → U5_gaa(T64, T70, T71, deleteD_in_aga(T70, void, T71))
deleteD_in_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_aga(T102, T103, deleteD_in_gga(0, void, T103))
U18_aga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
deleteD_in_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_aga(T114, T113, T115, lessA_in_ag(T114, T113))
U19_aga(T114, T113, T115, lessA_out_ag(T114, T113)) → deleteD_out_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_aga(T118, T113, T119, lessA_in_ag(T118, T113))
U20_aga(T118, T113, T119, lessA_out_ag(T118, T113)) → U21_aga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
U21_aga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
deleteD_in_aga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_aga(T135, T133, T136, pC_in_gaa(T133, T135, T136))
U22_aga(T135, T133, T136, pC_out_gaa(T133, T135, T136)) → deleteD_out_aga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_aga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_aga(T153, T152, deleteD_in_aga(s(T153), void, T152))
deleteD_in_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_aga(T162, T160, T163, lessB_in_ga(T160, T162))
U24_aga(T162, T160, T163, lessB_out_ga(T160, T162)) → deleteD_out_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_aga(T166, T160, T167, lessB_in_ga(T160, T166))
U25_aga(T166, T160, T167, lessB_out_ga(T160, T166)) → U26_aga(T166, T160, T167, deleteD_in_aga(s(T166), void, T167))
deleteD_in_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_aga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_aga(T284, T281, T282, T285, pF_in_aga(T284, T281, T285))
U28_aga(T284, T281, T282, T285, pF_out_aga(T284, T281, T285)) → deleteD_out_aga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_aga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_aga(T300, T297, T298, T301, pG_in_gaga(T297, T300, T298, T301))
pG_in_gaga(T297, T300, T298, T301) → U10_gaga(T297, T300, T298, T301, lessB_in_ga(T297, T300))
U10_gaga(T297, T300, T298, T301, lessB_out_ga(T297, T300)) → pG_out_gaga(T297, T300, T298, T301)
pG_in_gaga(T297, T304, T298, T305) → U11_gaga(T297, T304, T298, T305, lessB_in_ga(T297, T304))
U11_gaga(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → U12_gaga(T297, T304, T298, T305, deleteD_in_aga(T304, T298, T305))
deleteD_in_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_aga(T328, T320, T329, deleteD_in_gga(0, void, T329))
U30_aga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
deleteD_in_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_aga(T340, T339, T320, T341, lessA_in_ag(T340, T339))
U31_aga(T340, T339, T320, T341, lessA_out_ag(T340, T339)) → deleteD_out_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_aga(T344, T339, T320, T345, lessA_in_ag(T344, T339))
U32_aga(T344, T339, T320, T345, lessA_out_ag(T344, T339)) → U33_aga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
U33_aga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
deleteD_in_aga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_aga(T364, T361, T362, T365, pG_in_gaga(T361, T364, T362, T365))
U34_aga(T364, T361, T362, T365, pG_out_gaga(T361, T364, T362, T365)) → deleteD_out_aga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_aga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_aga(T384, T374, T383, deleteD_in_aga(s(T384), T374, T383))
deleteD_in_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_aga(T395, T393, T374, T396, lessB_in_ga(T393, T395))
U36_aga(T395, T393, T374, T396, lessB_out_ga(T393, T395)) → deleteD_out_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_aga(T399, T393, T374, T400, lessB_in_ga(T393, T399))
U37_aga(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → U38_aga(T399, T393, T374, T400, deleteD_in_aga(s(T399), T374, T400))
deleteD_in_aga(T411, tree(T411, T412, void), T412) → deleteD_out_aga(T411, tree(T411, T412, void), T412)
deleteD_in_aga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_aga(T443, T440, T441, T444, lessA_in_ag(T443, T440))
U39_aga(T443, T440, T441, T444, lessA_out_ag(T443, T440)) → deleteD_out_aga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_aga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_aga(T447, T440, T441, T448, lessA_in_ag(T447, T440))
U40_aga(T447, T440, T441, T448, lessA_out_ag(T447, T440)) → U41_aga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
U41_aga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_aga(T447, tree(T440, T441, void), tree(T440, T448, void))
deleteD_in_aga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_aga(T469, T466, T467, T470, pC_in_gaa(T466, T469, T470))
U42_aga(T469, T466, T467, T470, pC_out_gaa(T466, T469, T470)) → deleteD_out_aga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_aga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
U43_aga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
deleteD_in_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_aga(T501, T500, T479, T502, lessA_in_ag(T501, T500))
U44_aga(T501, T500, T479, T502, lessA_out_ag(T501, T500)) → deleteD_out_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_aga(T505, T500, T479, T506, lessA_in_ag(T505, T500))
U45_aga(T505, T500, T479, T506, lessA_out_ag(T505, T500)) → U46_aga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
U46_aga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
deleteD_in_aga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_aga(T527, T524, T525, T528, pC_in_gaa(T524, T527, T528))
U47_aga(T527, T524, T525, T528, pC_out_gaa(T524, T527, T528)) → deleteD_out_aga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_aga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_aga(T547, T537, T546, deleteD_in_aga(s(T547), void, T546))
deleteD_in_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_aga(T556, T554, T537, T557, lessB_in_ga(T554, T556))
U49_aga(T556, T554, T537, T557, lessB_out_ga(T554, T556)) → deleteD_out_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_aga(T560, T554, T537, T561, lessB_in_ga(T554, T560))
U50_aga(T560, T554, T537, T561, lessB_out_ga(T554, T560)) → U51_aga(T560, T554, T537, T561, deleteD_in_aga(s(T560), void, T561))
deleteD_in_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_aga(T651, T647, T648, T649, T652, lessA_in_ag(T651, T647))
U53_aga(T651, T647, T648, T649, T652, lessA_out_ag(T651, T647)) → deleteD_out_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_aga(T655, T647, T648, T649, T656, lessA_in_ag(T655, T647))
U54_aga(T655, T647, T648, T649, T656, lessA_out_ag(T655, T647)) → U55_aga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
U55_aga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
deleteD_in_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_aga(T680, T676, T677, T678, T681, pH_in_gaga(T676, T680, T678, T681))
pH_in_gaga(T676, T680, T678, T681) → U13_gaga(T676, T680, T678, T681, lessB_in_ga(T676, T680))
U13_gaga(T676, T680, T678, T681, lessB_out_ga(T676, T680)) → pH_out_gaga(T676, T680, T678, T681)
pH_in_gaga(T676, T684, T678, T685) → U14_gaga(T676, T684, T678, T685, lessB_in_ga(T676, T684))
U14_gaga(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → U15_gaga(T676, T684, T678, T685, deleteD_in_aga(T684, T678, T685))
deleteD_in_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_aga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
U57_aga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
deleteD_in_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_aga(T724, T723, T701, T702, T725, lessA_in_ag(T724, T723))
U58_aga(T724, T723, T701, T702, T725, lessA_out_ag(T724, T723)) → deleteD_out_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_aga(T728, T723, T701, T702, T729, lessA_in_ag(T728, T723))
U59_aga(T728, T723, T701, T702, T729, lessA_out_ag(T728, T723)) → U60_aga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
U60_aga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
deleteD_in_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_aga(T753, T749, T750, T751, T754, pH_in_gaga(T749, T753, T751, T754))
U61_aga(T753, T749, T750, T751, T754, pH_out_gaga(T749, T753, T751, T754)) → deleteD_out_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_aga(T775, T764, T765, T774, deleteD_in_aga(s(T775), T765, T774))
deleteD_in_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_aga(T786, T784, T764, T765, T787, lessB_in_ga(T784, T786))
U63_aga(T786, T784, T764, T765, T787, lessB_out_ga(T784, T786)) → deleteD_out_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_aga(T790, T784, T764, T765, T791, lessB_in_ga(T784, T790))
U64_aga(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → U65_aga(T790, T784, T764, T765, T791, deleteD_in_aga(s(T790), T765, T791))
U65_aga(T790, T784, T764, T765, T791, deleteD_out_aga(s(T790), T765, T791)) → deleteD_out_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_aga(T775, T764, T765, T774, deleteD_out_aga(s(T775), T765, T774)) → deleteD_out_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U15_gaga(T676, T684, T678, T685, deleteD_out_aga(T684, T678, T685)) → pH_out_gaga(T676, T684, T678, T685)
U56_aga(T680, T676, T677, T678, T681, pH_out_gaga(T676, T680, T678, T681)) → deleteD_out_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U51_aga(T560, T554, T537, T561, deleteD_out_aga(s(T560), void, T561)) → deleteD_out_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_aga(T547, T537, T546, deleteD_out_aga(s(T547), void, T546)) → deleteD_out_aga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U38_aga(T399, T393, T374, T400, deleteD_out_aga(s(T399), T374, T400)) → deleteD_out_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_aga(T384, T374, T383, deleteD_out_aga(s(T384), T374, T383)) → deleteD_out_aga(s(T384), tree(0, void, T374), tree(0, void, T383))
U12_gaga(T297, T304, T298, T305, deleteD_out_aga(T304, T298, T305)) → pG_out_gaga(T297, T304, T298, T305)
U29_aga(T300, T297, T298, T301, pG_out_gaga(T297, T300, T298, T301)) → deleteD_out_aga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_aga(T166, T160, T167, deleteD_out_aga(s(T166), void, T167)) → deleteD_out_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_aga(T153, T152, deleteD_out_aga(s(T153), void, T152)) → deleteD_out_aga(s(T153), tree(0, void, void), tree(0, void, T152))
U5_gaa(T64, T70, T71, deleteD_out_aga(T70, void, T71)) → pC_out_gaa(T64, T70, T71)
U17_aga(T66, T64, T67, pC_out_gaa(T64, T66, T67)) → deleteD_out_aga(T66, tree(T64, void, void), tree(T64, void, T67))

The argument filtering Pi contains the following mapping:
deleteD_in_aga(x1, x2, x3) = deleteD_in_aga(x2)
tree(x1, x2, x3) = tree(x1, x2, x3)
void = void
deleteD_out_aga(x1, x2, x3) = deleteD_out_aga(x2)
U16_aga(x1, x2, x3, x4) = U16_aga(x2, x4)
pF_in_aga(x1, x2, x3) = pF_in_aga(x2)
U7_aga(x1, x2, x3, x4) = U7_aga(x2, x4)
lessA_in_ag(x1, x2) = lessA_in_ag(x2)
s(x1) = s(x1)
lessA_out_ag(x1, x2) = lessA_out_ag(x1, x2)
U1_ag(x1, x2, x3) = U1_ag(x2, x3)
pF_out_aga(x1, x2, x3) = pF_out_aga(x1, x2)
U8_aga(x1, x2, x3, x4) = U8_aga(x2, x4)
U9_aga(x1, x2, x3, x4) = U9_aga(x1, x2, x4)
deleteD_in_gga(x1, x2, x3) = deleteD_in_gga(x1, x2)
deleteD_out_gga(x1, x2, x3) = deleteD_out_gga(x1, x2)
U16_gga(x1, x2, x3, x4) = U16_gga(x1, x2, x4)
pF_in_gga(x1, x2, x3) = pF_in_gga(x1, x2)
U7_gga(x1, x2, x3, x4) = U7_gga(x1, x2, x4)
lessA_in_gg(x1, x2) = lessA_in_gg(x1, x2)
0 = 0
lessA_out_gg(x1, x2) = lessA_out_gg(x1, x2)
U1_gg(x1, x2, x3) = U1_gg(x1, x2, x3)
pF_out_gga(x1, x2, x3) = pF_out_gga(x1, x2)
U8_gga(x1, x2, x3, x4) = U8_gga(x1, x2, x4)
U9_gga(x1, x2, x3, x4) = U9_gga(x1, x2, x4)
U17_gga(x1, x2, x3, x4) = U17_gga(x1, x2, x4)
pC_in_gga(x1, x2, x3) = pC_in_gga(x1, x2)
U3_gga(x1, x2, x3, x4) = U3_gga(x1, x2, x4)
lessB_in_gg(x1, x2) = lessB_in_gg(x1, x2)
lessB_out_gg(x1, x2) = lessB_out_gg(x1, x2)
U2_gg(x1, x2, x3) = U2_gg(x1, x2, x3)
pC_out_gga(x1, x2, x3) = pC_out_gga(x1, x2)
U4_gga(x1, x2, x3, x4) = U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4) = U5_gga(x1, x2, x4)
U18_gga(x1, x2, x3) = U18_gga(x1, x3)
U19_gga(x1, x2, x3, x4) = U19_gga(x1, x2, x4)
U20_gga(x1, x2, x3, x4) = U20_gga(x1, x2, x4)
U21_gga(x1, x2, x3, x4) = U21_gga(x1, x2, x4)
U22_gga(x1, x2, x3, x4) = U22_gga(x1, x2, x4)
U23_gga(x1, x2, x3) = U23_gga(x1, x3)
U24_gga(x1, x2, x3, x4) = U24_gga(x1, x2, x4)
U25_gga(x1, x2, x3, x4) = U25_gga(x1, x2, x4)
U26_gga(x1, x2, x3, x4) = U26_gga(x1, x2, x4)
U27_gga(x1, x2, x3, x4, x5, x6, x7, x8) = U27_gga(x1, x2, x3, x4, x8)
delminE_in_gaa(x1, x2, x3) = delminE_in_gaa(x1)
delminE_out_gaa(x1, x2, x3) = delminE_out_gaa(x1, x2)
U6_gaa(x1, x2, x3, x4, x5, x6, x7) = U6_gaa(x1, x2, x3, x7)
U28_gga(x1, x2, x3, x4, x5) = U28_gga(x1, x2, x3, x5)
U29_gga(x1, x2, x3, x4, x5) = U29_gga(x1, x2, x3, x5)
pG_in_ggga(x1, x2, x3, x4) = pG_in_ggga(x1, x2, x3)
U10_ggga(x1, x2, x3, x4, x5) = U10_ggga(x1, x2, x3, x5)
pG_out_ggga(x1, x2, x3, x4) = pG_out_ggga(x1, x2, x3)
U11_ggga(x1, x2, x3, x4, x5) = U11_ggga(x1, x2, x3, x5)
U12_ggga(x1, x2, x3, x4, x5) = U12_ggga(x1, x2, x3, x5)
U30_gga(x1, x2, x3, x4) = U30_gga(x1, x2, x4)
U31_gga(x1, x2, x3, x4, x5) = U31_gga(x1, x2, x3, x5)
U32_gga(x1, x2, x3, x4, x5) = U32_gga(x1, x2, x3, x5)
U33_gga(x1, x2, x3, x4, x5) = U33_gga(x1, x2, x3, x5)
U34_gga(x1, x2, x3, x4, x5) = U34_gga(x1, x2, x3, x5)
U35_gga(x1, x2, x3, x4) = U35_gga(x1, x2, x4)
U36_gga(x1, x2, x3, x4, x5) = U36_gga(x1, x2, x3, x5)
U37_gga(x1, x2, x3, x4, x5) = U37_gga(x1, x2, x3, x5)
U38_gga(x1, x2, x3, x4, x5) = U38_gga(x1, x2, x3, x5)
U39_gga(x1, x2, x3, x4, x5) = U39_gga(x1, x2, x3, x5)
U40_gga(x1, x2, x3, x4, x5) = U40_gga(x1, x2, x3, x5)
U41_gga(x1, x2, x3, x4, x5) = U41_gga(x1, x2, x3, x5)
U42_gga(x1, x2, x3, x4, x5) = U42_gga(x1, x2, x3, x5)
U43_gga(x1, x2, x3, x4) = U43_gga(x1, x2, x4)
U44_gga(x1, x2, x3, x4, x5) = U44_gga(x1, x2, x3, x5)
U45_gga(x1, x2, x3, x4, x5) = U45_gga(x1, x2, x3, x5)
U46_gga(x1, x2, x3, x4, x5) = U46_gga(x1, x2, x3, x5)
U47_gga(x1, x2, x3, x4, x5) = U47_gga(x1, x2, x3, x5)
U48_gga(x1, x2, x3, x4) = U48_gga(x1, x2, x4)
U49_gga(x1, x2, x3, x4, x5) = U49_gga(x1, x2, x3, x5)
U50_gga(x1, x2, x3, x4, x5) = U50_gga(x1, x2, x3, x5)
U51_gga(x1, x2, x3, x4, x5) = U51_gga(x1, x2, x3, x5)
U52_gga(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U52_gga(x1, x2, x3, x4, x5, x9)
U53_gga(x1, x2, x3, x4, x5, x6) = U53_gga(x1, x2, x3, x4, x6)
U54_gga(x1, x2, x3, x4, x5, x6) = U54_gga(x1, x2, x3, x4, x6)
U55_gga(x1, x2, x3, x4, x5, x6) = U55_gga(x1, x2, x3, x4, x6)
U56_gga(x1, x2, x3, x4, x5, x6) = U56_gga(x1, x2, x3, x4, x6)
pH_in_ggga(x1, x2, x3, x4) = pH_in_ggga(x1, x2, x3)
U13_ggga(x1, x2, x3, x4, x5) = U13_ggga(x1, x2, x3, x5)
pH_out_ggga(x1, x2, x3, x4) = pH_out_ggga(x1, x2, x3)
U14_ggga(x1, x2, x3, x4, x5) = U14_ggga(x1, x2, x3, x5)
U15_ggga(x1, x2, x3, x4, x5) = U15_ggga(x1, x2, x3, x5)
U57_gga(x1, x2, x3, x4, x5) = U57_gga(x1, x2, x3, x5)
U58_gga(x1, x2, x3, x4, x5, x6) = U58_gga(x1, x2, x3, x4, x6)
U59_gga(x1, x2, x3, x4, x5, x6) = U59_gga(x1, x2, x3, x4, x6)
U60_gga(x1, x2, x3, x4, x5, x6) = U60_gga(x1, x2, x3, x4, x6)
U61_gga(x1, x2, x3, x4, x5, x6) = U61_gga(x1, x2, x3, x4, x6)
U62_gga(x1, x2, x3, x4, x5) = U62_gga(x1, x2, x3, x5)
U63_gga(x1, x2, x3, x4, x5, x6) = U63_gga(x1, x2, x3, x4, x6)
U64_gga(x1, x2, x3, x4, x5, x6) = U64_gga(x1, x2, x3, x4, x6)
U65_gga(x1, x2, x3, x4, x5, x6) = U65_gga(x1, x2, x3, x4, x6)
U17_aga(x1, x2, x3, x4) = U17_aga(x2, x4)
pC_in_gaa(x1, x2, x3) = pC_in_gaa(x1)
U3_gaa(x1, x2, x3, x4) = U3_gaa(x1, x4)
lessB_in_ga(x1, x2) = lessB_in_ga(x1)
lessB_out_ga(x1, x2) = lessB_out_ga(x1)
U2_ga(x1, x2, x3) = U2_ga(x1, x3)
pC_out_gaa(x1, x2, x3) = pC_out_gaa(x1)
U4_gaa(x1, x2, x3, x4) = U4_gaa(x1, x4)
U5_gaa(x1, x2, x3, x4) = U5_gaa(x1, x4)
U18_aga(x1, x2, x3) = U18_aga(x1, x3)
U19_aga(x1, x2, x3, x4) = U19_aga(x2, x4)
U20_aga(x1, x2, x3, x4) = U20_aga(x2, x4)
U21_aga(x1, x2, x3, x4) = U21_aga(x2, x4)
U22_aga(x1, x2, x3, x4) = U22_aga(x2, x4)
U23_aga(x1, x2, x3) = U23_aga(x3)
U24_aga(x1, x2, x3, x4) = U24_aga(x2, x4)
U25_aga(x1, x2, x3, x4) = U25_aga(x2, x4)
U26_aga(x1, x2, x3, x4) = U26_aga(x2, x4)
U27_aga(x1, x2, x3, x4, x5, x6, x7, x8) = U27_aga(x1, x2, x3, x4, x8)
U28_aga(x1, x2, x3, x4, x5) = U28_aga(x2, x3, x5)
U29_aga(x1, x2, x3, x4, x5) = U29_aga(x2, x3, x5)
pG_in_gaga(x1, x2, x3, x4) = pG_in_gaga(x1, x3)
U10_gaga(x1, x2, x3, x4, x5) = U10_gaga(x1, x3, x5)
pG_out_gaga(x1, x2, x3, x4) = pG_out_gaga(x1, x3)
U11_gaga(x1, x2, x3, x4, x5) = U11_gaga(x1, x3, x5)
U12_gaga(x1, x2, x3, x4, x5) = U12_gaga(x1, x3, x5)
U30_aga(x1, x2, x3, x4) = U30_aga(x1, x2, x4)
U31_aga(x1, x2, x3, x4, x5) = U31_aga(x2, x3, x5)
U32_aga(x1, x2, x3, x4, x5) = U32_aga(x2, x3, x5)
U33_aga(x1, x2, x3, x4, x5) = U33_aga(x2, x3, x5)
U34_aga(x1, x2, x3, x4, x5) = U34_aga(x2, x3, x5)
U35_aga(x1, x2, x3, x4) = U35_aga(x2, x4)
U36_aga(x1, x2, x3, x4, x5) = U36_aga(x2, x3, x5)
U37_aga(x1, x2, x3, x4, x5) = U37_aga(x2, x3, x5)
U38_aga(x1, x2, x3, x4, x5) = U38_aga(x2, x3, x5)
U39_aga(x1, x2, x3, x4, x5) = U39_aga(x2, x3, x5)
U40_aga(x1, x2, x3, x4, x5) = U40_aga(x2, x3, x5)
U41_aga(x1, x2, x3, x4, x5) = U41_aga(x2, x3, x5)
U42_aga(x1, x2, x3, x4, x5) = U42_aga(x2, x3, x5)
U43_aga(x1, x2, x3, x4) = U43_aga(x1, x2, x4)
U44_aga(x1, x2, x3, x4, x5) = U44_aga(x2, x3, x5)
U45_aga(x1, x2, x3, x4, x5) = U45_aga(x2, x3, x5)
U46_aga(x1, x2, x3, x4, x5) = U46_aga(x2, x3, x5)
U47_aga(x1, x2, x3, x4, x5) = U47_aga(x2, x3, x5)
U48_aga(x1, x2, x3, x4) = U48_aga(x2, x4)
U49_aga(x1, x2, x3, x4, x5) = U49_aga(x2, x3, x5)
U50_aga(x1, x2, x3, x4, x5) = U50_aga(x2, x3, x5)
U51_aga(x1, x2, x3, x4, x5) = U51_aga(x2, x3, x5)
U52_aga(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U52_aga(x1, x2, x3, x4, x5, x9)
U53_aga(x1, x2, x3, x4, x5, x6) = U53_aga(x2, x3, x4, x6)
U54_aga(x1, x2, x3, x4, x5, x6) = U54_aga(x2, x3, x4, x6)
U55_aga(x1, x2, x3, x4, x5, x6) = U55_aga(x2, x3, x4, x6)
U56_aga(x1, x2, x3, x4, x5, x6) = U56_aga(x2, x3, x4, x6)
pH_in_gaga(x1, x2, x3, x4) = pH_in_gaga(x1, x3)
U13_gaga(x1, x2, x3, x4, x5) = U13_gaga(x1, x3, x5)
pH_out_gaga(x1, x2, x3, x4) = pH_out_gaga(x1, x3)
U14_gaga(x1, x2, x3, x4, x5) = U14_gaga(x1, x3, x5)
U15_gaga(x1, x2, x3, x4, x5) = U15_gaga(x1, x3, x5)
U57_aga(x1, x2, x3, x4, x5) = U57_aga(x1, x2, x3, x5)
U58_aga(x1, x2, x3, x4, x5, x6) = U58_aga(x2, x3, x4, x6)
U59_aga(x1, x2, x3, x4, x5, x6) = U59_aga(x2, x3, x4, x6)
U60_aga(x1, x2, x3, x4, x5, x6) = U60_aga(x2, x3, x4, x6)
U61_aga(x1, x2, x3, x4, x5, x6) = U61_aga(x2, x3, x4, x6)
U62_aga(x1, x2, x3, x4, x5) = U62_aga(x2, x3, x5)
U63_aga(x1, x2, x3, x4, x5, x6) = U63_aga(x2, x3, x4, x6)
U64_aga(x1, x2, x3, x4, x5, x6) = U64_aga(x2, x3, x4, x6)
U65_aga(x1, x2, x3, x4, x5, x6) = U65_aga(x2, x3, x4, x6)
DELETED_IN_AGA(x1, x2, x3) = DELETED_IN_AGA(x2)
U16_AGA(x1, x2, x3, x4) = U16_AGA(x2, x4)
PF_IN_AGA(x1, x2, x3) = PF_IN_AGA(x2)
U7_AGA(x1, x2, x3, x4) = U7_AGA(x2, x4)
LESSA_IN_AG(x1, x2) = LESSA_IN_AG(x2)
U1_AG(x1, x2, x3) = U1_AG(x2, x3)
U8_AGA(x1, x2, x3, x4) = U8_AGA(x2, x4)
U9_AGA(x1, x2, x3, x4) = U9_AGA(x1, x2, x4)
DELETED_IN_GGA(x1, x2, x3) = DELETED_IN_GGA(x1, x2)
U16_GGA(x1, x2, x3, x4) = U16_GGA(x1, x2, x4)
PF_IN_GGA(x1, x2, x3) = PF_IN_GGA(x1, x2)
U7_GGA(x1, x2, x3, x4) = U7_GGA(x1, x2, x4)
LESSA_IN_GG(x1, x2) = LESSA_IN_GG(x1, x2)
U1_GG(x1, x2, x3) = U1_GG(x1, x2, x3)
U8_GGA(x1, x2, x3, x4) = U8_GGA(x1, x2, x4)
U9_GGA(x1, x2, x3, x4) = U9_GGA(x1, x2, x4)
U17_GGA(x1, x2, x3, x4) = U17_GGA(x1, x2, x4)
PC_IN_GGA(x1, x2, x3) = PC_IN_GGA(x1, x2)
U3_GGA(x1, x2, x3, x4) = U3_GGA(x1, x2, x4)
LESSB_IN_GG(x1, x2) = LESSB_IN_GG(x1, x2)
U2_GG(x1, x2, x3) = U2_GG(x1, x2, x3)
U4_GGA(x1, x2, x3, x4) = U4_GGA(x1, x2, x4)
U5_GGA(x1, x2, x3, x4) = U5_GGA(x1, x2, x4)
U18_GGA(x1, x2, x3) = U18_GGA(x1, x3)
U19_GGA(x1, x2, x3, x4) = U19_GGA(x1, x2, x4)
U20_GGA(x1, x2, x3, x4) = U20_GGA(x1, x2, x4)
U21_GGA(x1, x2, x3, x4) = U21_GGA(x1, x2, x4)
U22_GGA(x1, x2, x3, x4) = U22_GGA(x1, x2, x4)
U23_GGA(x1, x2, x3) = U23_GGA(x1, x3)
U24_GGA(x1, x2, x3, x4) = U24_GGA(x1, x2, x4)
U25_GGA(x1, x2, x3, x4) = U25_GGA(x1, x2, x4)
U26_GGA(x1, x2, x3, x4) = U26_GGA(x1, x2, x4)
U27_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U27_GGA(x1, x2, x3, x4, x8)
DELMINE_IN_GAA(x1, x2, x3) = DELMINE_IN_GAA(x1)
U6_GAA(x1, x2, x3, x4, x5, x6, x7) = U6_GAA(x1, x2, x3, x7)
U28_GGA(x1, x2, x3, x4, x5) = U28_GGA(x1, x2, x3, x5)
U29_GGA(x1, x2, x3, x4, x5) = U29_GGA(x1, x2, x3, x5)
PG_IN_GGGA(x1, x2, x3, x4) = PG_IN_GGGA(x1, x2, x3)
U10_GGGA(x1, x2, x3, x4, x5) = U10_GGGA(x1, x2, x3, x5)
U11_GGGA(x1, x2, x3, x4, x5) = U11_GGGA(x1, x2, x3, x5)
U12_GGGA(x1, x2, x3, x4, x5) = U12_GGGA(x1, x2, x3, x5)
U30_GGA(x1, x2, x3, x4) = U30_GGA(x1, x2, x4)
U31_GGA(x1, x2, x3, x4, x5) = U31_GGA(x1, x2, x3, x5)
U32_GGA(x1, x2, x3, x4, x5) = U32_GGA(x1, x2, x3, x5)
U33_GGA(x1, x2, x3, x4, x5) = U33_GGA(x1, x2, x3, x5)
U34_GGA(x1, x2, x3, x4, x5) = U34_GGA(x1, x2, x3, x5)
U35_GGA(x1, x2, x3, x4) = U35_GGA(x1, x2, x4)
U36_GGA(x1, x2, x3, x4, x5) = U36_GGA(x1, x2, x3, x5)
U37_GGA(x1, x2, x3, x4, x5) = U37_GGA(x1, x2, x3, x5)
U38_GGA(x1, x2, x3, x4, x5) = U38_GGA(x1, x2, x3, x5)
U39_GGA(x1, x2, x3, x4, x5) = U39_GGA(x1, x2, x3, x5)
U40_GGA(x1, x2, x3, x4, x5) = U40_GGA(x1, x2, x3, x5)
U41_GGA(x1, x2, x3, x4, x5) = U41_GGA(x1, x2, x3, x5)
U42_GGA(x1, x2, x3, x4, x5) = U42_GGA(x1, x2, x3, x5)
U43_GGA(x1, x2, x3, x4) = U43_GGA(x1, x2, x4)
U44_GGA(x1, x2, x3, x4, x5) = U44_GGA(x1, x2, x3, x5)
U45_GGA(x1, x2, x3, x4, x5) = U45_GGA(x1, x2, x3, x5)
U46_GGA(x1, x2, x3, x4, x5) = U46_GGA(x1, x2, x3, x5)
U47_GGA(x1, x2, x3, x4, x5) = U47_GGA(x1, x2, x3, x5)
U48_GGA(x1, x2, x3, x4) = U48_GGA(x1, x2, x4)
U49_GGA(x1, x2, x3, x4, x5) = U49_GGA(x1, x2, x3, x5)
U50_GGA(x1, x2, x3, x4, x5) = U50_GGA(x1, x2, x3, x5)
U51_GGA(x1, x2, x3, x4, x5) = U51_GGA(x1, x2, x3, x5)
U52_GGA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U52_GGA(x1, x2, x3, x4, x5, x9)
U53_GGA(x1, x2, x3, x4, x5, x6) = U53_GGA(x1, x2, x3, x4, x6)
U54_GGA(x1, x2, x3, x4, x5, x6) = U54_GGA(x1, x2, x3, x4, x6)
U55_GGA(x1, x2, x3, x4, x5, x6) = U55_GGA(x1, x2, x3, x4, x6)
U56_GGA(x1, x2, x3, x4, x5, x6) = U56_GGA(x1, x2, x3, x4, x6)
PH_IN_GGGA(x1, x2, x3, x4) = PH_IN_GGGA(x1, x2, x3)
U13_GGGA(x1, x2, x3, x4, x5) = U13_GGGA(x1, x2, x3, x5)
U14_GGGA(x1, x2, x3, x4, x5) = U14_GGGA(x1, x2, x3, x5)
U15_GGGA(x1, x2, x3, x4, x5) = U15_GGGA(x1, x2, x3, x5)
U57_GGA(x1, x2, x3, x4, x5) = U57_GGA(x1, x2, x3, x5)
U58_GGA(x1, x2, x3, x4, x5, x6) = U58_GGA(x1, x2, x3, x4, x6)
U59_GGA(x1, x2, x3, x4, x5, x6) = U59_GGA(x1, x2, x3, x4, x6)
U60_GGA(x1, x2, x3, x4, x5, x6) = U60_GGA(x1, x2, x3, x4, x6)
U61_GGA(x1, x2, x3, x4, x5, x6) = U61_GGA(x1, x2, x3, x4, x6)
U62_GGA(x1, x2, x3, x4, x5) = U62_GGA(x1, x2, x3, x5)
U63_GGA(x1, x2, x3, x4, x5, x6) = U63_GGA(x1, x2, x3, x4, x6)
U64_GGA(x1, x2, x3, x4, x5, x6) = U64_GGA(x1, x2, x3, x4, x6)
U65_GGA(x1, x2, x3, x4, x5, x6) = U65_GGA(x1, x2, x3, x4, x6)
U17_AGA(x1, x2, x3, x4) = U17_AGA(x2, x4)
PC_IN_GAA(x1, x2, x3) = PC_IN_GAA(x1)
U3_GAA(x1, x2, x3, x4) = U3_GAA(x1, x4)
LESSB_IN_GA(x1, x2) = LESSB_IN_GA(x1)
U2_GA(x1, x2, x3) = U2_GA(x1, x3)
U4_GAA(x1, x2, x3, x4) = U4_GAA(x1, x4)
U5_GAA(x1, x2, x3, x4) = U5_GAA(x1, x4)
U18_AGA(x1, x2, x3) = U18_AGA(x1, x3)
U19_AGA(x1, x2, x3, x4) = U19_AGA(x2, x4)
U20_AGA(x1, x2, x3, x4) = U20_AGA(x2, x4)
U21_AGA(x1, x2, x3, x4) = U21_AGA(x2, x4)
U22_AGA(x1, x2, x3, x4) = U22_AGA(x2, x4)
U23_AGA(x1, x2, x3) = U23_AGA(x3)
U24_AGA(x1, x2, x3, x4) = U24_AGA(x2, x4)
U25_AGA(x1, x2, x3, x4) = U25_AGA(x2, x4)
U26_AGA(x1, x2, x3, x4) = U26_AGA(x2, x4)
U27_AGA(x1, x2, x3, x4, x5, x6, x7, x8) = U27_AGA(x1, x2, x3, x4, x8)
U28_AGA(x1, x2, x3, x4, x5) = U28_AGA(x2, x3, x5)
U29_AGA(x1, x2, x3, x4, x5) = U29_AGA(x2, x3, x5)
PG_IN_GAGA(x1, x2, x3, x4) = PG_IN_GAGA(x1, x3)
U10_GAGA(x1, x2, x3, x4, x5) = U10_GAGA(x1, x3, x5)
U11_GAGA(x1, x2, x3, x4, x5) = U11_GAGA(x1, x3, x5)
U12_GAGA(x1, x2, x3, x4, x5) = U12_GAGA(x1, x3, x5)
U30_AGA(x1, x2, x3, x4) = U30_AGA(x1, x2, x4)
U31_AGA(x1, x2, x3, x4, x5) = U31_AGA(x2, x3, x5)
U32_AGA(x1, x2, x3, x4, x5) = U32_AGA(x2, x3, x5)
U33_AGA(x1, x2, x3, x4, x5) = U33_AGA(x2, x3, x5)
U34_AGA(x1, x2, x3, x4, x5) = U34_AGA(x2, x3, x5)
U35_AGA(x1, x2, x3, x4) = U35_AGA(x2, x4)
U36_AGA(x1, x2, x3, x4, x5) = U36_AGA(x2, x3, x5)
U37_AGA(x1, x2, x3, x4, x5) = U37_AGA(x2, x3, x5)
U38_AGA(x1, x2, x3, x4, x5) = U38_AGA(x2, x3, x5)
U39_AGA(x1, x2, x3, x4, x5) = U39_AGA(x2, x3, x5)
U40_AGA(x1, x2, x3, x4, x5) = U40_AGA(x2, x3, x5)
U41_AGA(x1, x2, x3, x4, x5) = U41_AGA(x2, x3, x5)
U42_AGA(x1, x2, x3, x4, x5) = U42_AGA(x2, x3, x5)
U43_AGA(x1, x2, x3, x4) = U43_AGA(x1, x2, x4)
U44_AGA(x1, x2, x3, x4, x5) = U44_AGA(x2, x3, x5)
U45_AGA(x1, x2, x3, x4, x5) = U45_AGA(x2, x3, x5)
U46_AGA(x1, x2, x3, x4, x5) = U46_AGA(x2, x3, x5)
U47_AGA(x1, x2, x3, x4, x5) = U47_AGA(x2, x3, x5)
U48_AGA(x1, x2, x3, x4) = U48_AGA(x2, x4)
U49_AGA(x1, x2, x3, x4, x5) = U49_AGA(x2, x3, x5)
U50_AGA(x1, x2, x3, x4, x5) = U50_AGA(x2, x3, x5)
U51_AGA(x1, x2, x3, x4, x5) = U51_AGA(x2, x3, x5)
U52_AGA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U52_AGA(x1, x2, x3, x4, x5, x9)
U53_AGA(x1, x2, x3, x4, x5, x6) = U53_AGA(x2, x3, x4, x6)
U54_AGA(x1, x2, x3, x4, x5, x6) = U54_AGA(x2, x3, x4, x6)
U55_AGA(x1, x2, x3, x4, x5, x6) = U55_AGA(x2, x3, x4, x6)
U56_AGA(x1, x2, x3, x4, x5, x6) = U56_AGA(x2, x3, x4, x6)
PH_IN_GAGA(x1, x2, x3, x4) = PH_IN_GAGA(x1, x3)
U13_GAGA(x1, x2, x3, x4, x5) = U13_GAGA(x1, x3, x5)
U14_GAGA(x1, x2, x3, x4, x5) = U14_GAGA(x1, x3, x5)
U15_GAGA(x1, x2, x3, x4, x5) = U15_GAGA(x1, x3, x5)
U57_AGA(x1, x2, x3, x4, x5) = U57_AGA(x1, x2, x3, x5)
U58_AGA(x1, x2, x3, x4, x5, x6) = U58_AGA(x2, x3, x4, x6)
U59_AGA(x1, x2, x3, x4, x5, x6) = U59_AGA(x2, x3, x4, x6)
U60_AGA(x1, x2, x3, x4, x5, x6) = U60_AGA(x2, x3, x4, x6)
U61_AGA(x1, x2, x3, x4, x5, x6) = U61_AGA(x2, x3, x4, x6)
U62_AGA(x1, x2, x3, x4, x5) = U62_AGA(x2, x3, x5)
U63_AGA(x1, x2, x3, x4, x5, x6) = U63_AGA(x2, x3, x4, x6)
U64_AGA(x1, x2, x3, x4, x5, x6) = U64_AGA(x2, x3, x4, x6)
U65_AGA(x1, x2, x3, x4, x5, x6) = U65_AGA(x2, x3, x4, 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_AGA(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_AGA(T33, T31, T34, pF_in_aga(T33, T31, T34))
DELETED_IN_AGA(T33, tree(T31, void, void), tree(T31, T34, void)) → PF_IN_AGA(T33, T31, T34)
PF_IN_AGA(T33, T31, T34) → U7_AGA(T33, T31, T34, lessA_in_ag(T33, T31))
PF_IN_AGA(T33, T31, T34) → LESSA_IN_AG(T33, T31)
LESSA_IN_AG(s(T52), s(T51)) → U1_AG(T52, T51, lessA_in_ag(T52, T51))
LESSA_IN_AG(s(T52), s(T51)) → LESSA_IN_AG(T52, T51)
PF_IN_AGA(T37, T31, T38) → U8_AGA(T37, T31, T38, lessA_in_ag(T37, T31))
U8_AGA(T37, T31, T38, lessA_out_ag(T37, T31)) → U9_AGA(T37, T31, T38, deleteD_in_gga(T37, void, T38))
U8_AGA(T37, T31, T38, lessA_out_ag(T37, T31)) → DELETED_IN_GGA(T37, void, T38)
DELETED_IN_GGA(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_GGA(T33, T31, T34, pF_in_gga(T33, T31, T34))
DELETED_IN_GGA(T33, tree(T31, void, void), tree(T31, T34, void)) → PF_IN_GGA(T33, T31, T34)
PF_IN_GGA(T33, T31, T34) → U7_GGA(T33, T31, T34, lessA_in_gg(T33, T31))
PF_IN_GGA(T33, T31, T34) → LESSA_IN_GG(T33, T31)
LESSA_IN_GG(s(T52), s(T51)) → U1_GG(T52, T51, lessA_in_gg(T52, T51))
LESSA_IN_GG(s(T52), s(T51)) → LESSA_IN_GG(T52, T51)
PF_IN_GGA(T37, T31, T38) → U8_GGA(T37, T31, T38, lessA_in_gg(T37, T31))
U8_GGA(T37, T31, T38, lessA_out_gg(T37, T31)) → U9_GGA(T37, T31, T38, deleteD_in_gga(T37, void, T38))
U8_GGA(T37, T31, T38, lessA_out_gg(T37, T31)) → DELETED_IN_GGA(T37, void, T38)
DELETED_IN_GGA(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_GGA(T66, T64, T67, pC_in_gga(T64, T66, T67))
DELETED_IN_GGA(T66, tree(T64, void, void), tree(T64, void, T67)) → PC_IN_GGA(T64, T66, T67)
PC_IN_GGA(T64, T66, T67) → U3_GGA(T64, T66, T67, lessB_in_gg(T64, T66))
PC_IN_GGA(T64, T66, T67) → LESSB_IN_GG(T64, T66)
LESSB_IN_GG(s(T83), s(T85)) → U2_GG(T83, T85, lessB_in_gg(T83, T85))
LESSB_IN_GG(s(T83), s(T85)) → LESSB_IN_GG(T83, T85)
PC_IN_GGA(T64, T70, T71) → U4_GGA(T64, T70, T71, lessB_in_gg(T64, T70))
U4_GGA(T64, T70, T71, lessB_out_gg(T64, T70)) → U5_GGA(T64, T70, T71, deleteD_in_gga(T70, void, T71))
U4_GGA(T64, T70, T71, lessB_out_gg(T64, T70)) → DELETED_IN_GGA(T70, void, T71)
DELETED_IN_GGA(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_GGA(T102, T103, deleteD_in_gga(0, void, T103))
DELETED_IN_GGA(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → DELETED_IN_GGA(0, void, T103)
DELETED_IN_GGA(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_GGA(T114, T113, T115, lessA_in_gg(T114, T113))
DELETED_IN_GGA(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → LESSA_IN_GG(T114, T113)
DELETED_IN_GGA(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_GGA(T118, T113, T119, lessA_in_gg(T118, T113))
U20_GGA(T118, T113, T119, lessA_out_gg(T118, T113)) → U21_GGA(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
U20_GGA(T118, T113, T119, lessA_out_gg(T118, T113)) → DELETED_IN_GGA(s(T118), void, T119)
DELETED_IN_GGA(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_GGA(T135, T133, T136, pC_in_gga(T133, T135, T136))
DELETED_IN_GGA(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_GGA(T153, T152, deleteD_in_gga(s(T153), void, T152))
DELETED_IN_GGA(s(T153), tree(0, void, void), tree(0, void, T152)) → DELETED_IN_GGA(s(T153), void, T152)
DELETED_IN_GGA(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_GGA(T162, T160, T163, lessB_in_gg(T160, T162))
DELETED_IN_GGA(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → LESSB_IN_GG(T160, T162)
DELETED_IN_GGA(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_GGA(T166, T160, T167, lessB_in_gg(T160, T166))
U25_GGA(T166, T160, T167, lessB_out_gg(T160, T166)) → U26_GGA(T166, T160, T167, deleteD_in_gga(s(T166), void, T167))
U25_GGA(T166, T160, T167, lessB_out_gg(T160, T166)) → DELETED_IN_GGA(s(T166), void, T167)
DELETED_IN_GGA(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_GGA(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
DELETED_IN_GGA(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → DELMINE_IN_GAA(T219, T224, T225)
DELMINE_IN_GAA(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → U6_GAA(T252, T253, T254, T258, T259, T257, delminE_in_gaa(T253, T258, T259))
DELMINE_IN_GAA(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → DELMINE_IN_GAA(T253, T258, T259)
DELETED_IN_GGA(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_GGA(T284, T281, T282, T285, pF_in_gga(T284, T281, T285))
DELETED_IN_GGA(T284, tree(T281, void, T282), tree(T281, T285, T282)) → PF_IN_GGA(T284, T281, T285)
DELETED_IN_GGA(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_GGA(T300, T297, T298, T301, pG_in_ggga(T297, T300, T298, T301))
DELETED_IN_GGA(T300, tree(T297, void, T298), tree(T297, void, T301)) → PG_IN_GGGA(T297, T300, T298, T301)
PG_IN_GGGA(T297, T300, T298, T301) → U10_GGGA(T297, T300, T298, T301, lessB_in_gg(T297, T300))
PG_IN_GGGA(T297, T300, T298, T301) → LESSB_IN_GG(T297, T300)
PG_IN_GGGA(T297, T304, T298, T305) → U11_GGGA(T297, T304, T298, T305, lessB_in_gg(T297, T304))
U11_GGGA(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → U12_GGGA(T297, T304, T298, T305, deleteD_in_gga(T304, T298, T305))
U11_GGGA(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → DELETED_IN_GGA(T304, T298, T305)
DELETED_IN_GGA(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_GGA(T328, T320, T329, deleteD_in_gga(0, void, T329))
DELETED_IN_GGA(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → DELETED_IN_GGA(0, void, T329)
DELETED_IN_GGA(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_GGA(T340, T339, T320, T341, lessA_in_gg(T340, T339))
DELETED_IN_GGA(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → LESSA_IN_GG(T340, T339)
DELETED_IN_GGA(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_GGA(T344, T339, T320, T345, lessA_in_gg(T344, T339))
U32_GGA(T344, T339, T320, T345, lessA_out_gg(T344, T339)) → U33_GGA(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
U32_GGA(T344, T339, T320, T345, lessA_out_gg(T344, T339)) → DELETED_IN_GGA(s(T344), void, T345)
DELETED_IN_GGA(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_GGA(T364, T361, T362, T365, pG_in_ggga(T361, T364, T362, T365))
DELETED_IN_GGA(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_GGA(T384, T374, T383, deleteD_in_gga(s(T384), T374, T383))
DELETED_IN_GGA(s(T384), tree(0, void, T374), tree(0, void, T383)) → DELETED_IN_GGA(s(T384), T374, T383)
DELETED_IN_GGA(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_GGA(T395, T393, T374, T396, lessB_in_gg(T393, T395))
DELETED_IN_GGA(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → LESSB_IN_GG(T393, T395)
DELETED_IN_GGA(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_GGA(T399, T393, T374, T400, lessB_in_gg(T393, T399))
U37_GGA(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → U38_GGA(T399, T393, T374, T400, deleteD_in_gga(s(T399), T374, T400))
U37_GGA(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → DELETED_IN_GGA(s(T399), T374, T400)
DELETED_IN_GGA(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_GGA(T443, T440, T441, T444, lessA_in_gg(T443, T440))
DELETED_IN_GGA(T443, tree(T440, T441, void), tree(T440, T444, void)) → LESSA_IN_GG(T443, T440)
DELETED_IN_GGA(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_GGA(T447, T440, T441, T448, lessA_in_gg(T447, T440))
U40_GGA(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → U41_GGA(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
U40_GGA(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → DELETED_IN_GGA(T447, T441, T448)
DELETED_IN_GGA(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_GGA(T469, T466, T467, T470, pC_in_gga(T466, T469, T470))
DELETED_IN_GGA(T469, tree(T466, T467, void), tree(T466, T467, T470)) → PC_IN_GGA(T466, T469, T470)
DELETED_IN_GGA(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_GGA(T487, T479, T488, deleteD_in_gga(0, T479, T488))
DELETED_IN_GGA(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → DELETED_IN_GGA(0, T479, T488)
DELETED_IN_GGA(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_GGA(T501, T500, T479, T502, lessA_in_gg(T501, T500))
DELETED_IN_GGA(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → LESSA_IN_GG(T501, T500)
DELETED_IN_GGA(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_GGA(T505, T500, T479, T506, lessA_in_gg(T505, T500))
U45_GGA(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → U46_GGA(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
U45_GGA(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → DELETED_IN_GGA(s(T505), T479, T506)
DELETED_IN_GGA(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_GGA(T527, T524, T525, T528, pC_in_gga(T524, T527, T528))
DELETED_IN_GGA(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_GGA(T547, T537, T546, deleteD_in_gga(s(T547), void, T546))
DELETED_IN_GGA(s(T547), tree(0, T537, void), tree(0, T537, T546)) → DELETED_IN_GGA(s(T547), void, T546)
DELETED_IN_GGA(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_GGA(T556, T554, T537, T557, lessB_in_gg(T554, T556))
DELETED_IN_GGA(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → LESSB_IN_GG(T554, T556)
DELETED_IN_GGA(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_GGA(T560, T554, T537, T561, lessB_in_gg(T554, T560))
U50_GGA(T560, T554, T537, T561, lessB_out_gg(T554, T560)) → U51_GGA(T560, T554, T537, T561, deleteD_in_gga(s(T560), void, T561))
U50_GGA(T560, T554, T537, T561, lessB_out_gg(T554, T560)) → DELETED_IN_GGA(s(T560), void, T561)
DELETED_IN_GGA(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_GGA(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
DELETED_IN_GGA(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → DELMINE_IN_GAA(T615, T620, T621)
DELETED_IN_GGA(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_GGA(T651, T647, T648, T649, T652, lessA_in_gg(T651, T647))
DELETED_IN_GGA(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → LESSA_IN_GG(T651, T647)
DELETED_IN_GGA(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_GGA(T655, T647, T648, T649, T656, lessA_in_gg(T655, T647))
U54_GGA(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → U55_GGA(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
U54_GGA(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → DELETED_IN_GGA(T655, T648, T656)
DELETED_IN_GGA(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_GGA(T680, T676, T677, T678, T681, pH_in_ggga(T676, T680, T678, T681))
DELETED_IN_GGA(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → PH_IN_GGGA(T676, T680, T678, T681)
PH_IN_GGGA(T676, T680, T678, T681) → U13_GGGA(T676, T680, T678, T681, lessB_in_gg(T676, T680))
PH_IN_GGGA(T676, T680, T678, T681) → LESSB_IN_GG(T676, T680)
PH_IN_GGGA(T676, T684, T678, T685) → U14_GGGA(T676, T684, T678, T685, lessB_in_gg(T676, T684))
U14_GGGA(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → U15_GGGA(T676, T684, T678, T685, deleteD_in_gga(T684, T678, T685))
U14_GGGA(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → DELETED_IN_GGA(T684, T678, T685)
DELETED_IN_GGA(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_GGA(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
DELETED_IN_GGA(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → DELETED_IN_GGA(0, T701, T711)
DELETED_IN_GGA(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_GGA(T724, T723, T701, T702, T725, lessA_in_gg(T724, T723))
DELETED_IN_GGA(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → LESSA_IN_GG(T724, T723)
DELETED_IN_GGA(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_GGA(T728, T723, T701, T702, T729, lessA_in_gg(T728, T723))
U59_GGA(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → U60_GGA(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
U59_GGA(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → DELETED_IN_GGA(s(T728), T701, T729)
DELETED_IN_GGA(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_GGA(T753, T749, T750, T751, T754, pH_in_ggga(T749, T753, T751, T754))
DELETED_IN_GGA(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_GGA(T775, T764, T765, T774, deleteD_in_gga(s(T775), T765, T774))
DELETED_IN_GGA(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → DELETED_IN_GGA(s(T775), T765, T774)
DELETED_IN_GGA(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_GGA(T786, T784, T764, T765, T787, lessB_in_gg(T784, T786))
DELETED_IN_GGA(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → LESSB_IN_GG(T784, T786)
DELETED_IN_GGA(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_GGA(T790, T784, T764, T765, T791, lessB_in_gg(T784, T790))
U64_GGA(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → U65_GGA(T790, T784, T764, T765, T791, deleteD_in_gga(s(T790), T765, T791))
U64_GGA(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → DELETED_IN_GGA(s(T790), T765, T791)
DELETED_IN_AGA(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_AGA(T66, T64, T67, pC_in_gaa(T64, T66, T67))
DELETED_IN_AGA(T66, tree(T64, void, void), tree(T64, void, T67)) → PC_IN_GAA(T64, T66, T67)
PC_IN_GAA(T64, T66, T67) → U3_GAA(T64, T66, T67, lessB_in_ga(T64, T66))
PC_IN_GAA(T64, T66, T67) → LESSB_IN_GA(T64, T66)
LESSB_IN_GA(s(T83), s(T85)) → U2_GA(T83, T85, lessB_in_ga(T83, T85))
LESSB_IN_GA(s(T83), s(T85)) → LESSB_IN_GA(T83, T85)
PC_IN_GAA(T64, T70, T71) → U4_GAA(T64, T70, T71, lessB_in_ga(T64, T70))
U4_GAA(T64, T70, T71, lessB_out_ga(T64, T70)) → U5_GAA(T64, T70, T71, deleteD_in_aga(T70, void, T71))
U4_GAA(T64, T70, T71, lessB_out_ga(T64, T70)) → DELETED_IN_AGA(T70, void, T71)
DELETED_IN_AGA(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_AGA(T102, T103, deleteD_in_gga(0, void, T103))
DELETED_IN_AGA(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → DELETED_IN_GGA(0, void, T103)
DELETED_IN_AGA(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_AGA(T114, T113, T115, lessA_in_ag(T114, T113))
DELETED_IN_AGA(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → LESSA_IN_AG(T114, T113)
DELETED_IN_AGA(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_AGA(T118, T113, T119, lessA_in_ag(T118, T113))
U20_AGA(T118, T113, T119, lessA_out_ag(T118, T113)) → U21_AGA(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
U20_AGA(T118, T113, T119, lessA_out_ag(T118, T113)) → DELETED_IN_GGA(s(T118), void, T119)
DELETED_IN_AGA(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_AGA(T135, T133, T136, pC_in_gaa(T133, T135, T136))
DELETED_IN_AGA(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_AGA(T153, T152, deleteD_in_aga(s(T153), void, T152))
DELETED_IN_AGA(s(T153), tree(0, void, void), tree(0, void, T152)) → DELETED_IN_AGA(s(T153), void, T152)
DELETED_IN_AGA(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_AGA(T162, T160, T163, lessB_in_ga(T160, T162))
DELETED_IN_AGA(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → LESSB_IN_GA(T160, T162)
DELETED_IN_AGA(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_AGA(T166, T160, T167, lessB_in_ga(T160, T166))
U25_AGA(T166, T160, T167, lessB_out_ga(T160, T166)) → U26_AGA(T166, T160, T167, deleteD_in_aga(s(T166), void, T167))
U25_AGA(T166, T160, T167, lessB_out_ga(T160, T166)) → DELETED_IN_AGA(s(T166), void, T167)
DELETED_IN_AGA(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_AGA(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
DELETED_IN_AGA(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → DELMINE_IN_GAA(T219, T224, T225)
DELETED_IN_AGA(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_AGA(T284, T281, T282, T285, pF_in_aga(T284, T281, T285))
DELETED_IN_AGA(T284, tree(T281, void, T282), tree(T281, T285, T282)) → PF_IN_AGA(T284, T281, T285)
DELETED_IN_AGA(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_AGA(T300, T297, T298, T301, pG_in_gaga(T297, T300, T298, T301))
DELETED_IN_AGA(T300, tree(T297, void, T298), tree(T297, void, T301)) → PG_IN_GAGA(T297, T300, T298, T301)
PG_IN_GAGA(T297, T300, T298, T301) → U10_GAGA(T297, T300, T298, T301, lessB_in_ga(T297, T300))
PG_IN_GAGA(T297, T300, T298, T301) → LESSB_IN_GA(T297, T300)
PG_IN_GAGA(T297, T304, T298, T305) → U11_GAGA(T297, T304, T298, T305, lessB_in_ga(T297, T304))
U11_GAGA(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → U12_GAGA(T297, T304, T298, T305, deleteD_in_aga(T304, T298, T305))
U11_GAGA(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → DELETED_IN_AGA(T304, T298, T305)
DELETED_IN_AGA(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_AGA(T328, T320, T329, deleteD_in_gga(0, void, T329))
DELETED_IN_AGA(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → DELETED_IN_GGA(0, void, T329)
DELETED_IN_AGA(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_AGA(T340, T339, T320, T341, lessA_in_ag(T340, T339))
DELETED_IN_AGA(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → LESSA_IN_AG(T340, T339)
DELETED_IN_AGA(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_AGA(T344, T339, T320, T345, lessA_in_ag(T344, T339))
U32_AGA(T344, T339, T320, T345, lessA_out_ag(T344, T339)) → U33_AGA(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
U32_AGA(T344, T339, T320, T345, lessA_out_ag(T344, T339)) → DELETED_IN_GGA(s(T344), void, T345)
DELETED_IN_AGA(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_AGA(T364, T361, T362, T365, pG_in_gaga(T361, T364, T362, T365))
DELETED_IN_AGA(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_AGA(T384, T374, T383, deleteD_in_aga(s(T384), T374, T383))
DELETED_IN_AGA(s(T384), tree(0, void, T374), tree(0, void, T383)) → DELETED_IN_AGA(s(T384), T374, T383)
DELETED_IN_AGA(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_AGA(T395, T393, T374, T396, lessB_in_ga(T393, T395))
DELETED_IN_AGA(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → LESSB_IN_GA(T393, T395)
DELETED_IN_AGA(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_AGA(T399, T393, T374, T400, lessB_in_ga(T393, T399))
U37_AGA(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → U38_AGA(T399, T393, T374, T400, deleteD_in_aga(s(T399), T374, T400))
U37_AGA(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → DELETED_IN_AGA(s(T399), T374, T400)
DELETED_IN_AGA(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_AGA(T443, T440, T441, T444, lessA_in_ag(T443, T440))
DELETED_IN_AGA(T443, tree(T440, T441, void), tree(T440, T444, void)) → LESSA_IN_AG(T443, T440)
DELETED_IN_AGA(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_AGA(T447, T440, T441, T448, lessA_in_ag(T447, T440))
U40_AGA(T447, T440, T441, T448, lessA_out_ag(T447, T440)) → U41_AGA(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
U40_AGA(T447, T440, T441, T448, lessA_out_ag(T447, T440)) → DELETED_IN_GGA(T447, T441, T448)
DELETED_IN_AGA(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_AGA(T469, T466, T467, T470, pC_in_gaa(T466, T469, T470))
DELETED_IN_AGA(T469, tree(T466, T467, void), tree(T466, T467, T470)) → PC_IN_GAA(T466, T469, T470)
DELETED_IN_AGA(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_AGA(T487, T479, T488, deleteD_in_gga(0, T479, T488))
DELETED_IN_AGA(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → DELETED_IN_GGA(0, T479, T488)
DELETED_IN_AGA(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_AGA(T501, T500, T479, T502, lessA_in_ag(T501, T500))
DELETED_IN_AGA(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → LESSA_IN_AG(T501, T500)
DELETED_IN_AGA(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_AGA(T505, T500, T479, T506, lessA_in_ag(T505, T500))
U45_AGA(T505, T500, T479, T506, lessA_out_ag(T505, T500)) → U46_AGA(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
U45_AGA(T505, T500, T479, T506, lessA_out_ag(T505, T500)) → DELETED_IN_GGA(s(T505), T479, T506)
DELETED_IN_AGA(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_AGA(T527, T524, T525, T528, pC_in_gaa(T524, T527, T528))
DELETED_IN_AGA(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_AGA(T547, T537, T546, deleteD_in_aga(s(T547), void, T546))
DELETED_IN_AGA(s(T547), tree(0, T537, void), tree(0, T537, T546)) → DELETED_IN_AGA(s(T547), void, T546)
DELETED_IN_AGA(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_AGA(T556, T554, T537, T557, lessB_in_ga(T554, T556))
DELETED_IN_AGA(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → LESSB_IN_GA(T554, T556)
DELETED_IN_AGA(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_AGA(T560, T554, T537, T561, lessB_in_ga(T554, T560))
U50_AGA(T560, T554, T537, T561, lessB_out_ga(T554, T560)) → U51_AGA(T560, T554, T537, T561, deleteD_in_aga(s(T560), void, T561))
U50_AGA(T560, T554, T537, T561, lessB_out_ga(T554, T560)) → DELETED_IN_AGA(s(T560), void, T561)
DELETED_IN_AGA(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_AGA(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
DELETED_IN_AGA(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → DELMINE_IN_GAA(T615, T620, T621)
DELETED_IN_AGA(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_AGA(T651, T647, T648, T649, T652, lessA_in_ag(T651, T647))
DELETED_IN_AGA(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → LESSA_IN_AG(T651, T647)
DELETED_IN_AGA(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_AGA(T655, T647, T648, T649, T656, lessA_in_ag(T655, T647))
U54_AGA(T655, T647, T648, T649, T656, lessA_out_ag(T655, T647)) → U55_AGA(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
U54_AGA(T655, T647, T648, T649, T656, lessA_out_ag(T655, T647)) → DELETED_IN_GGA(T655, T648, T656)
DELETED_IN_AGA(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_AGA(T680, T676, T677, T678, T681, pH_in_gaga(T676, T680, T678, T681))
DELETED_IN_AGA(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → PH_IN_GAGA(T676, T680, T678, T681)
PH_IN_GAGA(T676, T680, T678, T681) → U13_GAGA(T676, T680, T678, T681, lessB_in_ga(T676, T680))
PH_IN_GAGA(T676, T680, T678, T681) → LESSB_IN_GA(T676, T680)
PH_IN_GAGA(T676, T684, T678, T685) → U14_GAGA(T676, T684, T678, T685, lessB_in_ga(T676, T684))
U14_GAGA(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → U15_GAGA(T676, T684, T678, T685, deleteD_in_aga(T684, T678, T685))
U14_GAGA(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → DELETED_IN_AGA(T684, T678, T685)
DELETED_IN_AGA(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_AGA(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
DELETED_IN_AGA(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → DELETED_IN_GGA(0, T701, T711)
DELETED_IN_AGA(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_AGA(T724, T723, T701, T702, T725, lessA_in_ag(T724, T723))
DELETED_IN_AGA(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → LESSA_IN_AG(T724, T723)
DELETED_IN_AGA(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_AGA(T728, T723, T701, T702, T729, lessA_in_ag(T728, T723))
U59_AGA(T728, T723, T701, T702, T729, lessA_out_ag(T728, T723)) → U60_AGA(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
U59_AGA(T728, T723, T701, T702, T729, lessA_out_ag(T728, T723)) → DELETED_IN_GGA(s(T728), T701, T729)
DELETED_IN_AGA(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_AGA(T753, T749, T750, T751, T754, pH_in_gaga(T749, T753, T751, T754))
DELETED_IN_AGA(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_AGA(T775, T764, T765, T774, deleteD_in_aga(s(T775), T765, T774))
DELETED_IN_AGA(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → DELETED_IN_AGA(s(T775), T765, T774)
DELETED_IN_AGA(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_AGA(T786, T784, T764, T765, T787, lessB_in_ga(T784, T786))
DELETED_IN_AGA(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → LESSB_IN_GA(T784, T786)
DELETED_IN_AGA(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_AGA(T790, T784, T764, T765, T791, lessB_in_ga(T784, T790))
U64_AGA(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → U65_AGA(T790, T784, T764, T765, T791, deleteD_in_aga(s(T790), T765, T791))
U64_AGA(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → DELETED_IN_AGA(s(T790), T765, T791)

The TRS R consists of the following rules:

deleteD_in_aga(T6, tree(T6, void, T7), T7) → deleteD_out_aga(T6, tree(T6, void, T7), T7)
deleteD_in_aga(T9, tree(T9, void, void), void) → deleteD_out_aga(T9, tree(T9, void, void), void)
deleteD_in_aga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_aga(T33, T31, T34, pF_in_aga(T33, T31, T34))
pF_in_aga(T33, T31, T34) → U7_aga(T33, T31, T34, lessA_in_ag(T33, T31))
lessA_in_ag(0, s(T45)) → lessA_out_ag(0, s(T45))
lessA_in_ag(s(T52), s(T51)) → U1_ag(T52, T51, lessA_in_ag(T52, T51))
U1_ag(T52, T51, lessA_out_ag(T52, T51)) → lessA_out_ag(s(T52), s(T51))
U7_aga(T33, T31, T34, lessA_out_ag(T33, T31)) → pF_out_aga(T33, T31, T34)
pF_in_aga(T37, T31, T38) → U8_aga(T37, T31, T38, lessA_in_ag(T37, T31))
U8_aga(T37, T31, T38, lessA_out_ag(T37, T31)) → U9_aga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T6, tree(T6, void, T7), T7) → deleteD_out_gga(T6, tree(T6, void, T7), T7)
deleteD_in_gga(T9, tree(T9, void, void), void) → deleteD_out_gga(T9, tree(T9, void, void), void)
deleteD_in_gga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_gga(T33, T31, T34, pF_in_gga(T33, T31, T34))
pF_in_gga(T33, T31, T34) → U7_gga(T33, T31, T34, lessA_in_gg(T33, T31))
lessA_in_gg(0, s(T45)) → lessA_out_gg(0, s(T45))
lessA_in_gg(s(T52), s(T51)) → U1_gg(T52, T51, lessA_in_gg(T52, T51))
U1_gg(T52, T51, lessA_out_gg(T52, T51)) → lessA_out_gg(s(T52), s(T51))
U7_gga(T33, T31, T34, lessA_out_gg(T33, T31)) → pF_out_gga(T33, T31, T34)
pF_in_gga(T37, T31, T38) → U8_gga(T37, T31, T38, lessA_in_gg(T37, T31))
U8_gga(T37, T31, T38, lessA_out_gg(T37, T31)) → U9_gga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_gga(T66, T64, T67, pC_in_gga(T64, T66, T67))
pC_in_gga(T64, T66, T67) → U3_gga(T64, T66, T67, lessB_in_gg(T64, T66))
lessB_in_gg(0, s(T78)) → lessB_out_gg(0, s(T78))
lessB_in_gg(s(T83), s(T85)) → U2_gg(T83, T85, lessB_in_gg(T83, T85))
U2_gg(T83, T85, lessB_out_gg(T83, T85)) → lessB_out_gg(s(T83), s(T85))
U3_gga(T64, T66, T67, lessB_out_gg(T64, T66)) → pC_out_gga(T64, T66, T67)
pC_in_gga(T64, T70, T71) → U4_gga(T64, T70, T71, lessB_in_gg(T64, T70))
U4_gga(T64, T70, T71, lessB_out_gg(T64, T70)) → U5_gga(T64, T70, T71, deleteD_in_gga(T70, void, T71))
deleteD_in_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_gga(T102, T103, deleteD_in_gga(0, void, T103))
deleteD_in_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_gga(T114, T113, T115, lessA_in_gg(T114, T113))
U19_gga(T114, T113, T115, lessA_out_gg(T114, T113)) → deleteD_out_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_gga(T118, T113, T119, lessA_in_gg(T118, T113))
U20_gga(T118, T113, T119, lessA_out_gg(T118, T113)) → U21_gga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
deleteD_in_gga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_gga(T135, T133, T136, pC_in_gga(T133, T135, T136))
U22_gga(T135, T133, T136, pC_out_gga(T133, T135, T136)) → deleteD_out_gga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_gga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_gga(T153, T152, deleteD_in_gga(s(T153), void, T152))
deleteD_in_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_gga(T162, T160, T163, lessB_in_gg(T160, T162))
U24_gga(T162, T160, T163, lessB_out_gg(T160, T162)) → deleteD_out_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_gga(T166, T160, T167, lessB_in_gg(T160, T166))
U25_gga(T166, T160, T167, lessB_out_gg(T160, T166)) → U26_gga(T166, T160, T167, deleteD_in_gga(s(T166), void, T167))
deleteD_in_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
delminE_in_gaa(tree(T238, void, T239), T238, T239) → delminE_out_gaa(tree(T238, void, T239), T238, T239)
delminE_in_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → U6_gaa(T252, T253, T254, T258, T259, T257, delminE_in_gaa(T253, T258, T259))
U6_gaa(T252, T253, T254, T258, T259, T257, delminE_out_gaa(T253, T258, T259)) → delminE_out_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257))
U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_gga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_gga(T284, T281, T282, T285, pF_in_gga(T284, T281, T285))
U28_gga(T284, T281, T282, T285, pF_out_gga(T284, T281, T285)) → deleteD_out_gga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_gga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_gga(T300, T297, T298, T301, pG_in_ggga(T297, T300, T298, T301))
pG_in_ggga(T297, T300, T298, T301) → U10_ggga(T297, T300, T298, T301, lessB_in_gg(T297, T300))
U10_ggga(T297, T300, T298, T301, lessB_out_gg(T297, T300)) → pG_out_ggga(T297, T300, T298, T301)
pG_in_ggga(T297, T304, T298, T305) → U11_ggga(T297, T304, T298, T305, lessB_in_gg(T297, T304))
U11_ggga(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → U12_ggga(T297, T304, T298, T305, deleteD_in_gga(T304, T298, T305))
deleteD_in_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_gga(T328, T320, T329, deleteD_in_gga(0, void, T329))
deleteD_in_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_gga(T340, T339, T320, T341, lessA_in_gg(T340, T339))
U31_gga(T340, T339, T320, T341, lessA_out_gg(T340, T339)) → deleteD_out_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_gga(T344, T339, T320, T345, lessA_in_gg(T344, T339))
U32_gga(T344, T339, T320, T345, lessA_out_gg(T344, T339)) → U33_gga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
deleteD_in_gga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_gga(T364, T361, T362, T365, pG_in_ggga(T361, T364, T362, T365))
U34_gga(T364, T361, T362, T365, pG_out_ggga(T361, T364, T362, T365)) → deleteD_out_gga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_gga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_gga(T384, T374, T383, deleteD_in_gga(s(T384), T374, T383))
deleteD_in_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_gga(T395, T393, T374, T396, lessB_in_gg(T393, T395))
U36_gga(T395, T393, T374, T396, lessB_out_gg(T393, T395)) → deleteD_out_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_gga(T399, T393, T374, T400, lessB_in_gg(T393, T399))
U37_gga(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → U38_gga(T399, T393, T374, T400, deleteD_in_gga(s(T399), T374, T400))
deleteD_in_gga(T411, tree(T411, T412, void), T412) → deleteD_out_gga(T411, tree(T411, T412, void), T412)
deleteD_in_gga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_gga(T443, T440, T441, T444, lessA_in_gg(T443, T440))
U39_gga(T443, T440, T441, T444, lessA_out_gg(T443, T440)) → deleteD_out_gga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_gga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_gga(T447, T440, T441, T448, lessA_in_gg(T447, T440))
U40_gga(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → U41_gga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
deleteD_in_gga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_gga(T469, T466, T467, T470, pC_in_gga(T466, T469, T470))
U42_gga(T469, T466, T467, T470, pC_out_gga(T466, T469, T470)) → deleteD_out_gga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_gga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
deleteD_in_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_gga(T501, T500, T479, T502, lessA_in_gg(T501, T500))
U44_gga(T501, T500, T479, T502, lessA_out_gg(T501, T500)) → deleteD_out_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_gga(T505, T500, T479, T506, lessA_in_gg(T505, T500))
U45_gga(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → U46_gga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
deleteD_in_gga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_gga(T527, T524, T525, T528, pC_in_gga(T524, T527, T528))
U47_gga(T527, T524, T525, T528, pC_out_gga(T524, T527, T528)) → deleteD_out_gga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_gga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_gga(T547, T537, T546, deleteD_in_gga(s(T547), void, T546))
deleteD_in_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_gga(T556, T554, T537, T557, lessB_in_gg(T554, T556))
U49_gga(T556, T554, T537, T557, lessB_out_gg(T554, T556)) → deleteD_out_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_gga(T560, T554, T537, T561, lessB_in_gg(T554, T560))
U50_gga(T560, T554, T537, T561, lessB_out_gg(T554, T560)) → U51_gga(T560, T554, T537, T561, deleteD_in_gga(s(T560), void, T561))
deleteD_in_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_gga(T651, T647, T648, T649, T652, lessA_in_gg(T651, T647))
U53_gga(T651, T647, T648, T649, T652, lessA_out_gg(T651, T647)) → deleteD_out_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_gga(T655, T647, T648, T649, T656, lessA_in_gg(T655, T647))
U54_gga(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → U55_gga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
deleteD_in_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_gga(T680, T676, T677, T678, T681, pH_in_ggga(T676, T680, T678, T681))
pH_in_ggga(T676, T680, T678, T681) → U13_ggga(T676, T680, T678, T681, lessB_in_gg(T676, T680))
U13_ggga(T676, T680, T678, T681, lessB_out_gg(T676, T680)) → pH_out_ggga(T676, T680, T678, T681)
pH_in_ggga(T676, T684, T678, T685) → U14_ggga(T676, T684, T678, T685, lessB_in_gg(T676, T684))
U14_ggga(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → U15_ggga(T676, T684, T678, T685, deleteD_in_gga(T684, T678, T685))
deleteD_in_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_gga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
deleteD_in_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_gga(T724, T723, T701, T702, T725, lessA_in_gg(T724, T723))
U58_gga(T724, T723, T701, T702, T725, lessA_out_gg(T724, T723)) → deleteD_out_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_gga(T728, T723, T701, T702, T729, lessA_in_gg(T728, T723))
U59_gga(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → U60_gga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
deleteD_in_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_gga(T753, T749, T750, T751, T754, pH_in_ggga(T749, T753, T751, T754))
U61_gga(T753, T749, T750, T751, T754, pH_out_ggga(T749, T753, T751, T754)) → deleteD_out_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_gga(T775, T764, T765, T774, deleteD_in_gga(s(T775), T765, T774))
deleteD_in_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_gga(T786, T784, T764, T765, T787, lessB_in_gg(T784, T786))
U63_gga(T786, T784, T764, T765, T787, lessB_out_gg(T784, T786)) → deleteD_out_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_gga(T790, T784, T764, T765, T791, lessB_in_gg(T784, T790))
U64_gga(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → U65_gga(T790, T784, T764, T765, T791, deleteD_in_gga(s(T790), T765, T791))
U65_gga(T790, T784, T764, T765, T791, deleteD_out_gga(s(T790), T765, T791)) → deleteD_out_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_gga(T775, T764, T765, T774, deleteD_out_gga(s(T775), T765, T774)) → deleteD_out_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U60_gga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
U57_gga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
U15_ggga(T676, T684, T678, T685, deleteD_out_gga(T684, T678, T685)) → pH_out_ggga(T676, T684, T678, T685)
U56_gga(T680, T676, T677, T678, T681, pH_out_ggga(T676, T680, T678, T681)) → deleteD_out_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U55_gga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
U51_gga(T560, T554, T537, T561, deleteD_out_gga(s(T560), void, T561)) → deleteD_out_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_gga(T547, T537, T546, deleteD_out_gga(s(T547), void, T546)) → deleteD_out_gga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U46_gga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
U43_gga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
U41_gga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_gga(T447, tree(T440, T441, void), tree(T440, T448, void))
U38_gga(T399, T393, T374, T400, deleteD_out_gga(s(T399), T374, T400)) → deleteD_out_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_gga(T384, T374, T383, deleteD_out_gga(s(T384), T374, T383)) → deleteD_out_gga(s(T384), tree(0, void, T374), tree(0, void, T383))
U33_gga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
U30_gga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
U12_ggga(T297, T304, T298, T305, deleteD_out_gga(T304, T298, T305)) → pG_out_ggga(T297, T304, T298, T305)
U29_gga(T300, T297, T298, T301, pG_out_ggga(T297, T300, T298, T301)) → deleteD_out_gga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_gga(T166, T160, T167, deleteD_out_gga(s(T166), void, T167)) → deleteD_out_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_gga(T153, T152, deleteD_out_gga(s(T153), void, T152)) → deleteD_out_gga(s(T153), tree(0, void, void), tree(0, void, T152))
U21_gga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
U18_gga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
U5_gga(T64, T70, T71, deleteD_out_gga(T70, void, T71)) → pC_out_gga(T64, T70, T71)
U17_gga(T66, T64, T67, pC_out_gga(T64, T66, T67)) → deleteD_out_gga(T66, tree(T64, void, void), tree(T64, void, T67))
U9_gga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_gga(T37, T31, T38)
U16_gga(T33, T31, T34, pF_out_gga(T33, T31, T34)) → deleteD_out_gga(T33, tree(T31, void, void), tree(T31, T34, void))
U9_aga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_aga(T37, T31, T38)
U16_aga(T33, T31, T34, pF_out_aga(T33, T31, T34)) → deleteD_out_aga(T33, tree(T31, void, void), tree(T31, T34, void))
deleteD_in_aga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_aga(T66, T64, T67, pC_in_gaa(T64, T66, T67))
pC_in_gaa(T64, T66, T67) → U3_gaa(T64, T66, T67, lessB_in_ga(T64, T66))
lessB_in_ga(0, s(T78)) → lessB_out_ga(0, s(T78))
lessB_in_ga(s(T83), s(T85)) → U2_ga(T83, T85, lessB_in_ga(T83, T85))
U2_ga(T83, T85, lessB_out_ga(T83, T85)) → lessB_out_ga(s(T83), s(T85))
U3_gaa(T64, T66, T67, lessB_out_ga(T64, T66)) → pC_out_gaa(T64, T66, T67)
pC_in_gaa(T64, T70, T71) → U4_gaa(T64, T70, T71, lessB_in_ga(T64, T70))
U4_gaa(T64, T70, T71, lessB_out_ga(T64, T70)) → U5_gaa(T64, T70, T71, deleteD_in_aga(T70, void, T71))
deleteD_in_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_aga(T102, T103, deleteD_in_gga(0, void, T103))
U18_aga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
deleteD_in_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_aga(T114, T113, T115, lessA_in_ag(T114, T113))
U19_aga(T114, T113, T115, lessA_out_ag(T114, T113)) → deleteD_out_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_aga(T118, T113, T119, lessA_in_ag(T118, T113))
U20_aga(T118, T113, T119, lessA_out_ag(T118, T113)) → U21_aga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
U21_aga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
deleteD_in_aga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_aga(T135, T133, T136, pC_in_gaa(T133, T135, T136))
U22_aga(T135, T133, T136, pC_out_gaa(T133, T135, T136)) → deleteD_out_aga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_aga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_aga(T153, T152, deleteD_in_aga(s(T153), void, T152))
deleteD_in_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_aga(T162, T160, T163, lessB_in_ga(T160, T162))
U24_aga(T162, T160, T163, lessB_out_ga(T160, T162)) → deleteD_out_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_aga(T166, T160, T167, lessB_in_ga(T160, T166))
U25_aga(T166, T160, T167, lessB_out_ga(T160, T166)) → U26_aga(T166, T160, T167, deleteD_in_aga(s(T166), void, T167))
deleteD_in_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_aga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_aga(T284, T281, T282, T285, pF_in_aga(T284, T281, T285))
U28_aga(T284, T281, T282, T285, pF_out_aga(T284, T281, T285)) → deleteD_out_aga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_aga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_aga(T300, T297, T298, T301, pG_in_gaga(T297, T300, T298, T301))
pG_in_gaga(T297, T300, T298, T301) → U10_gaga(T297, T300, T298, T301, lessB_in_ga(T297, T300))
U10_gaga(T297, T300, T298, T301, lessB_out_ga(T297, T300)) → pG_out_gaga(T297, T300, T298, T301)
pG_in_gaga(T297, T304, T298, T305) → U11_gaga(T297, T304, T298, T305, lessB_in_ga(T297, T304))
U11_gaga(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → U12_gaga(T297, T304, T298, T305, deleteD_in_aga(T304, T298, T305))
deleteD_in_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_aga(T328, T320, T329, deleteD_in_gga(0, void, T329))
U30_aga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
deleteD_in_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_aga(T340, T339, T320, T341, lessA_in_ag(T340, T339))
U31_aga(T340, T339, T320, T341, lessA_out_ag(T340, T339)) → deleteD_out_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_aga(T344, T339, T320, T345, lessA_in_ag(T344, T339))
U32_aga(T344, T339, T320, T345, lessA_out_ag(T344, T339)) → U33_aga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
U33_aga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
deleteD_in_aga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_aga(T364, T361, T362, T365, pG_in_gaga(T361, T364, T362, T365))
U34_aga(T364, T361, T362, T365, pG_out_gaga(T361, T364, T362, T365)) → deleteD_out_aga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_aga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_aga(T384, T374, T383, deleteD_in_aga(s(T384), T374, T383))
deleteD_in_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_aga(T395, T393, T374, T396, lessB_in_ga(T393, T395))
U36_aga(T395, T393, T374, T396, lessB_out_ga(T393, T395)) → deleteD_out_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_aga(T399, T393, T374, T400, lessB_in_ga(T393, T399))
U37_aga(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → U38_aga(T399, T393, T374, T400, deleteD_in_aga(s(T399), T374, T400))
deleteD_in_aga(T411, tree(T411, T412, void), T412) → deleteD_out_aga(T411, tree(T411, T412, void), T412)
deleteD_in_aga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_aga(T443, T440, T441, T444, lessA_in_ag(T443, T440))
U39_aga(T443, T440, T441, T444, lessA_out_ag(T443, T440)) → deleteD_out_aga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_aga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_aga(T447, T440, T441, T448, lessA_in_ag(T447, T440))
U40_aga(T447, T440, T441, T448, lessA_out_ag(T447, T440)) → U41_aga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
U41_aga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_aga(T447, tree(T440, T441, void), tree(T440, T448, void))
deleteD_in_aga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_aga(T469, T466, T467, T470, pC_in_gaa(T466, T469, T470))
U42_aga(T469, T466, T467, T470, pC_out_gaa(T466, T469, T470)) → deleteD_out_aga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_aga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
U43_aga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
deleteD_in_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_aga(T501, T500, T479, T502, lessA_in_ag(T501, T500))
U44_aga(T501, T500, T479, T502, lessA_out_ag(T501, T500)) → deleteD_out_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_aga(T505, T500, T479, T506, lessA_in_ag(T505, T500))
U45_aga(T505, T500, T479, T506, lessA_out_ag(T505, T500)) → U46_aga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
U46_aga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
deleteD_in_aga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_aga(T527, T524, T525, T528, pC_in_gaa(T524, T527, T528))
U47_aga(T527, T524, T525, T528, pC_out_gaa(T524, T527, T528)) → deleteD_out_aga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_aga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_aga(T547, T537, T546, deleteD_in_aga(s(T547), void, T546))
deleteD_in_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_aga(T556, T554, T537, T557, lessB_in_ga(T554, T556))
U49_aga(T556, T554, T537, T557, lessB_out_ga(T554, T556)) → deleteD_out_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_aga(T560, T554, T537, T561, lessB_in_ga(T554, T560))
U50_aga(T560, T554, T537, T561, lessB_out_ga(T554, T560)) → U51_aga(T560, T554, T537, T561, deleteD_in_aga(s(T560), void, T561))
deleteD_in_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_aga(T651, T647, T648, T649, T652, lessA_in_ag(T651, T647))
U53_aga(T651, T647, T648, T649, T652, lessA_out_ag(T651, T647)) → deleteD_out_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_aga(T655, T647, T648, T649, T656, lessA_in_ag(T655, T647))
U54_aga(T655, T647, T648, T649, T656, lessA_out_ag(T655, T647)) → U55_aga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
U55_aga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
deleteD_in_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_aga(T680, T676, T677, T678, T681, pH_in_gaga(T676, T680, T678, T681))
pH_in_gaga(T676, T680, T678, T681) → U13_gaga(T676, T680, T678, T681, lessB_in_ga(T676, T680))
U13_gaga(T676, T680, T678, T681, lessB_out_ga(T676, T680)) → pH_out_gaga(T676, T680, T678, T681)
pH_in_gaga(T676, T684, T678, T685) → U14_gaga(T676, T684, T678, T685, lessB_in_ga(T676, T684))
U14_gaga(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → U15_gaga(T676, T684, T678, T685, deleteD_in_aga(T684, T678, T685))
deleteD_in_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_aga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
U57_aga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
deleteD_in_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_aga(T724, T723, T701, T702, T725, lessA_in_ag(T724, T723))
U58_aga(T724, T723, T701, T702, T725, lessA_out_ag(T724, T723)) → deleteD_out_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_aga(T728, T723, T701, T702, T729, lessA_in_ag(T728, T723))
U59_aga(T728, T723, T701, T702, T729, lessA_out_ag(T728, T723)) → U60_aga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
U60_aga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
deleteD_in_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_aga(T753, T749, T750, T751, T754, pH_in_gaga(T749, T753, T751, T754))
U61_aga(T753, T749, T750, T751, T754, pH_out_gaga(T749, T753, T751, T754)) → deleteD_out_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_aga(T775, T764, T765, T774, deleteD_in_aga(s(T775), T765, T774))
deleteD_in_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_aga(T786, T784, T764, T765, T787, lessB_in_ga(T784, T786))
U63_aga(T786, T784, T764, T765, T787, lessB_out_ga(T784, T786)) → deleteD_out_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_aga(T790, T784, T764, T765, T791, lessB_in_ga(T784, T790))
U64_aga(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → U65_aga(T790, T784, T764, T765, T791, deleteD_in_aga(s(T790), T765, T791))
U65_aga(T790, T784, T764, T765, T791, deleteD_out_aga(s(T790), T765, T791)) → deleteD_out_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_aga(T775, T764, T765, T774, deleteD_out_aga(s(T775), T765, T774)) → deleteD_out_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U15_gaga(T676, T684, T678, T685, deleteD_out_aga(T684, T678, T685)) → pH_out_gaga(T676, T684, T678, T685)
U56_aga(T680, T676, T677, T678, T681, pH_out_gaga(T676, T680, T678, T681)) → deleteD_out_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U51_aga(T560, T554, T537, T561, deleteD_out_aga(s(T560), void, T561)) → deleteD_out_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_aga(T547, T537, T546, deleteD_out_aga(s(T547), void, T546)) → deleteD_out_aga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U38_aga(T399, T393, T374, T400, deleteD_out_aga(s(T399), T374, T400)) → deleteD_out_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_aga(T384, T374, T383, deleteD_out_aga(s(T384), T374, T383)) → deleteD_out_aga(s(T384), tree(0, void, T374), tree(0, void, T383))
U12_gaga(T297, T304, T298, T305, deleteD_out_aga(T304, T298, T305)) → pG_out_gaga(T297, T304, T298, T305)
U29_aga(T300, T297, T298, T301, pG_out_gaga(T297, T300, T298, T301)) → deleteD_out_aga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_aga(T166, T160, T167, deleteD_out_aga(s(T166), void, T167)) → deleteD_out_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_aga(T153, T152, deleteD_out_aga(s(T153), void, T152)) → deleteD_out_aga(s(T153), tree(0, void, void), tree(0, void, T152))
U5_gaa(T64, T70, T71, deleteD_out_aga(T70, void, T71)) → pC_out_gaa(T64, T70, T71)
U17_aga(T66, T64, T67, pC_out_gaa(T64, T66, T67)) → deleteD_out_aga(T66, tree(T64, void, void), tree(T64, void, T67))

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 7 SCCs with 183 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

LESSB_IN_GA(s(T83), s(T85)) → LESSB_IN_GA(T83, T85)

The TRS R consists of the following rules:

deleteD_in_aga(T6, tree(T6, void, T7), T7) → deleteD_out_aga(T6, tree(T6, void, T7), T7)
deleteD_in_aga(T9, tree(T9, void, void), void) → deleteD_out_aga(T9, tree(T9, void, void), void)
deleteD_in_aga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_aga(T33, T31, T34, pF_in_aga(T33, T31, T34))
pF_in_aga(T33, T31, T34) → U7_aga(T33, T31, T34, lessA_in_ag(T33, T31))
lessA_in_ag(0, s(T45)) → lessA_out_ag(0, s(T45))
lessA_in_ag(s(T52), s(T51)) → U1_ag(T52, T51, lessA_in_ag(T52, T51))
U1_ag(T52, T51, lessA_out_ag(T52, T51)) → lessA_out_ag(s(T52), s(T51))
U7_aga(T33, T31, T34, lessA_out_ag(T33, T31)) → pF_out_aga(T33, T31, T34)
pF_in_aga(T37, T31, T38) → U8_aga(T37, T31, T38, lessA_in_ag(T37, T31))
U8_aga(T37, T31, T38, lessA_out_ag(T37, T31)) → U9_aga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T6, tree(T6, void, T7), T7) → deleteD_out_gga(T6, tree(T6, void, T7), T7)
deleteD_in_gga(T9, tree(T9, void, void), void) → deleteD_out_gga(T9, tree(T9, void, void), void)
deleteD_in_gga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_gga(T33, T31, T34, pF_in_gga(T33, T31, T34))
pF_in_gga(T33, T31, T34) → U7_gga(T33, T31, T34, lessA_in_gg(T33, T31))
lessA_in_gg(0, s(T45)) → lessA_out_gg(0, s(T45))
lessA_in_gg(s(T52), s(T51)) → U1_gg(T52, T51, lessA_in_gg(T52, T51))
U1_gg(T52, T51, lessA_out_gg(T52, T51)) → lessA_out_gg(s(T52), s(T51))
U7_gga(T33, T31, T34, lessA_out_gg(T33, T31)) → pF_out_gga(T33, T31, T34)
pF_in_gga(T37, T31, T38) → U8_gga(T37, T31, T38, lessA_in_gg(T37, T31))
U8_gga(T37, T31, T38, lessA_out_gg(T37, T31)) → U9_gga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_gga(T66, T64, T67, pC_in_gga(T64, T66, T67))
pC_in_gga(T64, T66, T67) → U3_gga(T64, T66, T67, lessB_in_gg(T64, T66))
lessB_in_gg(0, s(T78)) → lessB_out_gg(0, s(T78))
lessB_in_gg(s(T83), s(T85)) → U2_gg(T83, T85, lessB_in_gg(T83, T85))
U2_gg(T83, T85, lessB_out_gg(T83, T85)) → lessB_out_gg(s(T83), s(T85))
U3_gga(T64, T66, T67, lessB_out_gg(T64, T66)) → pC_out_gga(T64, T66, T67)
pC_in_gga(T64, T70, T71) → U4_gga(T64, T70, T71, lessB_in_gg(T64, T70))
U4_gga(T64, T70, T71, lessB_out_gg(T64, T70)) → U5_gga(T64, T70, T71, deleteD_in_gga(T70, void, T71))
deleteD_in_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_gga(T102, T103, deleteD_in_gga(0, void, T103))
deleteD_in_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_gga(T114, T113, T115, lessA_in_gg(T114, T113))
U19_gga(T114, T113, T115, lessA_out_gg(T114, T113)) → deleteD_out_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_gga(T118, T113, T119, lessA_in_gg(T118, T113))
U20_gga(T118, T113, T119, lessA_out_gg(T118, T113)) → U21_gga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
deleteD_in_gga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_gga(T135, T133, T136, pC_in_gga(T133, T135, T136))
U22_gga(T135, T133, T136, pC_out_gga(T133, T135, T136)) → deleteD_out_gga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_gga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_gga(T153, T152, deleteD_in_gga(s(T153), void, T152))
deleteD_in_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_gga(T162, T160, T163, lessB_in_gg(T160, T162))
U24_gga(T162, T160, T163, lessB_out_gg(T160, T162)) → deleteD_out_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_gga(T166, T160, T167, lessB_in_gg(T160, T166))
U25_gga(T166, T160, T167, lessB_out_gg(T160, T166)) → U26_gga(T166, T160, T167, deleteD_in_gga(s(T166), void, T167))
deleteD_in_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
delminE_in_gaa(tree(T238, void, T239), T238, T239) → delminE_out_gaa(tree(T238, void, T239), T238, T239)
delminE_in_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → U6_gaa(T252, T253, T254, T258, T259, T257, delminE_in_gaa(T253, T258, T259))
U6_gaa(T252, T253, T254, T258, T259, T257, delminE_out_gaa(T253, T258, T259)) → delminE_out_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257))
U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_gga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_gga(T284, T281, T282, T285, pF_in_gga(T284, T281, T285))
U28_gga(T284, T281, T282, T285, pF_out_gga(T284, T281, T285)) → deleteD_out_gga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_gga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_gga(T300, T297, T298, T301, pG_in_ggga(T297, T300, T298, T301))
pG_in_ggga(T297, T300, T298, T301) → U10_ggga(T297, T300, T298, T301, lessB_in_gg(T297, T300))
U10_ggga(T297, T300, T298, T301, lessB_out_gg(T297, T300)) → pG_out_ggga(T297, T300, T298, T301)
pG_in_ggga(T297, T304, T298, T305) → U11_ggga(T297, T304, T298, T305, lessB_in_gg(T297, T304))
U11_ggga(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → U12_ggga(T297, T304, T298, T305, deleteD_in_gga(T304, T298, T305))
deleteD_in_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_gga(T328, T320, T329, deleteD_in_gga(0, void, T329))
deleteD_in_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_gga(T340, T339, T320, T341, lessA_in_gg(T340, T339))
U31_gga(T340, T339, T320, T341, lessA_out_gg(T340, T339)) → deleteD_out_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_gga(T344, T339, T320, T345, lessA_in_gg(T344, T339))
U32_gga(T344, T339, T320, T345, lessA_out_gg(T344, T339)) → U33_gga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
deleteD_in_gga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_gga(T364, T361, T362, T365, pG_in_ggga(T361, T364, T362, T365))
U34_gga(T364, T361, T362, T365, pG_out_ggga(T361, T364, T362, T365)) → deleteD_out_gga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_gga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_gga(T384, T374, T383, deleteD_in_gga(s(T384), T374, T383))
deleteD_in_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_gga(T395, T393, T374, T396, lessB_in_gg(T393, T395))
U36_gga(T395, T393, T374, T396, lessB_out_gg(T393, T395)) → deleteD_out_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_gga(T399, T393, T374, T400, lessB_in_gg(T393, T399))
U37_gga(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → U38_gga(T399, T393, T374, T400, deleteD_in_gga(s(T399), T374, T400))
deleteD_in_gga(T411, tree(T411, T412, void), T412) → deleteD_out_gga(T411, tree(T411, T412, void), T412)
deleteD_in_gga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_gga(T443, T440, T441, T444, lessA_in_gg(T443, T440))
U39_gga(T443, T440, T441, T444, lessA_out_gg(T443, T440)) → deleteD_out_gga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_gga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_gga(T447, T440, T441, T448, lessA_in_gg(T447, T440))
U40_gga(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → U41_gga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
deleteD_in_gga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_gga(T469, T466, T467, T470, pC_in_gga(T466, T469, T470))
U42_gga(T469, T466, T467, T470, pC_out_gga(T466, T469, T470)) → deleteD_out_gga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_gga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
deleteD_in_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_gga(T501, T500, T479, T502, lessA_in_gg(T501, T500))
U44_gga(T501, T500, T479, T502, lessA_out_gg(T501, T500)) → deleteD_out_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_gga(T505, T500, T479, T506, lessA_in_gg(T505, T500))
U45_gga(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → U46_gga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
deleteD_in_gga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_gga(T527, T524, T525, T528, pC_in_gga(T524, T527, T528))
U47_gga(T527, T524, T525, T528, pC_out_gga(T524, T527, T528)) → deleteD_out_gga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_gga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_gga(T547, T537, T546, deleteD_in_gga(s(T547), void, T546))
deleteD_in_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_gga(T556, T554, T537, T557, lessB_in_gg(T554, T556))
U49_gga(T556, T554, T537, T557, lessB_out_gg(T554, T556)) → deleteD_out_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_gga(T560, T554, T537, T561, lessB_in_gg(T554, T560))
U50_gga(T560, T554, T537, T561, lessB_out_gg(T554, T560)) → U51_gga(T560, T554, T537, T561, deleteD_in_gga(s(T560), void, T561))
deleteD_in_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_gga(T651, T647, T648, T649, T652, lessA_in_gg(T651, T647))
U53_gga(T651, T647, T648, T649, T652, lessA_out_gg(T651, T647)) → deleteD_out_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_gga(T655, T647, T648, T649, T656, lessA_in_gg(T655, T647))
U54_gga(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → U55_gga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
deleteD_in_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_gga(T680, T676, T677, T678, T681, pH_in_ggga(T676, T680, T678, T681))
pH_in_ggga(T676, T680, T678, T681) → U13_ggga(T676, T680, T678, T681, lessB_in_gg(T676, T680))
U13_ggga(T676, T680, T678, T681, lessB_out_gg(T676, T680)) → pH_out_ggga(T676, T680, T678, T681)
pH_in_ggga(T676, T684, T678, T685) → U14_ggga(T676, T684, T678, T685, lessB_in_gg(T676, T684))
U14_ggga(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → U15_ggga(T676, T684, T678, T685, deleteD_in_gga(T684, T678, T685))
deleteD_in_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_gga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
deleteD_in_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_gga(T724, T723, T701, T702, T725, lessA_in_gg(T724, T723))
U58_gga(T724, T723, T701, T702, T725, lessA_out_gg(T724, T723)) → deleteD_out_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_gga(T728, T723, T701, T702, T729, lessA_in_gg(T728, T723))
U59_gga(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → U60_gga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
deleteD_in_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_gga(T753, T749, T750, T751, T754, pH_in_ggga(T749, T753, T751, T754))
U61_gga(T753, T749, T750, T751, T754, pH_out_ggga(T749, T753, T751, T754)) → deleteD_out_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_gga(T775, T764, T765, T774, deleteD_in_gga(s(T775), T765, T774))
deleteD_in_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_gga(T786, T784, T764, T765, T787, lessB_in_gg(T784, T786))
U63_gga(T786, T784, T764, T765, T787, lessB_out_gg(T784, T786)) → deleteD_out_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_gga(T790, T784, T764, T765, T791, lessB_in_gg(T784, T790))
U64_gga(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → U65_gga(T790, T784, T764, T765, T791, deleteD_in_gga(s(T790), T765, T791))
U65_gga(T790, T784, T764, T765, T791, deleteD_out_gga(s(T790), T765, T791)) → deleteD_out_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_gga(T775, T764, T765, T774, deleteD_out_gga(s(T775), T765, T774)) → deleteD_out_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U60_gga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
U57_gga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
U15_ggga(T676, T684, T678, T685, deleteD_out_gga(T684, T678, T685)) → pH_out_ggga(T676, T684, T678, T685)
U56_gga(T680, T676, T677, T678, T681, pH_out_ggga(T676, T680, T678, T681)) → deleteD_out_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U55_gga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
U51_gga(T560, T554, T537, T561, deleteD_out_gga(s(T560), void, T561)) → deleteD_out_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_gga(T547, T537, T546, deleteD_out_gga(s(T547), void, T546)) → deleteD_out_gga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U46_gga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
U43_gga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
U41_gga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_gga(T447, tree(T440, T441, void), tree(T440, T448, void))
U38_gga(T399, T393, T374, T400, deleteD_out_gga(s(T399), T374, T400)) → deleteD_out_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_gga(T384, T374, T383, deleteD_out_gga(s(T384), T374, T383)) → deleteD_out_gga(s(T384), tree(0, void, T374), tree(0, void, T383))
U33_gga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
U30_gga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
U12_ggga(T297, T304, T298, T305, deleteD_out_gga(T304, T298, T305)) → pG_out_ggga(T297, T304, T298, T305)
U29_gga(T300, T297, T298, T301, pG_out_ggga(T297, T300, T298, T301)) → deleteD_out_gga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_gga(T166, T160, T167, deleteD_out_gga(s(T166), void, T167)) → deleteD_out_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_gga(T153, T152, deleteD_out_gga(s(T153), void, T152)) → deleteD_out_gga(s(T153), tree(0, void, void), tree(0, void, T152))
U21_gga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
U18_gga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
U5_gga(T64, T70, T71, deleteD_out_gga(T70, void, T71)) → pC_out_gga(T64, T70, T71)
U17_gga(T66, T64, T67, pC_out_gga(T64, T66, T67)) → deleteD_out_gga(T66, tree(T64, void, void), tree(T64, void, T67))
U9_gga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_gga(T37, T31, T38)
U16_gga(T33, T31, T34, pF_out_gga(T33, T31, T34)) → deleteD_out_gga(T33, tree(T31, void, void), tree(T31, T34, void))
U9_aga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_aga(T37, T31, T38)
U16_aga(T33, T31, T34, pF_out_aga(T33, T31, T34)) → deleteD_out_aga(T33, tree(T31, void, void), tree(T31, T34, void))
deleteD_in_aga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_aga(T66, T64, T67, pC_in_gaa(T64, T66, T67))
pC_in_gaa(T64, T66, T67) → U3_gaa(T64, T66, T67, lessB_in_ga(T64, T66))
lessB_in_ga(0, s(T78)) → lessB_out_ga(0, s(T78))
lessB_in_ga(s(T83), s(T85)) → U2_ga(T83, T85, lessB_in_ga(T83, T85))
U2_ga(T83, T85, lessB_out_ga(T83, T85)) → lessB_out_ga(s(T83), s(T85))
U3_gaa(T64, T66, T67, lessB_out_ga(T64, T66)) → pC_out_gaa(T64, T66, T67)
pC_in_gaa(T64, T70, T71) → U4_gaa(T64, T70, T71, lessB_in_ga(T64, T70))
U4_gaa(T64, T70, T71, lessB_out_ga(T64, T70)) → U5_gaa(T64, T70, T71, deleteD_in_aga(T70, void, T71))
deleteD_in_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_aga(T102, T103, deleteD_in_gga(0, void, T103))
U18_aga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
deleteD_in_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_aga(T114, T113, T115, lessA_in_ag(T114, T113))
U19_aga(T114, T113, T115, lessA_out_ag(T114, T113)) → deleteD_out_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_aga(T118, T113, T119, lessA_in_ag(T118, T113))
U20_aga(T118, T113, T119, lessA_out_ag(T118, T113)) → U21_aga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
U21_aga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
deleteD_in_aga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_aga(T135, T133, T136, pC_in_gaa(T133, T135, T136))
U22_aga(T135, T133, T136, pC_out_gaa(T133, T135, T136)) → deleteD_out_aga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_aga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_aga(T153, T152, deleteD_in_aga(s(T153), void, T152))
deleteD_in_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_aga(T162, T160, T163, lessB_in_ga(T160, T162))
U24_aga(T162, T160, T163, lessB_out_ga(T160, T162)) → deleteD_out_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_aga(T166, T160, T167, lessB_in_ga(T160, T166))
U25_aga(T166, T160, T167, lessB_out_ga(T160, T166)) → U26_aga(T166, T160, T167, deleteD_in_aga(s(T166), void, T167))
deleteD_in_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_aga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_aga(T284, T281, T282, T285, pF_in_aga(T284, T281, T285))
U28_aga(T284, T281, T282, T285, pF_out_aga(T284, T281, T285)) → deleteD_out_aga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_aga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_aga(T300, T297, T298, T301, pG_in_gaga(T297, T300, T298, T301))
pG_in_gaga(T297, T300, T298, T301) → U10_gaga(T297, T300, T298, T301, lessB_in_ga(T297, T300))
U10_gaga(T297, T300, T298, T301, lessB_out_ga(T297, T300)) → pG_out_gaga(T297, T300, T298, T301)
pG_in_gaga(T297, T304, T298, T305) → U11_gaga(T297, T304, T298, T305, lessB_in_ga(T297, T304))
U11_gaga(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → U12_gaga(T297, T304, T298, T305, deleteD_in_aga(T304, T298, T305))
deleteD_in_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_aga(T328, T320, T329, deleteD_in_gga(0, void, T329))
U30_aga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
deleteD_in_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_aga(T340, T339, T320, T341, lessA_in_ag(T340, T339))
U31_aga(T340, T339, T320, T341, lessA_out_ag(T340, T339)) → deleteD_out_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_aga(T344, T339, T320, T345, lessA_in_ag(T344, T339))
U32_aga(T344, T339, T320, T345, lessA_out_ag(T344, T339)) → U33_aga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
U33_aga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
deleteD_in_aga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_aga(T364, T361, T362, T365, pG_in_gaga(T361, T364, T362, T365))
U34_aga(T364, T361, T362, T365, pG_out_gaga(T361, T364, T362, T365)) → deleteD_out_aga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_aga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_aga(T384, T374, T383, deleteD_in_aga(s(T384), T374, T383))
deleteD_in_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_aga(T395, T393, T374, T396, lessB_in_ga(T393, T395))
U36_aga(T395, T393, T374, T396, lessB_out_ga(T393, T395)) → deleteD_out_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_aga(T399, T393, T374, T400, lessB_in_ga(T393, T399))
U37_aga(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → U38_aga(T399, T393, T374, T400, deleteD_in_aga(s(T399), T374, T400))
deleteD_in_aga(T411, tree(T411, T412, void), T412) → deleteD_out_aga(T411, tree(T411, T412, void), T412)
deleteD_in_aga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_aga(T443, T440, T441, T444, lessA_in_ag(T443, T440))
U39_aga(T443, T440, T441, T444, lessA_out_ag(T443, T440)) → deleteD_out_aga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_aga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_aga(T447, T440, T441, T448, lessA_in_ag(T447, T440))
U40_aga(T447, T440, T441, T448, lessA_out_ag(T447, T440)) → U41_aga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
U41_aga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_aga(T447, tree(T440, T441, void), tree(T440, T448, void))
deleteD_in_aga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_aga(T469, T466, T467, T470, pC_in_gaa(T466, T469, T470))
U42_aga(T469, T466, T467, T470, pC_out_gaa(T466, T469, T470)) → deleteD_out_aga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_aga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
U43_aga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
deleteD_in_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_aga(T501, T500, T479, T502, lessA_in_ag(T501, T500))
U44_aga(T501, T500, T479, T502, lessA_out_ag(T501, T500)) → deleteD_out_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_aga(T505, T500, T479, T506, lessA_in_ag(T505, T500))
U45_aga(T505, T500, T479, T506, lessA_out_ag(T505, T500)) → U46_aga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
U46_aga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
deleteD_in_aga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_aga(T527, T524, T525, T528, pC_in_gaa(T524, T527, T528))
U47_aga(T527, T524, T525, T528, pC_out_gaa(T524, T527, T528)) → deleteD_out_aga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_aga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_aga(T547, T537, T546, deleteD_in_aga(s(T547), void, T546))
deleteD_in_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_aga(T556, T554, T537, T557, lessB_in_ga(T554, T556))
U49_aga(T556, T554, T537, T557, lessB_out_ga(T554, T556)) → deleteD_out_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_aga(T560, T554, T537, T561, lessB_in_ga(T554, T560))
U50_aga(T560, T554, T537, T561, lessB_out_ga(T554, T560)) → U51_aga(T560, T554, T537, T561, deleteD_in_aga(s(T560), void, T561))
deleteD_in_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_aga(T651, T647, T648, T649, T652, lessA_in_ag(T651, T647))
U53_aga(T651, T647, T648, T649, T652, lessA_out_ag(T651, T647)) → deleteD_out_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_aga(T655, T647, T648, T649, T656, lessA_in_ag(T655, T647))
U54_aga(T655, T647, T648, T649, T656, lessA_out_ag(T655, T647)) → U55_aga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
U55_aga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
deleteD_in_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_aga(T680, T676, T677, T678, T681, pH_in_gaga(T676, T680, T678, T681))
pH_in_gaga(T676, T680, T678, T681) → U13_gaga(T676, T680, T678, T681, lessB_in_ga(T676, T680))
U13_gaga(T676, T680, T678, T681, lessB_out_ga(T676, T680)) → pH_out_gaga(T676, T680, T678, T681)
pH_in_gaga(T676, T684, T678, T685) → U14_gaga(T676, T684, T678, T685, lessB_in_ga(T676, T684))
U14_gaga(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → U15_gaga(T676, T684, T678, T685, deleteD_in_aga(T684, T678, T685))
deleteD_in_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_aga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
U57_aga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
deleteD_in_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_aga(T724, T723, T701, T702, T725, lessA_in_ag(T724, T723))
U58_aga(T724, T723, T701, T702, T725, lessA_out_ag(T724, T723)) → deleteD_out_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_aga(T728, T723, T701, T702, T729, lessA_in_ag(T728, T723))
U59_aga(T728, T723, T701, T702, T729, lessA_out_ag(T728, T723)) → U60_aga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
U60_aga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
deleteD_in_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_aga(T753, T749, T750, T751, T754, pH_in_gaga(T749, T753, T751, T754))
U61_aga(T753, T749, T750, T751, T754, pH_out_gaga(T749, T753, T751, T754)) → deleteD_out_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_aga(T775, T764, T765, T774, deleteD_in_aga(s(T775), T765, T774))
deleteD_in_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_aga(T786, T784, T764, T765, T787, lessB_in_ga(T784, T786))
U63_aga(T786, T784, T764, T765, T787, lessB_out_ga(T784, T786)) → deleteD_out_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_aga(T790, T784, T764, T765, T791, lessB_in_ga(T784, T790))
U64_aga(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → U65_aga(T790, T784, T764, T765, T791, deleteD_in_aga(s(T790), T765, T791))
U65_aga(T790, T784, T764, T765, T791, deleteD_out_aga(s(T790), T765, T791)) → deleteD_out_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_aga(T775, T764, T765, T774, deleteD_out_aga(s(T775), T765, T774)) → deleteD_out_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U15_gaga(T676, T684, T678, T685, deleteD_out_aga(T684, T678, T685)) → pH_out_gaga(T676, T684, T678, T685)
U56_aga(T680, T676, T677, T678, T681, pH_out_gaga(T676, T680, T678, T681)) → deleteD_out_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U51_aga(T560, T554, T537, T561, deleteD_out_aga(s(T560), void, T561)) → deleteD_out_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_aga(T547, T537, T546, deleteD_out_aga(s(T547), void, T546)) → deleteD_out_aga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U38_aga(T399, T393, T374, T400, deleteD_out_aga(s(T399), T374, T400)) → deleteD_out_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_aga(T384, T374, T383, deleteD_out_aga(s(T384), T374, T383)) → deleteD_out_aga(s(T384), tree(0, void, T374), tree(0, void, T383))
U12_gaga(T297, T304, T298, T305, deleteD_out_aga(T304, T298, T305)) → pG_out_gaga(T297, T304, T298, T305)
U29_aga(T300, T297, T298, T301, pG_out_gaga(T297, T300, T298, T301)) → deleteD_out_aga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_aga(T166, T160, T167, deleteD_out_aga(s(T166), void, T167)) → deleteD_out_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_aga(T153, T152, deleteD_out_aga(s(T153), void, T152)) → deleteD_out_aga(s(T153), tree(0, void, void), tree(0, void, T152))
U5_gaa(T64, T70, T71, deleteD_out_aga(T70, void, T71)) → pC_out_gaa(T64, T70, T71)
U17_aga(T66, T64, T67, pC_out_gaa(T64, T66, T67)) → deleteD_out_aga(T66, tree(T64, void, void), tree(T64, void, T67))

(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_GA(s(T83), s(T85)) → LESSB_IN_GA(T83, T85)

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

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

(12) PiDPToQDPProof (SOUND transformation)

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

(13) Obligation:

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

LESSB_IN_GA(s(T83)) → LESSB_IN_GA(T83)

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_GA(s(T83)) → LESSB_IN_GA(T83)
The graph contains the following edges 1 > 1

(15) YES

(16) Obligation:

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

DELMINE_IN_GAA(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → DELMINE_IN_GAA(T253, T258, T259)

The TRS R consists of the following rules:

deleteD_in_aga(T6, tree(T6, void, T7), T7) → deleteD_out_aga(T6, tree(T6, void, T7), T7)
deleteD_in_aga(T9, tree(T9, void, void), void) → deleteD_out_aga(T9, tree(T9, void, void), void)
deleteD_in_aga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_aga(T33, T31, T34, pF_in_aga(T33, T31, T34))
pF_in_aga(T33, T31, T34) → U7_aga(T33, T31, T34, lessA_in_ag(T33, T31))
lessA_in_ag(0, s(T45)) → lessA_out_ag(0, s(T45))
lessA_in_ag(s(T52), s(T51)) → U1_ag(T52, T51, lessA_in_ag(T52, T51))
U1_ag(T52, T51, lessA_out_ag(T52, T51)) → lessA_out_ag(s(T52), s(T51))
U7_aga(T33, T31, T34, lessA_out_ag(T33, T31)) → pF_out_aga(T33, T31, T34)
pF_in_aga(T37, T31, T38) → U8_aga(T37, T31, T38, lessA_in_ag(T37, T31))
U8_aga(T37, T31, T38, lessA_out_ag(T37, T31)) → U9_aga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T6, tree(T6, void, T7), T7) → deleteD_out_gga(T6, tree(T6, void, T7), T7)
deleteD_in_gga(T9, tree(T9, void, void), void) → deleteD_out_gga(T9, tree(T9, void, void), void)
deleteD_in_gga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_gga(T33, T31, T34, pF_in_gga(T33, T31, T34))
pF_in_gga(T33, T31, T34) → U7_gga(T33, T31, T34, lessA_in_gg(T33, T31))
lessA_in_gg(0, s(T45)) → lessA_out_gg(0, s(T45))
lessA_in_gg(s(T52), s(T51)) → U1_gg(T52, T51, lessA_in_gg(T52, T51))
U1_gg(T52, T51, lessA_out_gg(T52, T51)) → lessA_out_gg(s(T52), s(T51))
U7_gga(T33, T31, T34, lessA_out_gg(T33, T31)) → pF_out_gga(T33, T31, T34)
pF_in_gga(T37, T31, T38) → U8_gga(T37, T31, T38, lessA_in_gg(T37, T31))
U8_gga(T37, T31, T38, lessA_out_gg(T37, T31)) → U9_gga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_gga(T66, T64, T67, pC_in_gga(T64, T66, T67))
pC_in_gga(T64, T66, T67) → U3_gga(T64, T66, T67, lessB_in_gg(T64, T66))
lessB_in_gg(0, s(T78)) → lessB_out_gg(0, s(T78))
lessB_in_gg(s(T83), s(T85)) → U2_gg(T83, T85, lessB_in_gg(T83, T85))
U2_gg(T83, T85, lessB_out_gg(T83, T85)) → lessB_out_gg(s(T83), s(T85))
U3_gga(T64, T66, T67, lessB_out_gg(T64, T66)) → pC_out_gga(T64, T66, T67)
pC_in_gga(T64, T70, T71) → U4_gga(T64, T70, T71, lessB_in_gg(T64, T70))
U4_gga(T64, T70, T71, lessB_out_gg(T64, T70)) → U5_gga(T64, T70, T71, deleteD_in_gga(T70, void, T71))
deleteD_in_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_gga(T102, T103, deleteD_in_gga(0, void, T103))
deleteD_in_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_gga(T114, T113, T115, lessA_in_gg(T114, T113))
U19_gga(T114, T113, T115, lessA_out_gg(T114, T113)) → deleteD_out_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_gga(T118, T113, T119, lessA_in_gg(T118, T113))
U20_gga(T118, T113, T119, lessA_out_gg(T118, T113)) → U21_gga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
deleteD_in_gga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_gga(T135, T133, T136, pC_in_gga(T133, T135, T136))
U22_gga(T135, T133, T136, pC_out_gga(T133, T135, T136)) → deleteD_out_gga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_gga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_gga(T153, T152, deleteD_in_gga(s(T153), void, T152))
deleteD_in_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_gga(T162, T160, T163, lessB_in_gg(T160, T162))
U24_gga(T162, T160, T163, lessB_out_gg(T160, T162)) → deleteD_out_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_gga(T166, T160, T167, lessB_in_gg(T160, T166))
U25_gga(T166, T160, T167, lessB_out_gg(T160, T166)) → U26_gga(T166, T160, T167, deleteD_in_gga(s(T166), void, T167))
deleteD_in_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
delminE_in_gaa(tree(T238, void, T239), T238, T239) → delminE_out_gaa(tree(T238, void, T239), T238, T239)
delminE_in_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → U6_gaa(T252, T253, T254, T258, T259, T257, delminE_in_gaa(T253, T258, T259))
U6_gaa(T252, T253, T254, T258, T259, T257, delminE_out_gaa(T253, T258, T259)) → delminE_out_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257))
U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_gga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_gga(T284, T281, T282, T285, pF_in_gga(T284, T281, T285))
U28_gga(T284, T281, T282, T285, pF_out_gga(T284, T281, T285)) → deleteD_out_gga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_gga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_gga(T300, T297, T298, T301, pG_in_ggga(T297, T300, T298, T301))
pG_in_ggga(T297, T300, T298, T301) → U10_ggga(T297, T300, T298, T301, lessB_in_gg(T297, T300))
U10_ggga(T297, T300, T298, T301, lessB_out_gg(T297, T300)) → pG_out_ggga(T297, T300, T298, T301)
pG_in_ggga(T297, T304, T298, T305) → U11_ggga(T297, T304, T298, T305, lessB_in_gg(T297, T304))
U11_ggga(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → U12_ggga(T297, T304, T298, T305, deleteD_in_gga(T304, T298, T305))
deleteD_in_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_gga(T328, T320, T329, deleteD_in_gga(0, void, T329))
deleteD_in_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_gga(T340, T339, T320, T341, lessA_in_gg(T340, T339))
U31_gga(T340, T339, T320, T341, lessA_out_gg(T340, T339)) → deleteD_out_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_gga(T344, T339, T320, T345, lessA_in_gg(T344, T339))
U32_gga(T344, T339, T320, T345, lessA_out_gg(T344, T339)) → U33_gga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
deleteD_in_gga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_gga(T364, T361, T362, T365, pG_in_ggga(T361, T364, T362, T365))
U34_gga(T364, T361, T362, T365, pG_out_ggga(T361, T364, T362, T365)) → deleteD_out_gga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_gga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_gga(T384, T374, T383, deleteD_in_gga(s(T384), T374, T383))
deleteD_in_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_gga(T395, T393, T374, T396, lessB_in_gg(T393, T395))
U36_gga(T395, T393, T374, T396, lessB_out_gg(T393, T395)) → deleteD_out_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_gga(T399, T393, T374, T400, lessB_in_gg(T393, T399))
U37_gga(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → U38_gga(T399, T393, T374, T400, deleteD_in_gga(s(T399), T374, T400))
deleteD_in_gga(T411, tree(T411, T412, void), T412) → deleteD_out_gga(T411, tree(T411, T412, void), T412)
deleteD_in_gga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_gga(T443, T440, T441, T444, lessA_in_gg(T443, T440))
U39_gga(T443, T440, T441, T444, lessA_out_gg(T443, T440)) → deleteD_out_gga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_gga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_gga(T447, T440, T441, T448, lessA_in_gg(T447, T440))
U40_gga(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → U41_gga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
deleteD_in_gga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_gga(T469, T466, T467, T470, pC_in_gga(T466, T469, T470))
U42_gga(T469, T466, T467, T470, pC_out_gga(T466, T469, T470)) → deleteD_out_gga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_gga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
deleteD_in_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_gga(T501, T500, T479, T502, lessA_in_gg(T501, T500))
U44_gga(T501, T500, T479, T502, lessA_out_gg(T501, T500)) → deleteD_out_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_gga(T505, T500, T479, T506, lessA_in_gg(T505, T500))
U45_gga(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → U46_gga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
deleteD_in_gga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_gga(T527, T524, T525, T528, pC_in_gga(T524, T527, T528))
U47_gga(T527, T524, T525, T528, pC_out_gga(T524, T527, T528)) → deleteD_out_gga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_gga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_gga(T547, T537, T546, deleteD_in_gga(s(T547), void, T546))
deleteD_in_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_gga(T556, T554, T537, T557, lessB_in_gg(T554, T556))
U49_gga(T556, T554, T537, T557, lessB_out_gg(T554, T556)) → deleteD_out_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_gga(T560, T554, T537, T561, lessB_in_gg(T554, T560))
U50_gga(T560, T554, T537, T561, lessB_out_gg(T554, T560)) → U51_gga(T560, T554, T537, T561, deleteD_in_gga(s(T560), void, T561))
deleteD_in_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_gga(T651, T647, T648, T649, T652, lessA_in_gg(T651, T647))
U53_gga(T651, T647, T648, T649, T652, lessA_out_gg(T651, T647)) → deleteD_out_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_gga(T655, T647, T648, T649, T656, lessA_in_gg(T655, T647))
U54_gga(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → U55_gga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
deleteD_in_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_gga(T680, T676, T677, T678, T681, pH_in_ggga(T676, T680, T678, T681))
pH_in_ggga(T676, T680, T678, T681) → U13_ggga(T676, T680, T678, T681, lessB_in_gg(T676, T680))
U13_ggga(T676, T680, T678, T681, lessB_out_gg(T676, T680)) → pH_out_ggga(T676, T680, T678, T681)
pH_in_ggga(T676, T684, T678, T685) → U14_ggga(T676, T684, T678, T685, lessB_in_gg(T676, T684))
U14_ggga(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → U15_ggga(T676, T684, T678, T685, deleteD_in_gga(T684, T678, T685))
deleteD_in_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_gga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
deleteD_in_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_gga(T724, T723, T701, T702, T725, lessA_in_gg(T724, T723))
U58_gga(T724, T723, T701, T702, T725, lessA_out_gg(T724, T723)) → deleteD_out_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_gga(T728, T723, T701, T702, T729, lessA_in_gg(T728, T723))
U59_gga(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → U60_gga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
deleteD_in_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_gga(T753, T749, T750, T751, T754, pH_in_ggga(T749, T753, T751, T754))
U61_gga(T753, T749, T750, T751, T754, pH_out_ggga(T749, T753, T751, T754)) → deleteD_out_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_gga(T775, T764, T765, T774, deleteD_in_gga(s(T775), T765, T774))
deleteD_in_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_gga(T786, T784, T764, T765, T787, lessB_in_gg(T784, T786))
U63_gga(T786, T784, T764, T765, T787, lessB_out_gg(T784, T786)) → deleteD_out_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_gga(T790, T784, T764, T765, T791, lessB_in_gg(T784, T790))
U64_gga(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → U65_gga(T790, T784, T764, T765, T791, deleteD_in_gga(s(T790), T765, T791))
U65_gga(T790, T784, T764, T765, T791, deleteD_out_gga(s(T790), T765, T791)) → deleteD_out_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_gga(T775, T764, T765, T774, deleteD_out_gga(s(T775), T765, T774)) → deleteD_out_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U60_gga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
U57_gga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
U15_ggga(T676, T684, T678, T685, deleteD_out_gga(T684, T678, T685)) → pH_out_ggga(T676, T684, T678, T685)
U56_gga(T680, T676, T677, T678, T681, pH_out_ggga(T676, T680, T678, T681)) → deleteD_out_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U55_gga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
U51_gga(T560, T554, T537, T561, deleteD_out_gga(s(T560), void, T561)) → deleteD_out_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_gga(T547, T537, T546, deleteD_out_gga(s(T547), void, T546)) → deleteD_out_gga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U46_gga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
U43_gga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
U41_gga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_gga(T447, tree(T440, T441, void), tree(T440, T448, void))
U38_gga(T399, T393, T374, T400, deleteD_out_gga(s(T399), T374, T400)) → deleteD_out_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_gga(T384, T374, T383, deleteD_out_gga(s(T384), T374, T383)) → deleteD_out_gga(s(T384), tree(0, void, T374), tree(0, void, T383))
U33_gga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
U30_gga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
U12_ggga(T297, T304, T298, T305, deleteD_out_gga(T304, T298, T305)) → pG_out_ggga(T297, T304, T298, T305)
U29_gga(T300, T297, T298, T301, pG_out_ggga(T297, T300, T298, T301)) → deleteD_out_gga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_gga(T166, T160, T167, deleteD_out_gga(s(T166), void, T167)) → deleteD_out_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_gga(T153, T152, deleteD_out_gga(s(T153), void, T152)) → deleteD_out_gga(s(T153), tree(0, void, void), tree(0, void, T152))
U21_gga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
U18_gga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
U5_gga(T64, T70, T71, deleteD_out_gga(T70, void, T71)) → pC_out_gga(T64, T70, T71)
U17_gga(T66, T64, T67, pC_out_gga(T64, T66, T67)) → deleteD_out_gga(T66, tree(T64, void, void), tree(T64, void, T67))
U9_gga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_gga(T37, T31, T38)
U16_gga(T33, T31, T34, pF_out_gga(T33, T31, T34)) → deleteD_out_gga(T33, tree(T31, void, void), tree(T31, T34, void))
U9_aga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_aga(T37, T31, T38)
U16_aga(T33, T31, T34, pF_out_aga(T33, T31, T34)) → deleteD_out_aga(T33, tree(T31, void, void), tree(T31, T34, void))
deleteD_in_aga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_aga(T66, T64, T67, pC_in_gaa(T64, T66, T67))
pC_in_gaa(T64, T66, T67) → U3_gaa(T64, T66, T67, lessB_in_ga(T64, T66))
lessB_in_ga(0, s(T78)) → lessB_out_ga(0, s(T78))
lessB_in_ga(s(T83), s(T85)) → U2_ga(T83, T85, lessB_in_ga(T83, T85))
U2_ga(T83, T85, lessB_out_ga(T83, T85)) → lessB_out_ga(s(T83), s(T85))
U3_gaa(T64, T66, T67, lessB_out_ga(T64, T66)) → pC_out_gaa(T64, T66, T67)
pC_in_gaa(T64, T70, T71) → U4_gaa(T64, T70, T71, lessB_in_ga(T64, T70))
U4_gaa(T64, T70, T71, lessB_out_ga(T64, T70)) → U5_gaa(T64, T70, T71, deleteD_in_aga(T70, void, T71))
deleteD_in_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_aga(T102, T103, deleteD_in_gga(0, void, T103))
U18_aga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
deleteD_in_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_aga(T114, T113, T115, lessA_in_ag(T114, T113))
U19_aga(T114, T113, T115, lessA_out_ag(T114, T113)) → deleteD_out_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_aga(T118, T113, T119, lessA_in_ag(T118, T113))
U20_aga(T118, T113, T119, lessA_out_ag(T118, T113)) → U21_aga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
U21_aga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
deleteD_in_aga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_aga(T135, T133, T136, pC_in_gaa(T133, T135, T136))
U22_aga(T135, T133, T136, pC_out_gaa(T133, T135, T136)) → deleteD_out_aga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_aga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_aga(T153, T152, deleteD_in_aga(s(T153), void, T152))
deleteD_in_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_aga(T162, T160, T163, lessB_in_ga(T160, T162))
U24_aga(T162, T160, T163, lessB_out_ga(T160, T162)) → deleteD_out_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_aga(T166, T160, T167, lessB_in_ga(T160, T166))
U25_aga(T166, T160, T167, lessB_out_ga(T160, T166)) → U26_aga(T166, T160, T167, deleteD_in_aga(s(T166), void, T167))
deleteD_in_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_aga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_aga(T284, T281, T282, T285, pF_in_aga(T284, T281, T285))
U28_aga(T284, T281, T282, T285, pF_out_aga(T284, T281, T285)) → deleteD_out_aga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_aga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_aga(T300, T297, T298, T301, pG_in_gaga(T297, T300, T298, T301))
pG_in_gaga(T297, T300, T298, T301) → U10_gaga(T297, T300, T298, T301, lessB_in_ga(T297, T300))
U10_gaga(T297, T300, T298, T301, lessB_out_ga(T297, T300)) → pG_out_gaga(T297, T300, T298, T301)
pG_in_gaga(T297, T304, T298, T305) → U11_gaga(T297, T304, T298, T305, lessB_in_ga(T297, T304))
U11_gaga(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → U12_gaga(T297, T304, T298, T305, deleteD_in_aga(T304, T298, T305))
deleteD_in_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_aga(T328, T320, T329, deleteD_in_gga(0, void, T329))
U30_aga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
deleteD_in_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_aga(T340, T339, T320, T341, lessA_in_ag(T340, T339))
U31_aga(T340, T339, T320, T341, lessA_out_ag(T340, T339)) → deleteD_out_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_aga(T344, T339, T320, T345, lessA_in_ag(T344, T339))
U32_aga(T344, T339, T320, T345, lessA_out_ag(T344, T339)) → U33_aga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
U33_aga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
deleteD_in_aga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_aga(T364, T361, T362, T365, pG_in_gaga(T361, T364, T362, T365))
U34_aga(T364, T361, T362, T365, pG_out_gaga(T361, T364, T362, T365)) → deleteD_out_aga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_aga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_aga(T384, T374, T383, deleteD_in_aga(s(T384), T374, T383))
deleteD_in_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_aga(T395, T393, T374, T396, lessB_in_ga(T393, T395))
U36_aga(T395, T393, T374, T396, lessB_out_ga(T393, T395)) → deleteD_out_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_aga(T399, T393, T374, T400, lessB_in_ga(T393, T399))
U37_aga(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → U38_aga(T399, T393, T374, T400, deleteD_in_aga(s(T399), T374, T400))
deleteD_in_aga(T411, tree(T411, T412, void), T412) → deleteD_out_aga(T411, tree(T411, T412, void), T412)
deleteD_in_aga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_aga(T443, T440, T441, T444, lessA_in_ag(T443, T440))
U39_aga(T443, T440, T441, T444, lessA_out_ag(T443, T440)) → deleteD_out_aga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_aga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_aga(T447, T440, T441, T448, lessA_in_ag(T447, T440))
U40_aga(T447, T440, T441, T448, lessA_out_ag(T447, T440)) → U41_aga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
U41_aga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_aga(T447, tree(T440, T441, void), tree(T440, T448, void))
deleteD_in_aga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_aga(T469, T466, T467, T470, pC_in_gaa(T466, T469, T470))
U42_aga(T469, T466, T467, T470, pC_out_gaa(T466, T469, T470)) → deleteD_out_aga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_aga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
U43_aga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
deleteD_in_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_aga(T501, T500, T479, T502, lessA_in_ag(T501, T500))
U44_aga(T501, T500, T479, T502, lessA_out_ag(T501, T500)) → deleteD_out_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_aga(T505, T500, T479, T506, lessA_in_ag(T505, T500))
U45_aga(T505, T500, T479, T506, lessA_out_ag(T505, T500)) → U46_aga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
U46_aga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
deleteD_in_aga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_aga(T527, T524, T525, T528, pC_in_gaa(T524, T527, T528))
U47_aga(T527, T524, T525, T528, pC_out_gaa(T524, T527, T528)) → deleteD_out_aga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_aga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_aga(T547, T537, T546, deleteD_in_aga(s(T547), void, T546))
deleteD_in_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_aga(T556, T554, T537, T557, lessB_in_ga(T554, T556))
U49_aga(T556, T554, T537, T557, lessB_out_ga(T554, T556)) → deleteD_out_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_aga(T560, T554, T537, T561, lessB_in_ga(T554, T560))
U50_aga(T560, T554, T537, T561, lessB_out_ga(T554, T560)) → U51_aga(T560, T554, T537, T561, deleteD_in_aga(s(T560), void, T561))
deleteD_in_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_aga(T651, T647, T648, T649, T652, lessA_in_ag(T651, T647))
U53_aga(T651, T647, T648, T649, T652, lessA_out_ag(T651, T647)) → deleteD_out_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_aga(T655, T647, T648, T649, T656, lessA_in_ag(T655, T647))
U54_aga(T655, T647, T648, T649, T656, lessA_out_ag(T655, T647)) → U55_aga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
U55_aga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
deleteD_in_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_aga(T680, T676, T677, T678, T681, pH_in_gaga(T676, T680, T678, T681))
pH_in_gaga(T676, T680, T678, T681) → U13_gaga(T676, T680, T678, T681, lessB_in_ga(T676, T680))
U13_gaga(T676, T680, T678, T681, lessB_out_ga(T676, T680)) → pH_out_gaga(T676, T680, T678, T681)
pH_in_gaga(T676, T684, T678, T685) → U14_gaga(T676, T684, T678, T685, lessB_in_ga(T676, T684))
U14_gaga(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → U15_gaga(T676, T684, T678, T685, deleteD_in_aga(T684, T678, T685))
deleteD_in_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_aga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
U57_aga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
deleteD_in_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_aga(T724, T723, T701, T702, T725, lessA_in_ag(T724, T723))
U58_aga(T724, T723, T701, T702, T725, lessA_out_ag(T724, T723)) → deleteD_out_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_aga(T728, T723, T701, T702, T729, lessA_in_ag(T728, T723))
U59_aga(T728, T723, T701, T702, T729, lessA_out_ag(T728, T723)) → U60_aga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
U60_aga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
deleteD_in_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_aga(T753, T749, T750, T751, T754, pH_in_gaga(T749, T753, T751, T754))
U61_aga(T753, T749, T750, T751, T754, pH_out_gaga(T749, T753, T751, T754)) → deleteD_out_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_aga(T775, T764, T765, T774, deleteD_in_aga(s(T775), T765, T774))
deleteD_in_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_aga(T786, T784, T764, T765, T787, lessB_in_ga(T784, T786))
U63_aga(T786, T784, T764, T765, T787, lessB_out_ga(T784, T786)) → deleteD_out_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_aga(T790, T784, T764, T765, T791, lessB_in_ga(T784, T790))
U64_aga(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → U65_aga(T790, T784, T764, T765, T791, deleteD_in_aga(s(T790), T765, T791))
U65_aga(T790, T784, T764, T765, T791, deleteD_out_aga(s(T790), T765, T791)) → deleteD_out_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_aga(T775, T764, T765, T774, deleteD_out_aga(s(T775), T765, T774)) → deleteD_out_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U15_gaga(T676, T684, T678, T685, deleteD_out_aga(T684, T678, T685)) → pH_out_gaga(T676, T684, T678, T685)
U56_aga(T680, T676, T677, T678, T681, pH_out_gaga(T676, T680, T678, T681)) → deleteD_out_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U51_aga(T560, T554, T537, T561, deleteD_out_aga(s(T560), void, T561)) → deleteD_out_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_aga(T547, T537, T546, deleteD_out_aga(s(T547), void, T546)) → deleteD_out_aga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U38_aga(T399, T393, T374, T400, deleteD_out_aga(s(T399), T374, T400)) → deleteD_out_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_aga(T384, T374, T383, deleteD_out_aga(s(T384), T374, T383)) → deleteD_out_aga(s(T384), tree(0, void, T374), tree(0, void, T383))
U12_gaga(T297, T304, T298, T305, deleteD_out_aga(T304, T298, T305)) → pG_out_gaga(T297, T304, T298, T305)
U29_aga(T300, T297, T298, T301, pG_out_gaga(T297, T300, T298, T301)) → deleteD_out_aga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_aga(T166, T160, T167, deleteD_out_aga(s(T166), void, T167)) → deleteD_out_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_aga(T153, T152, deleteD_out_aga(s(T153), void, T152)) → deleteD_out_aga(s(T153), tree(0, void, void), tree(0, void, T152))
U5_gaa(T64, T70, T71, deleteD_out_aga(T70, void, T71)) → pC_out_gaa(T64, T70, T71)
U17_aga(T66, T64, T67, pC_out_gaa(T64, T66, T67)) → deleteD_out_aga(T66, tree(T64, void, void), tree(T64, void, T67))

(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:

DELMINE_IN_GAA(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → DELMINE_IN_GAA(T253, T258, T259)

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

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:

DELMINE_IN_GAA(tree(T252, T253, T254)) → DELMINE_IN_GAA(T253)

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:

DELMINE_IN_GAA(tree(T252, T253, T254)) → DELMINE_IN_GAA(T253)
The graph contains the following edges 1 > 1

(22) YES

(23) Obligation:

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

LESSB_IN_GG(s(T83), s(T85)) → LESSB_IN_GG(T83, T85)

The TRS R consists of the following rules:

deleteD_in_aga(T6, tree(T6, void, T7), T7) → deleteD_out_aga(T6, tree(T6, void, T7), T7)
deleteD_in_aga(T9, tree(T9, void, void), void) → deleteD_out_aga(T9, tree(T9, void, void), void)
deleteD_in_aga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_aga(T33, T31, T34, pF_in_aga(T33, T31, T34))
pF_in_aga(T33, T31, T34) → U7_aga(T33, T31, T34, lessA_in_ag(T33, T31))
lessA_in_ag(0, s(T45)) → lessA_out_ag(0, s(T45))
lessA_in_ag(s(T52), s(T51)) → U1_ag(T52, T51, lessA_in_ag(T52, T51))
U1_ag(T52, T51, lessA_out_ag(T52, T51)) → lessA_out_ag(s(T52), s(T51))
U7_aga(T33, T31, T34, lessA_out_ag(T33, T31)) → pF_out_aga(T33, T31, T34)
pF_in_aga(T37, T31, T38) → U8_aga(T37, T31, T38, lessA_in_ag(T37, T31))
U8_aga(T37, T31, T38, lessA_out_ag(T37, T31)) → U9_aga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T6, tree(T6, void, T7), T7) → deleteD_out_gga(T6, tree(T6, void, T7), T7)
deleteD_in_gga(T9, tree(T9, void, void), void) → deleteD_out_gga(T9, tree(T9, void, void), void)
deleteD_in_gga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_gga(T33, T31, T34, pF_in_gga(T33, T31, T34))
pF_in_gga(T33, T31, T34) → U7_gga(T33, T31, T34, lessA_in_gg(T33, T31))
lessA_in_gg(0, s(T45)) → lessA_out_gg(0, s(T45))
lessA_in_gg(s(T52), s(T51)) → U1_gg(T52, T51, lessA_in_gg(T52, T51))
U1_gg(T52, T51, lessA_out_gg(T52, T51)) → lessA_out_gg(s(T52), s(T51))
U7_gga(T33, T31, T34, lessA_out_gg(T33, T31)) → pF_out_gga(T33, T31, T34)
pF_in_gga(T37, T31, T38) → U8_gga(T37, T31, T38, lessA_in_gg(T37, T31))
U8_gga(T37, T31, T38, lessA_out_gg(T37, T31)) → U9_gga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_gga(T66, T64, T67, pC_in_gga(T64, T66, T67))
pC_in_gga(T64, T66, T67) → U3_gga(T64, T66, T67, lessB_in_gg(T64, T66))
lessB_in_gg(0, s(T78)) → lessB_out_gg(0, s(T78))
lessB_in_gg(s(T83), s(T85)) → U2_gg(T83, T85, lessB_in_gg(T83, T85))
U2_gg(T83, T85, lessB_out_gg(T83, T85)) → lessB_out_gg(s(T83), s(T85))
U3_gga(T64, T66, T67, lessB_out_gg(T64, T66)) → pC_out_gga(T64, T66, T67)
pC_in_gga(T64, T70, T71) → U4_gga(T64, T70, T71, lessB_in_gg(T64, T70))
U4_gga(T64, T70, T71, lessB_out_gg(T64, T70)) → U5_gga(T64, T70, T71, deleteD_in_gga(T70, void, T71))
deleteD_in_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_gga(T102, T103, deleteD_in_gga(0, void, T103))
deleteD_in_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_gga(T114, T113, T115, lessA_in_gg(T114, T113))
U19_gga(T114, T113, T115, lessA_out_gg(T114, T113)) → deleteD_out_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_gga(T118, T113, T119, lessA_in_gg(T118, T113))
U20_gga(T118, T113, T119, lessA_out_gg(T118, T113)) → U21_gga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
deleteD_in_gga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_gga(T135, T133, T136, pC_in_gga(T133, T135, T136))
U22_gga(T135, T133, T136, pC_out_gga(T133, T135, T136)) → deleteD_out_gga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_gga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_gga(T153, T152, deleteD_in_gga(s(T153), void, T152))
deleteD_in_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_gga(T162, T160, T163, lessB_in_gg(T160, T162))
U24_gga(T162, T160, T163, lessB_out_gg(T160, T162)) → deleteD_out_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_gga(T166, T160, T167, lessB_in_gg(T160, T166))
U25_gga(T166, T160, T167, lessB_out_gg(T160, T166)) → U26_gga(T166, T160, T167, deleteD_in_gga(s(T166), void, T167))
deleteD_in_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
delminE_in_gaa(tree(T238, void, T239), T238, T239) → delminE_out_gaa(tree(T238, void, T239), T238, T239)
delminE_in_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → U6_gaa(T252, T253, T254, T258, T259, T257, delminE_in_gaa(T253, T258, T259))
U6_gaa(T252, T253, T254, T258, T259, T257, delminE_out_gaa(T253, T258, T259)) → delminE_out_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257))
U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_gga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_gga(T284, T281, T282, T285, pF_in_gga(T284, T281, T285))
U28_gga(T284, T281, T282, T285, pF_out_gga(T284, T281, T285)) → deleteD_out_gga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_gga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_gga(T300, T297, T298, T301, pG_in_ggga(T297, T300, T298, T301))
pG_in_ggga(T297, T300, T298, T301) → U10_ggga(T297, T300, T298, T301, lessB_in_gg(T297, T300))
U10_ggga(T297, T300, T298, T301, lessB_out_gg(T297, T300)) → pG_out_ggga(T297, T300, T298, T301)
pG_in_ggga(T297, T304, T298, T305) → U11_ggga(T297, T304, T298, T305, lessB_in_gg(T297, T304))
U11_ggga(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → U12_ggga(T297, T304, T298, T305, deleteD_in_gga(T304, T298, T305))
deleteD_in_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_gga(T328, T320, T329, deleteD_in_gga(0, void, T329))
deleteD_in_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_gga(T340, T339, T320, T341, lessA_in_gg(T340, T339))
U31_gga(T340, T339, T320, T341, lessA_out_gg(T340, T339)) → deleteD_out_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_gga(T344, T339, T320, T345, lessA_in_gg(T344, T339))
U32_gga(T344, T339, T320, T345, lessA_out_gg(T344, T339)) → U33_gga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
deleteD_in_gga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_gga(T364, T361, T362, T365, pG_in_ggga(T361, T364, T362, T365))
U34_gga(T364, T361, T362, T365, pG_out_ggga(T361, T364, T362, T365)) → deleteD_out_gga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_gga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_gga(T384, T374, T383, deleteD_in_gga(s(T384), T374, T383))
deleteD_in_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_gga(T395, T393, T374, T396, lessB_in_gg(T393, T395))
U36_gga(T395, T393, T374, T396, lessB_out_gg(T393, T395)) → deleteD_out_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_gga(T399, T393, T374, T400, lessB_in_gg(T393, T399))
U37_gga(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → U38_gga(T399, T393, T374, T400, deleteD_in_gga(s(T399), T374, T400))
deleteD_in_gga(T411, tree(T411, T412, void), T412) → deleteD_out_gga(T411, tree(T411, T412, void), T412)
deleteD_in_gga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_gga(T443, T440, T441, T444, lessA_in_gg(T443, T440))
U39_gga(T443, T440, T441, T444, lessA_out_gg(T443, T440)) → deleteD_out_gga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_gga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_gga(T447, T440, T441, T448, lessA_in_gg(T447, T440))
U40_gga(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → U41_gga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
deleteD_in_gga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_gga(T469, T466, T467, T470, pC_in_gga(T466, T469, T470))
U42_gga(T469, T466, T467, T470, pC_out_gga(T466, T469, T470)) → deleteD_out_gga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_gga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
deleteD_in_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_gga(T501, T500, T479, T502, lessA_in_gg(T501, T500))
U44_gga(T501, T500, T479, T502, lessA_out_gg(T501, T500)) → deleteD_out_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_gga(T505, T500, T479, T506, lessA_in_gg(T505, T500))
U45_gga(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → U46_gga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
deleteD_in_gga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_gga(T527, T524, T525, T528, pC_in_gga(T524, T527, T528))
U47_gga(T527, T524, T525, T528, pC_out_gga(T524, T527, T528)) → deleteD_out_gga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_gga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_gga(T547, T537, T546, deleteD_in_gga(s(T547), void, T546))
deleteD_in_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_gga(T556, T554, T537, T557, lessB_in_gg(T554, T556))
U49_gga(T556, T554, T537, T557, lessB_out_gg(T554, T556)) → deleteD_out_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_gga(T560, T554, T537, T561, lessB_in_gg(T554, T560))
U50_gga(T560, T554, T537, T561, lessB_out_gg(T554, T560)) → U51_gga(T560, T554, T537, T561, deleteD_in_gga(s(T560), void, T561))
deleteD_in_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_gga(T651, T647, T648, T649, T652, lessA_in_gg(T651, T647))
U53_gga(T651, T647, T648, T649, T652, lessA_out_gg(T651, T647)) → deleteD_out_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_gga(T655, T647, T648, T649, T656, lessA_in_gg(T655, T647))
U54_gga(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → U55_gga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
deleteD_in_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_gga(T680, T676, T677, T678, T681, pH_in_ggga(T676, T680, T678, T681))
pH_in_ggga(T676, T680, T678, T681) → U13_ggga(T676, T680, T678, T681, lessB_in_gg(T676, T680))
U13_ggga(T676, T680, T678, T681, lessB_out_gg(T676, T680)) → pH_out_ggga(T676, T680, T678, T681)
pH_in_ggga(T676, T684, T678, T685) → U14_ggga(T676, T684, T678, T685, lessB_in_gg(T676, T684))
U14_ggga(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → U15_ggga(T676, T684, T678, T685, deleteD_in_gga(T684, T678, T685))
deleteD_in_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_gga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
deleteD_in_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_gga(T724, T723, T701, T702, T725, lessA_in_gg(T724, T723))
U58_gga(T724, T723, T701, T702, T725, lessA_out_gg(T724, T723)) → deleteD_out_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_gga(T728, T723, T701, T702, T729, lessA_in_gg(T728, T723))
U59_gga(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → U60_gga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
deleteD_in_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_gga(T753, T749, T750, T751, T754, pH_in_ggga(T749, T753, T751, T754))
U61_gga(T753, T749, T750, T751, T754, pH_out_ggga(T749, T753, T751, T754)) → deleteD_out_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_gga(T775, T764, T765, T774, deleteD_in_gga(s(T775), T765, T774))
deleteD_in_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_gga(T786, T784, T764, T765, T787, lessB_in_gg(T784, T786))
U63_gga(T786, T784, T764, T765, T787, lessB_out_gg(T784, T786)) → deleteD_out_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_gga(T790, T784, T764, T765, T791, lessB_in_gg(T784, T790))
U64_gga(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → U65_gga(T790, T784, T764, T765, T791, deleteD_in_gga(s(T790), T765, T791))
U65_gga(T790, T784, T764, T765, T791, deleteD_out_gga(s(T790), T765, T791)) → deleteD_out_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_gga(T775, T764, T765, T774, deleteD_out_gga(s(T775), T765, T774)) → deleteD_out_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U60_gga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
U57_gga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
U15_ggga(T676, T684, T678, T685, deleteD_out_gga(T684, T678, T685)) → pH_out_ggga(T676, T684, T678, T685)
U56_gga(T680, T676, T677, T678, T681, pH_out_ggga(T676, T680, T678, T681)) → deleteD_out_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U55_gga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
U51_gga(T560, T554, T537, T561, deleteD_out_gga(s(T560), void, T561)) → deleteD_out_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_gga(T547, T537, T546, deleteD_out_gga(s(T547), void, T546)) → deleteD_out_gga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U46_gga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
U43_gga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
U41_gga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_gga(T447, tree(T440, T441, void), tree(T440, T448, void))
U38_gga(T399, T393, T374, T400, deleteD_out_gga(s(T399), T374, T400)) → deleteD_out_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_gga(T384, T374, T383, deleteD_out_gga(s(T384), T374, T383)) → deleteD_out_gga(s(T384), tree(0, void, T374), tree(0, void, T383))
U33_gga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
U30_gga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
U12_ggga(T297, T304, T298, T305, deleteD_out_gga(T304, T298, T305)) → pG_out_ggga(T297, T304, T298, T305)
U29_gga(T300, T297, T298, T301, pG_out_ggga(T297, T300, T298, T301)) → deleteD_out_gga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_gga(T166, T160, T167, deleteD_out_gga(s(T166), void, T167)) → deleteD_out_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_gga(T153, T152, deleteD_out_gga(s(T153), void, T152)) → deleteD_out_gga(s(T153), tree(0, void, void), tree(0, void, T152))
U21_gga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
U18_gga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
U5_gga(T64, T70, T71, deleteD_out_gga(T70, void, T71)) → pC_out_gga(T64, T70, T71)
U17_gga(T66, T64, T67, pC_out_gga(T64, T66, T67)) → deleteD_out_gga(T66, tree(T64, void, void), tree(T64, void, T67))
U9_gga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_gga(T37, T31, T38)
U16_gga(T33, T31, T34, pF_out_gga(T33, T31, T34)) → deleteD_out_gga(T33, tree(T31, void, void), tree(T31, T34, void))
U9_aga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_aga(T37, T31, T38)
U16_aga(T33, T31, T34, pF_out_aga(T33, T31, T34)) → deleteD_out_aga(T33, tree(T31, void, void), tree(T31, T34, void))
deleteD_in_aga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_aga(T66, T64, T67, pC_in_gaa(T64, T66, T67))
pC_in_gaa(T64, T66, T67) → U3_gaa(T64, T66, T67, lessB_in_ga(T64, T66))
lessB_in_ga(0, s(T78)) → lessB_out_ga(0, s(T78))
lessB_in_ga(s(T83), s(T85)) → U2_ga(T83, T85, lessB_in_ga(T83, T85))
U2_ga(T83, T85, lessB_out_ga(T83, T85)) → lessB_out_ga(s(T83), s(T85))
U3_gaa(T64, T66, T67, lessB_out_ga(T64, T66)) → pC_out_gaa(T64, T66, T67)
pC_in_gaa(T64, T70, T71) → U4_gaa(T64, T70, T71, lessB_in_ga(T64, T70))
U4_gaa(T64, T70, T71, lessB_out_ga(T64, T70)) → U5_gaa(T64, T70, T71, deleteD_in_aga(T70, void, T71))
deleteD_in_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_aga(T102, T103, deleteD_in_gga(0, void, T103))
U18_aga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
deleteD_in_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_aga(T114, T113, T115, lessA_in_ag(T114, T113))
U19_aga(T114, T113, T115, lessA_out_ag(T114, T113)) → deleteD_out_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_aga(T118, T113, T119, lessA_in_ag(T118, T113))
U20_aga(T118, T113, T119, lessA_out_ag(T118, T113)) → U21_aga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
U21_aga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
deleteD_in_aga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_aga(T135, T133, T136, pC_in_gaa(T133, T135, T136))
U22_aga(T135, T133, T136, pC_out_gaa(T133, T135, T136)) → deleteD_out_aga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_aga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_aga(T153, T152, deleteD_in_aga(s(T153), void, T152))
deleteD_in_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_aga(T162, T160, T163, lessB_in_ga(T160, T162))
U24_aga(T162, T160, T163, lessB_out_ga(T160, T162)) → deleteD_out_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_aga(T166, T160, T167, lessB_in_ga(T160, T166))
U25_aga(T166, T160, T167, lessB_out_ga(T160, T166)) → U26_aga(T166, T160, T167, deleteD_in_aga(s(T166), void, T167))
deleteD_in_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_aga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_aga(T284, T281, T282, T285, pF_in_aga(T284, T281, T285))
U28_aga(T284, T281, T282, T285, pF_out_aga(T284, T281, T285)) → deleteD_out_aga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_aga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_aga(T300, T297, T298, T301, pG_in_gaga(T297, T300, T298, T301))
pG_in_gaga(T297, T300, T298, T301) → U10_gaga(T297, T300, T298, T301, lessB_in_ga(T297, T300))
U10_gaga(T297, T300, T298, T301, lessB_out_ga(T297, T300)) → pG_out_gaga(T297, T300, T298, T301)
pG_in_gaga(T297, T304, T298, T305) → U11_gaga(T297, T304, T298, T305, lessB_in_ga(T297, T304))
U11_gaga(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → U12_gaga(T297, T304, T298, T305, deleteD_in_aga(T304, T298, T305))
deleteD_in_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_aga(T328, T320, T329, deleteD_in_gga(0, void, T329))
U30_aga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
deleteD_in_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_aga(T340, T339, T320, T341, lessA_in_ag(T340, T339))
U31_aga(T340, T339, T320, T341, lessA_out_ag(T340, T339)) → deleteD_out_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_aga(T344, T339, T320, T345, lessA_in_ag(T344, T339))
U32_aga(T344, T339, T320, T345, lessA_out_ag(T344, T339)) → U33_aga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
U33_aga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
deleteD_in_aga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_aga(T364, T361, T362, T365, pG_in_gaga(T361, T364, T362, T365))
U34_aga(T364, T361, T362, T365, pG_out_gaga(T361, T364, T362, T365)) → deleteD_out_aga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_aga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_aga(T384, T374, T383, deleteD_in_aga(s(T384), T374, T383))
deleteD_in_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_aga(T395, T393, T374, T396, lessB_in_ga(T393, T395))
U36_aga(T395, T393, T374, T396, lessB_out_ga(T393, T395)) → deleteD_out_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_aga(T399, T393, T374, T400, lessB_in_ga(T393, T399))
U37_aga(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → U38_aga(T399, T393, T374, T400, deleteD_in_aga(s(T399), T374, T400))
deleteD_in_aga(T411, tree(T411, T412, void), T412) → deleteD_out_aga(T411, tree(T411, T412, void), T412)
deleteD_in_aga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_aga(T443, T440, T441, T444, lessA_in_ag(T443, T440))
U39_aga(T443, T440, T441, T444, lessA_out_ag(T443, T440)) → deleteD_out_aga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_aga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_aga(T447, T440, T441, T448, lessA_in_ag(T447, T440))
U40_aga(T447, T440, T441, T448, lessA_out_ag(T447, T440)) → U41_aga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
U41_aga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_aga(T447, tree(T440, T441, void), tree(T440, T448, void))
deleteD_in_aga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_aga(T469, T466, T467, T470, pC_in_gaa(T466, T469, T470))
U42_aga(T469, T466, T467, T470, pC_out_gaa(T466, T469, T470)) → deleteD_out_aga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_aga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
U43_aga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
deleteD_in_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_aga(T501, T500, T479, T502, lessA_in_ag(T501, T500))
U44_aga(T501, T500, T479, T502, lessA_out_ag(T501, T500)) → deleteD_out_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_aga(T505, T500, T479, T506, lessA_in_ag(T505, T500))
U45_aga(T505, T500, T479, T506, lessA_out_ag(T505, T500)) → U46_aga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
U46_aga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
deleteD_in_aga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_aga(T527, T524, T525, T528, pC_in_gaa(T524, T527, T528))
U47_aga(T527, T524, T525, T528, pC_out_gaa(T524, T527, T528)) → deleteD_out_aga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_aga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_aga(T547, T537, T546, deleteD_in_aga(s(T547), void, T546))
deleteD_in_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_aga(T556, T554, T537, T557, lessB_in_ga(T554, T556))
U49_aga(T556, T554, T537, T557, lessB_out_ga(T554, T556)) → deleteD_out_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_aga(T560, T554, T537, T561, lessB_in_ga(T554, T560))
U50_aga(T560, T554, T537, T561, lessB_out_ga(T554, T560)) → U51_aga(T560, T554, T537, T561, deleteD_in_aga(s(T560), void, T561))
deleteD_in_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_aga(T651, T647, T648, T649, T652, lessA_in_ag(T651, T647))
U53_aga(T651, T647, T648, T649, T652, lessA_out_ag(T651, T647)) → deleteD_out_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_aga(T655, T647, T648, T649, T656, lessA_in_ag(T655, T647))
U54_aga(T655, T647, T648, T649, T656, lessA_out_ag(T655, T647)) → U55_aga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
U55_aga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
deleteD_in_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_aga(T680, T676, T677, T678, T681, pH_in_gaga(T676, T680, T678, T681))
pH_in_gaga(T676, T680, T678, T681) → U13_gaga(T676, T680, T678, T681, lessB_in_ga(T676, T680))
U13_gaga(T676, T680, T678, T681, lessB_out_ga(T676, T680)) → pH_out_gaga(T676, T680, T678, T681)
pH_in_gaga(T676, T684, T678, T685) → U14_gaga(T676, T684, T678, T685, lessB_in_ga(T676, T684))
U14_gaga(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → U15_gaga(T676, T684, T678, T685, deleteD_in_aga(T684, T678, T685))
deleteD_in_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_aga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
U57_aga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
deleteD_in_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_aga(T724, T723, T701, T702, T725, lessA_in_ag(T724, T723))
U58_aga(T724, T723, T701, T702, T725, lessA_out_ag(T724, T723)) → deleteD_out_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_aga(T728, T723, T701, T702, T729, lessA_in_ag(T728, T723))
U59_aga(T728, T723, T701, T702, T729, lessA_out_ag(T728, T723)) → U60_aga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
U60_aga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
deleteD_in_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_aga(T753, T749, T750, T751, T754, pH_in_gaga(T749, T753, T751, T754))
U61_aga(T753, T749, T750, T751, T754, pH_out_gaga(T749, T753, T751, T754)) → deleteD_out_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_aga(T775, T764, T765, T774, deleteD_in_aga(s(T775), T765, T774))
deleteD_in_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_aga(T786, T784, T764, T765, T787, lessB_in_ga(T784, T786))
U63_aga(T786, T784, T764, T765, T787, lessB_out_ga(T784, T786)) → deleteD_out_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_aga(T790, T784, T764, T765, T791, lessB_in_ga(T784, T790))
U64_aga(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → U65_aga(T790, T784, T764, T765, T791, deleteD_in_aga(s(T790), T765, T791))
U65_aga(T790, T784, T764, T765, T791, deleteD_out_aga(s(T790), T765, T791)) → deleteD_out_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_aga(T775, T764, T765, T774, deleteD_out_aga(s(T775), T765, T774)) → deleteD_out_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U15_gaga(T676, T684, T678, T685, deleteD_out_aga(T684, T678, T685)) → pH_out_gaga(T676, T684, T678, T685)
U56_aga(T680, T676, T677, T678, T681, pH_out_gaga(T676, T680, T678, T681)) → deleteD_out_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U51_aga(T560, T554, T537, T561, deleteD_out_aga(s(T560), void, T561)) → deleteD_out_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_aga(T547, T537, T546, deleteD_out_aga(s(T547), void, T546)) → deleteD_out_aga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U38_aga(T399, T393, T374, T400, deleteD_out_aga(s(T399), T374, T400)) → deleteD_out_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_aga(T384, T374, T383, deleteD_out_aga(s(T384), T374, T383)) → deleteD_out_aga(s(T384), tree(0, void, T374), tree(0, void, T383))
U12_gaga(T297, T304, T298, T305, deleteD_out_aga(T304, T298, T305)) → pG_out_gaga(T297, T304, T298, T305)
U29_aga(T300, T297, T298, T301, pG_out_gaga(T297, T300, T298, T301)) → deleteD_out_aga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_aga(T166, T160, T167, deleteD_out_aga(s(T166), void, T167)) → deleteD_out_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_aga(T153, T152, deleteD_out_aga(s(T153), void, T152)) → deleteD_out_aga(s(T153), tree(0, void, void), tree(0, void, T152))
U5_gaa(T64, T70, T71, deleteD_out_aga(T70, void, T71)) → pC_out_gaa(T64, T70, T71)
U17_aga(T66, T64, T67, pC_out_gaa(T64, T66, T67)) → deleteD_out_aga(T66, tree(T64, void, void), tree(T64, void, T67))

(24) UsableRulesProof (EQUIVALENT transformation)

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

(25) Obligation:

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

LESSB_IN_GG(s(T83), s(T85)) → LESSB_IN_GG(T83, T85)

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

(26) PiDPToQDPProof (EQUIVALENT transformation)

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

(27) Obligation:

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

LESSB_IN_GG(s(T83), s(T85)) → LESSB_IN_GG(T83, T85)

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

(28) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

LESSB_IN_GG(s(T83), s(T85)) → LESSB_IN_GG(T83, T85)
The graph contains the following edges 1 > 1, 2 > 2

(29) YES

(30) Obligation:

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

LESSA_IN_GG(s(T52), s(T51)) → LESSA_IN_GG(T52, T51)

The TRS R consists of the following rules:

deleteD_in_aga(T6, tree(T6, void, T7), T7) → deleteD_out_aga(T6, tree(T6, void, T7), T7)
deleteD_in_aga(T9, tree(T9, void, void), void) → deleteD_out_aga(T9, tree(T9, void, void), void)
deleteD_in_aga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_aga(T33, T31, T34, pF_in_aga(T33, T31, T34))
pF_in_aga(T33, T31, T34) → U7_aga(T33, T31, T34, lessA_in_ag(T33, T31))
lessA_in_ag(0, s(T45)) → lessA_out_ag(0, s(T45))
lessA_in_ag(s(T52), s(T51)) → U1_ag(T52, T51, lessA_in_ag(T52, T51))
U1_ag(T52, T51, lessA_out_ag(T52, T51)) → lessA_out_ag(s(T52), s(T51))
U7_aga(T33, T31, T34, lessA_out_ag(T33, T31)) → pF_out_aga(T33, T31, T34)
pF_in_aga(T37, T31, T38) → U8_aga(T37, T31, T38, lessA_in_ag(T37, T31))
U8_aga(T37, T31, T38, lessA_out_ag(T37, T31)) → U9_aga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T6, tree(T6, void, T7), T7) → deleteD_out_gga(T6, tree(T6, void, T7), T7)
deleteD_in_gga(T9, tree(T9, void, void), void) → deleteD_out_gga(T9, tree(T9, void, void), void)
deleteD_in_gga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_gga(T33, T31, T34, pF_in_gga(T33, T31, T34))
pF_in_gga(T33, T31, T34) → U7_gga(T33, T31, T34, lessA_in_gg(T33, T31))
lessA_in_gg(0, s(T45)) → lessA_out_gg(0, s(T45))
lessA_in_gg(s(T52), s(T51)) → U1_gg(T52, T51, lessA_in_gg(T52, T51))
U1_gg(T52, T51, lessA_out_gg(T52, T51)) → lessA_out_gg(s(T52), s(T51))
U7_gga(T33, T31, T34, lessA_out_gg(T33, T31)) → pF_out_gga(T33, T31, T34)
pF_in_gga(T37, T31, T38) → U8_gga(T37, T31, T38, lessA_in_gg(T37, T31))
U8_gga(T37, T31, T38, lessA_out_gg(T37, T31)) → U9_gga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_gga(T66, T64, T67, pC_in_gga(T64, T66, T67))
pC_in_gga(T64, T66, T67) → U3_gga(T64, T66, T67, lessB_in_gg(T64, T66))
lessB_in_gg(0, s(T78)) → lessB_out_gg(0, s(T78))
lessB_in_gg(s(T83), s(T85)) → U2_gg(T83, T85, lessB_in_gg(T83, T85))
U2_gg(T83, T85, lessB_out_gg(T83, T85)) → lessB_out_gg(s(T83), s(T85))
U3_gga(T64, T66, T67, lessB_out_gg(T64, T66)) → pC_out_gga(T64, T66, T67)
pC_in_gga(T64, T70, T71) → U4_gga(T64, T70, T71, lessB_in_gg(T64, T70))
U4_gga(T64, T70, T71, lessB_out_gg(T64, T70)) → U5_gga(T64, T70, T71, deleteD_in_gga(T70, void, T71))
deleteD_in_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_gga(T102, T103, deleteD_in_gga(0, void, T103))
deleteD_in_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_gga(T114, T113, T115, lessA_in_gg(T114, T113))
U19_gga(T114, T113, T115, lessA_out_gg(T114, T113)) → deleteD_out_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_gga(T118, T113, T119, lessA_in_gg(T118, T113))
U20_gga(T118, T113, T119, lessA_out_gg(T118, T113)) → U21_gga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
deleteD_in_gga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_gga(T135, T133, T136, pC_in_gga(T133, T135, T136))
U22_gga(T135, T133, T136, pC_out_gga(T133, T135, T136)) → deleteD_out_gga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_gga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_gga(T153, T152, deleteD_in_gga(s(T153), void, T152))
deleteD_in_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_gga(T162, T160, T163, lessB_in_gg(T160, T162))
U24_gga(T162, T160, T163, lessB_out_gg(T160, T162)) → deleteD_out_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_gga(T166, T160, T167, lessB_in_gg(T160, T166))
U25_gga(T166, T160, T167, lessB_out_gg(T160, T166)) → U26_gga(T166, T160, T167, deleteD_in_gga(s(T166), void, T167))
deleteD_in_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
delminE_in_gaa(tree(T238, void, T239), T238, T239) → delminE_out_gaa(tree(T238, void, T239), T238, T239)
delminE_in_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → U6_gaa(T252, T253, T254, T258, T259, T257, delminE_in_gaa(T253, T258, T259))
U6_gaa(T252, T253, T254, T258, T259, T257, delminE_out_gaa(T253, T258, T259)) → delminE_out_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257))
U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_gga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_gga(T284, T281, T282, T285, pF_in_gga(T284, T281, T285))
U28_gga(T284, T281, T282, T285, pF_out_gga(T284, T281, T285)) → deleteD_out_gga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_gga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_gga(T300, T297, T298, T301, pG_in_ggga(T297, T300, T298, T301))
pG_in_ggga(T297, T300, T298, T301) → U10_ggga(T297, T300, T298, T301, lessB_in_gg(T297, T300))
U10_ggga(T297, T300, T298, T301, lessB_out_gg(T297, T300)) → pG_out_ggga(T297, T300, T298, T301)
pG_in_ggga(T297, T304, T298, T305) → U11_ggga(T297, T304, T298, T305, lessB_in_gg(T297, T304))
U11_ggga(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → U12_ggga(T297, T304, T298, T305, deleteD_in_gga(T304, T298, T305))
deleteD_in_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_gga(T328, T320, T329, deleteD_in_gga(0, void, T329))
deleteD_in_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_gga(T340, T339, T320, T341, lessA_in_gg(T340, T339))
U31_gga(T340, T339, T320, T341, lessA_out_gg(T340, T339)) → deleteD_out_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_gga(T344, T339, T320, T345, lessA_in_gg(T344, T339))
U32_gga(T344, T339, T320, T345, lessA_out_gg(T344, T339)) → U33_gga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
deleteD_in_gga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_gga(T364, T361, T362, T365, pG_in_ggga(T361, T364, T362, T365))
U34_gga(T364, T361, T362, T365, pG_out_ggga(T361, T364, T362, T365)) → deleteD_out_gga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_gga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_gga(T384, T374, T383, deleteD_in_gga(s(T384), T374, T383))
deleteD_in_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_gga(T395, T393, T374, T396, lessB_in_gg(T393, T395))
U36_gga(T395, T393, T374, T396, lessB_out_gg(T393, T395)) → deleteD_out_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_gga(T399, T393, T374, T400, lessB_in_gg(T393, T399))
U37_gga(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → U38_gga(T399, T393, T374, T400, deleteD_in_gga(s(T399), T374, T400))
deleteD_in_gga(T411, tree(T411, T412, void), T412) → deleteD_out_gga(T411, tree(T411, T412, void), T412)
deleteD_in_gga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_gga(T443, T440, T441, T444, lessA_in_gg(T443, T440))
U39_gga(T443, T440, T441, T444, lessA_out_gg(T443, T440)) → deleteD_out_gga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_gga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_gga(T447, T440, T441, T448, lessA_in_gg(T447, T440))
U40_gga(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → U41_gga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
deleteD_in_gga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_gga(T469, T466, T467, T470, pC_in_gga(T466, T469, T470))
U42_gga(T469, T466, T467, T470, pC_out_gga(T466, T469, T470)) → deleteD_out_gga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_gga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
deleteD_in_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_gga(T501, T500, T479, T502, lessA_in_gg(T501, T500))
U44_gga(T501, T500, T479, T502, lessA_out_gg(T501, T500)) → deleteD_out_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_gga(T505, T500, T479, T506, lessA_in_gg(T505, T500))
U45_gga(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → U46_gga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
deleteD_in_gga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_gga(T527, T524, T525, T528, pC_in_gga(T524, T527, T528))
U47_gga(T527, T524, T525, T528, pC_out_gga(T524, T527, T528)) → deleteD_out_gga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_gga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_gga(T547, T537, T546, deleteD_in_gga(s(T547), void, T546))
deleteD_in_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_gga(T556, T554, T537, T557, lessB_in_gg(T554, T556))
U49_gga(T556, T554, T537, T557, lessB_out_gg(T554, T556)) → deleteD_out_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_gga(T560, T554, T537, T561, lessB_in_gg(T554, T560))
U50_gga(T560, T554, T537, T561, lessB_out_gg(T554, T560)) → U51_gga(T560, T554, T537, T561, deleteD_in_gga(s(T560), void, T561))
deleteD_in_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_gga(T651, T647, T648, T649, T652, lessA_in_gg(T651, T647))
U53_gga(T651, T647, T648, T649, T652, lessA_out_gg(T651, T647)) → deleteD_out_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_gga(T655, T647, T648, T649, T656, lessA_in_gg(T655, T647))
U54_gga(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → U55_gga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
deleteD_in_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_gga(T680, T676, T677, T678, T681, pH_in_ggga(T676, T680, T678, T681))
pH_in_ggga(T676, T680, T678, T681) → U13_ggga(T676, T680, T678, T681, lessB_in_gg(T676, T680))
U13_ggga(T676, T680, T678, T681, lessB_out_gg(T676, T680)) → pH_out_ggga(T676, T680, T678, T681)
pH_in_ggga(T676, T684, T678, T685) → U14_ggga(T676, T684, T678, T685, lessB_in_gg(T676, T684))
U14_ggga(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → U15_ggga(T676, T684, T678, T685, deleteD_in_gga(T684, T678, T685))
deleteD_in_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_gga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
deleteD_in_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_gga(T724, T723, T701, T702, T725, lessA_in_gg(T724, T723))
U58_gga(T724, T723, T701, T702, T725, lessA_out_gg(T724, T723)) → deleteD_out_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_gga(T728, T723, T701, T702, T729, lessA_in_gg(T728, T723))
U59_gga(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → U60_gga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
deleteD_in_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_gga(T753, T749, T750, T751, T754, pH_in_ggga(T749, T753, T751, T754))
U61_gga(T753, T749, T750, T751, T754, pH_out_ggga(T749, T753, T751, T754)) → deleteD_out_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_gga(T775, T764, T765, T774, deleteD_in_gga(s(T775), T765, T774))
deleteD_in_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_gga(T786, T784, T764, T765, T787, lessB_in_gg(T784, T786))
U63_gga(T786, T784, T764, T765, T787, lessB_out_gg(T784, T786)) → deleteD_out_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_gga(T790, T784, T764, T765, T791, lessB_in_gg(T784, T790))
U64_gga(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → U65_gga(T790, T784, T764, T765, T791, deleteD_in_gga(s(T790), T765, T791))
U65_gga(T790, T784, T764, T765, T791, deleteD_out_gga(s(T790), T765, T791)) → deleteD_out_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_gga(T775, T764, T765, T774, deleteD_out_gga(s(T775), T765, T774)) → deleteD_out_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U60_gga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
U57_gga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
U15_ggga(T676, T684, T678, T685, deleteD_out_gga(T684, T678, T685)) → pH_out_ggga(T676, T684, T678, T685)
U56_gga(T680, T676, T677, T678, T681, pH_out_ggga(T676, T680, T678, T681)) → deleteD_out_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U55_gga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
U51_gga(T560, T554, T537, T561, deleteD_out_gga(s(T560), void, T561)) → deleteD_out_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_gga(T547, T537, T546, deleteD_out_gga(s(T547), void, T546)) → deleteD_out_gga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U46_gga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
U43_gga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
U41_gga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_gga(T447, tree(T440, T441, void), tree(T440, T448, void))
U38_gga(T399, T393, T374, T400, deleteD_out_gga(s(T399), T374, T400)) → deleteD_out_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_gga(T384, T374, T383, deleteD_out_gga(s(T384), T374, T383)) → deleteD_out_gga(s(T384), tree(0, void, T374), tree(0, void, T383))
U33_gga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
U30_gga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
U12_ggga(T297, T304, T298, T305, deleteD_out_gga(T304, T298, T305)) → pG_out_ggga(T297, T304, T298, T305)
U29_gga(T300, T297, T298, T301, pG_out_ggga(T297, T300, T298, T301)) → deleteD_out_gga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_gga(T166, T160, T167, deleteD_out_gga(s(T166), void, T167)) → deleteD_out_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_gga(T153, T152, deleteD_out_gga(s(T153), void, T152)) → deleteD_out_gga(s(T153), tree(0, void, void), tree(0, void, T152))
U21_gga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
U18_gga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
U5_gga(T64, T70, T71, deleteD_out_gga(T70, void, T71)) → pC_out_gga(T64, T70, T71)
U17_gga(T66, T64, T67, pC_out_gga(T64, T66, T67)) → deleteD_out_gga(T66, tree(T64, void, void), tree(T64, void, T67))
U9_gga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_gga(T37, T31, T38)
U16_gga(T33, T31, T34, pF_out_gga(T33, T31, T34)) → deleteD_out_gga(T33, tree(T31, void, void), tree(T31, T34, void))
U9_aga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_aga(T37, T31, T38)
U16_aga(T33, T31, T34, pF_out_aga(T33, T31, T34)) → deleteD_out_aga(T33, tree(T31, void, void), tree(T31, T34, void))
deleteD_in_aga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_aga(T66, T64, T67, pC_in_gaa(T64, T66, T67))
pC_in_gaa(T64, T66, T67) → U3_gaa(T64, T66, T67, lessB_in_ga(T64, T66))
lessB_in_ga(0, s(T78)) → lessB_out_ga(0, s(T78))
lessB_in_ga(s(T83), s(T85)) → U2_ga(T83, T85, lessB_in_ga(T83, T85))
U2_ga(T83, T85, lessB_out_ga(T83, T85)) → lessB_out_ga(s(T83), s(T85))
U3_gaa(T64, T66, T67, lessB_out_ga(T64, T66)) → pC_out_gaa(T64, T66, T67)
pC_in_gaa(T64, T70, T71) → U4_gaa(T64, T70, T71, lessB_in_ga(T64, T70))
U4_gaa(T64, T70, T71, lessB_out_ga(T64, T70)) → U5_gaa(T64, T70, T71, deleteD_in_aga(T70, void, T71))
deleteD_in_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_aga(T102, T103, deleteD_in_gga(0, void, T103))
U18_aga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
deleteD_in_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_aga(T114, T113, T115, lessA_in_ag(T114, T113))
U19_aga(T114, T113, T115, lessA_out_ag(T114, T113)) → deleteD_out_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_aga(T118, T113, T119, lessA_in_ag(T118, T113))
U20_aga(T118, T113, T119, lessA_out_ag(T118, T113)) → U21_aga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
U21_aga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
deleteD_in_aga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_aga(T135, T133, T136, pC_in_gaa(T133, T135, T136))
U22_aga(T135, T133, T136, pC_out_gaa(T133, T135, T136)) → deleteD_out_aga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_aga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_aga(T153, T152, deleteD_in_aga(s(T153), void, T152))
deleteD_in_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_aga(T162, T160, T163, lessB_in_ga(T160, T162))
U24_aga(T162, T160, T163, lessB_out_ga(T160, T162)) → deleteD_out_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_aga(T166, T160, T167, lessB_in_ga(T160, T166))
U25_aga(T166, T160, T167, lessB_out_ga(T160, T166)) → U26_aga(T166, T160, T167, deleteD_in_aga(s(T166), void, T167))
deleteD_in_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_aga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_aga(T284, T281, T282, T285, pF_in_aga(T284, T281, T285))
U28_aga(T284, T281, T282, T285, pF_out_aga(T284, T281, T285)) → deleteD_out_aga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_aga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_aga(T300, T297, T298, T301, pG_in_gaga(T297, T300, T298, T301))
pG_in_gaga(T297, T300, T298, T301) → U10_gaga(T297, T300, T298, T301, lessB_in_ga(T297, T300))
U10_gaga(T297, T300, T298, T301, lessB_out_ga(T297, T300)) → pG_out_gaga(T297, T300, T298, T301)
pG_in_gaga(T297, T304, T298, T305) → U11_gaga(T297, T304, T298, T305, lessB_in_ga(T297, T304))
U11_gaga(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → U12_gaga(T297, T304, T298, T305, deleteD_in_aga(T304, T298, T305))
deleteD_in_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_aga(T328, T320, T329, deleteD_in_gga(0, void, T329))
U30_aga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
deleteD_in_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_aga(T340, T339, T320, T341, lessA_in_ag(T340, T339))
U31_aga(T340, T339, T320, T341, lessA_out_ag(T340, T339)) → deleteD_out_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_aga(T344, T339, T320, T345, lessA_in_ag(T344, T339))
U32_aga(T344, T339, T320, T345, lessA_out_ag(T344, T339)) → U33_aga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
U33_aga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
deleteD_in_aga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_aga(T364, T361, T362, T365, pG_in_gaga(T361, T364, T362, T365))
U34_aga(T364, T361, T362, T365, pG_out_gaga(T361, T364, T362, T365)) → deleteD_out_aga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_aga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_aga(T384, T374, T383, deleteD_in_aga(s(T384), T374, T383))
deleteD_in_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_aga(T395, T393, T374, T396, lessB_in_ga(T393, T395))
U36_aga(T395, T393, T374, T396, lessB_out_ga(T393, T395)) → deleteD_out_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_aga(T399, T393, T374, T400, lessB_in_ga(T393, T399))
U37_aga(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → U38_aga(T399, T393, T374, T400, deleteD_in_aga(s(T399), T374, T400))
deleteD_in_aga(T411, tree(T411, T412, void), T412) → deleteD_out_aga(T411, tree(T411, T412, void), T412)
deleteD_in_aga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_aga(T443, T440, T441, T444, lessA_in_ag(T443, T440))
U39_aga(T443, T440, T441, T444, lessA_out_ag(T443, T440)) → deleteD_out_aga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_aga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_aga(T447, T440, T441, T448, lessA_in_ag(T447, T440))
U40_aga(T447, T440, T441, T448, lessA_out_ag(T447, T440)) → U41_aga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
U41_aga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_aga(T447, tree(T440, T441, void), tree(T440, T448, void))
deleteD_in_aga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_aga(T469, T466, T467, T470, pC_in_gaa(T466, T469, T470))
U42_aga(T469, T466, T467, T470, pC_out_gaa(T466, T469, T470)) → deleteD_out_aga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_aga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
U43_aga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
deleteD_in_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_aga(T501, T500, T479, T502, lessA_in_ag(T501, T500))
U44_aga(T501, T500, T479, T502, lessA_out_ag(T501, T500)) → deleteD_out_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_aga(T505, T500, T479, T506, lessA_in_ag(T505, T500))
U45_aga(T505, T500, T479, T506, lessA_out_ag(T505, T500)) → U46_aga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
U46_aga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
deleteD_in_aga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_aga(T527, T524, T525, T528, pC_in_gaa(T524, T527, T528))
U47_aga(T527, T524, T525, T528, pC_out_gaa(T524, T527, T528)) → deleteD_out_aga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_aga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_aga(T547, T537, T546, deleteD_in_aga(s(T547), void, T546))
deleteD_in_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_aga(T556, T554, T537, T557, lessB_in_ga(T554, T556))
U49_aga(T556, T554, T537, T557, lessB_out_ga(T554, T556)) → deleteD_out_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_aga(T560, T554, T537, T561, lessB_in_ga(T554, T560))
U50_aga(T560, T554, T537, T561, lessB_out_ga(T554, T560)) → U51_aga(T560, T554, T537, T561, deleteD_in_aga(s(T560), void, T561))
deleteD_in_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_aga(T651, T647, T648, T649, T652, lessA_in_ag(T651, T647))
U53_aga(T651, T647, T648, T649, T652, lessA_out_ag(T651, T647)) → deleteD_out_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_aga(T655, T647, T648, T649, T656, lessA_in_ag(T655, T647))
U54_aga(T655, T647, T648, T649, T656, lessA_out_ag(T655, T647)) → U55_aga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
U55_aga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
deleteD_in_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_aga(T680, T676, T677, T678, T681, pH_in_gaga(T676, T680, T678, T681))
pH_in_gaga(T676, T680, T678, T681) → U13_gaga(T676, T680, T678, T681, lessB_in_ga(T676, T680))
U13_gaga(T676, T680, T678, T681, lessB_out_ga(T676, T680)) → pH_out_gaga(T676, T680, T678, T681)
pH_in_gaga(T676, T684, T678, T685) → U14_gaga(T676, T684, T678, T685, lessB_in_ga(T676, T684))
U14_gaga(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → U15_gaga(T676, T684, T678, T685, deleteD_in_aga(T684, T678, T685))
deleteD_in_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_aga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
U57_aga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
deleteD_in_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_aga(T724, T723, T701, T702, T725, lessA_in_ag(T724, T723))
U58_aga(T724, T723, T701, T702, T725, lessA_out_ag(T724, T723)) → deleteD_out_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_aga(T728, T723, T701, T702, T729, lessA_in_ag(T728, T723))
U59_aga(T728, T723, T701, T702, T729, lessA_out_ag(T728, T723)) → U60_aga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
U60_aga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
deleteD_in_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_aga(T753, T749, T750, T751, T754, pH_in_gaga(T749, T753, T751, T754))
U61_aga(T753, T749, T750, T751, T754, pH_out_gaga(T749, T753, T751, T754)) → deleteD_out_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_aga(T775, T764, T765, T774, deleteD_in_aga(s(T775), T765, T774))
deleteD_in_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_aga(T786, T784, T764, T765, T787, lessB_in_ga(T784, T786))
U63_aga(T786, T784, T764, T765, T787, lessB_out_ga(T784, T786)) → deleteD_out_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_aga(T790, T784, T764, T765, T791, lessB_in_ga(T784, T790))
U64_aga(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → U65_aga(T790, T784, T764, T765, T791, deleteD_in_aga(s(T790), T765, T791))
U65_aga(T790, T784, T764, T765, T791, deleteD_out_aga(s(T790), T765, T791)) → deleteD_out_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_aga(T775, T764, T765, T774, deleteD_out_aga(s(T775), T765, T774)) → deleteD_out_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U15_gaga(T676, T684, T678, T685, deleteD_out_aga(T684, T678, T685)) → pH_out_gaga(T676, T684, T678, T685)
U56_aga(T680, T676, T677, T678, T681, pH_out_gaga(T676, T680, T678, T681)) → deleteD_out_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U51_aga(T560, T554, T537, T561, deleteD_out_aga(s(T560), void, T561)) → deleteD_out_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_aga(T547, T537, T546, deleteD_out_aga(s(T547), void, T546)) → deleteD_out_aga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U38_aga(T399, T393, T374, T400, deleteD_out_aga(s(T399), T374, T400)) → deleteD_out_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_aga(T384, T374, T383, deleteD_out_aga(s(T384), T374, T383)) → deleteD_out_aga(s(T384), tree(0, void, T374), tree(0, void, T383))
U12_gaga(T297, T304, T298, T305, deleteD_out_aga(T304, T298, T305)) → pG_out_gaga(T297, T304, T298, T305)
U29_aga(T300, T297, T298, T301, pG_out_gaga(T297, T300, T298, T301)) → deleteD_out_aga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_aga(T166, T160, T167, deleteD_out_aga(s(T166), void, T167)) → deleteD_out_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_aga(T153, T152, deleteD_out_aga(s(T153), void, T152)) → deleteD_out_aga(s(T153), tree(0, void, void), tree(0, void, T152))
U5_gaa(T64, T70, T71, deleteD_out_aga(T70, void, T71)) → pC_out_gaa(T64, T70, T71)
U17_aga(T66, T64, T67, pC_out_gaa(T64, T66, T67)) → deleteD_out_aga(T66, tree(T64, void, void), tree(T64, void, T67))

(31) UsableRulesProof (EQUIVALENT transformation)

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

(32) Obligation:

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

LESSA_IN_GG(s(T52), s(T51)) → LESSA_IN_GG(T52, T51)

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

(33) PiDPToQDPProof (EQUIVALENT transformation)

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

(34) Obligation:

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

LESSA_IN_GG(s(T52), s(T51)) → LESSA_IN_GG(T52, T51)

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

(35) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

LESSA_IN_GG(s(T52), s(T51)) → LESSA_IN_GG(T52, T51)
The graph contains the following edges 1 > 1, 2 > 2

(36) YES

(37) Obligation:

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

DELETED_IN_GGA(T300, tree(T297, void, T298), tree(T297, void, T301)) → PG_IN_GGGA(T297, T300, T298, T301)
PG_IN_GGGA(T297, T304, T298, T305) → U11_GGGA(T297, T304, T298, T305, lessB_in_gg(T297, T304))
U11_GGGA(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → DELETED_IN_GGA(T304, T298, T305)
DELETED_IN_GGA(s(T384), tree(0, void, T374), tree(0, void, T383)) → DELETED_IN_GGA(s(T384), T374, T383)
DELETED_IN_GGA(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_GGA(T399, T393, T374, T400, lessB_in_gg(T393, T399))
U37_GGA(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → DELETED_IN_GGA(s(T399), T374, T400)
DELETED_IN_GGA(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_GGA(T447, T440, T441, T448, lessA_in_gg(T447, T440))
U40_GGA(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → DELETED_IN_GGA(T447, T441, T448)
DELETED_IN_GGA(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → DELETED_IN_GGA(0, T479, T488)
DELETED_IN_GGA(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_GGA(T655, T647, T648, T649, T656, lessA_in_gg(T655, T647))
U54_GGA(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → DELETED_IN_GGA(T655, T648, T656)
DELETED_IN_GGA(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_GGA(T505, T500, T479, T506, lessA_in_gg(T505, T500))
U45_GGA(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → DELETED_IN_GGA(s(T505), T479, T506)
DELETED_IN_GGA(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → PH_IN_GGGA(T676, T680, T678, T681)
PH_IN_GGGA(T676, T684, T678, T685) → U14_GGGA(T676, T684, T678, T685, lessB_in_gg(T676, T684))
U14_GGGA(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → DELETED_IN_GGA(T684, T678, T685)
DELETED_IN_GGA(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → DELETED_IN_GGA(0, T701, T711)
DELETED_IN_GGA(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_GGA(T728, T723, T701, T702, T729, lessA_in_gg(T728, T723))
U59_GGA(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → DELETED_IN_GGA(s(T728), T701, T729)
DELETED_IN_GGA(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → DELETED_IN_GGA(s(T775), T765, T774)
DELETED_IN_GGA(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_GGA(T790, T784, T764, T765, T791, lessB_in_gg(T784, T790))
U64_GGA(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → DELETED_IN_GGA(s(T790), T765, T791)

The TRS R consists of the following rules:

deleteD_in_aga(T6, tree(T6, void, T7), T7) → deleteD_out_aga(T6, tree(T6, void, T7), T7)
deleteD_in_aga(T9, tree(T9, void, void), void) → deleteD_out_aga(T9, tree(T9, void, void), void)
deleteD_in_aga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_aga(T33, T31, T34, pF_in_aga(T33, T31, T34))
pF_in_aga(T33, T31, T34) → U7_aga(T33, T31, T34, lessA_in_ag(T33, T31))
lessA_in_ag(0, s(T45)) → lessA_out_ag(0, s(T45))
lessA_in_ag(s(T52), s(T51)) → U1_ag(T52, T51, lessA_in_ag(T52, T51))
U1_ag(T52, T51, lessA_out_ag(T52, T51)) → lessA_out_ag(s(T52), s(T51))
U7_aga(T33, T31, T34, lessA_out_ag(T33, T31)) → pF_out_aga(T33, T31, T34)
pF_in_aga(T37, T31, T38) → U8_aga(T37, T31, T38, lessA_in_ag(T37, T31))
U8_aga(T37, T31, T38, lessA_out_ag(T37, T31)) → U9_aga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T6, tree(T6, void, T7), T7) → deleteD_out_gga(T6, tree(T6, void, T7), T7)
deleteD_in_gga(T9, tree(T9, void, void), void) → deleteD_out_gga(T9, tree(T9, void, void), void)
deleteD_in_gga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_gga(T33, T31, T34, pF_in_gga(T33, T31, T34))
pF_in_gga(T33, T31, T34) → U7_gga(T33, T31, T34, lessA_in_gg(T33, T31))
lessA_in_gg(0, s(T45)) → lessA_out_gg(0, s(T45))
lessA_in_gg(s(T52), s(T51)) → U1_gg(T52, T51, lessA_in_gg(T52, T51))
U1_gg(T52, T51, lessA_out_gg(T52, T51)) → lessA_out_gg(s(T52), s(T51))
U7_gga(T33, T31, T34, lessA_out_gg(T33, T31)) → pF_out_gga(T33, T31, T34)
pF_in_gga(T37, T31, T38) → U8_gga(T37, T31, T38, lessA_in_gg(T37, T31))
U8_gga(T37, T31, T38, lessA_out_gg(T37, T31)) → U9_gga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_gga(T66, T64, T67, pC_in_gga(T64, T66, T67))
pC_in_gga(T64, T66, T67) → U3_gga(T64, T66, T67, lessB_in_gg(T64, T66))
lessB_in_gg(0, s(T78)) → lessB_out_gg(0, s(T78))
lessB_in_gg(s(T83), s(T85)) → U2_gg(T83, T85, lessB_in_gg(T83, T85))
U2_gg(T83, T85, lessB_out_gg(T83, T85)) → lessB_out_gg(s(T83), s(T85))
U3_gga(T64, T66, T67, lessB_out_gg(T64, T66)) → pC_out_gga(T64, T66, T67)
pC_in_gga(T64, T70, T71) → U4_gga(T64, T70, T71, lessB_in_gg(T64, T70))
U4_gga(T64, T70, T71, lessB_out_gg(T64, T70)) → U5_gga(T64, T70, T71, deleteD_in_gga(T70, void, T71))
deleteD_in_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_gga(T102, T103, deleteD_in_gga(0, void, T103))
deleteD_in_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_gga(T114, T113, T115, lessA_in_gg(T114, T113))
U19_gga(T114, T113, T115, lessA_out_gg(T114, T113)) → deleteD_out_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_gga(T118, T113, T119, lessA_in_gg(T118, T113))
U20_gga(T118, T113, T119, lessA_out_gg(T118, T113)) → U21_gga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
deleteD_in_gga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_gga(T135, T133, T136, pC_in_gga(T133, T135, T136))
U22_gga(T135, T133, T136, pC_out_gga(T133, T135, T136)) → deleteD_out_gga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_gga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_gga(T153, T152, deleteD_in_gga(s(T153), void, T152))
deleteD_in_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_gga(T162, T160, T163, lessB_in_gg(T160, T162))
U24_gga(T162, T160, T163, lessB_out_gg(T160, T162)) → deleteD_out_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_gga(T166, T160, T167, lessB_in_gg(T160, T166))
U25_gga(T166, T160, T167, lessB_out_gg(T160, T166)) → U26_gga(T166, T160, T167, deleteD_in_gga(s(T166), void, T167))
deleteD_in_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
delminE_in_gaa(tree(T238, void, T239), T238, T239) → delminE_out_gaa(tree(T238, void, T239), T238, T239)
delminE_in_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → U6_gaa(T252, T253, T254, T258, T259, T257, delminE_in_gaa(T253, T258, T259))
U6_gaa(T252, T253, T254, T258, T259, T257, delminE_out_gaa(T253, T258, T259)) → delminE_out_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257))
U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_gga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_gga(T284, T281, T282, T285, pF_in_gga(T284, T281, T285))
U28_gga(T284, T281, T282, T285, pF_out_gga(T284, T281, T285)) → deleteD_out_gga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_gga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_gga(T300, T297, T298, T301, pG_in_ggga(T297, T300, T298, T301))
pG_in_ggga(T297, T300, T298, T301) → U10_ggga(T297, T300, T298, T301, lessB_in_gg(T297, T300))
U10_ggga(T297, T300, T298, T301, lessB_out_gg(T297, T300)) → pG_out_ggga(T297, T300, T298, T301)
pG_in_ggga(T297, T304, T298, T305) → U11_ggga(T297, T304, T298, T305, lessB_in_gg(T297, T304))
U11_ggga(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → U12_ggga(T297, T304, T298, T305, deleteD_in_gga(T304, T298, T305))
deleteD_in_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_gga(T328, T320, T329, deleteD_in_gga(0, void, T329))
deleteD_in_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_gga(T340, T339, T320, T341, lessA_in_gg(T340, T339))
U31_gga(T340, T339, T320, T341, lessA_out_gg(T340, T339)) → deleteD_out_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_gga(T344, T339, T320, T345, lessA_in_gg(T344, T339))
U32_gga(T344, T339, T320, T345, lessA_out_gg(T344, T339)) → U33_gga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
deleteD_in_gga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_gga(T364, T361, T362, T365, pG_in_ggga(T361, T364, T362, T365))
U34_gga(T364, T361, T362, T365, pG_out_ggga(T361, T364, T362, T365)) → deleteD_out_gga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_gga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_gga(T384, T374, T383, deleteD_in_gga(s(T384), T374, T383))
deleteD_in_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_gga(T395, T393, T374, T396, lessB_in_gg(T393, T395))
U36_gga(T395, T393, T374, T396, lessB_out_gg(T393, T395)) → deleteD_out_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_gga(T399, T393, T374, T400, lessB_in_gg(T393, T399))
U37_gga(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → U38_gga(T399, T393, T374, T400, deleteD_in_gga(s(T399), T374, T400))
deleteD_in_gga(T411, tree(T411, T412, void), T412) → deleteD_out_gga(T411, tree(T411, T412, void), T412)
deleteD_in_gga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_gga(T443, T440, T441, T444, lessA_in_gg(T443, T440))
U39_gga(T443, T440, T441, T444, lessA_out_gg(T443, T440)) → deleteD_out_gga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_gga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_gga(T447, T440, T441, T448, lessA_in_gg(T447, T440))
U40_gga(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → U41_gga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
deleteD_in_gga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_gga(T469, T466, T467, T470, pC_in_gga(T466, T469, T470))
U42_gga(T469, T466, T467, T470, pC_out_gga(T466, T469, T470)) → deleteD_out_gga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_gga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
deleteD_in_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_gga(T501, T500, T479, T502, lessA_in_gg(T501, T500))
U44_gga(T501, T500, T479, T502, lessA_out_gg(T501, T500)) → deleteD_out_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_gga(T505, T500, T479, T506, lessA_in_gg(T505, T500))
U45_gga(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → U46_gga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
deleteD_in_gga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_gga(T527, T524, T525, T528, pC_in_gga(T524, T527, T528))
U47_gga(T527, T524, T525, T528, pC_out_gga(T524, T527, T528)) → deleteD_out_gga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_gga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_gga(T547, T537, T546, deleteD_in_gga(s(T547), void, T546))
deleteD_in_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_gga(T556, T554, T537, T557, lessB_in_gg(T554, T556))
U49_gga(T556, T554, T537, T557, lessB_out_gg(T554, T556)) → deleteD_out_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_gga(T560, T554, T537, T561, lessB_in_gg(T554, T560))
U50_gga(T560, T554, T537, T561, lessB_out_gg(T554, T560)) → U51_gga(T560, T554, T537, T561, deleteD_in_gga(s(T560), void, T561))
deleteD_in_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_gga(T651, T647, T648, T649, T652, lessA_in_gg(T651, T647))
U53_gga(T651, T647, T648, T649, T652, lessA_out_gg(T651, T647)) → deleteD_out_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_gga(T655, T647, T648, T649, T656, lessA_in_gg(T655, T647))
U54_gga(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → U55_gga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
deleteD_in_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_gga(T680, T676, T677, T678, T681, pH_in_ggga(T676, T680, T678, T681))
pH_in_ggga(T676, T680, T678, T681) → U13_ggga(T676, T680, T678, T681, lessB_in_gg(T676, T680))
U13_ggga(T676, T680, T678, T681, lessB_out_gg(T676, T680)) → pH_out_ggga(T676, T680, T678, T681)
pH_in_ggga(T676, T684, T678, T685) → U14_ggga(T676, T684, T678, T685, lessB_in_gg(T676, T684))
U14_ggga(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → U15_ggga(T676, T684, T678, T685, deleteD_in_gga(T684, T678, T685))
deleteD_in_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_gga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
deleteD_in_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_gga(T724, T723, T701, T702, T725, lessA_in_gg(T724, T723))
U58_gga(T724, T723, T701, T702, T725, lessA_out_gg(T724, T723)) → deleteD_out_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_gga(T728, T723, T701, T702, T729, lessA_in_gg(T728, T723))
U59_gga(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → U60_gga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
deleteD_in_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_gga(T753, T749, T750, T751, T754, pH_in_ggga(T749, T753, T751, T754))
U61_gga(T753, T749, T750, T751, T754, pH_out_ggga(T749, T753, T751, T754)) → deleteD_out_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_gga(T775, T764, T765, T774, deleteD_in_gga(s(T775), T765, T774))
deleteD_in_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_gga(T786, T784, T764, T765, T787, lessB_in_gg(T784, T786))
U63_gga(T786, T784, T764, T765, T787, lessB_out_gg(T784, T786)) → deleteD_out_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_gga(T790, T784, T764, T765, T791, lessB_in_gg(T784, T790))
U64_gga(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → U65_gga(T790, T784, T764, T765, T791, deleteD_in_gga(s(T790), T765, T791))
U65_gga(T790, T784, T764, T765, T791, deleteD_out_gga(s(T790), T765, T791)) → deleteD_out_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_gga(T775, T764, T765, T774, deleteD_out_gga(s(T775), T765, T774)) → deleteD_out_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U60_gga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
U57_gga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
U15_ggga(T676, T684, T678, T685, deleteD_out_gga(T684, T678, T685)) → pH_out_ggga(T676, T684, T678, T685)
U56_gga(T680, T676, T677, T678, T681, pH_out_ggga(T676, T680, T678, T681)) → deleteD_out_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U55_gga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
U51_gga(T560, T554, T537, T561, deleteD_out_gga(s(T560), void, T561)) → deleteD_out_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_gga(T547, T537, T546, deleteD_out_gga(s(T547), void, T546)) → deleteD_out_gga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U46_gga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
U43_gga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
U41_gga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_gga(T447, tree(T440, T441, void), tree(T440, T448, void))
U38_gga(T399, T393, T374, T400, deleteD_out_gga(s(T399), T374, T400)) → deleteD_out_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_gga(T384, T374, T383, deleteD_out_gga(s(T384), T374, T383)) → deleteD_out_gga(s(T384), tree(0, void, T374), tree(0, void, T383))
U33_gga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
U30_gga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
U12_ggga(T297, T304, T298, T305, deleteD_out_gga(T304, T298, T305)) → pG_out_ggga(T297, T304, T298, T305)
U29_gga(T300, T297, T298, T301, pG_out_ggga(T297, T300, T298, T301)) → deleteD_out_gga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_gga(T166, T160, T167, deleteD_out_gga(s(T166), void, T167)) → deleteD_out_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_gga(T153, T152, deleteD_out_gga(s(T153), void, T152)) → deleteD_out_gga(s(T153), tree(0, void, void), tree(0, void, T152))
U21_gga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
U18_gga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
U5_gga(T64, T70, T71, deleteD_out_gga(T70, void, T71)) → pC_out_gga(T64, T70, T71)
U17_gga(T66, T64, T67, pC_out_gga(T64, T66, T67)) → deleteD_out_gga(T66, tree(T64, void, void), tree(T64, void, T67))
U9_gga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_gga(T37, T31, T38)
U16_gga(T33, T31, T34, pF_out_gga(T33, T31, T34)) → deleteD_out_gga(T33, tree(T31, void, void), tree(T31, T34, void))
U9_aga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_aga(T37, T31, T38)
U16_aga(T33, T31, T34, pF_out_aga(T33, T31, T34)) → deleteD_out_aga(T33, tree(T31, void, void), tree(T31, T34, void))
deleteD_in_aga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_aga(T66, T64, T67, pC_in_gaa(T64, T66, T67))
pC_in_gaa(T64, T66, T67) → U3_gaa(T64, T66, T67, lessB_in_ga(T64, T66))
lessB_in_ga(0, s(T78)) → lessB_out_ga(0, s(T78))
lessB_in_ga(s(T83), s(T85)) → U2_ga(T83, T85, lessB_in_ga(T83, T85))
U2_ga(T83, T85, lessB_out_ga(T83, T85)) → lessB_out_ga(s(T83), s(T85))
U3_gaa(T64, T66, T67, lessB_out_ga(T64, T66)) → pC_out_gaa(T64, T66, T67)
pC_in_gaa(T64, T70, T71) → U4_gaa(T64, T70, T71, lessB_in_ga(T64, T70))
U4_gaa(T64, T70, T71, lessB_out_ga(T64, T70)) → U5_gaa(T64, T70, T71, deleteD_in_aga(T70, void, T71))
deleteD_in_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_aga(T102, T103, deleteD_in_gga(0, void, T103))
U18_aga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
deleteD_in_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_aga(T114, T113, T115, lessA_in_ag(T114, T113))
U19_aga(T114, T113, T115, lessA_out_ag(T114, T113)) → deleteD_out_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_aga(T118, T113, T119, lessA_in_ag(T118, T113))
U20_aga(T118, T113, T119, lessA_out_ag(T118, T113)) → U21_aga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
U21_aga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
deleteD_in_aga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_aga(T135, T133, T136, pC_in_gaa(T133, T135, T136))
U22_aga(T135, T133, T136, pC_out_gaa(T133, T135, T136)) → deleteD_out_aga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_aga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_aga(T153, T152, deleteD_in_aga(s(T153), void, T152))
deleteD_in_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_aga(T162, T160, T163, lessB_in_ga(T160, T162))
U24_aga(T162, T160, T163, lessB_out_ga(T160, T162)) → deleteD_out_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_aga(T166, T160, T167, lessB_in_ga(T160, T166))
U25_aga(T166, T160, T167, lessB_out_ga(T160, T166)) → U26_aga(T166, T160, T167, deleteD_in_aga(s(T166), void, T167))
deleteD_in_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_aga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_aga(T284, T281, T282, T285, pF_in_aga(T284, T281, T285))
U28_aga(T284, T281, T282, T285, pF_out_aga(T284, T281, T285)) → deleteD_out_aga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_aga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_aga(T300, T297, T298, T301, pG_in_gaga(T297, T300, T298, T301))
pG_in_gaga(T297, T300, T298, T301) → U10_gaga(T297, T300, T298, T301, lessB_in_ga(T297, T300))
U10_gaga(T297, T300, T298, T301, lessB_out_ga(T297, T300)) → pG_out_gaga(T297, T300, T298, T301)
pG_in_gaga(T297, T304, T298, T305) → U11_gaga(T297, T304, T298, T305, lessB_in_ga(T297, T304))
U11_gaga(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → U12_gaga(T297, T304, T298, T305, deleteD_in_aga(T304, T298, T305))
deleteD_in_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_aga(T328, T320, T329, deleteD_in_gga(0, void, T329))
U30_aga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
deleteD_in_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_aga(T340, T339, T320, T341, lessA_in_ag(T340, T339))
U31_aga(T340, T339, T320, T341, lessA_out_ag(T340, T339)) → deleteD_out_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_aga(T344, T339, T320, T345, lessA_in_ag(T344, T339))
U32_aga(T344, T339, T320, T345, lessA_out_ag(T344, T339)) → U33_aga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
U33_aga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
deleteD_in_aga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_aga(T364, T361, T362, T365, pG_in_gaga(T361, T364, T362, T365))
U34_aga(T364, T361, T362, T365, pG_out_gaga(T361, T364, T362, T365)) → deleteD_out_aga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_aga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_aga(T384, T374, T383, deleteD_in_aga(s(T384), T374, T383))
deleteD_in_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_aga(T395, T393, T374, T396, lessB_in_ga(T393, T395))
U36_aga(T395, T393, T374, T396, lessB_out_ga(T393, T395)) → deleteD_out_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_aga(T399, T393, T374, T400, lessB_in_ga(T393, T399))
U37_aga(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → U38_aga(T399, T393, T374, T400, deleteD_in_aga(s(T399), T374, T400))
deleteD_in_aga(T411, tree(T411, T412, void), T412) → deleteD_out_aga(T411, tree(T411, T412, void), T412)
deleteD_in_aga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_aga(T443, T440, T441, T444, lessA_in_ag(T443, T440))
U39_aga(T443, T440, T441, T444, lessA_out_ag(T443, T440)) → deleteD_out_aga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_aga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_aga(T447, T440, T441, T448, lessA_in_ag(T447, T440))
U40_aga(T447, T440, T441, T448, lessA_out_ag(T447, T440)) → U41_aga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
U41_aga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_aga(T447, tree(T440, T441, void), tree(T440, T448, void))
deleteD_in_aga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_aga(T469, T466, T467, T470, pC_in_gaa(T466, T469, T470))
U42_aga(T469, T466, T467, T470, pC_out_gaa(T466, T469, T470)) → deleteD_out_aga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_aga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
U43_aga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
deleteD_in_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_aga(T501, T500, T479, T502, lessA_in_ag(T501, T500))
U44_aga(T501, T500, T479, T502, lessA_out_ag(T501, T500)) → deleteD_out_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_aga(T505, T500, T479, T506, lessA_in_ag(T505, T500))
U45_aga(T505, T500, T479, T506, lessA_out_ag(T505, T500)) → U46_aga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
U46_aga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
deleteD_in_aga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_aga(T527, T524, T525, T528, pC_in_gaa(T524, T527, T528))
U47_aga(T527, T524, T525, T528, pC_out_gaa(T524, T527, T528)) → deleteD_out_aga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_aga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_aga(T547, T537, T546, deleteD_in_aga(s(T547), void, T546))
deleteD_in_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_aga(T556, T554, T537, T557, lessB_in_ga(T554, T556))
U49_aga(T556, T554, T537, T557, lessB_out_ga(T554, T556)) → deleteD_out_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_aga(T560, T554, T537, T561, lessB_in_ga(T554, T560))
U50_aga(T560, T554, T537, T561, lessB_out_ga(T554, T560)) → U51_aga(T560, T554, T537, T561, deleteD_in_aga(s(T560), void, T561))
deleteD_in_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_aga(T651, T647, T648, T649, T652, lessA_in_ag(T651, T647))
U53_aga(T651, T647, T648, T649, T652, lessA_out_ag(T651, T647)) → deleteD_out_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_aga(T655, T647, T648, T649, T656, lessA_in_ag(T655, T647))
U54_aga(T655, T647, T648, T649, T656, lessA_out_ag(T655, T647)) → U55_aga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
U55_aga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
deleteD_in_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_aga(T680, T676, T677, T678, T681, pH_in_gaga(T676, T680, T678, T681))
pH_in_gaga(T676, T680, T678, T681) → U13_gaga(T676, T680, T678, T681, lessB_in_ga(T676, T680))
U13_gaga(T676, T680, T678, T681, lessB_out_ga(T676, T680)) → pH_out_gaga(T676, T680, T678, T681)
pH_in_gaga(T676, T684, T678, T685) → U14_gaga(T676, T684, T678, T685, lessB_in_ga(T676, T684))
U14_gaga(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → U15_gaga(T676, T684, T678, T685, deleteD_in_aga(T684, T678, T685))
deleteD_in_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_aga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
U57_aga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
deleteD_in_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_aga(T724, T723, T701, T702, T725, lessA_in_ag(T724, T723))
U58_aga(T724, T723, T701, T702, T725, lessA_out_ag(T724, T723)) → deleteD_out_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_aga(T728, T723, T701, T702, T729, lessA_in_ag(T728, T723))
U59_aga(T728, T723, T701, T702, T729, lessA_out_ag(T728, T723)) → U60_aga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
U60_aga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
deleteD_in_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_aga(T753, T749, T750, T751, T754, pH_in_gaga(T749, T753, T751, T754))
U61_aga(T753, T749, T750, T751, T754, pH_out_gaga(T749, T753, T751, T754)) → deleteD_out_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_aga(T775, T764, T765, T774, deleteD_in_aga(s(T775), T765, T774))
deleteD_in_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_aga(T786, T784, T764, T765, T787, lessB_in_ga(T784, T786))
U63_aga(T786, T784, T764, T765, T787, lessB_out_ga(T784, T786)) → deleteD_out_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_aga(T790, T784, T764, T765, T791, lessB_in_ga(T784, T790))
U64_aga(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → U65_aga(T790, T784, T764, T765, T791, deleteD_in_aga(s(T790), T765, T791))
U65_aga(T790, T784, T764, T765, T791, deleteD_out_aga(s(T790), T765, T791)) → deleteD_out_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_aga(T775, T764, T765, T774, deleteD_out_aga(s(T775), T765, T774)) → deleteD_out_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U15_gaga(T676, T684, T678, T685, deleteD_out_aga(T684, T678, T685)) → pH_out_gaga(T676, T684, T678, T685)
U56_aga(T680, T676, T677, T678, T681, pH_out_gaga(T676, T680, T678, T681)) → deleteD_out_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U51_aga(T560, T554, T537, T561, deleteD_out_aga(s(T560), void, T561)) → deleteD_out_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_aga(T547, T537, T546, deleteD_out_aga(s(T547), void, T546)) → deleteD_out_aga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U38_aga(T399, T393, T374, T400, deleteD_out_aga(s(T399), T374, T400)) → deleteD_out_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_aga(T384, T374, T383, deleteD_out_aga(s(T384), T374, T383)) → deleteD_out_aga(s(T384), tree(0, void, T374), tree(0, void, T383))
U12_gaga(T297, T304, T298, T305, deleteD_out_aga(T304, T298, T305)) → pG_out_gaga(T297, T304, T298, T305)
U29_aga(T300, T297, T298, T301, pG_out_gaga(T297, T300, T298, T301)) → deleteD_out_aga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_aga(T166, T160, T167, deleteD_out_aga(s(T166), void, T167)) → deleteD_out_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_aga(T153, T152, deleteD_out_aga(s(T153), void, T152)) → deleteD_out_aga(s(T153), tree(0, void, void), tree(0, void, T152))
U5_gaa(T64, T70, T71, deleteD_out_aga(T70, void, T71)) → pC_out_gaa(T64, T70, T71)
U17_aga(T66, T64, T67, pC_out_gaa(T64, T66, T67)) → deleteD_out_aga(T66, tree(T64, void, void), tree(T64, void, T67))

(38) UsableRulesProof (EQUIVALENT transformation)

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

(39) Obligation:

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

DELETED_IN_GGA(T300, tree(T297, void, T298), tree(T297, void, T301)) → PG_IN_GGGA(T297, T300, T298, T301)
PG_IN_GGGA(T297, T304, T298, T305) → U11_GGGA(T297, T304, T298, T305, lessB_in_gg(T297, T304))
U11_GGGA(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → DELETED_IN_GGA(T304, T298, T305)
DELETED_IN_GGA(s(T384), tree(0, void, T374), tree(0, void, T383)) → DELETED_IN_GGA(s(T384), T374, T383)
DELETED_IN_GGA(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_GGA(T399, T393, T374, T400, lessB_in_gg(T393, T399))
U37_GGA(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → DELETED_IN_GGA(s(T399), T374, T400)
DELETED_IN_GGA(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_GGA(T447, T440, T441, T448, lessA_in_gg(T447, T440))
U40_GGA(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → DELETED_IN_GGA(T447, T441, T448)
DELETED_IN_GGA(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → DELETED_IN_GGA(0, T479, T488)
DELETED_IN_GGA(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_GGA(T655, T647, T648, T649, T656, lessA_in_gg(T655, T647))
U54_GGA(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → DELETED_IN_GGA(T655, T648, T656)
DELETED_IN_GGA(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_GGA(T505, T500, T479, T506, lessA_in_gg(T505, T500))
U45_GGA(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → DELETED_IN_GGA(s(T505), T479, T506)
DELETED_IN_GGA(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → PH_IN_GGGA(T676, T680, T678, T681)
PH_IN_GGGA(T676, T684, T678, T685) → U14_GGGA(T676, T684, T678, T685, lessB_in_gg(T676, T684))
U14_GGGA(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → DELETED_IN_GGA(T684, T678, T685)
DELETED_IN_GGA(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → DELETED_IN_GGA(0, T701, T711)
DELETED_IN_GGA(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_GGA(T728, T723, T701, T702, T729, lessA_in_gg(T728, T723))
U59_GGA(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → DELETED_IN_GGA(s(T728), T701, T729)
DELETED_IN_GGA(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → DELETED_IN_GGA(s(T775), T765, T774)
DELETED_IN_GGA(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_GGA(T790, T784, T764, T765, T791, lessB_in_gg(T784, T790))
U64_GGA(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → DELETED_IN_GGA(s(T790), T765, T791)

The TRS R consists of the following rules:

lessB_in_gg(0, s(T78)) → lessB_out_gg(0, s(T78))
lessB_in_gg(s(T83), s(T85)) → U2_gg(T83, T85, lessB_in_gg(T83, T85))
lessA_in_gg(0, s(T45)) → lessA_out_gg(0, s(T45))
lessA_in_gg(s(T52), s(T51)) → U1_gg(T52, T51, lessA_in_gg(T52, T51))
U2_gg(T83, T85, lessB_out_gg(T83, T85)) → lessB_out_gg(s(T83), s(T85))
U1_gg(T52, T51, lessA_out_gg(T52, T51)) → lessA_out_gg(s(T52), s(T51))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
void = void
s(x1) = s(x1)
lessA_in_gg(x1, x2) = lessA_in_gg(x1, x2)
0 = 0
lessA_out_gg(x1, x2) = lessA_out_gg(x1, x2)
U1_gg(x1, x2, x3) = U1_gg(x1, x2, x3)
lessB_in_gg(x1, x2) = lessB_in_gg(x1, x2)
lessB_out_gg(x1, x2) = lessB_out_gg(x1, x2)
U2_gg(x1, x2, x3) = U2_gg(x1, x2, x3)
DELETED_IN_GGA(x1, x2, x3) = DELETED_IN_GGA(x1, x2)
PG_IN_GGGA(x1, x2, x3, x4) = PG_IN_GGGA(x1, x2, x3)
U11_GGGA(x1, x2, x3, x4, x5) = U11_GGGA(x1, x2, x3, x5)
U37_GGA(x1, x2, x3, x4, x5) = U37_GGA(x1, x2, x3, x5)
U40_GGA(x1, x2, x3, x4, x5) = U40_GGA(x1, x2, x3, x5)
U45_GGA(x1, x2, x3, x4, x5) = U45_GGA(x1, x2, x3, x5)
U54_GGA(x1, x2, x3, x4, x5, x6) = U54_GGA(x1, x2, x3, x4, x6)
PH_IN_GGGA(x1, x2, x3, x4) = PH_IN_GGGA(x1, x2, x3)
U14_GGGA(x1, x2, x3, x4, x5) = U14_GGGA(x1, x2, x3, x5)
U59_GGA(x1, x2, x3, x4, x5, x6) = U59_GGA(x1, x2, x3, x4, x6)
U64_GGA(x1, x2, x3, x4, x5, x6) = U64_GGA(x1, x2, x3, x4, x6)

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

(40) PiDPToQDPProof (SOUND transformation)

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

(41) Obligation:

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

DELETED_IN_GGA(T300, tree(T297, void, T298)) → PG_IN_GGGA(T297, T300, T298)
PG_IN_GGGA(T297, T304, T298) → U11_GGGA(T297, T304, T298, lessB_in_gg(T297, T304))
U11_GGGA(T297, T304, T298, lessB_out_gg(T297, T304)) → DELETED_IN_GGA(T304, T298)
DELETED_IN_GGA(s(T384), tree(0, void, T374)) → DELETED_IN_GGA(s(T384), T374)
DELETED_IN_GGA(s(T399), tree(s(T393), void, T374)) → U37_GGA(T399, T393, T374, lessB_in_gg(T393, T399))
U37_GGA(T399, T393, T374, lessB_out_gg(T393, T399)) → DELETED_IN_GGA(s(T399), T374)
DELETED_IN_GGA(T447, tree(T440, T441, void)) → U40_GGA(T447, T440, T441, lessA_in_gg(T447, T440))
U40_GGA(T447, T440, T441, lessA_out_gg(T447, T440)) → DELETED_IN_GGA(T447, T441)
DELETED_IN_GGA(0, tree(s(T487), T479, void)) → DELETED_IN_GGA(0, T479)
DELETED_IN_GGA(T655, tree(T647, T648, T649)) → U54_GGA(T655, T647, T648, T649, lessA_in_gg(T655, T647))
U54_GGA(T655, T647, T648, T649, lessA_out_gg(T655, T647)) → DELETED_IN_GGA(T655, T648)
DELETED_IN_GGA(s(T505), tree(s(T500), T479, void)) → U45_GGA(T505, T500, T479, lessA_in_gg(T505, T500))
U45_GGA(T505, T500, T479, lessA_out_gg(T505, T500)) → DELETED_IN_GGA(s(T505), T479)
DELETED_IN_GGA(T680, tree(T676, T677, T678)) → PH_IN_GGGA(T676, T680, T678)
PH_IN_GGGA(T676, T684, T678) → U14_GGGA(T676, T684, T678, lessB_in_gg(T676, T684))
U14_GGGA(T676, T684, T678, lessB_out_gg(T676, T684)) → DELETED_IN_GGA(T684, T678)
DELETED_IN_GGA(0, tree(s(T710), T701, T702)) → DELETED_IN_GGA(0, T701)
DELETED_IN_GGA(s(T728), tree(s(T723), T701, T702)) → U59_GGA(T728, T723, T701, T702, lessA_in_gg(T728, T723))
U59_GGA(T728, T723, T701, T702, lessA_out_gg(T728, T723)) → DELETED_IN_GGA(s(T728), T701)
DELETED_IN_GGA(s(T775), tree(0, T764, T765)) → DELETED_IN_GGA(s(T775), T765)
DELETED_IN_GGA(s(T790), tree(s(T784), T764, T765)) → U64_GGA(T790, T784, T764, T765, lessB_in_gg(T784, T790))
U64_GGA(T790, T784, T764, T765, lessB_out_gg(T784, T790)) → DELETED_IN_GGA(s(T790), T765)

The TRS R consists of the following rules:

lessB_in_gg(0, s(T78)) → lessB_out_gg(0, s(T78))
lessB_in_gg(s(T83), s(T85)) → U2_gg(T83, T85, lessB_in_gg(T83, T85))
lessA_in_gg(0, s(T45)) → lessA_out_gg(0, s(T45))
lessA_in_gg(s(T52), s(T51)) → U1_gg(T52, T51, lessA_in_gg(T52, T51))
U2_gg(T83, T85, lessB_out_gg(T83, T85)) → lessB_out_gg(s(T83), s(T85))
U1_gg(T52, T51, lessA_out_gg(T52, T51)) → lessA_out_gg(s(T52), s(T51))

The set Q consists of the following terms:

lessB_in_gg(x0, x1)
lessA_in_gg(x0, x1)
U2_gg(x0, x1, x2)
U1_gg(x0, x1, x2)

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

(42) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

PG_IN_GGGA(T297, T304, T298) → U11_GGGA(T297, T304, T298, lessB_in_gg(T297, T304))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
U11_GGGA(T297, T304, T298, lessB_out_gg(T297, T304)) → DELETED_IN_GGA(T304, T298)
The graph contains the following edges 2 >= 1, 4 > 1, 3 >= 2
DELETED_IN_GGA(T300, tree(T297, void, T298)) → PG_IN_GGGA(T297, T300, T298)
The graph contains the following edges 2 > 1, 1 >= 2, 2 > 3
PH_IN_GGGA(T676, T684, T678) → U14_GGGA(T676, T684, T678, lessB_in_gg(T676, T684))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
U37_GGA(T399, T393, T374, lessB_out_gg(T393, T399)) → DELETED_IN_GGA(s(T399), T374)
The graph contains the following edges 3 >= 2
DELETED_IN_GGA(s(T399), tree(s(T393), void, T374)) → U37_GGA(T399, T393, T374, lessB_in_gg(T393, T399))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3
U40_GGA(T447, T440, T441, lessA_out_gg(T447, T440)) → DELETED_IN_GGA(T447, T441)
The graph contains the following edges 1 >= 1, 4 > 1, 3 >= 2
DELETED_IN_GGA(T447, tree(T440, T441, void)) → U40_GGA(T447, T440, T441, lessA_in_gg(T447, T440))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
U54_GGA(T655, T647, T648, T649, lessA_out_gg(T655, T647)) → DELETED_IN_GGA(T655, T648)
The graph contains the following edges 1 >= 1, 5 > 1, 3 >= 2
U14_GGGA(T676, T684, T678, lessB_out_gg(T676, T684)) → DELETED_IN_GGA(T684, T678)
The graph contains the following edges 2 >= 1, 4 > 1, 3 >= 2
DELETED_IN_GGA(T655, tree(T647, T648, T649)) → U54_GGA(T655, T647, T648, T649, lessA_in_gg(T655, T647))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4
DELETED_IN_GGA(T680, tree(T676, T677, T678)) → PH_IN_GGGA(T676, T680, T678)
The graph contains the following edges 2 > 1, 1 >= 2, 2 > 3
U45_GGA(T505, T500, T479, lessA_out_gg(T505, T500)) → DELETED_IN_GGA(s(T505), T479)
The graph contains the following edges 3 >= 2
DELETED_IN_GGA(s(T505), tree(s(T500), T479, void)) → U45_GGA(T505, T500, T479, lessA_in_gg(T505, T500))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3
U59_GGA(T728, T723, T701, T702, lessA_out_gg(T728, T723)) → DELETED_IN_GGA(s(T728), T701)
The graph contains the following edges 3 >= 2
U64_GGA(T790, T784, T764, T765, lessB_out_gg(T784, T790)) → DELETED_IN_GGA(s(T790), T765)
The graph contains the following edges 4 >= 2
DELETED_IN_GGA(s(T728), tree(s(T723), T701, T702)) → U59_GGA(T728, T723, T701, T702, lessA_in_gg(T728, T723))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4
DELETED_IN_GGA(s(T790), tree(s(T784), T764, T765)) → U64_GGA(T790, T784, T764, T765, lessB_in_gg(T784, T790))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4
DELETED_IN_GGA(s(T384), tree(0, void, T374)) → DELETED_IN_GGA(s(T384), T374)
The graph contains the following edges 1 >= 1, 2 > 2
DELETED_IN_GGA(s(T775), tree(0, T764, T765)) → DELETED_IN_GGA(s(T775), T765)
The graph contains the following edges 1 >= 1, 2 > 2
DELETED_IN_GGA(0, tree(s(T487), T479, void)) → DELETED_IN_GGA(0, T479)
The graph contains the following edges 1 >= 1, 2 > 2
DELETED_IN_GGA(0, tree(s(T710), T701, T702)) → DELETED_IN_GGA(0, T701)
The graph contains the following edges 1 >= 1, 2 > 2

(43) YES

(44) Obligation:

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

LESSA_IN_AG(s(T52), s(T51)) → LESSA_IN_AG(T52, T51)

The TRS R consists of the following rules:

deleteD_in_aga(T6, tree(T6, void, T7), T7) → deleteD_out_aga(T6, tree(T6, void, T7), T7)
deleteD_in_aga(T9, tree(T9, void, void), void) → deleteD_out_aga(T9, tree(T9, void, void), void)
deleteD_in_aga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_aga(T33, T31, T34, pF_in_aga(T33, T31, T34))
pF_in_aga(T33, T31, T34) → U7_aga(T33, T31, T34, lessA_in_ag(T33, T31))
lessA_in_ag(0, s(T45)) → lessA_out_ag(0, s(T45))
lessA_in_ag(s(T52), s(T51)) → U1_ag(T52, T51, lessA_in_ag(T52, T51))
U1_ag(T52, T51, lessA_out_ag(T52, T51)) → lessA_out_ag(s(T52), s(T51))
U7_aga(T33, T31, T34, lessA_out_ag(T33, T31)) → pF_out_aga(T33, T31, T34)
pF_in_aga(T37, T31, T38) → U8_aga(T37, T31, T38, lessA_in_ag(T37, T31))
U8_aga(T37, T31, T38, lessA_out_ag(T37, T31)) → U9_aga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T6, tree(T6, void, T7), T7) → deleteD_out_gga(T6, tree(T6, void, T7), T7)
deleteD_in_gga(T9, tree(T9, void, void), void) → deleteD_out_gga(T9, tree(T9, void, void), void)
deleteD_in_gga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_gga(T33, T31, T34, pF_in_gga(T33, T31, T34))
pF_in_gga(T33, T31, T34) → U7_gga(T33, T31, T34, lessA_in_gg(T33, T31))
lessA_in_gg(0, s(T45)) → lessA_out_gg(0, s(T45))
lessA_in_gg(s(T52), s(T51)) → U1_gg(T52, T51, lessA_in_gg(T52, T51))
U1_gg(T52, T51, lessA_out_gg(T52, T51)) → lessA_out_gg(s(T52), s(T51))
U7_gga(T33, T31, T34, lessA_out_gg(T33, T31)) → pF_out_gga(T33, T31, T34)
pF_in_gga(T37, T31, T38) → U8_gga(T37, T31, T38, lessA_in_gg(T37, T31))
U8_gga(T37, T31, T38, lessA_out_gg(T37, T31)) → U9_gga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_gga(T66, T64, T67, pC_in_gga(T64, T66, T67))
pC_in_gga(T64, T66, T67) → U3_gga(T64, T66, T67, lessB_in_gg(T64, T66))
lessB_in_gg(0, s(T78)) → lessB_out_gg(0, s(T78))
lessB_in_gg(s(T83), s(T85)) → U2_gg(T83, T85, lessB_in_gg(T83, T85))
U2_gg(T83, T85, lessB_out_gg(T83, T85)) → lessB_out_gg(s(T83), s(T85))
U3_gga(T64, T66, T67, lessB_out_gg(T64, T66)) → pC_out_gga(T64, T66, T67)
pC_in_gga(T64, T70, T71) → U4_gga(T64, T70, T71, lessB_in_gg(T64, T70))
U4_gga(T64, T70, T71, lessB_out_gg(T64, T70)) → U5_gga(T64, T70, T71, deleteD_in_gga(T70, void, T71))
deleteD_in_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_gga(T102, T103, deleteD_in_gga(0, void, T103))
deleteD_in_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_gga(T114, T113, T115, lessA_in_gg(T114, T113))
U19_gga(T114, T113, T115, lessA_out_gg(T114, T113)) → deleteD_out_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_gga(T118, T113, T119, lessA_in_gg(T118, T113))
U20_gga(T118, T113, T119, lessA_out_gg(T118, T113)) → U21_gga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
deleteD_in_gga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_gga(T135, T133, T136, pC_in_gga(T133, T135, T136))
U22_gga(T135, T133, T136, pC_out_gga(T133, T135, T136)) → deleteD_out_gga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_gga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_gga(T153, T152, deleteD_in_gga(s(T153), void, T152))
deleteD_in_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_gga(T162, T160, T163, lessB_in_gg(T160, T162))
U24_gga(T162, T160, T163, lessB_out_gg(T160, T162)) → deleteD_out_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_gga(T166, T160, T167, lessB_in_gg(T160, T166))
U25_gga(T166, T160, T167, lessB_out_gg(T160, T166)) → U26_gga(T166, T160, T167, deleteD_in_gga(s(T166), void, T167))
deleteD_in_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
delminE_in_gaa(tree(T238, void, T239), T238, T239) → delminE_out_gaa(tree(T238, void, T239), T238, T239)
delminE_in_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → U6_gaa(T252, T253, T254, T258, T259, T257, delminE_in_gaa(T253, T258, T259))
U6_gaa(T252, T253, T254, T258, T259, T257, delminE_out_gaa(T253, T258, T259)) → delminE_out_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257))
U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_gga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_gga(T284, T281, T282, T285, pF_in_gga(T284, T281, T285))
U28_gga(T284, T281, T282, T285, pF_out_gga(T284, T281, T285)) → deleteD_out_gga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_gga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_gga(T300, T297, T298, T301, pG_in_ggga(T297, T300, T298, T301))
pG_in_ggga(T297, T300, T298, T301) → U10_ggga(T297, T300, T298, T301, lessB_in_gg(T297, T300))
U10_ggga(T297, T300, T298, T301, lessB_out_gg(T297, T300)) → pG_out_ggga(T297, T300, T298, T301)
pG_in_ggga(T297, T304, T298, T305) → U11_ggga(T297, T304, T298, T305, lessB_in_gg(T297, T304))
U11_ggga(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → U12_ggga(T297, T304, T298, T305, deleteD_in_gga(T304, T298, T305))
deleteD_in_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_gga(T328, T320, T329, deleteD_in_gga(0, void, T329))
deleteD_in_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_gga(T340, T339, T320, T341, lessA_in_gg(T340, T339))
U31_gga(T340, T339, T320, T341, lessA_out_gg(T340, T339)) → deleteD_out_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_gga(T344, T339, T320, T345, lessA_in_gg(T344, T339))
U32_gga(T344, T339, T320, T345, lessA_out_gg(T344, T339)) → U33_gga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
deleteD_in_gga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_gga(T364, T361, T362, T365, pG_in_ggga(T361, T364, T362, T365))
U34_gga(T364, T361, T362, T365, pG_out_ggga(T361, T364, T362, T365)) → deleteD_out_gga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_gga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_gga(T384, T374, T383, deleteD_in_gga(s(T384), T374, T383))
deleteD_in_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_gga(T395, T393, T374, T396, lessB_in_gg(T393, T395))
U36_gga(T395, T393, T374, T396, lessB_out_gg(T393, T395)) → deleteD_out_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_gga(T399, T393, T374, T400, lessB_in_gg(T393, T399))
U37_gga(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → U38_gga(T399, T393, T374, T400, deleteD_in_gga(s(T399), T374, T400))
deleteD_in_gga(T411, tree(T411, T412, void), T412) → deleteD_out_gga(T411, tree(T411, T412, void), T412)
deleteD_in_gga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_gga(T443, T440, T441, T444, lessA_in_gg(T443, T440))
U39_gga(T443, T440, T441, T444, lessA_out_gg(T443, T440)) → deleteD_out_gga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_gga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_gga(T447, T440, T441, T448, lessA_in_gg(T447, T440))
U40_gga(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → U41_gga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
deleteD_in_gga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_gga(T469, T466, T467, T470, pC_in_gga(T466, T469, T470))
U42_gga(T469, T466, T467, T470, pC_out_gga(T466, T469, T470)) → deleteD_out_gga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_gga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
deleteD_in_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_gga(T501, T500, T479, T502, lessA_in_gg(T501, T500))
U44_gga(T501, T500, T479, T502, lessA_out_gg(T501, T500)) → deleteD_out_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_gga(T505, T500, T479, T506, lessA_in_gg(T505, T500))
U45_gga(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → U46_gga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
deleteD_in_gga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_gga(T527, T524, T525, T528, pC_in_gga(T524, T527, T528))
U47_gga(T527, T524, T525, T528, pC_out_gga(T524, T527, T528)) → deleteD_out_gga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_gga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_gga(T547, T537, T546, deleteD_in_gga(s(T547), void, T546))
deleteD_in_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_gga(T556, T554, T537, T557, lessB_in_gg(T554, T556))
U49_gga(T556, T554, T537, T557, lessB_out_gg(T554, T556)) → deleteD_out_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_gga(T560, T554, T537, T561, lessB_in_gg(T554, T560))
U50_gga(T560, T554, T537, T561, lessB_out_gg(T554, T560)) → U51_gga(T560, T554, T537, T561, deleteD_in_gga(s(T560), void, T561))
deleteD_in_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_gga(T651, T647, T648, T649, T652, lessA_in_gg(T651, T647))
U53_gga(T651, T647, T648, T649, T652, lessA_out_gg(T651, T647)) → deleteD_out_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_gga(T655, T647, T648, T649, T656, lessA_in_gg(T655, T647))
U54_gga(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → U55_gga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
deleteD_in_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_gga(T680, T676, T677, T678, T681, pH_in_ggga(T676, T680, T678, T681))
pH_in_ggga(T676, T680, T678, T681) → U13_ggga(T676, T680, T678, T681, lessB_in_gg(T676, T680))
U13_ggga(T676, T680, T678, T681, lessB_out_gg(T676, T680)) → pH_out_ggga(T676, T680, T678, T681)
pH_in_ggga(T676, T684, T678, T685) → U14_ggga(T676, T684, T678, T685, lessB_in_gg(T676, T684))
U14_ggga(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → U15_ggga(T676, T684, T678, T685, deleteD_in_gga(T684, T678, T685))
deleteD_in_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_gga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
deleteD_in_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_gga(T724, T723, T701, T702, T725, lessA_in_gg(T724, T723))
U58_gga(T724, T723, T701, T702, T725, lessA_out_gg(T724, T723)) → deleteD_out_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_gga(T728, T723, T701, T702, T729, lessA_in_gg(T728, T723))
U59_gga(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → U60_gga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
deleteD_in_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_gga(T753, T749, T750, T751, T754, pH_in_ggga(T749, T753, T751, T754))
U61_gga(T753, T749, T750, T751, T754, pH_out_ggga(T749, T753, T751, T754)) → deleteD_out_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_gga(T775, T764, T765, T774, deleteD_in_gga(s(T775), T765, T774))
deleteD_in_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_gga(T786, T784, T764, T765, T787, lessB_in_gg(T784, T786))
U63_gga(T786, T784, T764, T765, T787, lessB_out_gg(T784, T786)) → deleteD_out_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_gga(T790, T784, T764, T765, T791, lessB_in_gg(T784, T790))
U64_gga(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → U65_gga(T790, T784, T764, T765, T791, deleteD_in_gga(s(T790), T765, T791))
U65_gga(T790, T784, T764, T765, T791, deleteD_out_gga(s(T790), T765, T791)) → deleteD_out_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_gga(T775, T764, T765, T774, deleteD_out_gga(s(T775), T765, T774)) → deleteD_out_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U60_gga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
U57_gga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
U15_ggga(T676, T684, T678, T685, deleteD_out_gga(T684, T678, T685)) → pH_out_ggga(T676, T684, T678, T685)
U56_gga(T680, T676, T677, T678, T681, pH_out_ggga(T676, T680, T678, T681)) → deleteD_out_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U55_gga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
U51_gga(T560, T554, T537, T561, deleteD_out_gga(s(T560), void, T561)) → deleteD_out_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_gga(T547, T537, T546, deleteD_out_gga(s(T547), void, T546)) → deleteD_out_gga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U46_gga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
U43_gga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
U41_gga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_gga(T447, tree(T440, T441, void), tree(T440, T448, void))
U38_gga(T399, T393, T374, T400, deleteD_out_gga(s(T399), T374, T400)) → deleteD_out_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_gga(T384, T374, T383, deleteD_out_gga(s(T384), T374, T383)) → deleteD_out_gga(s(T384), tree(0, void, T374), tree(0, void, T383))
U33_gga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
U30_gga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
U12_ggga(T297, T304, T298, T305, deleteD_out_gga(T304, T298, T305)) → pG_out_ggga(T297, T304, T298, T305)
U29_gga(T300, T297, T298, T301, pG_out_ggga(T297, T300, T298, T301)) → deleteD_out_gga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_gga(T166, T160, T167, deleteD_out_gga(s(T166), void, T167)) → deleteD_out_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_gga(T153, T152, deleteD_out_gga(s(T153), void, T152)) → deleteD_out_gga(s(T153), tree(0, void, void), tree(0, void, T152))
U21_gga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
U18_gga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
U5_gga(T64, T70, T71, deleteD_out_gga(T70, void, T71)) → pC_out_gga(T64, T70, T71)
U17_gga(T66, T64, T67, pC_out_gga(T64, T66, T67)) → deleteD_out_gga(T66, tree(T64, void, void), tree(T64, void, T67))
U9_gga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_gga(T37, T31, T38)
U16_gga(T33, T31, T34, pF_out_gga(T33, T31, T34)) → deleteD_out_gga(T33, tree(T31, void, void), tree(T31, T34, void))
U9_aga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_aga(T37, T31, T38)
U16_aga(T33, T31, T34, pF_out_aga(T33, T31, T34)) → deleteD_out_aga(T33, tree(T31, void, void), tree(T31, T34, void))
deleteD_in_aga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_aga(T66, T64, T67, pC_in_gaa(T64, T66, T67))
pC_in_gaa(T64, T66, T67) → U3_gaa(T64, T66, T67, lessB_in_ga(T64, T66))
lessB_in_ga(0, s(T78)) → lessB_out_ga(0, s(T78))
lessB_in_ga(s(T83), s(T85)) → U2_ga(T83, T85, lessB_in_ga(T83, T85))
U2_ga(T83, T85, lessB_out_ga(T83, T85)) → lessB_out_ga(s(T83), s(T85))
U3_gaa(T64, T66, T67, lessB_out_ga(T64, T66)) → pC_out_gaa(T64, T66, T67)
pC_in_gaa(T64, T70, T71) → U4_gaa(T64, T70, T71, lessB_in_ga(T64, T70))
U4_gaa(T64, T70, T71, lessB_out_ga(T64, T70)) → U5_gaa(T64, T70, T71, deleteD_in_aga(T70, void, T71))
deleteD_in_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_aga(T102, T103, deleteD_in_gga(0, void, T103))
U18_aga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
deleteD_in_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_aga(T114, T113, T115, lessA_in_ag(T114, T113))
U19_aga(T114, T113, T115, lessA_out_ag(T114, T113)) → deleteD_out_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_aga(T118, T113, T119, lessA_in_ag(T118, T113))
U20_aga(T118, T113, T119, lessA_out_ag(T118, T113)) → U21_aga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
U21_aga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
deleteD_in_aga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_aga(T135, T133, T136, pC_in_gaa(T133, T135, T136))
U22_aga(T135, T133, T136, pC_out_gaa(T133, T135, T136)) → deleteD_out_aga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_aga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_aga(T153, T152, deleteD_in_aga(s(T153), void, T152))
deleteD_in_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_aga(T162, T160, T163, lessB_in_ga(T160, T162))
U24_aga(T162, T160, T163, lessB_out_ga(T160, T162)) → deleteD_out_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_aga(T166, T160, T167, lessB_in_ga(T160, T166))
U25_aga(T166, T160, T167, lessB_out_ga(T160, T166)) → U26_aga(T166, T160, T167, deleteD_in_aga(s(T166), void, T167))
deleteD_in_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_aga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_aga(T284, T281, T282, T285, pF_in_aga(T284, T281, T285))
U28_aga(T284, T281, T282, T285, pF_out_aga(T284, T281, T285)) → deleteD_out_aga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_aga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_aga(T300, T297, T298, T301, pG_in_gaga(T297, T300, T298, T301))
pG_in_gaga(T297, T300, T298, T301) → U10_gaga(T297, T300, T298, T301, lessB_in_ga(T297, T300))
U10_gaga(T297, T300, T298, T301, lessB_out_ga(T297, T300)) → pG_out_gaga(T297, T300, T298, T301)
pG_in_gaga(T297, T304, T298, T305) → U11_gaga(T297, T304, T298, T305, lessB_in_ga(T297, T304))
U11_gaga(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → U12_gaga(T297, T304, T298, T305, deleteD_in_aga(T304, T298, T305))
deleteD_in_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_aga(T328, T320, T329, deleteD_in_gga(0, void, T329))
U30_aga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
deleteD_in_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_aga(T340, T339, T320, T341, lessA_in_ag(T340, T339))
U31_aga(T340, T339, T320, T341, lessA_out_ag(T340, T339)) → deleteD_out_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_aga(T344, T339, T320, T345, lessA_in_ag(T344, T339))
U32_aga(T344, T339, T320, T345, lessA_out_ag(T344, T339)) → U33_aga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
U33_aga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
deleteD_in_aga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_aga(T364, T361, T362, T365, pG_in_gaga(T361, T364, T362, T365))
U34_aga(T364, T361, T362, T365, pG_out_gaga(T361, T364, T362, T365)) → deleteD_out_aga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_aga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_aga(T384, T374, T383, deleteD_in_aga(s(T384), T374, T383))
deleteD_in_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_aga(T395, T393, T374, T396, lessB_in_ga(T393, T395))
U36_aga(T395, T393, T374, T396, lessB_out_ga(T393, T395)) → deleteD_out_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_aga(T399, T393, T374, T400, lessB_in_ga(T393, T399))
U37_aga(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → U38_aga(T399, T393, T374, T400, deleteD_in_aga(s(T399), T374, T400))
deleteD_in_aga(T411, tree(T411, T412, void), T412) → deleteD_out_aga(T411, tree(T411, T412, void), T412)
deleteD_in_aga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_aga(T443, T440, T441, T444, lessA_in_ag(T443, T440))
U39_aga(T443, T440, T441, T444, lessA_out_ag(T443, T440)) → deleteD_out_aga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_aga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_aga(T447, T440, T441, T448, lessA_in_ag(T447, T440))
U40_aga(T447, T440, T441, T448, lessA_out_ag(T447, T440)) → U41_aga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
U41_aga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_aga(T447, tree(T440, T441, void), tree(T440, T448, void))
deleteD_in_aga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_aga(T469, T466, T467, T470, pC_in_gaa(T466, T469, T470))
U42_aga(T469, T466, T467, T470, pC_out_gaa(T466, T469, T470)) → deleteD_out_aga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_aga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
U43_aga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
deleteD_in_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_aga(T501, T500, T479, T502, lessA_in_ag(T501, T500))
U44_aga(T501, T500, T479, T502, lessA_out_ag(T501, T500)) → deleteD_out_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_aga(T505, T500, T479, T506, lessA_in_ag(T505, T500))
U45_aga(T505, T500, T479, T506, lessA_out_ag(T505, T500)) → U46_aga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
U46_aga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
deleteD_in_aga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_aga(T527, T524, T525, T528, pC_in_gaa(T524, T527, T528))
U47_aga(T527, T524, T525, T528, pC_out_gaa(T524, T527, T528)) → deleteD_out_aga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_aga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_aga(T547, T537, T546, deleteD_in_aga(s(T547), void, T546))
deleteD_in_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_aga(T556, T554, T537, T557, lessB_in_ga(T554, T556))
U49_aga(T556, T554, T537, T557, lessB_out_ga(T554, T556)) → deleteD_out_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_aga(T560, T554, T537, T561, lessB_in_ga(T554, T560))
U50_aga(T560, T554, T537, T561, lessB_out_ga(T554, T560)) → U51_aga(T560, T554, T537, T561, deleteD_in_aga(s(T560), void, T561))
deleteD_in_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_aga(T651, T647, T648, T649, T652, lessA_in_ag(T651, T647))
U53_aga(T651, T647, T648, T649, T652, lessA_out_ag(T651, T647)) → deleteD_out_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_aga(T655, T647, T648, T649, T656, lessA_in_ag(T655, T647))
U54_aga(T655, T647, T648, T649, T656, lessA_out_ag(T655, T647)) → U55_aga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
U55_aga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
deleteD_in_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_aga(T680, T676, T677, T678, T681, pH_in_gaga(T676, T680, T678, T681))
pH_in_gaga(T676, T680, T678, T681) → U13_gaga(T676, T680, T678, T681, lessB_in_ga(T676, T680))
U13_gaga(T676, T680, T678, T681, lessB_out_ga(T676, T680)) → pH_out_gaga(T676, T680, T678, T681)
pH_in_gaga(T676, T684, T678, T685) → U14_gaga(T676, T684, T678, T685, lessB_in_ga(T676, T684))
U14_gaga(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → U15_gaga(T676, T684, T678, T685, deleteD_in_aga(T684, T678, T685))
deleteD_in_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_aga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
U57_aga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
deleteD_in_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_aga(T724, T723, T701, T702, T725, lessA_in_ag(T724, T723))
U58_aga(T724, T723, T701, T702, T725, lessA_out_ag(T724, T723)) → deleteD_out_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_aga(T728, T723, T701, T702, T729, lessA_in_ag(T728, T723))
U59_aga(T728, T723, T701, T702, T729, lessA_out_ag(T728, T723)) → U60_aga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
U60_aga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
deleteD_in_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_aga(T753, T749, T750, T751, T754, pH_in_gaga(T749, T753, T751, T754))
U61_aga(T753, T749, T750, T751, T754, pH_out_gaga(T749, T753, T751, T754)) → deleteD_out_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_aga(T775, T764, T765, T774, deleteD_in_aga(s(T775), T765, T774))
deleteD_in_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_aga(T786, T784, T764, T765, T787, lessB_in_ga(T784, T786))
U63_aga(T786, T784, T764, T765, T787, lessB_out_ga(T784, T786)) → deleteD_out_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_aga(T790, T784, T764, T765, T791, lessB_in_ga(T784, T790))
U64_aga(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → U65_aga(T790, T784, T764, T765, T791, deleteD_in_aga(s(T790), T765, T791))
U65_aga(T790, T784, T764, T765, T791, deleteD_out_aga(s(T790), T765, T791)) → deleteD_out_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_aga(T775, T764, T765, T774, deleteD_out_aga(s(T775), T765, T774)) → deleteD_out_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U15_gaga(T676, T684, T678, T685, deleteD_out_aga(T684, T678, T685)) → pH_out_gaga(T676, T684, T678, T685)
U56_aga(T680, T676, T677, T678, T681, pH_out_gaga(T676, T680, T678, T681)) → deleteD_out_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U51_aga(T560, T554, T537, T561, deleteD_out_aga(s(T560), void, T561)) → deleteD_out_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_aga(T547, T537, T546, deleteD_out_aga(s(T547), void, T546)) → deleteD_out_aga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U38_aga(T399, T393, T374, T400, deleteD_out_aga(s(T399), T374, T400)) → deleteD_out_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_aga(T384, T374, T383, deleteD_out_aga(s(T384), T374, T383)) → deleteD_out_aga(s(T384), tree(0, void, T374), tree(0, void, T383))
U12_gaga(T297, T304, T298, T305, deleteD_out_aga(T304, T298, T305)) → pG_out_gaga(T297, T304, T298, T305)
U29_aga(T300, T297, T298, T301, pG_out_gaga(T297, T300, T298, T301)) → deleteD_out_aga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_aga(T166, T160, T167, deleteD_out_aga(s(T166), void, T167)) → deleteD_out_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_aga(T153, T152, deleteD_out_aga(s(T153), void, T152)) → deleteD_out_aga(s(T153), tree(0, void, void), tree(0, void, T152))
U5_gaa(T64, T70, T71, deleteD_out_aga(T70, void, T71)) → pC_out_gaa(T64, T70, T71)
U17_aga(T66, T64, T67, pC_out_gaa(T64, T66, T67)) → deleteD_out_aga(T66, tree(T64, void, void), tree(T64, void, T67))

(45) UsableRulesProof (EQUIVALENT transformation)

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

(46) Obligation:

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

LESSA_IN_AG(s(T52), s(T51)) → LESSA_IN_AG(T52, T51)

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

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

(47) PiDPToQDPProof (SOUND transformation)

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

(48) Obligation:

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

LESSA_IN_AG(s(T51)) → LESSA_IN_AG(T51)

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

(49) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

LESSA_IN_AG(s(T51)) → LESSA_IN_AG(T51)
The graph contains the following edges 1 > 1

(50) YES

(51) Obligation:

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

DELETED_IN_AGA(T300, tree(T297, void, T298), tree(T297, void, T301)) → PG_IN_GAGA(T297, T300, T298, T301)
PG_IN_GAGA(T297, T304, T298, T305) → U11_GAGA(T297, T304, T298, T305, lessB_in_ga(T297, T304))
U11_GAGA(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → DELETED_IN_AGA(T304, T298, T305)
DELETED_IN_AGA(s(T384), tree(0, void, T374), tree(0, void, T383)) → DELETED_IN_AGA(s(T384), T374, T383)
DELETED_IN_AGA(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_AGA(T399, T393, T374, T400, lessB_in_ga(T393, T399))
U37_AGA(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → DELETED_IN_AGA(s(T399), T374, T400)
DELETED_IN_AGA(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → PH_IN_GAGA(T676, T680, T678, T681)
PH_IN_GAGA(T676, T684, T678, T685) → U14_GAGA(T676, T684, T678, T685, lessB_in_ga(T676, T684))
U14_GAGA(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → DELETED_IN_AGA(T684, T678, T685)
DELETED_IN_AGA(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → DELETED_IN_AGA(s(T775), T765, T774)
DELETED_IN_AGA(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_AGA(T790, T784, T764, T765, T791, lessB_in_ga(T784, T790))
U64_AGA(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → DELETED_IN_AGA(s(T790), T765, T791)

The TRS R consists of the following rules:

deleteD_in_aga(T6, tree(T6, void, T7), T7) → deleteD_out_aga(T6, tree(T6, void, T7), T7)
deleteD_in_aga(T9, tree(T9, void, void), void) → deleteD_out_aga(T9, tree(T9, void, void), void)
deleteD_in_aga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_aga(T33, T31, T34, pF_in_aga(T33, T31, T34))
pF_in_aga(T33, T31, T34) → U7_aga(T33, T31, T34, lessA_in_ag(T33, T31))
lessA_in_ag(0, s(T45)) → lessA_out_ag(0, s(T45))
lessA_in_ag(s(T52), s(T51)) → U1_ag(T52, T51, lessA_in_ag(T52, T51))
U1_ag(T52, T51, lessA_out_ag(T52, T51)) → lessA_out_ag(s(T52), s(T51))
U7_aga(T33, T31, T34, lessA_out_ag(T33, T31)) → pF_out_aga(T33, T31, T34)
pF_in_aga(T37, T31, T38) → U8_aga(T37, T31, T38, lessA_in_ag(T37, T31))
U8_aga(T37, T31, T38, lessA_out_ag(T37, T31)) → U9_aga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T6, tree(T6, void, T7), T7) → deleteD_out_gga(T6, tree(T6, void, T7), T7)
deleteD_in_gga(T9, tree(T9, void, void), void) → deleteD_out_gga(T9, tree(T9, void, void), void)
deleteD_in_gga(T33, tree(T31, void, void), tree(T31, T34, void)) → U16_gga(T33, T31, T34, pF_in_gga(T33, T31, T34))
pF_in_gga(T33, T31, T34) → U7_gga(T33, T31, T34, lessA_in_gg(T33, T31))
lessA_in_gg(0, s(T45)) → lessA_out_gg(0, s(T45))
lessA_in_gg(s(T52), s(T51)) → U1_gg(T52, T51, lessA_in_gg(T52, T51))
U1_gg(T52, T51, lessA_out_gg(T52, T51)) → lessA_out_gg(s(T52), s(T51))
U7_gga(T33, T31, T34, lessA_out_gg(T33, T31)) → pF_out_gga(T33, T31, T34)
pF_in_gga(T37, T31, T38) → U8_gga(T37, T31, T38, lessA_in_gg(T37, T31))
U8_gga(T37, T31, T38, lessA_out_gg(T37, T31)) → U9_gga(T37, T31, T38, deleteD_in_gga(T37, void, T38))
deleteD_in_gga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_gga(T66, T64, T67, pC_in_gga(T64, T66, T67))
pC_in_gga(T64, T66, T67) → U3_gga(T64, T66, T67, lessB_in_gg(T64, T66))
lessB_in_gg(0, s(T78)) → lessB_out_gg(0, s(T78))
lessB_in_gg(s(T83), s(T85)) → U2_gg(T83, T85, lessB_in_gg(T83, T85))
U2_gg(T83, T85, lessB_out_gg(T83, T85)) → lessB_out_gg(s(T83), s(T85))
U3_gga(T64, T66, T67, lessB_out_gg(T64, T66)) → pC_out_gga(T64, T66, T67)
pC_in_gga(T64, T70, T71) → U4_gga(T64, T70, T71, lessB_in_gg(T64, T70))
U4_gga(T64, T70, T71, lessB_out_gg(T64, T70)) → U5_gga(T64, T70, T71, deleteD_in_gga(T70, void, T71))
deleteD_in_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_gga(T102, T103, deleteD_in_gga(0, void, T103))
deleteD_in_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_gga(T114, T113, T115, lessA_in_gg(T114, T113))
U19_gga(T114, T113, T115, lessA_out_gg(T114, T113)) → deleteD_out_gga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_gga(T118, T113, T119, lessA_in_gg(T118, T113))
U20_gga(T118, T113, T119, lessA_out_gg(T118, T113)) → U21_gga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
deleteD_in_gga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_gga(T135, T133, T136, pC_in_gga(T133, T135, T136))
U22_gga(T135, T133, T136, pC_out_gga(T133, T135, T136)) → deleteD_out_gga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_gga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_gga(T153, T152, deleteD_in_gga(s(T153), void, T152))
deleteD_in_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_gga(T162, T160, T163, lessB_in_gg(T160, T162))
U24_gga(T162, T160, T163, lessB_out_gg(T160, T162)) → deleteD_out_gga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_gga(T166, T160, T167, lessB_in_gg(T160, T166))
U25_gga(T166, T160, T167, lessB_out_gg(T160, T166)) → U26_gga(T166, T160, T167, deleteD_in_gga(s(T166), void, T167))
deleteD_in_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_gga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
delminE_in_gaa(tree(T238, void, T239), T238, T239) → delminE_out_gaa(tree(T238, void, T239), T238, T239)
delminE_in_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257)) → U6_gaa(T252, T253, T254, T258, T259, T257, delminE_in_gaa(T253, T258, T259))
U6_gaa(T252, T253, T254, T258, T259, T257, delminE_out_gaa(T253, T258, T259)) → delminE_out_gaa(tree(T252, T253, T254), T258, tree(T252, T259, T257))
U27_gga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_gga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_gga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_gga(T284, T281, T282, T285, pF_in_gga(T284, T281, T285))
U28_gga(T284, T281, T282, T285, pF_out_gga(T284, T281, T285)) → deleteD_out_gga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_gga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_gga(T300, T297, T298, T301, pG_in_ggga(T297, T300, T298, T301))
pG_in_ggga(T297, T300, T298, T301) → U10_ggga(T297, T300, T298, T301, lessB_in_gg(T297, T300))
U10_ggga(T297, T300, T298, T301, lessB_out_gg(T297, T300)) → pG_out_ggga(T297, T300, T298, T301)
pG_in_ggga(T297, T304, T298, T305) → U11_ggga(T297, T304, T298, T305, lessB_in_gg(T297, T304))
U11_ggga(T297, T304, T298, T305, lessB_out_gg(T297, T304)) → U12_ggga(T297, T304, T298, T305, deleteD_in_gga(T304, T298, T305))
deleteD_in_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_gga(T328, T320, T329, deleteD_in_gga(0, void, T329))
deleteD_in_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_gga(T340, T339, T320, T341, lessA_in_gg(T340, T339))
U31_gga(T340, T339, T320, T341, lessA_out_gg(T340, T339)) → deleteD_out_gga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_gga(T344, T339, T320, T345, lessA_in_gg(T344, T339))
U32_gga(T344, T339, T320, T345, lessA_out_gg(T344, T339)) → U33_gga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
deleteD_in_gga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_gga(T364, T361, T362, T365, pG_in_ggga(T361, T364, T362, T365))
U34_gga(T364, T361, T362, T365, pG_out_ggga(T361, T364, T362, T365)) → deleteD_out_gga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_gga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_gga(T384, T374, T383, deleteD_in_gga(s(T384), T374, T383))
deleteD_in_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_gga(T395, T393, T374, T396, lessB_in_gg(T393, T395))
U36_gga(T395, T393, T374, T396, lessB_out_gg(T393, T395)) → deleteD_out_gga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_gga(T399, T393, T374, T400, lessB_in_gg(T393, T399))
U37_gga(T399, T393, T374, T400, lessB_out_gg(T393, T399)) → U38_gga(T399, T393, T374, T400, deleteD_in_gga(s(T399), T374, T400))
deleteD_in_gga(T411, tree(T411, T412, void), T412) → deleteD_out_gga(T411, tree(T411, T412, void), T412)
deleteD_in_gga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_gga(T443, T440, T441, T444, lessA_in_gg(T443, T440))
U39_gga(T443, T440, T441, T444, lessA_out_gg(T443, T440)) → deleteD_out_gga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_gga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_gga(T447, T440, T441, T448, lessA_in_gg(T447, T440))
U40_gga(T447, T440, T441, T448, lessA_out_gg(T447, T440)) → U41_gga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
deleteD_in_gga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_gga(T469, T466, T467, T470, pC_in_gga(T466, T469, T470))
U42_gga(T469, T466, T467, T470, pC_out_gga(T466, T469, T470)) → deleteD_out_gga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_gga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
deleteD_in_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_gga(T501, T500, T479, T502, lessA_in_gg(T501, T500))
U44_gga(T501, T500, T479, T502, lessA_out_gg(T501, T500)) → deleteD_out_gga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_gga(T505, T500, T479, T506, lessA_in_gg(T505, T500))
U45_gga(T505, T500, T479, T506, lessA_out_gg(T505, T500)) → U46_gga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
deleteD_in_gga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_gga(T527, T524, T525, T528, pC_in_gga(T524, T527, T528))
U47_gga(T527, T524, T525, T528, pC_out_gga(T524, T527, T528)) → deleteD_out_gga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_gga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_gga(T547, T537, T546, deleteD_in_gga(s(T547), void, T546))
deleteD_in_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_gga(T556, T554, T537, T557, lessB_in_gg(T554, T556))
U49_gga(T556, T554, T537, T557, lessB_out_gg(T554, T556)) → deleteD_out_gga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_gga(T560, T554, T537, T561, lessB_in_gg(T554, T560))
U50_gga(T560, T554, T537, T561, lessB_out_gg(T554, T560)) → U51_gga(T560, T554, T537, T561, deleteD_in_gga(s(T560), void, T561))
deleteD_in_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_gga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_gga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_gga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_gga(T651, T647, T648, T649, T652, lessA_in_gg(T651, T647))
U53_gga(T651, T647, T648, T649, T652, lessA_out_gg(T651, T647)) → deleteD_out_gga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_gga(T655, T647, T648, T649, T656, lessA_in_gg(T655, T647))
U54_gga(T655, T647, T648, T649, T656, lessA_out_gg(T655, T647)) → U55_gga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
deleteD_in_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_gga(T680, T676, T677, T678, T681, pH_in_ggga(T676, T680, T678, T681))
pH_in_ggga(T676, T680, T678, T681) → U13_ggga(T676, T680, T678, T681, lessB_in_gg(T676, T680))
U13_ggga(T676, T680, T678, T681, lessB_out_gg(T676, T680)) → pH_out_ggga(T676, T680, T678, T681)
pH_in_ggga(T676, T684, T678, T685) → U14_ggga(T676, T684, T678, T685, lessB_in_gg(T676, T684))
U14_ggga(T676, T684, T678, T685, lessB_out_gg(T676, T684)) → U15_ggga(T676, T684, T678, T685, deleteD_in_gga(T684, T678, T685))
deleteD_in_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_gga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
deleteD_in_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_gga(T724, T723, T701, T702, T725, lessA_in_gg(T724, T723))
U58_gga(T724, T723, T701, T702, T725, lessA_out_gg(T724, T723)) → deleteD_out_gga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_gga(T728, T723, T701, T702, T729, lessA_in_gg(T728, T723))
U59_gga(T728, T723, T701, T702, T729, lessA_out_gg(T728, T723)) → U60_gga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
deleteD_in_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_gga(T753, T749, T750, T751, T754, pH_in_ggga(T749, T753, T751, T754))
U61_gga(T753, T749, T750, T751, T754, pH_out_ggga(T749, T753, T751, T754)) → deleteD_out_gga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_gga(T775, T764, T765, T774, deleteD_in_gga(s(T775), T765, T774))
deleteD_in_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_gga(T786, T784, T764, T765, T787, lessB_in_gg(T784, T786))
U63_gga(T786, T784, T764, T765, T787, lessB_out_gg(T784, T786)) → deleteD_out_gga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_gga(T790, T784, T764, T765, T791, lessB_in_gg(T784, T790))
U64_gga(T790, T784, T764, T765, T791, lessB_out_gg(T784, T790)) → U65_gga(T790, T784, T764, T765, T791, deleteD_in_gga(s(T790), T765, T791))
U65_gga(T790, T784, T764, T765, T791, deleteD_out_gga(s(T790), T765, T791)) → deleteD_out_gga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_gga(T775, T764, T765, T774, deleteD_out_gga(s(T775), T765, T774)) → deleteD_out_gga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U60_gga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_gga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
U57_gga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_gga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
U15_ggga(T676, T684, T678, T685, deleteD_out_gga(T684, T678, T685)) → pH_out_ggga(T676, T684, T678, T685)
U56_gga(T680, T676, T677, T678, T681, pH_out_ggga(T676, T680, T678, T681)) → deleteD_out_gga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U55_gga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_gga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
U51_gga(T560, T554, T537, T561, deleteD_out_gga(s(T560), void, T561)) → deleteD_out_gga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_gga(T547, T537, T546, deleteD_out_gga(s(T547), void, T546)) → deleteD_out_gga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U46_gga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_gga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
U43_gga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_gga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
U41_gga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_gga(T447, tree(T440, T441, void), tree(T440, T448, void))
U38_gga(T399, T393, T374, T400, deleteD_out_gga(s(T399), T374, T400)) → deleteD_out_gga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_gga(T384, T374, T383, deleteD_out_gga(s(T384), T374, T383)) → deleteD_out_gga(s(T384), tree(0, void, T374), tree(0, void, T383))
U33_gga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_gga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
U30_gga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_gga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
U12_ggga(T297, T304, T298, T305, deleteD_out_gga(T304, T298, T305)) → pG_out_ggga(T297, T304, T298, T305)
U29_gga(T300, T297, T298, T301, pG_out_ggga(T297, T300, T298, T301)) → deleteD_out_gga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_gga(T166, T160, T167, deleteD_out_gga(s(T166), void, T167)) → deleteD_out_gga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_gga(T153, T152, deleteD_out_gga(s(T153), void, T152)) → deleteD_out_gga(s(T153), tree(0, void, void), tree(0, void, T152))
U21_gga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_gga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
U18_gga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_gga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
U5_gga(T64, T70, T71, deleteD_out_gga(T70, void, T71)) → pC_out_gga(T64, T70, T71)
U17_gga(T66, T64, T67, pC_out_gga(T64, T66, T67)) → deleteD_out_gga(T66, tree(T64, void, void), tree(T64, void, T67))
U9_gga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_gga(T37, T31, T38)
U16_gga(T33, T31, T34, pF_out_gga(T33, T31, T34)) → deleteD_out_gga(T33, tree(T31, void, void), tree(T31, T34, void))
U9_aga(T37, T31, T38, deleteD_out_gga(T37, void, T38)) → pF_out_aga(T37, T31, T38)
U16_aga(T33, T31, T34, pF_out_aga(T33, T31, T34)) → deleteD_out_aga(T33, tree(T31, void, void), tree(T31, T34, void))
deleteD_in_aga(T66, tree(T64, void, void), tree(T64, void, T67)) → U17_aga(T66, T64, T67, pC_in_gaa(T64, T66, T67))
pC_in_gaa(T64, T66, T67) → U3_gaa(T64, T66, T67, lessB_in_ga(T64, T66))
lessB_in_ga(0, s(T78)) → lessB_out_ga(0, s(T78))
lessB_in_ga(s(T83), s(T85)) → U2_ga(T83, T85, lessB_in_ga(T83, T85))
U2_ga(T83, T85, lessB_out_ga(T83, T85)) → lessB_out_ga(s(T83), s(T85))
U3_gaa(T64, T66, T67, lessB_out_ga(T64, T66)) → pC_out_gaa(T64, T66, T67)
pC_in_gaa(T64, T70, T71) → U4_gaa(T64, T70, T71, lessB_in_ga(T64, T70))
U4_gaa(T64, T70, T71, lessB_out_ga(T64, T70)) → U5_gaa(T64, T70, T71, deleteD_in_aga(T70, void, T71))
deleteD_in_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void)) → U18_aga(T102, T103, deleteD_in_gga(0, void, T103))
U18_aga(T102, T103, deleteD_out_gga(0, void, T103)) → deleteD_out_aga(0, tree(s(T102), void, void), tree(s(T102), T103, void))
deleteD_in_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void)) → U19_aga(T114, T113, T115, lessA_in_ag(T114, T113))
U19_aga(T114, T113, T115, lessA_out_ag(T114, T113)) → deleteD_out_aga(s(T114), tree(s(T113), void, void), tree(s(T113), T115, void))
deleteD_in_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void)) → U20_aga(T118, T113, T119, lessA_in_ag(T118, T113))
U20_aga(T118, T113, T119, lessA_out_ag(T118, T113)) → U21_aga(T118, T113, T119, deleteD_in_gga(s(T118), void, T119))
U21_aga(T118, T113, T119, deleteD_out_gga(s(T118), void, T119)) → deleteD_out_aga(s(T118), tree(s(T113), void, void), tree(s(T113), T119, void))
deleteD_in_aga(T135, tree(T133, void, void), tree(T133, void, T136)) → U22_aga(T135, T133, T136, pC_in_gaa(T133, T135, T136))
U22_aga(T135, T133, T136, pC_out_gaa(T133, T135, T136)) → deleteD_out_aga(T135, tree(T133, void, void), tree(T133, void, T136))
deleteD_in_aga(s(T153), tree(0, void, void), tree(0, void, T152)) → U23_aga(T153, T152, deleteD_in_aga(s(T153), void, T152))
deleteD_in_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163)) → U24_aga(T162, T160, T163, lessB_in_ga(T160, T162))
U24_aga(T162, T160, T163, lessB_out_ga(T160, T162)) → deleteD_out_aga(s(T162), tree(s(T160), void, void), tree(s(T160), void, T163))
deleteD_in_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167)) → U25_aga(T166, T160, T167, lessB_in_ga(T160, T166))
U25_aga(T166, T160, T167, lessB_out_ga(T160, T166)) → U26_aga(T166, T160, T167, deleteD_in_aga(s(T166), void, T167))
deleteD_in_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193)) → deleteD_out_aga(T178, tree(T178, void, tree(T192, void, T193)), tree(T192, void, T193))
deleteD_in_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223))) → U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_in_gaa(T219, T224, T225))
U27_aga(T178, T218, T219, T220, T224, T225, T223, delminE_out_gaa(T219, T224, T225)) → deleteD_out_aga(T178, tree(T178, void, tree(T218, T219, T220)), tree(T224, void, tree(T218, T225, T223)))
deleteD_in_aga(T284, tree(T281, void, T282), tree(T281, T285, T282)) → U28_aga(T284, T281, T282, T285, pF_in_aga(T284, T281, T285))
U28_aga(T284, T281, T282, T285, pF_out_aga(T284, T281, T285)) → deleteD_out_aga(T284, tree(T281, void, T282), tree(T281, T285, T282))
deleteD_in_aga(T300, tree(T297, void, T298), tree(T297, void, T301)) → U29_aga(T300, T297, T298, T301, pG_in_gaga(T297, T300, T298, T301))
pG_in_gaga(T297, T300, T298, T301) → U10_gaga(T297, T300, T298, T301, lessB_in_ga(T297, T300))
U10_gaga(T297, T300, T298, T301, lessB_out_ga(T297, T300)) → pG_out_gaga(T297, T300, T298, T301)
pG_in_gaga(T297, T304, T298, T305) → U11_gaga(T297, T304, T298, T305, lessB_in_ga(T297, T304))
U11_gaga(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → U12_gaga(T297, T304, T298, T305, deleteD_in_aga(T304, T298, T305))
deleteD_in_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320)) → U30_aga(T328, T320, T329, deleteD_in_gga(0, void, T329))
U30_aga(T328, T320, T329, deleteD_out_gga(0, void, T329)) → deleteD_out_aga(0, tree(s(T328), void, T320), tree(s(T328), T329, T320))
deleteD_in_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320)) → U31_aga(T340, T339, T320, T341, lessA_in_ag(T340, T339))
U31_aga(T340, T339, T320, T341, lessA_out_ag(T340, T339)) → deleteD_out_aga(s(T340), tree(s(T339), void, T320), tree(s(T339), T341, T320))
deleteD_in_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320)) → U32_aga(T344, T339, T320, T345, lessA_in_ag(T344, T339))
U32_aga(T344, T339, T320, T345, lessA_out_ag(T344, T339)) → U33_aga(T344, T339, T320, T345, deleteD_in_gga(s(T344), void, T345))
U33_aga(T344, T339, T320, T345, deleteD_out_gga(s(T344), void, T345)) → deleteD_out_aga(s(T344), tree(s(T339), void, T320), tree(s(T339), T345, T320))
deleteD_in_aga(T364, tree(T361, void, T362), tree(T361, void, T365)) → U34_aga(T364, T361, T362, T365, pG_in_gaga(T361, T364, T362, T365))
U34_aga(T364, T361, T362, T365, pG_out_gaga(T361, T364, T362, T365)) → deleteD_out_aga(T364, tree(T361, void, T362), tree(T361, void, T365))
deleteD_in_aga(s(T384), tree(0, void, T374), tree(0, void, T383)) → U35_aga(T384, T374, T383, deleteD_in_aga(s(T384), T374, T383))
deleteD_in_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396)) → U36_aga(T395, T393, T374, T396, lessB_in_ga(T393, T395))
U36_aga(T395, T393, T374, T396, lessB_out_ga(T393, T395)) → deleteD_out_aga(s(T395), tree(s(T393), void, T374), tree(s(T393), void, T396))
deleteD_in_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_aga(T399, T393, T374, T400, lessB_in_ga(T393, T399))
U37_aga(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → U38_aga(T399, T393, T374, T400, deleteD_in_aga(s(T399), T374, T400))
deleteD_in_aga(T411, tree(T411, T412, void), T412) → deleteD_out_aga(T411, tree(T411, T412, void), T412)
deleteD_in_aga(T443, tree(T440, T441, void), tree(T440, T444, void)) → U39_aga(T443, T440, T441, T444, lessA_in_ag(T443, T440))
U39_aga(T443, T440, T441, T444, lessA_out_ag(T443, T440)) → deleteD_out_aga(T443, tree(T440, T441, void), tree(T440, T444, void))
deleteD_in_aga(T447, tree(T440, T441, void), tree(T440, T448, void)) → U40_aga(T447, T440, T441, T448, lessA_in_ag(T447, T440))
U40_aga(T447, T440, T441, T448, lessA_out_ag(T447, T440)) → U41_aga(T447, T440, T441, T448, deleteD_in_gga(T447, T441, T448))
U41_aga(T447, T440, T441, T448, deleteD_out_gga(T447, T441, T448)) → deleteD_out_aga(T447, tree(T440, T441, void), tree(T440, T448, void))
deleteD_in_aga(T469, tree(T466, T467, void), tree(T466, T467, T470)) → U42_aga(T469, T466, T467, T470, pC_in_gaa(T466, T469, T470))
U42_aga(T469, T466, T467, T470, pC_out_gaa(T466, T469, T470)) → deleteD_out_aga(T469, tree(T466, T467, void), tree(T466, T467, T470))
deleteD_in_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void)) → U43_aga(T487, T479, T488, deleteD_in_gga(0, T479, T488))
U43_aga(T487, T479, T488, deleteD_out_gga(0, T479, T488)) → deleteD_out_aga(0, tree(s(T487), T479, void), tree(s(T487), T488, void))
deleteD_in_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void)) → U44_aga(T501, T500, T479, T502, lessA_in_ag(T501, T500))
U44_aga(T501, T500, T479, T502, lessA_out_ag(T501, T500)) → deleteD_out_aga(s(T501), tree(s(T500), T479, void), tree(s(T500), T502, void))
deleteD_in_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void)) → U45_aga(T505, T500, T479, T506, lessA_in_ag(T505, T500))
U45_aga(T505, T500, T479, T506, lessA_out_ag(T505, T500)) → U46_aga(T505, T500, T479, T506, deleteD_in_gga(s(T505), T479, T506))
U46_aga(T505, T500, T479, T506, deleteD_out_gga(s(T505), T479, T506)) → deleteD_out_aga(s(T505), tree(s(T500), T479, void), tree(s(T500), T506, void))
deleteD_in_aga(T527, tree(T524, T525, void), tree(T524, T525, T528)) → U47_aga(T527, T524, T525, T528, pC_in_gaa(T524, T527, T528))
U47_aga(T527, T524, T525, T528, pC_out_gaa(T524, T527, T528)) → deleteD_out_aga(T527, tree(T524, T525, void), tree(T524, T525, T528))
deleteD_in_aga(s(T547), tree(0, T537, void), tree(0, T537, T546)) → U48_aga(T547, T537, T546, deleteD_in_aga(s(T547), void, T546))
deleteD_in_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557)) → U49_aga(T556, T554, T537, T557, lessB_in_ga(T554, T556))
U49_aga(T556, T554, T537, T557, lessB_out_ga(T554, T556)) → deleteD_out_aga(s(T556), tree(s(T554), T537, void), tree(s(T554), T537, T557))
deleteD_in_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561)) → U50_aga(T560, T554, T537, T561, lessB_in_ga(T554, T560))
U50_aga(T560, T554, T537, T561, lessB_out_ga(T554, T560)) → U51_aga(T560, T554, T537, T561, deleteD_in_aga(s(T560), void, T561))
deleteD_in_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589)) → deleteD_out_aga(T573, tree(T573, T574, tree(T588, void, T589)), tree(T588, T574, T589))
deleteD_in_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619))) → U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_in_gaa(T615, T620, T621))
U52_aga(T573, T574, T614, T615, T616, T620, T621, T619, delminE_out_gaa(T615, T620, T621)) → deleteD_out_aga(T573, tree(T573, T574, tree(T614, T615, T616)), tree(T620, T574, tree(T614, T621, T619)))
deleteD_in_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649)) → U53_aga(T651, T647, T648, T649, T652, lessA_in_ag(T651, T647))
U53_aga(T651, T647, T648, T649, T652, lessA_out_ag(T651, T647)) → deleteD_out_aga(T651, tree(T647, T648, T649), tree(T647, T652, T649))
deleteD_in_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649)) → U54_aga(T655, T647, T648, T649, T656, lessA_in_ag(T655, T647))
U54_aga(T655, T647, T648, T649, T656, lessA_out_ag(T655, T647)) → U55_aga(T655, T647, T648, T649, T656, deleteD_in_gga(T655, T648, T656))
U55_aga(T655, T647, T648, T649, T656, deleteD_out_gga(T655, T648, T656)) → deleteD_out_aga(T655, tree(T647, T648, T649), tree(T647, T656, T649))
deleteD_in_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → U56_aga(T680, T676, T677, T678, T681, pH_in_gaga(T676, T680, T678, T681))
pH_in_gaga(T676, T680, T678, T681) → U13_gaga(T676, T680, T678, T681, lessB_in_ga(T676, T680))
U13_gaga(T676, T680, T678, T681, lessB_out_ga(T676, T680)) → pH_out_gaga(T676, T680, T678, T681)
pH_in_gaga(T676, T684, T678, T685) → U14_gaga(T676, T684, T678, T685, lessB_in_ga(T676, T684))
U14_gaga(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → U15_gaga(T676, T684, T678, T685, deleteD_in_aga(T684, T678, T685))
deleteD_in_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702)) → U57_aga(T710, T701, T702, T711, deleteD_in_gga(0, T701, T711))
U57_aga(T710, T701, T702, T711, deleteD_out_gga(0, T701, T711)) → deleteD_out_aga(0, tree(s(T710), T701, T702), tree(s(T710), T711, T702))
deleteD_in_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702)) → U58_aga(T724, T723, T701, T702, T725, lessA_in_ag(T724, T723))
U58_aga(T724, T723, T701, T702, T725, lessA_out_ag(T724, T723)) → deleteD_out_aga(s(T724), tree(s(T723), T701, T702), tree(s(T723), T725, T702))
deleteD_in_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702)) → U59_aga(T728, T723, T701, T702, T729, lessA_in_ag(T728, T723))
U59_aga(T728, T723, T701, T702, T729, lessA_out_ag(T728, T723)) → U60_aga(T728, T723, T701, T702, T729, deleteD_in_gga(s(T728), T701, T729))
U60_aga(T728, T723, T701, T702, T729, deleteD_out_gga(s(T728), T701, T729)) → deleteD_out_aga(s(T728), tree(s(T723), T701, T702), tree(s(T723), T729, T702))
deleteD_in_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754)) → U61_aga(T753, T749, T750, T751, T754, pH_in_gaga(T749, T753, T751, T754))
U61_aga(T753, T749, T750, T751, T754, pH_out_gaga(T749, T753, T751, T754)) → deleteD_out_aga(T753, tree(T749, T750, T751), tree(T749, T750, T754))
deleteD_in_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → U62_aga(T775, T764, T765, T774, deleteD_in_aga(s(T775), T765, T774))
deleteD_in_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787)) → U63_aga(T786, T784, T764, T765, T787, lessB_in_ga(T784, T786))
U63_aga(T786, T784, T764, T765, T787, lessB_out_ga(T784, T786)) → deleteD_out_aga(s(T786), tree(s(T784), T764, T765), tree(s(T784), T764, T787))
deleteD_in_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_aga(T790, T784, T764, T765, T791, lessB_in_ga(T784, T790))
U64_aga(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → U65_aga(T790, T784, T764, T765, T791, deleteD_in_aga(s(T790), T765, T791))
U65_aga(T790, T784, T764, T765, T791, deleteD_out_aga(s(T790), T765, T791)) → deleteD_out_aga(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791))
U62_aga(T775, T764, T765, T774, deleteD_out_aga(s(T775), T765, T774)) → deleteD_out_aga(s(T775), tree(0, T764, T765), tree(0, T764, T774))
U15_gaga(T676, T684, T678, T685, deleteD_out_aga(T684, T678, T685)) → pH_out_gaga(T676, T684, T678, T685)
U56_aga(T680, T676, T677, T678, T681, pH_out_gaga(T676, T680, T678, T681)) → deleteD_out_aga(T680, tree(T676, T677, T678), tree(T676, T677, T681))
U51_aga(T560, T554, T537, T561, deleteD_out_aga(s(T560), void, T561)) → deleteD_out_aga(s(T560), tree(s(T554), T537, void), tree(s(T554), T537, T561))
U48_aga(T547, T537, T546, deleteD_out_aga(s(T547), void, T546)) → deleteD_out_aga(s(T547), tree(0, T537, void), tree(0, T537, T546))
U38_aga(T399, T393, T374, T400, deleteD_out_aga(s(T399), T374, T400)) → deleteD_out_aga(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400))
U35_aga(T384, T374, T383, deleteD_out_aga(s(T384), T374, T383)) → deleteD_out_aga(s(T384), tree(0, void, T374), tree(0, void, T383))
U12_gaga(T297, T304, T298, T305, deleteD_out_aga(T304, T298, T305)) → pG_out_gaga(T297, T304, T298, T305)
U29_aga(T300, T297, T298, T301, pG_out_gaga(T297, T300, T298, T301)) → deleteD_out_aga(T300, tree(T297, void, T298), tree(T297, void, T301))
U26_aga(T166, T160, T167, deleteD_out_aga(s(T166), void, T167)) → deleteD_out_aga(s(T166), tree(s(T160), void, void), tree(s(T160), void, T167))
U23_aga(T153, T152, deleteD_out_aga(s(T153), void, T152)) → deleteD_out_aga(s(T153), tree(0, void, void), tree(0, void, T152))
U5_gaa(T64, T70, T71, deleteD_out_aga(T70, void, T71)) → pC_out_gaa(T64, T70, T71)
U17_aga(T66, T64, T67, pC_out_gaa(T64, T66, T67)) → deleteD_out_aga(T66, tree(T64, void, void), tree(T64, void, T67))

(52) UsableRulesProof (EQUIVALENT transformation)

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

(53) Obligation:

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

DELETED_IN_AGA(T300, tree(T297, void, T298), tree(T297, void, T301)) → PG_IN_GAGA(T297, T300, T298, T301)
PG_IN_GAGA(T297, T304, T298, T305) → U11_GAGA(T297, T304, T298, T305, lessB_in_ga(T297, T304))
U11_GAGA(T297, T304, T298, T305, lessB_out_ga(T297, T304)) → DELETED_IN_AGA(T304, T298, T305)
DELETED_IN_AGA(s(T384), tree(0, void, T374), tree(0, void, T383)) → DELETED_IN_AGA(s(T384), T374, T383)
DELETED_IN_AGA(s(T399), tree(s(T393), void, T374), tree(s(T393), void, T400)) → U37_AGA(T399, T393, T374, T400, lessB_in_ga(T393, T399))
U37_AGA(T399, T393, T374, T400, lessB_out_ga(T393, T399)) → DELETED_IN_AGA(s(T399), T374, T400)
DELETED_IN_AGA(T680, tree(T676, T677, T678), tree(T676, T677, T681)) → PH_IN_GAGA(T676, T680, T678, T681)
PH_IN_GAGA(T676, T684, T678, T685) → U14_GAGA(T676, T684, T678, T685, lessB_in_ga(T676, T684))
U14_GAGA(T676, T684, T678, T685, lessB_out_ga(T676, T684)) → DELETED_IN_AGA(T684, T678, T685)
DELETED_IN_AGA(s(T775), tree(0, T764, T765), tree(0, T764, T774)) → DELETED_IN_AGA(s(T775), T765, T774)
DELETED_IN_AGA(s(T790), tree(s(T784), T764, T765), tree(s(T784), T764, T791)) → U64_AGA(T790, T784, T764, T765, T791, lessB_in_ga(T784, T790))
U64_AGA(T790, T784, T764, T765, T791, lessB_out_ga(T784, T790)) → DELETED_IN_AGA(s(T790), T765, T791)

The TRS R consists of the following rules:

lessB_in_ga(0, s(T78)) → lessB_out_ga(0, s(T78))
lessB_in_ga(s(T83), s(T85)) → U2_ga(T83, T85, lessB_in_ga(T83, T85))
U2_ga(T83, T85, lessB_out_ga(T83, T85)) → lessB_out_ga(s(T83), s(T85))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
void = void
s(x1) = s(x1)
0 = 0
lessB_in_ga(x1, x2) = lessB_in_ga(x1)
lessB_out_ga(x1, x2) = lessB_out_ga(x1)
U2_ga(x1, x2, x3) = U2_ga(x1, x3)
DELETED_IN_AGA(x1, x2, x3) = DELETED_IN_AGA(x2)
PG_IN_GAGA(x1, x2, x3, x4) = PG_IN_GAGA(x1, x3)
U11_GAGA(x1, x2, x3, x4, x5) = U11_GAGA(x1, x3, x5)
U37_AGA(x1, x2, x3, x4, x5) = U37_AGA(x2, x3, x5)
PH_IN_GAGA(x1, x2, x3, x4) = PH_IN_GAGA(x1, x3)
U14_GAGA(x1, x2, x3, x4, x5) = U14_GAGA(x1, x3, x5)
U64_AGA(x1, x2, x3, x4, x5, x6) = U64_AGA(x2, x3, x4, x6)

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

(54) PiDPToQDPProof (SOUND transformation)

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

(55) Obligation:

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

DELETED_IN_AGA(tree(T297, void, T298)) → PG_IN_GAGA(T297, T298)
PG_IN_GAGA(T297, T298) → U11_GAGA(T297, T298, lessB_in_ga(T297))
U11_GAGA(T297, T298, lessB_out_ga(T297)) → DELETED_IN_AGA(T298)
DELETED_IN_AGA(tree(0, void, T374)) → DELETED_IN_AGA(T374)
DELETED_IN_AGA(tree(s(T393), void, T374)) → U37_AGA(T393, T374, lessB_in_ga(T393))
U37_AGA(T393, T374, lessB_out_ga(T393)) → DELETED_IN_AGA(T374)
DELETED_IN_AGA(tree(T676, T677, T678)) → PH_IN_GAGA(T676, T678)
PH_IN_GAGA(T676, T678) → U14_GAGA(T676, T678, lessB_in_ga(T676))
U14_GAGA(T676, T678, lessB_out_ga(T676)) → DELETED_IN_AGA(T678)
DELETED_IN_AGA(tree(0, T764, T765)) → DELETED_IN_AGA(T765)
DELETED_IN_AGA(tree(s(T784), T764, T765)) → U64_AGA(T784, T764, T765, lessB_in_ga(T784))
U64_AGA(T784, T764, T765, lessB_out_ga(T784)) → DELETED_IN_AGA(T765)

The TRS R consists of the following rules:

lessB_in_ga(0) → lessB_out_ga(0)
lessB_in_ga(s(T83)) → U2_ga(T83, lessB_in_ga(T83))
U2_ga(T83, lessB_out_ga(T83)) → lessB_out_ga(s(T83))

The set Q consists of the following terms:

lessB_in_ga(x0)
U2_ga(x0, x1)

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

(56) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

PG_IN_GAGA(T297, T298) → U11_GAGA(T297, T298, lessB_in_ga(T297))
The graph contains the following edges 1 >= 1, 2 >= 2
U11_GAGA(T297, T298, lessB_out_ga(T297)) → DELETED_IN_AGA(T298)
The graph contains the following edges 2 >= 1
DELETED_IN_AGA(tree(T297, void, T298)) → PG_IN_GAGA(T297, T298)
The graph contains the following edges 1 > 1, 1 > 2
PH_IN_GAGA(T676, T678) → U14_GAGA(T676, T678, lessB_in_ga(T676))
The graph contains the following edges 1 >= 1, 2 >= 2
U37_AGA(T393, T374, lessB_out_ga(T393)) → DELETED_IN_AGA(T374)
The graph contains the following edges 2 >= 1
DELETED_IN_AGA(tree(s(T393), void, T374)) → U37_AGA(T393, T374, lessB_in_ga(T393))
The graph contains the following edges 1 > 1, 1 > 2
U14_GAGA(T676, T678, lessB_out_ga(T676)) → DELETED_IN_AGA(T678)
The graph contains the following edges 2 >= 1
U64_AGA(T784, T764, T765, lessB_out_ga(T784)) → DELETED_IN_AGA(T765)
The graph contains the following edges 3 >= 1
DELETED_IN_AGA(tree(T676, T677, T678)) → PH_IN_GAGA(T676, T678)
The graph contains the following edges 1 > 1, 1 > 2
DELETED_IN_AGA(tree(s(T784), T764, T765)) → U64_AGA(T784, T764, T765, lessB_in_ga(T784))
The graph contains the following edges 1 > 1, 1 > 2, 1 > 3
DELETED_IN_AGA(tree(0, void, T374)) → DELETED_IN_AGA(T374)
The graph contains the following edges 1 > 1
DELETED_IN_AGA(tree(0, T764, T765)) → DELETED_IN_AGA(T765)
The graph contains the following edges 1 > 1

(0) Obligation:

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) PrologToPiTRSProof (SOUND transformation)

(4) Obligation:

(5) DependencyPairsProof (EQUIVALENT transformation)

(6) Obligation:

(7) DependencyGraphProof (EQUIVALENT transformation)

(8) Complex Obligation (AND)

(9) Obligation:

(10) UsableRulesProof (EQUIVALENT transformation)

(11) Obligation:

(12) PiDPToQDPProof (SOUND transformation)

(13) Obligation:

(14) QDPSizeChangeProof (EQUIVALENT transformation)

(15) YES

(16) Obligation:

(17) UsableRulesProof (EQUIVALENT transformation)

(18) Obligation:

(19) PiDPToQDPProof (SOUND transformation)

(20) Obligation:

(21) QDPSizeChangeProof (EQUIVALENT transformation)

(22) YES

(23) Obligation:

(24) UsableRulesProof (EQUIVALENT transformation)

(25) Obligation:

(26) PiDPToQDPProof (EQUIVALENT transformation)

(27) Obligation:

(28) QDPSizeChangeProof (EQUIVALENT transformation)

(29) YES

(30) Obligation:

(31) UsableRulesProof (EQUIVALENT transformation)

(32) Obligation:

(33) PiDPToQDPProof (EQUIVALENT transformation)

(34) Obligation:

(35) QDPSizeChangeProof (EQUIVALENT transformation)

(36) YES

(37) Obligation:

(38) UsableRulesProof (EQUIVALENT transformation)

(39) Obligation:

(40) PiDPToQDPProof (SOUND transformation)

(41) Obligation:

(42) QDPSizeChangeProof (EQUIVALENT transformation)

(43) YES

(44) Obligation:

(45) UsableRulesProof (EQUIVALENT transformation)

(46) Obligation:

(47) PiDPToQDPProof (SOUND transformation)

(48) Obligation:

(49) QDPSizeChangeProof (EQUIVALENT transformation)

(50) YES

(51) Obligation:

(52) UsableRulesProof (EQUIVALENT transformation)

(53) Obligation:

(54) PiDPToQDPProof (SOUND transformation)

(55) Obligation:

(56) QDPSizeChangeProof (EQUIVALENT transformation)

(57) YES