Left Termination proof of /tmp/tmpwG6JVK/delete-fbf.pl

Left Termination of the query pattern delete_in_3(a, g, a) w.r.t. the given Prolog program could successfully be proven:

0 Prolog

↳1 PrologToDTProblemTransformerProof (⇐)

↳2 TRIPLES

↳3 TriplesToPiDPProof (⇐)

↳4 PiDP

↳5 DependencyGraphProof (⇔)

↳6 AND

    ↳7 PiDP

        ↳8 UsableRulesProof (⇔)

        ↳9 PiDP

        ↳10 PiDPToQDPProof (⇐)

        ↳11 QDP

        ↳12 QDPSizeChangeProof (⇔)

        ↳13 YES

    ↳14 PiDP

        ↳15 UsableRulesProof (⇔)

        ↳16 PiDP

        ↳17 PiDPToQDPProof (⇐)

        ↳18 QDP

        ↳19 QDPSizeChangeProof (⇔)

        ↳20 YES

    ↳21 PiDP

        ↳22 UsableRulesProof (⇔)

        ↳23 PiDP

        ↳24 PiDPToQDPProof (⇔)

        ↳25 QDP

        ↳26 QDPSizeChangeProof (⇔)

        ↳27 YES

    ↳28 PiDP

        ↳29 UsableRulesProof (⇔)

        ↳30 PiDP

        ↳31 PiDPToQDPProof (⇔)

        ↳32 QDP

        ↳33 QDPSizeChangeProof (⇔)

        ↳34 YES

    ↳35 PiDP

        ↳36 UsableRulesProof (⇔)

        ↳37 PiDP

        ↳38 PiDPToQDPProof (⇐)

        ↳39 QDP

        ↳40 QDPSizeChangeProof (⇔)

        ↳41 YES

    ↳42 PiDP

        ↳43 UsableRulesProof (⇔)

        ↳44 PiDP

        ↳45 PiDPToQDPProof (⇐)

        ↳46 QDP

        ↳47 QDPSizeChangeProof (⇔)

        ↳48 YES

    ↳49 PiDP

        ↳50 UsableRulesProof (⇔)

        ↳51 PiDP

        ↳52 PiDPToQDPProof (⇐)

        ↳53 QDP

        ↳54 QDPSizeChangeProof (⇔)

        ↳55 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).

Queries:

delete(a,g,a).

(1) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph.

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\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\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X12, tree(X12, X13, void), X13)", 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\ndelete(T1, tree(T9, void, void), T3) !=? delete(X21, tree(X21, X22, X23), tree(X24, X22, X25))", 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(T69, T71), delete(T71, void, T72))\n\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: less(T69, T71)\n\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: delete(T75, void, T76)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: less(T69, T71), SCOPE: 4, CLAUSE: 7 | less(T69, T71), SCOPE: 4, CLAUSE: 8\n\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: less(T69, T71), SCOPE: 4, CLAUSE: 7\n\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: less(T69, T71), SCOPE: 4, CLAUSE: 8\n\nT69 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(T88, T90)\n\nT88 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: ','(less(T106, T104), delete(T106, void, T107)) | delete(T1, tree(T104, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT104 is ground\ndelete(T1, tree(T104, void, void), T3) !=? delete(X21, tree(X21, X22, X23), tree(X24, X22, X25))", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT9 is ground\ndelete(T1, tree(T9, void, void), T3) !=? delete(X21, tree(X21, X22, X23), tree(X24, X22, X25))\ndelete(T1, tree(T9, void, void), T3) !=? delete(X180, tree(X181, X182, X183), tree(X181, X184, X183))", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: ','(less(T106, T104), delete(T106, void, T107)), SCOPE: 5, CLAUSE: 7 | ','(less(T106, T104), delete(T106, void, T107)), SCOPE: 5, CLAUSE: 8 | ?_5 | delete(T1, tree(T104, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT104 is ground\ndelete(T1, tree(T104, void, void), T3) !=? delete(X21, tree(X21, X22, X23), tree(X24, X22, X25))", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: ','(less(T106, T104), delete(T106, void, T107)), SCOPE: 5, CLAUSE: 7\n\nT104 is ground\ndelete(T1, tree(T104, void, void), T3) !=? delete(X21, tree(X21, X22, X23), tree(X24, X22, X25))", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(less(T106, T104), delete(T106, void, T107)), SCOPE: 5, CLAUSE: 8 | ?_5 | delete(T1, tree(T104, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT104 is ground\ndelete(T1, tree(T104, void, void), T3) !=? delete(X21, tree(X21, X22, X23), tree(X24, X22, X25))", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: delete(0, void, T113)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: ','(less(T106, T104), delete(T106, void, T107)), SCOPE: 5, CLAUSE: 8\n\nT104 is ground\ndelete(T1, tree(T104, void, void), T3) !=? delete(X21, tree(X21, X22, X23), tree(X24, X22, X25))", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: ?_5 | delete(T1, tree(T104, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT104 is ground\ndelete(T1, tree(T104, void, void), T3) !=? delete(X21, tree(X21, X22, X23), tree(X24, X22, X25))", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(less(T124, T123), delete(s(T124), void, T125))\n\nT123 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: less(T124, T123)\n\nT123 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: delete(s(T128), void, T129)\n\nT128 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: delete(T1, tree(T104, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT104 is ground\ndelete(T1, tree(T104, void, void), T3) !=? delete(X21, tree(X21, X22, X23), tree(X24, X22, X25))", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: ','(less(T146, T148), delete(T148, void, T149))\n\nT146 is ground\ndelete(T1, tree(T146, void, void), T3) !=? delete(X21, tree(X21, X22, X23), tree(X24, X22, X25))", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: ','(less(T156, T158), delete(T158, void, T159))\n\nT156 is ground\ndelete(T1, tree(T156, void, void), T3) !=? delete(X21, tree(X21, X22, X23), tree(X24, X22, X25))", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ','(less(T156, T158), delete(T158, void, T159)), SCOPE: 6, CLAUSE: 7 | ','(less(T156, T158), delete(T158, void, T159)), SCOPE: 6, CLAUSE: 8\n\nT156 is ground\ndelete(T1, tree(T156, void, void), T3) !=? delete(X21, tree(X21, X22, X23), tree(X24, X22, X25))", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: ','(less(T156, T158), delete(T158, void, T159)), SCOPE: 6, CLAUSE: 7\n\nT156 is ground\ndelete(T1, tree(T156, void, void), T3) !=? delete(X21, tree(X21, X22, X23), tree(X24, X22, X25))", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(less(T156, T158), delete(T158, void, T159)), SCOPE: 6, CLAUSE: 8\n\nT156 is ground\ndelete(T1, tree(T156, void, void), T3) !=? delete(X21, tree(X21, X22, X23), tree(X24, X22, X25))", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: delete(s(T166), void, T165)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: ','(less(T178, T180), delete(s(T180), void, T181))\n\nT178 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: less(T178, T180)\n\nT178 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: delete(s(T184), void, T185)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: delmin(T200, T203, T204) | delete(T1, tree(T199, void, T200), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T199, void, T200), T3), SCOPE: 1, CLAUSE: 4\n\nT199 is ground\nT200 is ground\ndelete(T1, tree(T199, void, T200), T3) !=? delete(X12, tree(X12, X13, void), X13)", 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\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X12, tree(X12, X13, void), X13)\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X364, tree(X364, X365, X366), tree(X367, X365, X368))", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: delmin(T200, T203, T204), SCOPE: 7, CLAUSE: 5 | delmin(T200, T203, T204), SCOPE: 7, CLAUSE: 6 | ?_7 | delete(T1, tree(T199, void, T200), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T199, void, T200), T3), SCOPE: 1, CLAUSE: 4\n\nT199 is ground\nT200 is ground\ndelete(T1, tree(T199, void, T200), T3) !=? delete(X12, tree(X12, X13, void), X13)", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: delmin(T200, T203, T204), SCOPE: 7, CLAUSE: 5\n\nT200 is ground\ndelete(T1, tree(T199, void, T200), T3) !=? delete(X12, tree(X12, X13, void), X13)", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: delmin(T200, T203, T204), SCOPE: 7, CLAUSE: 6 | ?_7 | delete(T1, tree(T199, void, T200), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T199, void, T200), T3), SCOPE: 1, CLAUSE: 4\n\nT199 is ground\nT200 is ground\ndelete(T1, tree(T199, void, T200), T3) !=? delete(X12, tree(X12, X13, void), X13)", 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(T200, T203, T204), SCOPE: 7, CLAUSE: 6\n\nT200 is ground\ndelete(T1, tree(T199, void, T200), T3) !=? delete(X12, tree(X12, X13, void), X13)", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: ?_7 | delete(T1, tree(T199, void, T200), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T199, void, T200), T3), SCOPE: 1, CLAUSE: 4\n\nT199 is ground\nT200 is ground\ndelete(T1, tree(T199, void, T200), T3) !=? delete(X12, tree(X12, X13, void), X13)", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: delmin(T240, T245, T246)\n\nT240 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: delmin(T240, T245, T246), SCOPE: 8, CLAUSE: 5 | delmin(T240, T245, T246), SCOPE: 8, CLAUSE: 6\n\nT240 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: delmin(T240, T245, T246), SCOPE: 8, CLAUSE: 5\n\nT240 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: delmin(T240, T245, T246), SCOPE: 8, CLAUSE: 6\n\nT240 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(T274, T279, T280)\n\nT274 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(T199, void, T200), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T199, void, T200), T3), SCOPE: 1, CLAUSE: 4\n\nT199 is ground\nT200 is ground\ndelete(T1, tree(T199, void, T200), T3) !=? delete(X12, tree(X12, X13, void), X13)", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: delete(T1, tree(T199, void, T200), T3), SCOPE: 1, CLAUSE: 3\n\nT199 is ground\nT200 is ground\ndelete(T1, tree(T199, void, T200), T3) !=? delete(X12, tree(X12, X13, void), X13)", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: delete(T1, tree(T199, void, T200), T3), SCOPE: 1, CLAUSE: 4\n\nT199 is ground\nT200 is ground\ndelete(T1, tree(T199, void, T200), T3) !=? delete(X12, tree(X12, X13, void), X13)", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: ','(less(T305, T302), delete(T305, void, T306))\n\nT302 is ground\ndelete(T1, tree(T302, void, T303), T3) !=? delete(X12, tree(X12, X13, void), X13)", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: ','(less(T318, T321), delete(T321, T319, T322))\n\nT318 is ground\nT319 is ground\ndelete(T1, tree(T318, void, T319), T3) !=? delete(X12, tree(X12, X13, void), X13)", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: less(T318, T321)\n\nT318 is ground\ndelete(T1, tree(T318, void, T319), T3) !=? delete(X12, tree(X12, X13, void), X13)", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: delete(T325, T319, T326)\n\nT319 is ground\ndelete(T327, tree(T318, void, T319), T328) !=? delete(T329, tree(T329, T330, void), T330)", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: ','(less(T345, T342), delete(T345, void, T346)) | delete(T1, tree(T342, void, T343), T3), SCOPE: 1, CLAUSE: 4\n\nT342 is ground\nT343 is ground\ndelete(T1, tree(T342, void, T343), T3) !=? delete(X12, tree(X12, X13, void), X13)\ndelete(T1, tree(T342, void, T343), T3) !=? delete(X364, tree(X364, X365, X366), tree(X367, X365, X368))", 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\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X12, tree(X12, X13, void), X13)\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X364, tree(X364, X365, X366), tree(X367, X365, X368))\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X531, tree(X532, X533, X534), tree(X532, X535, X534))", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: ','(less(T345, T342), delete(T345, void, T346)), SCOPE: 9, CLAUSE: 7 | ','(less(T345, T342), delete(T345, void, T346)), SCOPE: 9, CLAUSE: 8 | ?_9 | delete(T1, tree(T342, void, T343), T3), SCOPE: 1, CLAUSE: 4\n\nT342 is ground\nT343 is ground\ndelete(T1, tree(T342, void, T343), T3) !=? delete(X12, tree(X12, X13, void), X13)\ndelete(T1, tree(T342, void, T343), T3) !=? delete(X364, tree(X364, X365, X366), tree(X367, X365, X368))", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: ','(less(T345, T342), delete(T345, void, T346)), SCOPE: 9, CLAUSE: 7\n\nT342 is ground\ndelete(T1, tree(T342, void, T343), T3) !=? delete(X12, tree(X12, X13, void), X13)\ndelete(T1, tree(T342, void, T343), T3) !=? delete(X364, tree(X364, X365, X366), tree(X367, X365, X368))", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: ','(less(T345, T342), delete(T345, void, T346)), SCOPE: 9, CLAUSE: 8 | ?_9 | delete(T1, tree(T342, void, T343), T3), SCOPE: 1, CLAUSE: 4\n\nT342 is ground\nT343 is ground\ndelete(T1, tree(T342, void, T343), T3) !=? delete(X12, tree(X12, X13, void), X13)\ndelete(T1, tree(T342, void, T343), T3) !=? delete(X364, tree(X364, X365, X366), tree(X367, X365, X368))", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: delete(0, void, T352)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: ','(less(T345, T342), delete(T345, void, T346)), SCOPE: 9, CLAUSE: 8\n\nT342 is ground\ndelete(T1, tree(T342, void, T343), T3) !=? delete(X12, tree(X12, X13, void), X13)\ndelete(T1, tree(T342, void, T343), T3) !=? delete(X364, tree(X364, X365, X366), tree(X367, X365, X368))", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: ?_9 | delete(T1, tree(T342, void, T343), T3), SCOPE: 1, CLAUSE: 4\n\nT342 is ground\nT343 is ground\ndelete(T1, tree(T342, void, T343), T3) !=? delete(X12, tree(X12, X13, void), X13)\ndelete(T1, tree(T342, void, T343), T3) !=? delete(X364, tree(X364, X365, X366), tree(X367, X365, X368))", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: ','(less(T363, T362), delete(s(T363), void, T364))\n\nT362 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: delete(T1, tree(T342, void, T343), T3), SCOPE: 1, CLAUSE: 4\n\nT342 is ground\nT343 is ground\ndelete(T1, tree(T342, void, T343), T3) !=? delete(X12, tree(X12, X13, void), X13)\ndelete(T1, tree(T342, void, T343), T3) !=? delete(X364, tree(X364, X365, X366), tree(X367, X365, X368))", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: ','(less(T376, T379), delete(T379, T377, T380))\n\nT376 is ground\nT377 is ground\ndelete(T1, tree(T376, void, T377), T3) !=? delete(X12, tree(X12, X13, void), X13)\ndelete(T1, tree(T376, void, T377), T3) !=? delete(X364, tree(X364, X365, X366), tree(X367, X365, X368))", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ','(less(T388, T391), delete(T391, T389, T392))\n\nT388 is ground\nT389 is ground\ndelete(T1, tree(T388, void, T389), T3) !=? delete(X12, tree(X12, X13, void), X13)\ndelete(T1, tree(T388, void, T389), T3) !=? delete(X364, tree(X364, X365, X366), tree(X367, X365, X368))", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: ','(less(T388, T391), delete(T391, T389, T392)), SCOPE: 10, CLAUSE: 7 | ','(less(T388, T391), delete(T391, T389, T392)), SCOPE: 10, CLAUSE: 8\n\nT388 is ground\nT389 is ground\ndelete(T1, tree(T388, void, T389), T3) !=? delete(X12, tree(X12, X13, void), X13)\ndelete(T1, tree(T388, void, T389), T3) !=? delete(X364, tree(X364, X365, X366), tree(X367, X365, X368))", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: ','(less(T388, T391), delete(T391, T389, T392)), SCOPE: 10, CLAUSE: 7\n\nT388 is ground\nT389 is ground\ndelete(T1, tree(T388, void, T389), T3) !=? delete(X12, tree(X12, X13, void), X13)\ndelete(T1, tree(T388, void, T389), T3) !=? delete(X364, tree(X364, X365, X366), tree(X367, X365, X368))", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: ','(less(T388, T391), delete(T391, T389, T392)), SCOPE: 10, CLAUSE: 8\n\nT388 is ground\nT389 is ground\ndelete(T1, tree(T388, void, T389), T3) !=? delete(X12, tree(X12, X13, void), X13)\ndelete(T1, tree(T388, void, T389), T3) !=? delete(X364, tree(X364, X365, X366), tree(X367, X365, X368))", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: delete(s(T399), T389, T398)\n\nT389 is ground\ndelete(T1, tree(0, void, T389), T3) !=? delete(X12, tree(X12, X13, void), X13)", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: ','(less(T408, T410), delete(s(T410), T389, T411))\n\nT389 is ground\nT408 is ground\ndelete(T1, tree(s(T408), void, T389), T3) !=? delete(X12, tree(X12, X13, void), X13)", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: less(T408, T410)\n\nT408 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: delete(s(T414), T389, T415)\n\nT389 is ground\ndelete(T416, tree(s(T408), void, T389), T417) !=? delete(T418, tree(T418, T419, void), T419)", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: true | delete(T1, tree(T428, T429, void), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T428, T429, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T428, T429, void), T3), SCOPE: 1, CLAUSE: 4\n\nT428 is ground\nT429 is ground\ndelete(T1, tree(T428, T429, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: 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\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: delete(T1, tree(T428, T429, void), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T428, T429, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T428, T429, void), T3), SCOPE: 1, CLAUSE: 4\n\nT428 is ground\nT429 is ground\ndelete(T1, tree(T428, T429, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: delmin(void, T438, T439) | delete(T1, tree(T434, T435, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T434, T435, void), T3), SCOPE: 1, CLAUSE: 4\n\nT434 is ground\nT435 is ground\ndelete(T1, tree(T434, T435, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: delete(T1, tree(T428, T429, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T428, T429, void), T3), SCOPE: 1, CLAUSE: 4\n\nT428 is ground\nT429 is ground\ndelete(T1, tree(T428, T429, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T428, T429, void), T3) !=? delete(X658, tree(X658, X659, X660), tree(X661, X659, X662))", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: delmin(void, T438, T439), SCOPE: 11, CLAUSE: 5 | delmin(void, T438, T439), SCOPE: 11, CLAUSE: 6 | ?_11 | delete(T1, tree(T434, T435, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T434, T435, void), T3), SCOPE: 1, CLAUSE: 4\n\nT434 is ground\nT435 is ground\ndelete(T1, tree(T434, T435, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: delmin(void, T438, T439), SCOPE: 11, CLAUSE: 6 | ?_11 | delete(T1, tree(T434, T435, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T434, T435, void), T3), SCOPE: 1, CLAUSE: 4\n\nT434 is ground\nT435 is ground\ndelete(T1, tree(T434, T435, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: ?_11 | delete(T1, tree(T434, T435, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T434, T435, void), T3), SCOPE: 1, CLAUSE: 4\n\nT434 is ground\nT435 is ground\ndelete(T1, tree(T434, T435, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: delete(T1, tree(T434, T435, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T434, T435, void), T3), SCOPE: 1, CLAUSE: 4\n\nT434 is ground\nT435 is ground\ndelete(T1, tree(T434, T435, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: delete(T1, tree(T434, T435, void), T3), SCOPE: 1, CLAUSE: 3\n\nT434 is ground\nT435 is ground\ndelete(T1, tree(T434, T435, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: delete(T1, tree(T434, T435, void), T3), SCOPE: 1, CLAUSE: 4\n\nT434 is ground\nT435 is ground\ndelete(T1, tree(T434, T435, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: ','(less(T460, T457), delete(T460, T458, T461))\n\nT457 is ground\nT458 is ground\ndelete(T1, tree(T457, T458, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: less(T460, T457)\n\nT457 is ground\ndelete(T1, tree(T457, T458, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: delete(T464, T458, T465)\n\nT458 is ground\nT464 is ground\ndelete(T466, tree(T457, T458, void), T467) !=? delete(T468, tree(T468, void, T469), T469)", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: ','(less(T485, T488), delete(T488, void, T489))\n\nT485 is ground\ndelete(T1, tree(T485, T486, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: ','(less(T500, T497), delete(T500, T498, T501)) | delete(T1, tree(T497, T498, void), T3), SCOPE: 1, CLAUSE: 4\n\nT497 is ground\nT498 is ground\ndelete(T1, tree(T497, T498, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T497, T498, void), T3) !=? delete(X658, tree(X658, X659, X660), tree(X661, X659, X662))", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: delete(T1, tree(T428, T429, void), T3), SCOPE: 1, CLAUSE: 4\n\nT428 is ground\nT429 is ground\ndelete(T1, tree(T428, T429, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T428, T429, void), T3) !=? delete(X658, tree(X658, X659, X660), tree(X661, X659, X662))\ndelete(T1, tree(T428, T429, void), T3) !=? delete(X741, tree(X742, X743, X744), tree(X742, X745, X744))", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: ','(less(T500, T497), delete(T500, T498, T501)), SCOPE: 12, CLAUSE: 7 | ','(less(T500, T497), delete(T500, T498, T501)), SCOPE: 12, CLAUSE: 8 | ?_12 | delete(T1, tree(T497, T498, void), T3), SCOPE: 1, CLAUSE: 4\n\nT497 is ground\nT498 is ground\ndelete(T1, tree(T497, T498, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T497, T498, void), T3) !=? delete(X658, tree(X658, X659, X660), tree(X661, X659, X662))", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: ','(less(T500, T497), delete(T500, T498, T501)), SCOPE: 12, CLAUSE: 7\n\nT497 is ground\nT498 is ground\ndelete(T1, tree(T497, T498, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T497, T498, void), T3) !=? delete(X658, tree(X658, X659, X660), tree(X661, X659, X662))", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: ','(less(T500, T497), delete(T500, T498, T501)), SCOPE: 12, CLAUSE: 8 | ?_12 | delete(T1, tree(T497, T498, void), T3), SCOPE: 1, CLAUSE: 4\n\nT497 is ground\nT498 is ground\ndelete(T1, tree(T497, T498, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T497, T498, void), T3) !=? delete(X658, tree(X658, X659, X660), tree(X661, X659, X662))", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: delete(0, T498, T507)\n\nT498 is ground\ndelete(T1, tree(s(T506), T498, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: ','(less(T500, T497), delete(T500, T498, T501)), SCOPE: 12, CLAUSE: 8\n\nT497 is ground\nT498 is ground\ndelete(T1, tree(T497, T498, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T497, T498, void), T3) !=? delete(X658, tree(X658, X659, X660), tree(X661, X659, X662))", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: ?_12 | delete(T1, tree(T497, T498, void), T3), SCOPE: 1, CLAUSE: 4\n\nT497 is ground\nT498 is ground\ndelete(T1, tree(T497, T498, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T497, T498, void), T3) !=? delete(X658, tree(X658, X659, X660), tree(X661, X659, X662))", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: ','(less(T520, T519), delete(s(T520), T498, T521))\n\nT498 is ground\nT519 is ground\ndelete(T1, tree(s(T519), T498, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: less(T520, T519)\n\nT519 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: delete(s(T524), T498, T525)\n\nT498 is ground\nT524 is ground\ndelete(T526, tree(s(T519), T498, void), T527) !=? delete(T528, tree(T528, void, T529), T529)", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: delete(T1, tree(T497, T498, void), T3), SCOPE: 1, CLAUSE: 4\n\nT497 is ground\nT498 is ground\ndelete(T1, tree(T497, T498, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T497, T498, void), T3) !=? delete(X658, tree(X658, X659, X660), tree(X661, X659, X662))", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: ','(less(T545, T548), delete(T548, void, T549))\n\nT545 is ground\ndelete(T1, tree(T545, T546, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T545, T546, void), T3) !=? delete(X658, tree(X658, X659, X660), tree(X661, X659, X662))", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: ','(less(T557, T560), delete(T560, void, T561))\n\nT557 is ground\ndelete(T1, tree(T557, T558, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T557, T558, void), T3) !=? delete(X658, tree(X658, X659, X660), tree(X661, X659, X662))", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: ','(less(T557, T560), delete(T560, void, T561)), SCOPE: 13, CLAUSE: 7 | ','(less(T557, T560), delete(T560, void, T561)), SCOPE: 13, CLAUSE: 8\n\nT557 is ground\ndelete(T1, tree(T557, T558, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T557, T558, void), T3) !=? delete(X658, tree(X658, X659, X660), tree(X661, X659, X662))", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: ','(less(T557, T560), delete(T560, void, T561)), SCOPE: 13, CLAUSE: 7\n\nT557 is ground\ndelete(T1, tree(T557, T558, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T557, T558, void), T3) !=? delete(X658, tree(X658, X659, X660), tree(X661, X659, X662))", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: ','(less(T557, T560), delete(T560, void, T561)), SCOPE: 13, CLAUSE: 8\n\nT557 is ground\ndelete(T1, tree(T557, T558, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T557, T558, void), T3) !=? delete(X658, tree(X658, X659, X660), tree(X661, X659, X662))", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: delete(s(T568), void, T567)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: ','(less(T580, T582), delete(s(T582), void, T583))\n\nT580 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: delmin(T593, T596, T597) | delete(T1, tree(T591, T592, T593), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T591, T592, T593), T3), SCOPE: 1, CLAUSE: 4\n\nT591 is ground\nT592 is ground\nT593 is ground\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT2 is ground\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X649, tree(X649, X650, void), X650)\ndelete(T1, T2, T3) !=? delete(X862, tree(X862, X863, X864), tree(X865, X863, X866))", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: delmin(T593, T596, T597), SCOPE: 14, CLAUSE: 5 | delmin(T593, T596, T597), SCOPE: 14, CLAUSE: 6 | ?_14 | delete(T1, tree(T591, T592, T593), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T591, T592, T593), T3), SCOPE: 1, CLAUSE: 4\n\nT591 is ground\nT592 is ground\nT593 is ground\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: delmin(T593, T596, T597), SCOPE: 14, CLAUSE: 5\n\nT593 is ground\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: delmin(T593, T596, T597), SCOPE: 14, CLAUSE: 6 | ?_14 | delete(T1, tree(T591, T592, T593), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T591, T592, T593), T3), SCOPE: 1, CLAUSE: 4\n\nT591 is ground\nT592 is ground\nT593 is ground\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: delmin(T593, T596, T597), SCOPE: 14, CLAUSE: 6\n\nT593 is ground\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: ?_14 | delete(T1, tree(T591, T592, T593), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T591, T592, T593), T3), SCOPE: 1, CLAUSE: 4\n\nT591 is ground\nT592 is ground\nT593 is ground\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: delmin(T633, T638, T639)\n\nT633 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: delete(T1, tree(T591, T592, T593), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T591, T592, T593), T3), SCOPE: 1, CLAUSE: 4\n\nT591 is ground\nT592 is ground\nT593 is ground\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: delete(T1, tree(T591, T592, T593), T3), SCOPE: 1, CLAUSE: 3\n\nT591 is ground\nT592 is ground\nT593 is ground\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: delete(T1, tree(T591, T592, T593), T3), SCOPE: 1, CLAUSE: 4\n\nT591 is ground\nT592 is ground\nT593 is ground\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T591, T592, T593), T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: ','(less(T669, T665), delete(T669, T666, T670))\n\nT665 is ground\nT666 is ground\ndelete(T1, tree(T665, T666, T667), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T665, T666, T667), T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: less(T669, T665)\n\nT665 is ground\ndelete(T1, tree(T665, T666, T667), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T665, T666, T667), T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: delete(T673, T666, T674)\n\nT666 is ground\nT673 is ground\ndelete(T675, tree(T665, T666, T676), T677) !=? delete(T678, tree(T678, void, T679), T679)\ndelete(T675, tree(T665, T666, T676), T677) !=? delete(T680, tree(T680, T681, void), T681)", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: ','(less(T699, T703), delete(T703, T701, T704))\n\nT699 is ground\nT701 is ground\ndelete(T1, tree(T699, T700, T701), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T699, T700, T701), T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: less(T699, T703)\n\nT699 is ground\ndelete(T1, tree(T699, T700, T701), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T699, T700, T701), T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: delete(T707, T701, T708)\n\nT701 is ground\ndelete(T709, tree(T699, T710, T701), T711) !=? delete(T712, tree(T712, void, T713), T713)\ndelete(T709, tree(T699, T710, T701), T711) !=? delete(T714, tree(T714, T715, void), T715)", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: ','(less(T732, T728), delete(T732, T729, T733)) | delete(T1, tree(T728, T729, T730), T3), SCOPE: 1, CLAUSE: 4\n\nT728 is ground\nT729 is ground\nT730 is ground\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X649, tree(X649, X650, void), X650)\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X862, tree(X862, X863, X864), tree(X865, X863, X866))", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT2 is ground\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X649, tree(X649, X650, void), X650)\ndelete(T1, T2, T3) !=? delete(X862, tree(X862, X863, X864), tree(X865, X863, X866))\ndelete(T1, T2, T3) !=? delete(X995, tree(X996, X997, X998), tree(X996, X999, X998))", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: ','(less(T732, T728), delete(T732, T729, T733)), SCOPE: 15, CLAUSE: 7 | ','(less(T732, T728), delete(T732, T729, T733)), SCOPE: 15, CLAUSE: 8 | ?_15 | delete(T1, tree(T728, T729, T730), T3), SCOPE: 1, CLAUSE: 4\n\nT728 is ground\nT729 is ground\nT730 is ground\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X649, tree(X649, X650, void), X650)\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X862, tree(X862, X863, X864), tree(X865, X863, X866))", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: ','(less(T732, T728), delete(T732, T729, T733)), SCOPE: 15, CLAUSE: 7\n\nT728 is ground\nT729 is ground\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X649, tree(X649, X650, void), X650)\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X862, tree(X862, X863, X864), tree(X865, X863, X866))", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: ','(less(T732, T728), delete(T732, T729, T733)), SCOPE: 15, CLAUSE: 8 | ?_15 | delete(T1, tree(T728, T729, T730), T3), SCOPE: 1, CLAUSE: 4\n\nT728 is ground\nT729 is ground\nT730 is ground\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X649, tree(X649, X650, void), X650)\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X862, tree(X862, X863, X864), tree(X865, X863, X866))", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: delete(0, T729, T739)\n\nT729 is ground\ndelete(T1, tree(s(T738), T729, T730), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: ','(less(T732, T728), delete(T732, T729, T733)), SCOPE: 15, CLAUSE: 8\n\nT728 is ground\nT729 is ground\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X649, tree(X649, X650, void), X650)\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X862, tree(X862, X863, X864), tree(X865, X863, X866))", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: ?_15 | delete(T1, tree(T728, T729, T730), T3), SCOPE: 1, CLAUSE: 4\n\nT728 is ground\nT729 is ground\nT730 is ground\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X649, tree(X649, X650, void), X650)\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X862, tree(X862, X863, X864), tree(X865, X863, X866))", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: ','(less(T752, T751), delete(s(T752), T729, T753))\n\nT729 is ground\nT751 is ground\ndelete(T1, tree(s(T751), T729, T730), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: less(T752, T751)\n\nT751 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: delete(s(T756), T729, T757)\n\nT729 is ground\nT756 is ground\ndelete(T758, tree(s(T751), T729, T759), T760) !=? delete(T761, tree(T761, void, T762), T762)", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: delete(T1, tree(T728, T729, T730), T3), SCOPE: 1, CLAUSE: 4\n\nT728 is ground\nT729 is ground\nT730 is ground\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X649, tree(X649, X650, void), X650)\ndelete(T1, tree(T728, T729, T730), T3) !=? delete(X862, tree(X862, X863, X864), tree(X865, X863, X866))", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: ','(less(T780, T784), delete(T784, T782, T785))\n\nT780 is ground\nT782 is ground\ndelete(T1, tree(T780, T781, T782), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T780, T781, T782), T3) !=? delete(X649, tree(X649, X650, void), X650)\ndelete(T1, tree(T780, T781, T782), T3) !=? delete(X862, tree(X862, X863, X864), tree(X865, X863, X866))", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: less(T780, T784)\n\nT780 is ground\ndelete(T1, tree(T780, T781, T782), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T780, T781, T782), T3) !=? delete(X649, tree(X649, X650, void), X650)\ndelete(T1, tree(T780, T781, T782), T3) !=? delete(X862, tree(X862, X863, X864), tree(X865, X863, X866))", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: delete(T788, T782, T789)\n\nT782 is ground\ndelete(T790, tree(T780, T791, T782), T792) !=? delete(T793, tree(T793, void, T794), T794)\ndelete(T790, tree(T780, T791, T782), T792) !=? delete(T795, tree(T795, T796, void), T796)\ndelete(T790, tree(T780, T791, T782), T792) !=? delete(T797, tree(T797, T798, T799), tree(T800, T798, T801))", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: ','(less(T814, T818), delete(T818, T816, T819))\n\nT814 is ground\nT816 is ground\ndelete(T1, tree(T814, T815, T816), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T814, T815, T816), T3) !=? delete(X649, tree(X649, X650, void), X650)\ndelete(T1, tree(T814, T815, T816), T3) !=? delete(X862, tree(X862, X863, X864), tree(X865, X863, X866))", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: ','(less(T814, T818), delete(T818, T816, T819)), SCOPE: 16, CLAUSE: 7 | ','(less(T814, T818), delete(T818, T816, T819)), SCOPE: 16, CLAUSE: 8\n\nT814 is ground\nT816 is ground\ndelete(T1, tree(T814, T815, T816), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T814, T815, T816), T3) !=? delete(X649, tree(X649, X650, void), X650)\ndelete(T1, tree(T814, T815, T816), T3) !=? delete(X862, tree(X862, X863, X864), tree(X865, X863, X866))", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: ','(less(T814, T818), delete(T818, T816, T819)), SCOPE: 16, CLAUSE: 7\n\nT814 is ground\nT816 is ground\ndelete(T1, tree(T814, T815, T816), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T814, T815, T816), T3) !=? delete(X649, tree(X649, X650, void), X650)\ndelete(T1, tree(T814, T815, T816), T3) !=? delete(X862, tree(X862, X863, X864), tree(X865, X863, X866))", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: ','(less(T814, T818), delete(T818, T816, T819)), SCOPE: 16, CLAUSE: 8\n\nT814 is ground\nT816 is ground\ndelete(T1, tree(T814, T815, T816), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T814, T815, T816), T3) !=? delete(X649, tree(X649, X650, void), X650)\ndelete(T1, tree(T814, T815, T816), T3) !=? delete(X862, tree(X862, X863, X864), tree(X865, X863, X866))", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: delete(s(T826), T816, T825)\n\nT816 is ground\ndelete(T1, tree(0, T815, T816), T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: ','(less(T835, T837), delete(s(T837), T816, T838))\n\nT816 is ground\nT835 is ground\ndelete(T1, tree(s(T835), T815, T816), T3) !=? delete(X649, tree(X649, X650, void), X650)", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: less(T835, T837)\n\nT835 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: delete(s(T841), T816, T842)\n\nT816 is ground\ndelete(T843, tree(s(T835), T844, T816), T845) !=? delete(T846, tree(T846, T847, void), T847)", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 216 [arrowhead = none ];
216 -> 2;

217 [label="EVAL with clause\ndelete(X6, tree(X6, void, X7), X7).\nand substitution\nT1 -> T6\nX6 -> T6\nX7 -> T7\nT2 -> tree(T6, void, T7)\nT3 -> T7", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 217 [arrowhead = none ];
217 -> 3;

218 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 218 [arrowhead = none ];
218 -> 4;

219 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 219 [arrowhead = none ];
219 -> 5;

220 [label="EVAL with clause\ndelete(X649, tree(X649, X650, void), X650).\nand substitution\nT1 -> T428\nX649 -> T428\nX650 -> T429\nT2 -> tree(T428, T429, void)\nT3 -> T429", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 220 [arrowhead = none ];
220 -> 122;

221 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 221 [arrowhead = none ];
221 -> 123;

222 [label="EVAL with clause\ndelete(X12, tree(X12, X13, void), X13).\nand substitution\nT1 -> T9\nX12 -> T9\nT6 -> T9\nX13 -> void\nT7 -> void\nT3 -> void", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 222 [arrowhead = none ];
222 -> 6;

223 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 223 [arrowhead = none ];
223 -> 7;

224 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 224 [arrowhead = none ];
224 -> 8;

225 [label="EVAL with clause\ndelete(X364, tree(X364, X365, X366), tree(X367, X365, X368)) :- delmin(X366, X367, X368).\nand substitution\nT1 -> T199\nX364 -> T199\nT6 -> T199\nX365 -> void\nT7 -> T200\nX366 -> T200\nX367 -> T203\nX368 -> T204\nT3 -> tree(T203, void, T204)\nT201 -> T203\nT202 -> T204", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 225 [arrowhead = none ];
225 -> 68;

226 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 226 [arrowhead = none ];
226 -> 69;

227 [label="EVAL with clause\ndelete(X21, tree(X21, X22, X23), tree(X24, X22, X25)) :- delmin(X23, X24, X25).\nand substitution\nT1 -> T13\nX21 -> T13\nT9 -> T13\nX22 -> void\nX23 -> void\nX24 -> T16\nX25 -> T17\nT3 -> tree(T16, void, T17)\nT14 -> T16\nT15 -> T17", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 227 [arrowhead = none ];
227 -> 9;

228 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 228 [arrowhead = none ];
228 -> 10;

229 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 229 [arrowhead = none ];
229 -> 11;

230 [label="EVAL with clause\ndelete(X180, tree(X181, X182, X183), tree(X181, X184, X183)) :- ','(less(X180, X181), delete(X180, X182, X184)).\nand substitution\nT1 -> T106\nX180 -> T106\nT9 -> T104\nX181 -> T104\nX182 -> void\nX183 -> void\nX184 -> T107\nT3 -> tree(T104, T107, void)\nT103 -> T106\nT105 -> T107", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 230 [arrowhead = none ];
230 -> 41;

231 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 231 [arrowhead = none ];
231 -> 42;

232 [label="BACKTRACK\nfor clause: delmin(tree(Y, void, Right), Y, Right)because of non-unification", fontsize=14, style = filled, fillcolor = white];
11 -> 232 [arrowhead = none ];
232 -> 12;

233 [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 = white];
12 -> 233 [arrowhead = none ];
233 -> 13;

234 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
13 -> 234 [arrowhead = none ];
234 -> 14;

235 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 235 [arrowhead = none ];
235 -> 15;

236 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 236 [arrowhead = none ];
236 -> 16;

237 [label="EVAL with clause\ndelete(X59, tree(X60, X61, X62), tree(X60, X63, X62)) :- ','(less(X59, X60), delete(X59, X61, X63)).\nand substitution\nT1 -> T33\nX59 -> T33\nT13 -> T31\nX60 -> T31\nX61 -> void\nX62 -> void\nX63 -> T34\nT3 -> tree(T31, T34, void)\nT30 -> T33\nT32 -> T34", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 237 [arrowhead = none ];
237 -> 17;

238 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 238 [arrowhead = none ];
238 -> 18;

239 [label="EVAL with clause\ndelete(X122, tree(X123, X124, X125), tree(X123, X124, X126)) :- ','(less(X123, X122), delete(X122, X125, X126)).\nand substitution\nT1 -> T71\nX122 -> T71\nT13 -> T69\nX123 -> T69\nX124 -> void\nX125 -> void\nX126 -> T72\nT3 -> tree(T69, void, T72)\nT68 -> T71\nT70 -> T72", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 239 [arrowhead = none ];
239 -> 29;

240 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 240 [arrowhead = none ];
240 -> 30;

241 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
17 -> 241 [arrowhead = none ];
241 -> 19;

242 [label="SPLIT 2\nnew knowledge:\nT37 is ground\nreplacements:\nT33 -> T37\nT34 -> T38", fontsize=14, style = filled, fillcolor = violet];
17 -> 242 [arrowhead = none ];
242 -> 20;

243 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
19 -> 243 [arrowhead = none ];
243 -> 21;

244 [label="INSTANCE with matching:\nT1 -> T37\nT2 -> void\nT3 -> T38", fontsize=14, style = filled, fillcolor = lightgrey];
20 -> 244 [arrowhead = none , style=dashed];
244 -> 1[style=dashed];

245 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 245 [arrowhead = none ];
245 -> 22;

246 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 246 [arrowhead = none ];
246 -> 23;

247 [label="EVAL with clause\nless(0, s(X77)).\nand substitution\nT33 -> 0\nX77 -> T45\nT31 -> s(T45)", fontsize=14, style = filled, fillcolor = lightblue];
22 -> 247 [arrowhead = none ];
247 -> 24;

248 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
22 -> 248 [arrowhead = none ];
248 -> 25;

249 [label="EVAL with clause\nless(s(X83), s(X84)) :- less(X83, X84).\nand substitution\nX83 -> T52\nT33 -> s(T52)\nX84 -> T51\nT31 -> s(T51)\nT50 -> T52", fontsize=14, style = filled, fillcolor = lightblue];
23 -> 249 [arrowhead = none ];
249 -> 27;

250 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
23 -> 250 [arrowhead = none ];
250 -> 28;

251 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
24 -> 251 [arrowhead = none ];
251 -> 26;

252 [label="INSTANCE with matching:\nT33 -> T52\nT31 -> T51", fontsize=14, style = filled, fillcolor = lightgrey];
27 -> 252 [arrowhead = none , style=dashed];
252 -> 19[style=dashed];

253 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
29 -> 253 [arrowhead = none ];
253 -> 31;

254 [label="SPLIT 2\nreplacements:\nT71 -> T75\nT72 -> T76", fontsize=14, style = filled, fillcolor = violet];
29 -> 254 [arrowhead = none ];
254 -> 32;

255 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
31 -> 255 [arrowhead = none ];
255 -> 33;

256 [label="INSTANCE with matching:\nT1 -> T75\nT2 -> void\nT3 -> T76", fontsize=14, style = filled, fillcolor = lightgrey];
32 -> 256 [arrowhead = none , style=dashed];
256 -> 1[style=dashed];

257 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
33 -> 257 [arrowhead = none ];
257 -> 34;

258 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
33 -> 258 [arrowhead = none ];
258 -> 35;

259 [label="EVAL with clause\nless(0, s(X140)).\nand substitution\nT69 -> 0\nX140 -> T83\nT71 -> s(T83)", fontsize=14, style = filled, fillcolor = lightblue];
34 -> 259 [arrowhead = none ];
259 -> 36;

260 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
34 -> 260 [arrowhead = none ];
260 -> 37;

261 [label="EVAL with clause\nless(s(X146), s(X147)) :- less(X146, X147).\nand substitution\nX146 -> T88\nT69 -> s(T88)\nX147 -> T90\nT71 -> s(T90)\nT89 -> T90", fontsize=14, style = filled, fillcolor = lightblue];
35 -> 261 [arrowhead = none ];
261 -> 39;

262 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
35 -> 262 [arrowhead = none ];
262 -> 40;

263 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
36 -> 263 [arrowhead = none ];
263 -> 38;

264 [label="INSTANCE with matching:\nT69 -> T88\nT71 -> T90", fontsize=14, style = filled, fillcolor = lightgrey];
39 -> 264 [arrowhead = none , style=dashed];
264 -> 31[style=dashed];

265 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
41 -> 265 [arrowhead = none ];
265 -> 43;

266 [label="EVAL with clause\ndelete(X285, tree(X286, X287, X288), tree(X286, X287, X289)) :- ','(less(X286, X285), delete(X285, X288, X289)).\nand substitution\nT1 -> T158\nX285 -> T158\nT9 -> T156\nX286 -> T156\nX287 -> void\nX288 -> void\nX289 -> T159\nT3 -> tree(T156, void, T159)\nT155 -> T158\nT157 -> T159", fontsize=14, style = filled, fillcolor = lightblue];
42 -> 266 [arrowhead = none ];
266 -> 57;

267 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
42 -> 267 [arrowhead = none ];
267 -> 58;

268 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
43 -> 268 [arrowhead = none ];
268 -> 44;

269 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
43 -> 269 [arrowhead = none ];
269 -> 45;

270 [label="EVAL with clause\nless(0, s(X194)).\nand substitution\nT106 -> 0\nX194 -> T112\nT104 -> s(T112)\nT107 -> T113", fontsize=14, style = filled, fillcolor = lightblue];
44 -> 270 [arrowhead = none ];
270 -> 46;

271 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
44 -> 271 [arrowhead = none ];
271 -> 47;

272 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
45 -> 272 [arrowhead = none ];
272 -> 48;

273 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
45 -> 273 [arrowhead = none ];
273 -> 49;

274 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> void\nT3 -> T113", fontsize=14, style = filled, fillcolor = lightgrey];
46 -> 274 [arrowhead = none , style=dashed];
274 -> 1[style=dashed];

275 [label="EVAL with clause\nless(s(X227), s(X228)) :- less(X227, X228).\nand substitution\nX227 -> T124\nT106 -> s(T124)\nX228 -> T123\nT104 -> s(T123)\nT122 -> T124\nT107 -> T125", fontsize=14, style = filled, fillcolor = lightblue];
48 -> 275 [arrowhead = none ];
275 -> 50;

276 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
48 -> 276 [arrowhead = none ];
276 -> 51;

277 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
49 -> 277 [arrowhead = none ];
277 -> 54;

278 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
50 -> 278 [arrowhead = none ];
278 -> 52;

279 [label="SPLIT 2\nnew knowledge:\nT128 is ground\nreplacements:\nT124 -> T128\nT125 -> T129", fontsize=14, style = filled, fillcolor = violet];
50 -> 279 [arrowhead = none ];
279 -> 53;

280 [label="INSTANCE with matching:\nT33 -> T124\nT31 -> T123", fontsize=14, style = filled, fillcolor = lightgrey];
52 -> 280 [arrowhead = none , style=dashed];
280 -> 19[style=dashed];

281 [label="INSTANCE with matching:\nT1 -> s(T128)\nT2 -> void\nT3 -> T129", fontsize=14, style = filled, fillcolor = lightgrey];
53 -> 281 [arrowhead = none , style=dashed];
281 -> 1[style=dashed];

282 [label="EVAL with clause\ndelete(X268, tree(X269, X270, X271), tree(X269, X270, X272)) :- ','(less(X269, X268), delete(X268, X271, X272)).\nand substitution\nT1 -> T148\nX268 -> T148\nT104 -> T146\nX269 -> T146\nX270 -> void\nX271 -> void\nX272 -> T149\nT3 -> tree(T146, void, T149)\nT145 -> T148\nT147 -> T149", fontsize=14, style = filled, fillcolor = lightblue];
54 -> 282 [arrowhead = none ];
282 -> 55;

283 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
54 -> 283 [arrowhead = none ];
283 -> 56;

284 [label="INSTANCE with matching:\nT69 -> T146\nT71 -> T148\nT72 -> T149", fontsize=14, style = filled, fillcolor = lightgrey];
55 -> 284 [arrowhead = none , style=dashed];
284 -> 29[style=dashed];

285 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
57 -> 285 [arrowhead = none ];
285 -> 59;

286 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
59 -> 286 [arrowhead = none ];
286 -> 60;

287 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
59 -> 287 [arrowhead = none ];
287 -> 61;

288 [label="EVAL with clause\nless(0, s(X299)).\nand substitution\nT156 -> 0\nX299 -> T166\nT158 -> s(T166)\nT159 -> T165\nT164 -> T166", fontsize=14, style = filled, fillcolor = lightblue];
60 -> 288 [arrowhead = none ];
288 -> 62;

289 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
60 -> 289 [arrowhead = none ];
289 -> 63;

290 [label="EVAL with clause\nless(s(X328), s(X329)) :- less(X328, X329).\nand substitution\nX328 -> T178\nT156 -> s(T178)\nX329 -> T180\nT158 -> s(T180)\nT179 -> T180\nT159 -> T181", fontsize=14, style = filled, fillcolor = lightblue];
61 -> 290 [arrowhead = none ];
290 -> 64;

291 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
61 -> 291 [arrowhead = none ];
291 -> 65;

292 [label="INSTANCE with matching:\nT1 -> s(T166)\nT2 -> void\nT3 -> T165", fontsize=14, style = filled, fillcolor = lightgrey];
62 -> 292 [arrowhead = none , style=dashed];
292 -> 1[style=dashed];

293 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
64 -> 293 [arrowhead = none ];
293 -> 66;

294 [label="SPLIT 2\nreplacements:\nT180 -> T184\nT181 -> T185", fontsize=14, style = filled, fillcolor = violet];
64 -> 294 [arrowhead = none ];
294 -> 67;

295 [label="INSTANCE with matching:\nT69 -> T178\nT71 -> T180", fontsize=14, style = filled, fillcolor = lightgrey];
66 -> 295 [arrowhead = none , style=dashed];
295 -> 31[style=dashed];

296 [label="INSTANCE with matching:\nT1 -> s(T184)\nT2 -> void\nT3 -> T185", fontsize=14, style = filled, fillcolor = lightgrey];
67 -> 296 [arrowhead = none , style=dashed];
296 -> 1[style=dashed];

297 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
68 -> 297 [arrowhead = none ];
297 -> 70;

298 [label="EVAL with clause\ndelete(X531, tree(X532, X533, X534), tree(X532, X535, X534)) :- ','(less(X531, X532), delete(X531, X533, X535)).\nand substitution\nT1 -> T345\nX531 -> T345\nT6 -> T342\nX532 -> T342\nX533 -> void\nT7 -> T343\nX534 -> T343\nX535 -> T346\nT3 -> tree(T342, T346, T343)\nT341 -> T345\nT344 -> T346", fontsize=14, style = filled, fillcolor = lightblue];
69 -> 298 [arrowhead = none ];
298 -> 97;

299 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
69 -> 299 [arrowhead = none ];
299 -> 98;

300 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
70 -> 300 [arrowhead = none ];
300 -> 71;

301 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
70 -> 301 [arrowhead = none ];
301 -> 72;

302 [label="EVAL with clause\ndelmin(tree(X382, void, X383), X382, X383).\nand substitution\nX382 -> T213\nX383 -> T214\nT200 -> tree(T213, void, T214)\nT203 -> T213\nT204 -> T214", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 302 [arrowhead = none ];
302 -> 73;

303 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 303 [arrowhead = none ];
303 -> 74;

304 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
72 -> 304 [arrowhead = none ];
304 -> 76;

305 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
72 -> 305 [arrowhead = none ];
305 -> 77;

306 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
73 -> 306 [arrowhead = none ];
306 -> 75;

307 [label="EVAL with clause\ndelmin(tree(X410, X411, X412), X413, tree(X410, X414, X415)) :- delmin(X411, X413, X414).\nand substitution\nX410 -> T239\nX411 -> T240\nX412 -> T241\nT200 -> tree(T239, T240, T241)\nT203 -> T245\nX413 -> T245\nX414 -> T246\nX415 -> T244\nT204 -> tree(T239, T246, T244)\nT242 -> T245\nT243 -> T246", fontsize=14, style = filled, fillcolor = lightblue];
76 -> 307 [arrowhead = none ];
307 -> 78;

308 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
76 -> 308 [arrowhead = none ];
308 -> 79;

309 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
77 -> 309 [arrowhead = none ];
309 -> 88;

310 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
78 -> 310 [arrowhead = none ];
310 -> 80;

311 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
80 -> 311 [arrowhead = none ];
311 -> 81;

312 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
80 -> 312 [arrowhead = none ];
312 -> 82;

313 [label="EVAL with clause\ndelmin(tree(X434, void, X435), X434, X435).\nand substitution\nX434 -> T259\nX435 -> T260\nT240 -> tree(T259, void, T260)\nT245 -> T259\nT246 -> T260", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 313 [arrowhead = none ];
313 -> 83;

314 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 314 [arrowhead = none ];
314 -> 84;

315 [label="EVAL with clause\ndelmin(tree(X450, X451, X452), X453, tree(X450, X454, X455)) :- delmin(X451, X453, X454).\nand substitution\nX450 -> T273\nX451 -> T274\nX452 -> T275\nT240 -> tree(T273, T274, T275)\nT245 -> T279\nX453 -> T279\nX454 -> T280\nX455 -> T278\nT246 -> tree(T273, T280, T278)\nT276 -> T279\nT277 -> T280", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 315 [arrowhead = none ];
315 -> 86;

316 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 316 [arrowhead = none ];
316 -> 87;

317 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
83 -> 317 [arrowhead = none ];
317 -> 85;

318 [label="INSTANCE with matching:\nT240 -> T274\nT245 -> T279\nT246 -> T280", fontsize=14, style = filled, fillcolor = lightgrey];
86 -> 318 [arrowhead = none , style=dashed];
318 -> 78[style=dashed];

319 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
88 -> 319 [arrowhead = none ];
319 -> 89;

320 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
88 -> 320 [arrowhead = none ];
320 -> 90;

321 [label="EVAL with clause\ndelete(X486, tree(X487, X488, X489), tree(X487, X490, X489)) :- ','(less(X486, X487), delete(X486, X488, X490)).\nand substitution\nT1 -> T305\nX486 -> T305\nT199 -> T302\nX487 -> T302\nX488 -> void\nT200 -> T303\nX489 -> T303\nX490 -> T306\nT3 -> tree(T302, T306, T303)\nT301 -> T305\nT304 -> T306", fontsize=14, style = filled, fillcolor = lightblue];
89 -> 321 [arrowhead = none ];
321 -> 91;

322 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
89 -> 322 [arrowhead = none ];
322 -> 92;

323 [label="EVAL with clause\ndelete(X508, tree(X509, X510, X511), tree(X509, X510, X512)) :- ','(less(X509, X508), delete(X508, X511, X512)).\nand substitution\nT1 -> T321\nX508 -> T321\nT199 -> T318\nX509 -> T318\nX510 -> void\nT200 -> T319\nX511 -> T319\nX512 -> T322\nT3 -> tree(T318, void, T322)\nT317 -> T321\nT320 -> T322", fontsize=14, style = filled, fillcolor = lightblue];
90 -> 323 [arrowhead = none ];
323 -> 93;

324 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
90 -> 324 [arrowhead = none ];
324 -> 94;

325 [label="INSTANCE with matching:\nT33 -> T305\nT31 -> T302\nT34 -> T306", fontsize=14, style = filled, fillcolor = lightgrey];
91 -> 325 [arrowhead = none , style=dashed];
325 -> 17[style=dashed];

326 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
93 -> 326 [arrowhead = none ];
326 -> 95;

327 [label="SPLIT 2\nreplacements:\nT321 -> T325\nT322 -> T326\nT1 -> T327\nT3 -> T328\nX12 -> T329\nX13 -> T330", fontsize=14, style = filled, fillcolor = violet];
93 -> 327 [arrowhead = none ];
327 -> 96;

328 [label="INSTANCE with matching:\nT178 -> T318\nT180 -> T321", fontsize=14, style = filled, fillcolor = lightgrey];
95 -> 328 [arrowhead = none , style=dashed];
328 -> 66[style=dashed];

329 [label="INSTANCE with matching:\nT1 -> T325\nT2 -> T319\nT3 -> T326", fontsize=14, style = filled, fillcolor = lightgrey];
96 -> 329 [arrowhead = none , style=dashed];
329 -> 1[style=dashed];

330 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
97 -> 330 [arrowhead = none ];
330 -> 99;

331 [label="EVAL with clause\ndelete(X611, tree(X612, X613, X614), tree(X612, X613, X615)) :- ','(less(X612, X611), delete(X611, X614, X615)).\nand substitution\nT1 -> T391\nX611 -> T391\nT6 -> T388\nX612 -> T388\nX613 -> void\nT7 -> T389\nX614 -> T389\nX615 -> T392\nT3 -> tree(T388, void, T392)\nT387 -> T391\nT390 -> T392", fontsize=14, style = filled, fillcolor = lightblue];
98 -> 331 [arrowhead = none ];
331 -> 111;

332 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
98 -> 332 [arrowhead = none ];
332 -> 112;

333 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
99 -> 333 [arrowhead = none ];
333 -> 100;

334 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
99 -> 334 [arrowhead = none ];
334 -> 101;

335 [label="EVAL with clause\nless(0, s(X545)).\nand substitution\nT345 -> 0\nX545 -> T351\nT342 -> s(T351)\nT346 -> T352", fontsize=14, style = filled, fillcolor = lightblue];
100 -> 335 [arrowhead = none ];
335 -> 102;

336 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
100 -> 336 [arrowhead = none ];
336 -> 103;

337 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
101 -> 337 [arrowhead = none ];
337 -> 104;

338 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
101 -> 338 [arrowhead = none ];
338 -> 105;

339 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> void\nT3 -> T352", fontsize=14, style = filled, fillcolor = lightgrey];
102 -> 339 [arrowhead = none , style=dashed];
339 -> 1[style=dashed];

340 [label="EVAL with clause\nless(s(X578), s(X579)) :- less(X578, X579).\nand substitution\nX578 -> T363\nT345 -> s(T363)\nX579 -> T362\nT342 -> s(T362)\nT361 -> T363\nT346 -> T364", fontsize=14, style = filled, fillcolor = lightblue];
104 -> 340 [arrowhead = none ];
340 -> 106;

341 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
104 -> 341 [arrowhead = none ];
341 -> 107;

342 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
105 -> 342 [arrowhead = none ];
342 -> 108;

343 [label="INSTANCE with matching:\nT124 -> T363\nT123 -> T362\nT125 -> T364", fontsize=14, style = filled, fillcolor = lightgrey];
106 -> 343 [arrowhead = none , style=dashed];
343 -> 50[style=dashed];

344 [label="EVAL with clause\ndelete(X594, tree(X595, X596, X597), tree(X595, X596, X598)) :- ','(less(X595, X594), delete(X594, X597, X598)).\nand substitution\nT1 -> T379\nX594 -> T379\nT342 -> T376\nX595 -> T376\nX596 -> void\nT343 -> T377\nX597 -> T377\nX598 -> T380\nT3 -> tree(T376, void, T380)\nT375 -> T379\nT378 -> T380", fontsize=14, style = filled, fillcolor = lightblue];
108 -> 344 [arrowhead = none ];
344 -> 109;

345 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
108 -> 345 [arrowhead = none ];
345 -> 110;

346 [label="INSTANCE with matching:\nT318 -> T376\nT321 -> T379\nT319 -> T377\nT322 -> T380", fontsize=14, style = filled, fillcolor = lightgrey];
109 -> 346 [arrowhead = none , style=dashed];
346 -> 93[style=dashed];

347 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
111 -> 347 [arrowhead = none ];
347 -> 113;

348 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
113 -> 348 [arrowhead = none ];
348 -> 114;

349 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
113 -> 349 [arrowhead = none ];
349 -> 115;

350 [label="EVAL with clause\nless(0, s(X625)).\nand substitution\nT388 -> 0\nX625 -> T399\nT391 -> s(T399)\nT392 -> T398\nT397 -> T399", fontsize=14, style = filled, fillcolor = lightblue];
114 -> 350 [arrowhead = none ];
350 -> 116;

351 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
114 -> 351 [arrowhead = none ];
351 -> 117;

352 [label="EVAL with clause\nless(s(X635), s(X636)) :- less(X635, X636).\nand substitution\nX635 -> T408\nT388 -> s(T408)\nX636 -> T410\nT391 -> s(T410)\nT409 -> T410\nT392 -> T411", fontsize=14, style = filled, fillcolor = lightblue];
115 -> 352 [arrowhead = none ];
352 -> 118;

353 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
115 -> 353 [arrowhead = none ];
353 -> 119;

354 [label="INSTANCE with matching:\nT1 -> s(T399)\nT2 -> T389\nT3 -> T398", fontsize=14, style = filled, fillcolor = lightgrey];
116 -> 354 [arrowhead = none , style=dashed];
354 -> 1[style=dashed];

355 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
118 -> 355 [arrowhead = none ];
355 -> 120;

356 [label="SPLIT 2\nreplacements:\nT410 -> T414\nT411 -> T415\nT1 -> T416\nT3 -> T417\nX12 -> T418\nX13 -> T419", fontsize=14, style = filled, fillcolor = violet];
118 -> 356 [arrowhead = none ];
356 -> 121;

357 [label="INSTANCE with matching:\nT178 -> T408\nT180 -> T410", fontsize=14, style = filled, fillcolor = lightgrey];
120 -> 357 [arrowhead = none , style=dashed];
357 -> 66[style=dashed];

358 [label="INSTANCE with matching:\nT1 -> s(T414)\nT2 -> T389\nT3 -> T415", fontsize=14, style = filled, fillcolor = lightgrey];
121 -> 358 [arrowhead = none , style=dashed];
358 -> 1[style=dashed];

359 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
122 -> 359 [arrowhead = none ];
359 -> 124;

360 [label="EVAL with clause\ndelete(X862, tree(X862, X863, X864), tree(X865, X863, X866)) :- delmin(X864, X865, X866).\nand substitution\nT1 -> T591\nX862 -> T591\nX863 -> T592\nX864 -> T593\nT2 -> tree(T591, T592, T593)\nX865 -> T596\nX866 -> T597\nT3 -> tree(T596, T592, T597)\nT594 -> T596\nT595 -> T597", fontsize=14, style = filled, fillcolor = lightblue];
123 -> 360 [arrowhead = none ];
360 -> 164;

361 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
123 -> 361 [arrowhead = none ];
361 -> 165;

362 [label="EVAL with clause\ndelete(X658, tree(X658, X659, X660), tree(X661, X659, X662)) :- delmin(X660, X661, X662).\nand substitution\nT1 -> T434\nX658 -> T434\nT428 -> T434\nT429 -> T435\nX659 -> T435\nX660 -> void\nX661 -> T438\nX662 -> T439\nT3 -> tree(T438, T435, T439)\nT436 -> T438\nT437 -> T439", fontsize=14, style = filled, fillcolor = lightblue];
124 -> 362 [arrowhead = none ];
362 -> 125;

363 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
124 -> 363 [arrowhead = none ];
363 -> 126;

364 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
125 -> 364 [arrowhead = none ];
364 -> 127;

365 [label="EVAL with clause\ndelete(X741, tree(X742, X743, X744), tree(X742, X745, X744)) :- ','(less(X741, X742), delete(X741, X743, X745)).\nand substitution\nT1 -> T500\nX741 -> T500\nT428 -> T497\nX742 -> T497\nT429 -> T498\nX743 -> T498\nX744 -> void\nX745 -> T501\nT3 -> tree(T497, T501, void)\nT496 -> T500\nT499 -> T501", fontsize=14, style = filled, fillcolor = lightblue];
126 -> 365 [arrowhead = none ];
365 -> 139;

366 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
126 -> 366 [arrowhead = none ];
366 -> 140;

367 [label="BACKTRACK\nfor clause: delmin(tree(Y, void, Right), Y, Right)because of non-unification", fontsize=14, style = filled, fillcolor = white];
127 -> 367 [arrowhead = none ];
367 -> 128;

368 [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 = white];
128 -> 368 [arrowhead = none ];
368 -> 129;

369 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 369 [arrowhead = none ];
369 -> 130;

370 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
130 -> 370 [arrowhead = none ];
370 -> 131;

371 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
130 -> 371 [arrowhead = none ];
371 -> 132;

372 [label="EVAL with clause\ndelete(X696, tree(X697, X698, X699), tree(X697, X700, X699)) :- ','(less(X696, X697), delete(X696, X698, X700)).\nand substitution\nT1 -> T460\nX696 -> T460\nT434 -> T457\nX697 -> T457\nT435 -> T458\nX698 -> T458\nX699 -> void\nX700 -> T461\nT3 -> tree(T457, T461, void)\nT456 -> T460\nT459 -> T461", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 372 [arrowhead = none ];
372 -> 133;

373 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 373 [arrowhead = none ];
373 -> 134;

374 [label="EVAL with clause\ndelete(X724, tree(X725, X726, X727), tree(X725, X726, X728)) :- ','(less(X725, X724), delete(X724, X727, X728)).\nand substitution\nT1 -> T488\nX724 -> T488\nT434 -> T485\nX725 -> T485\nT435 -> T486\nX726 -> T486\nX727 -> void\nX728 -> T489\nT3 -> tree(T485, T486, T489)\nT484 -> T488\nT487 -> T489", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 374 [arrowhead = none ];
374 -> 137;

375 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 375 [arrowhead = none ];
375 -> 138;

376 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
133 -> 376 [arrowhead = none ];
376 -> 135;

377 [label="SPLIT 2\nnew knowledge:\nT464 is ground\nreplacements:\nT460 -> T464\nT461 -> T465\nT1 -> T466\nT3 -> T467\nX6 -> T468\nX7 -> T469", fontsize=14, style = filled, fillcolor = violet];
133 -> 377 [arrowhead = none ];
377 -> 136;

378 [label="INSTANCE with matching:\nT124 -> T460\nT123 -> T457", fontsize=14, style = filled, fillcolor = lightgrey];
135 -> 378 [arrowhead = none , style=dashed];
378 -> 52[style=dashed];

379 [label="INSTANCE with matching:\nT1 -> T464\nT2 -> T458\nT3 -> T465", fontsize=14, style = filled, fillcolor = lightgrey];
136 -> 379 [arrowhead = none , style=dashed];
379 -> 1[style=dashed];

380 [label="INSTANCE with matching:\nT69 -> T485\nT71 -> T488\nT72 -> T489", fontsize=14, style = filled, fillcolor = lightgrey];
137 -> 380 [arrowhead = none , style=dashed];
380 -> 29[style=dashed];

381 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
139 -> 381 [arrowhead = none ];
381 -> 141;

382 [label="EVAL with clause\ndelete(X808, tree(X809, X810, X811), tree(X809, X810, X812)) :- ','(less(X809, X808), delete(X808, X811, X812)).\nand substitution\nT1 -> T560\nX808 -> T560\nT428 -> T557\nX809 -> T557\nT429 -> T558\nX810 -> T558\nX811 -> void\nX812 -> T561\nT3 -> tree(T557, T558, T561)\nT556 -> T560\nT559 -> T561", fontsize=14, style = filled, fillcolor = lightblue];
140 -> 382 [arrowhead = none ];
382 -> 155;

383 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
140 -> 383 [arrowhead = none ];
383 -> 156;

384 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
141 -> 384 [arrowhead = none ];
384 -> 142;

385 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
141 -> 385 [arrowhead = none ];
385 -> 143;

386 [label="EVAL with clause\nless(0, s(X755)).\nand substitution\nT500 -> 0\nX755 -> T506\nT497 -> s(T506)\nT501 -> T507", fontsize=14, style = filled, fillcolor = lightblue];
142 -> 386 [arrowhead = none ];
386 -> 144;

387 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
142 -> 387 [arrowhead = none ];
387 -> 145;

388 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
143 -> 388 [arrowhead = none ];
388 -> 146;

389 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
143 -> 389 [arrowhead = none ];
389 -> 147;

390 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T498\nT3 -> T507", fontsize=14, style = filled, fillcolor = lightgrey];
144 -> 390 [arrowhead = none , style=dashed];
390 -> 1[style=dashed];

391 [label="EVAL with clause\nless(s(X769), s(X770)) :- less(X769, X770).\nand substitution\nX769 -> T520\nT500 -> s(T520)\nX770 -> T519\nT497 -> s(T519)\nT518 -> T520\nT501 -> T521", fontsize=14, style = filled, fillcolor = lightblue];
146 -> 391 [arrowhead = none ];
391 -> 148;

392 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
146 -> 392 [arrowhead = none ];
392 -> 149;

393 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
147 -> 393 [arrowhead = none ];
393 -> 152;

394 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
148 -> 394 [arrowhead = none ];
394 -> 150;

395 [label="SPLIT 2\nnew knowledge:\nT524 is ground\nreplacements:\nT520 -> T524\nT521 -> T525\nT1 -> T526\nT3 -> T527\nX6 -> T528\nX7 -> T529", fontsize=14, style = filled, fillcolor = violet];
148 -> 395 [arrowhead = none ];
395 -> 151;

396 [label="INSTANCE with matching:\nT124 -> T520\nT123 -> T519", fontsize=14, style = filled, fillcolor = lightgrey];
150 -> 396 [arrowhead = none , style=dashed];
396 -> 52[style=dashed];

397 [label="INSTANCE with matching:\nT1 -> s(T524)\nT2 -> T498\nT3 -> T525", fontsize=14, style = filled, fillcolor = lightgrey];
151 -> 397 [arrowhead = none , style=dashed];
397 -> 1[style=dashed];

398 [label="EVAL with clause\ndelete(X791, tree(X792, X793, X794), tree(X792, X793, X795)) :- ','(less(X792, X791), delete(X791, X794, X795)).\nand substitution\nT1 -> T548\nX791 -> T548\nT497 -> T545\nX792 -> T545\nT498 -> T546\nX793 -> T546\nX794 -> void\nX795 -> T549\nT3 -> tree(T545, T546, T549)\nT544 -> T548\nT547 -> T549", fontsize=14, style = filled, fillcolor = lightblue];
152 -> 398 [arrowhead = none ];
398 -> 153;

399 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
152 -> 399 [arrowhead = none ];
399 -> 154;

400 [label="INSTANCE with matching:\nT69 -> T545\nT71 -> T548\nT72 -> T549", fontsize=14, style = filled, fillcolor = lightgrey];
153 -> 400 [arrowhead = none , style=dashed];
400 -> 29[style=dashed];

401 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
155 -> 401 [arrowhead = none ];
401 -> 157;

402 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
157 -> 402 [arrowhead = none ];
402 -> 158;

403 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
157 -> 403 [arrowhead = none ];
403 -> 159;

404 [label="EVAL with clause\nless(0, s(X822)).\nand substitution\nT557 -> 0\nX822 -> T568\nT560 -> s(T568)\nT561 -> T567\nT566 -> T568", fontsize=14, style = filled, fillcolor = lightblue];
158 -> 404 [arrowhead = none ];
404 -> 160;

405 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
158 -> 405 [arrowhead = none ];
405 -> 161;

406 [label="EVAL with clause\nless(s(X851), s(X852)) :- less(X851, X852).\nand substitution\nX851 -> T580\nT557 -> s(T580)\nX852 -> T582\nT560 -> s(T582)\nT581 -> T582\nT561 -> T583", fontsize=14, style = filled, fillcolor = lightblue];
159 -> 406 [arrowhead = none ];
406 -> 162;

407 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
159 -> 407 [arrowhead = none ];
407 -> 163;

408 [label="INSTANCE with matching:\nT1 -> s(T568)\nT2 -> void\nT3 -> T567", fontsize=14, style = filled, fillcolor = lightgrey];
160 -> 408 [arrowhead = none , style=dashed];
408 -> 1[style=dashed];

409 [label="INSTANCE with matching:\nT178 -> T580\nT180 -> T582\nT181 -> T583", fontsize=14, style = filled, fillcolor = lightgrey];
162 -> 409 [arrowhead = none , style=dashed];
409 -> 64[style=dashed];

410 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
164 -> 410 [arrowhead = none ];
410 -> 166;

411 [label="EVAL with clause\ndelete(X995, tree(X996, X997, X998), tree(X996, X999, X998)) :- ','(less(X995, X996), delete(X995, X997, X999)).\nand substitution\nT1 -> T732\nX995 -> T732\nX996 -> T728\nX997 -> T729\nX998 -> T730\nT2 -> tree(T728, T729, T730)\nX999 -> T733\nT3 -> tree(T728, T733, T730)\nT727 -> T732\nT731 -> T733", fontsize=14, style = filled, fillcolor = lightblue];
165 -> 411 [arrowhead = none ];
411 -> 187;

412 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
165 -> 412 [arrowhead = none ];
412 -> 188;

413 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
166 -> 413 [arrowhead = none ];
413 -> 167;

414 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
166 -> 414 [arrowhead = none ];
414 -> 168;

415 [label="EVAL with clause\ndelmin(tree(X880, void, X881), X880, X881).\nand substitution\nX880 -> T606\nX881 -> T607\nT593 -> tree(T606, void, T607)\nT596 -> T606\nT597 -> T607", fontsize=14, style = filled, fillcolor = lightblue];
167 -> 415 [arrowhead = none ];
415 -> 169;

416 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
167 -> 416 [arrowhead = none ];
416 -> 170;

417 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
168 -> 417 [arrowhead = none ];
417 -> 172;

418 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
168 -> 418 [arrowhead = none ];
418 -> 173;

419 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
169 -> 419 [arrowhead = none ];
419 -> 171;

420 [label="EVAL with clause\ndelmin(tree(X908, X909, X910), X911, tree(X908, X912, X913)) :- delmin(X909, X911, X912).\nand substitution\nX908 -> T632\nX909 -> T633\nX910 -> T634\nT593 -> tree(T632, T633, T634)\nT596 -> T638\nX911 -> T638\nX912 -> T639\nX913 -> T637\nT597 -> tree(T632, T639, T637)\nT635 -> T638\nT636 -> T639", fontsize=14, style = filled, fillcolor = lightblue];
172 -> 420 [arrowhead = none ];
420 -> 174;

421 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
172 -> 421 [arrowhead = none ];
421 -> 175;

422 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
173 -> 422 [arrowhead = none ];
422 -> 176;

423 [label="INSTANCE with matching:\nT240 -> T633\nT245 -> T638\nT246 -> T639", fontsize=14, style = filled, fillcolor = lightgrey];
174 -> 423 [arrowhead = none , style=dashed];
423 -> 78[style=dashed];

424 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
176 -> 424 [arrowhead = none ];
424 -> 177;

425 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
176 -> 425 [arrowhead = none ];
425 -> 178;

426 [label="EVAL with clause\ndelete(X944, tree(X945, X946, X947), tree(X945, X948, X947)) :- ','(less(X944, X945), delete(X944, X946, X948)).\nand substitution\nT1 -> T669\nX944 -> T669\nT591 -> T665\nX945 -> T665\nT592 -> T666\nX946 -> T666\nT593 -> T667\nX947 -> T667\nX948 -> T670\nT3 -> tree(T665, T670, T667)\nT664 -> T669\nT668 -> T670", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 426 [arrowhead = none ];
426 -> 179;

427 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 427 [arrowhead = none ];
427 -> 180;

428 [label="EVAL with clause\ndelete(X972, tree(X973, X974, X975), tree(X973, X974, X976)) :- ','(less(X973, X972), delete(X972, X975, X976)).\nand substitution\nT1 -> T703\nX972 -> T703\nT591 -> T699\nX973 -> T699\nT592 -> T700\nX974 -> T700\nT593 -> T701\nX975 -> T701\nX976 -> T704\nT3 -> tree(T699, T700, T704)\nT698 -> T703\nT702 -> T704", fontsize=14, style = filled, fillcolor = lightblue];
178 -> 428 [arrowhead = none ];
428 -> 183;

429 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
178 -> 429 [arrowhead = none ];
429 -> 184;

430 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
179 -> 430 [arrowhead = none ];
430 -> 181;

431 [label="SPLIT 2\nnew knowledge:\nT673 is ground\nreplacements:\nT669 -> T673\nT670 -> T674\nT1 -> T675\nT667 -> T676\nT3 -> T677\nX6 -> T678\nX7 -> T679\nX649 -> T680\nX650 -> T681", fontsize=14, style = filled, fillcolor = violet];
179 -> 431 [arrowhead = none ];
431 -> 182;

432 [label="INSTANCE with matching:\nT520 -> T669\nT519 -> T665", fontsize=14, style = filled, fillcolor = lightgrey];
181 -> 432 [arrowhead = none , style=dashed];
432 -> 150[style=dashed];

433 [label="INSTANCE with matching:\nT1 -> T673\nT2 -> T666\nT3 -> T674", fontsize=14, style = filled, fillcolor = lightgrey];
182 -> 433 [arrowhead = none , style=dashed];
433 -> 1[style=dashed];

434 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
183 -> 434 [arrowhead = none ];
434 -> 185;

435 [label="SPLIT 2\nreplacements:\nT703 -> T707\nT704 -> T708\nT1 -> T709\nT700 -> T710\nT3 -> T711\nX6 -> T712\nX7 -> T713\nX649 -> T714\nX650 -> T715", fontsize=14, style = filled, fillcolor = violet];
183 -> 435 [arrowhead = none ];
435 -> 186;

436 [label="INSTANCE with matching:\nT408 -> T699\nT410 -> T703", fontsize=14, style = filled, fillcolor = lightgrey];
185 -> 436 [arrowhead = none , style=dashed];
436 -> 120[style=dashed];

437 [label="INSTANCE with matching:\nT1 -> T707\nT2 -> T701\nT3 -> T708", fontsize=14, style = filled, fillcolor = lightgrey];
186 -> 437 [arrowhead = none , style=dashed];
437 -> 1[style=dashed];

438 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
187 -> 438 [arrowhead = none ];
438 -> 189;

439 [label="EVAL with clause\ndelete(X1068, tree(X1069, X1070, X1071), tree(X1069, X1070, X1072)) :- ','(less(X1069, X1068), delete(X1068, X1071, X1072)).\nand substitution\nT1 -> T818\nX1068 -> T818\nX1069 -> T814\nX1070 -> T815\nX1071 -> T816\nT2 -> tree(T814, T815, T816)\nX1072 -> T819\nT3 -> tree(T814, T815, T819)\nT813 -> T818\nT817 -> T819", fontsize=14, style = filled, fillcolor = lightblue];
188 -> 439 [arrowhead = none ];
439 -> 205;

440 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
188 -> 440 [arrowhead = none ];
440 -> 206;

441 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
189 -> 441 [arrowhead = none ];
441 -> 190;

442 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
189 -> 442 [arrowhead = none ];
442 -> 191;

443 [label="EVAL with clause\nless(0, s(X1009)).\nand substitution\nT732 -> 0\nX1009 -> T738\nT728 -> s(T738)\nT733 -> T739", fontsize=14, style = filled, fillcolor = lightblue];
190 -> 443 [arrowhead = none ];
443 -> 192;

444 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
190 -> 444 [arrowhead = none ];
444 -> 193;

445 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
191 -> 445 [arrowhead = none ];
445 -> 194;

446 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
191 -> 446 [arrowhead = none ];
446 -> 195;

447 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T729\nT3 -> T739", fontsize=14, style = filled, fillcolor = lightgrey];
192 -> 447 [arrowhead = none , style=dashed];
447 -> 1[style=dashed];

448 [label="EVAL with clause\nless(s(X1023), s(X1024)) :- less(X1023, X1024).\nand substitution\nX1023 -> T752\nT732 -> s(T752)\nX1024 -> T751\nT728 -> s(T751)\nT750 -> T752\nT733 -> T753", fontsize=14, style = filled, fillcolor = lightblue];
194 -> 448 [arrowhead = none ];
448 -> 196;

449 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
194 -> 449 [arrowhead = none ];
449 -> 197;

450 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
195 -> 450 [arrowhead = none ];
450 -> 200;

451 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
196 -> 451 [arrowhead = none ];
451 -> 198;

452 [label="SPLIT 2\nnew knowledge:\nT756 is ground\nreplacements:\nT752 -> T756\nT753 -> T757\nT1 -> T758\nT730 -> T759\nT3 -> T760\nX6 -> T761\nX7 -> T762", fontsize=14, style = filled, fillcolor = violet];
196 -> 452 [arrowhead = none ];
452 -> 199;

453 [label="INSTANCE with matching:\nT520 -> T752\nT519 -> T751", fontsize=14, style = filled, fillcolor = lightgrey];
198 -> 453 [arrowhead = none , style=dashed];
453 -> 150[style=dashed];

454 [label="INSTANCE with matching:\nT1 -> s(T756)\nT2 -> T729\nT3 -> T757", fontsize=14, style = filled, fillcolor = lightgrey];
199 -> 454 [arrowhead = none , style=dashed];
454 -> 1[style=dashed];

455 [label="EVAL with clause\ndelete(X1045, tree(X1046, X1047, X1048), tree(X1046, X1047, X1049)) :- ','(less(X1046, X1045), delete(X1045, X1048, X1049)).\nand substitution\nT1 -> T784\nX1045 -> T784\nT728 -> T780\nX1046 -> T780\nT729 -> T781\nX1047 -> T781\nT730 -> T782\nX1048 -> T782\nX1049 -> T785\nT3 -> tree(T780, T781, T785)\nT779 -> T784\nT783 -> T785", fontsize=14, style = filled, fillcolor = lightblue];
200 -> 455 [arrowhead = none ];
455 -> 201;

456 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
200 -> 456 [arrowhead = none ];
456 -> 202;

457 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
201 -> 457 [arrowhead = none ];
457 -> 203;

458 [label="SPLIT 2\nreplacements:\nT784 -> T788\nT785 -> T789\nT1 -> T790\nT781 -> T791\nT3 -> T792\nX6 -> T793\nX7 -> T794\nX649 -> T795\nX650 -> T796\nX862 -> T797\nX863 -> T798\nX864 -> T799\nX865 -> T800\nX866 -> T801", fontsize=14, style = filled, fillcolor = violet];
201 -> 458 [arrowhead = none ];
458 -> 204;

459 [label="INSTANCE with matching:\nT408 -> T780\nT410 -> T784", fontsize=14, style = filled, fillcolor = lightgrey];
203 -> 459 [arrowhead = none , style=dashed];
459 -> 120[style=dashed];

460 [label="INSTANCE with matching:\nT1 -> T788\nT2 -> T782\nT3 -> T789", fontsize=14, style = filled, fillcolor = lightgrey];
204 -> 460 [arrowhead = none , style=dashed];
460 -> 1[style=dashed];

461 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
205 -> 461 [arrowhead = none ];
461 -> 207;

462 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
207 -> 462 [arrowhead = none ];
462 -> 208;

463 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
207 -> 463 [arrowhead = none ];
463 -> 209;

464 [label="EVAL with clause\nless(0, s(X1082)).\nand substitution\nT814 -> 0\nX1082 -> T826\nT818 -> s(T826)\nT819 -> T825\nT824 -> T826", fontsize=14, style = filled, fillcolor = lightblue];
208 -> 464 [arrowhead = none ];
464 -> 210;

465 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
208 -> 465 [arrowhead = none ];
465 -> 211;

466 [label="EVAL with clause\nless(s(X1092), s(X1093)) :- less(X1092, X1093).\nand substitution\nX1092 -> T835\nT814 -> s(T835)\nX1093 -> T837\nT818 -> s(T837)\nT836 -> T837\nT819 -> T838", fontsize=14, style = filled, fillcolor = lightblue];
209 -> 466 [arrowhead = none ];
466 -> 212;

467 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
209 -> 467 [arrowhead = none ];
467 -> 213;

468 [label="INSTANCE with matching:\nT1 -> s(T826)\nT2 -> T816\nT3 -> T825", fontsize=14, style = filled, fillcolor = lightgrey];
210 -> 468 [arrowhead = none , style=dashed];
468 -> 1[style=dashed];

469 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
212 -> 469 [arrowhead = none ];
469 -> 214;

470 [label="SPLIT 2\nreplacements:\nT837 -> T841\nT838 -> T842\nT1 -> T843\nT815 -> T844\nT3 -> T845\nX649 -> T846\nX650 -> T847", fontsize=14, style = filled, fillcolor = violet];
212 -> 470 [arrowhead = none ];
470 -> 215;

471 [label="INSTANCE with matching:\nT408 -> T835\nT410 -> T837", fontsize=14, style = filled, fillcolor = lightgrey];
214 -> 471 [arrowhead = none , style=dashed];
471 -> 120[style=dashed];

472 [label="INSTANCE with matching:\nT1 -> s(T841)\nT2 -> T816\nT3 -> T842", fontsize=14, style = filled, fillcolor = lightgrey];
215 -> 472 [arrowhead = none , style=dashed];
472 -> 1[style=dashed];

}

(2) Obligation:

Triples:

less19(s(T52), s(T51)) :- less19(T52, T51).
less31(s(T88), s(T90)) :- less31(T88, T90).
p29(T69, T71, T72) :- less31(T69, T71).
p29(T69, T75, T76) :- ','(lessc31(T69, T75), delete1(T75, void, T76)).
delmin78(tree(T273, T274, T275), T279, tree(T273, T280, T278)) :- delmin78(T274, T279, T280).
p17(T33, T31, T34) :- less19(T33, T31).
p17(T37, T31, T38) :- ','(lessc19(T37, T31), delete1(T37, void, T38)).
p50(T124, T123, T125) :- less19(T124, T123).
p50(T128, T123, T129) :- ','(lessc19(T128, T123), delete1(s(T128), void, T129)).
p93(T318, T321, T319, T322) :- less31(T318, T321).
p93(T318, T325, T319, T326) :- ','(lessc31(T318, T325), delete1(T325, T319, T326)).
p64(T178, T180, T181) :- less31(T178, T180).
p64(T178, T184, T185) :- ','(lessc31(T178, T184), delete1(s(T184), void, T185)).
delete1(T33, tree(T31, void, void), tree(T31, T34, void)) :- p17(T33, T31, T34).
delete1(T71, tree(T69, void, void), tree(T69, void, T72)) :- p29(T69, T71, T72).
delete1(0, tree(s(T112), void, void), tree(s(T112), T113, void)) :- delete1(0, void, T113).
delete1(s(T124), tree(s(T123), void, void), tree(s(T123), T125, void)) :- p50(T124, T123, T125).
delete1(T148, tree(T146, void, void), tree(T146, void, T149)) :- p29(T146, T148, T149).
delete1(s(T166), tree(0, void, void), tree(0, void, T165)) :- delete1(s(T166), void, T165).
delete1(s(T180), tree(s(T178), void, void), tree(s(T178), void, T181)) :- p64(T178, T180, T181).
delete1(T199, tree(T199, void, tree(T239, T240, T241)), tree(T245, void, tree(T239, T246, T244))) :- delmin78(T240, T245, T246).
delete1(T305, tree(T302, void, T303), tree(T302, T306, T303)) :- p17(T305, T302, T306).
delete1(T321, tree(T318, void, T319), tree(T318, void, T322)) :- p93(T318, T321, T319, T322).
delete1(0, tree(s(T351), void, T343), tree(s(T351), T352, T343)) :- delete1(0, void, T352).
delete1(s(T363), tree(s(T362), void, T343), tree(s(T362), T364, T343)) :- p50(T363, T362, T364).
delete1(T379, tree(T376, void, T377), tree(T376, void, T380)) :- p93(T376, T379, T377, T380).
delete1(s(T399), tree(0, void, T389), tree(0, void, T398)) :- delete1(s(T399), T389, T398).
delete1(s(T410), tree(s(T408), void, T389), tree(s(T408), void, T411)) :- less31(T408, T410).
delete1(s(T414), tree(s(T408), void, T389), tree(s(T408), void, T415)) :- ','(lessc31(T408, T414), delete1(s(T414), T389, T415)).
delete1(T460, tree(T457, T458, void), tree(T457, T461, void)) :- less19(T460, T457).
delete1(T464, tree(T457, T458, void), tree(T457, T465, void)) :- ','(lessc19(T464, T457), delete1(T464, T458, T465)).
delete1(T488, tree(T485, T486, void), tree(T485, T486, T489)) :- p29(T485, T488, T489).
delete1(0, tree(s(T506), T498, void), tree(s(T506), T507, void)) :- delete1(0, T498, T507).
delete1(s(T520), tree(s(T519), T498, void), tree(s(T519), T521, void)) :- less19(T520, T519).
delete1(s(T524), tree(s(T519), T498, void), tree(s(T519), T525, void)) :- ','(lessc19(T524, T519), delete1(s(T524), T498, T525)).
delete1(T548, tree(T545, T546, void), tree(T545, T546, T549)) :- p29(T545, T548, T549).
delete1(s(T568), tree(0, T558, void), tree(0, T558, T567)) :- delete1(s(T568), void, T567).
delete1(s(T582), tree(s(T580), T558, void), tree(s(T580), T558, T583)) :- p64(T580, T582, T583).
delete1(T591, tree(T591, T592, tree(T632, T633, T634)), tree(T638, T592, tree(T632, T639, T637))) :- delmin78(T633, T638, T639).
delete1(T669, tree(T665, T666, T667), tree(T665, T670, T667)) :- less19(T669, T665).
delete1(T673, tree(T665, T666, T676), tree(T665, T674, T676)) :- ','(lessc19(T673, T665), delete1(T673, T666, T674)).
delete1(T703, tree(T699, T700, T701), tree(T699, T700, T704)) :- less31(T699, T703).
delete1(T707, tree(T699, T710, T701), tree(T699, T710, T708)) :- ','(lessc31(T699, T707), delete1(T707, T701, T708)).
delete1(0, tree(s(T738), T729, T730), tree(s(T738), T739, T730)) :- delete1(0, T729, T739).
delete1(s(T752), tree(s(T751), T729, T730), tree(s(T751), T753, T730)) :- less19(T752, T751).
delete1(s(T756), tree(s(T751), T729, T759), tree(s(T751), T757, T759)) :- ','(lessc19(T756, T751), delete1(s(T756), T729, T757)).
delete1(T784, tree(T780, T781, T782), tree(T780, T781, T785)) :- less31(T780, T784).
delete1(T788, tree(T780, T791, T782), tree(T780, T791, T789)) :- ','(lessc31(T780, T788), delete1(T788, T782, T789)).
delete1(s(T826), tree(0, T815, T816), tree(0, T815, T825)) :- delete1(s(T826), T816, T825).
delete1(s(T837), tree(s(T835), T815, T816), tree(s(T835), T815, T838)) :- less31(T835, T837).
delete1(s(T841), tree(s(T835), T844, T816), tree(s(T835), T844, T842)) :- ','(lessc31(T835, T841), delete1(s(T841), T816, T842)).

Clauses:

deletec1(T6, tree(T6, void, T7), T7).
deletec1(T9, tree(T9, void, void), void).
deletec1(T33, tree(T31, void, void), tree(T31, T34, void)) :- qc17(T33, T31, T34).
deletec1(T71, tree(T69, void, void), tree(T69, void, T72)) :- qc29(T69, T71, T72).
deletec1(0, tree(s(T112), void, void), tree(s(T112), T113, void)) :- deletec1(0, void, T113).
deletec1(s(T124), tree(s(T123), void, void), tree(s(T123), T125, void)) :- qc50(T124, T123, T125).
deletec1(T148, tree(T146, void, void), tree(T146, void, T149)) :- qc29(T146, T148, T149).
deletec1(s(T166), tree(0, void, void), tree(0, void, T165)) :- deletec1(s(T166), void, T165).
deletec1(s(T180), tree(s(T178), void, void), tree(s(T178), void, T181)) :- qc64(T178, T180, T181).
deletec1(T199, tree(T199, void, tree(T213, void, T214)), tree(T213, void, T214)).
deletec1(T199, tree(T199, void, tree(T239, T240, T241)), tree(T245, void, tree(T239, T246, T244))) :- delminc78(T240, T245, T246).
deletec1(T305, tree(T302, void, T303), tree(T302, T306, T303)) :- qc17(T305, T302, T306).
deletec1(T321, tree(T318, void, T319), tree(T318, void, T322)) :- qc93(T318, T321, T319, T322).
deletec1(0, tree(s(T351), void, T343), tree(s(T351), T352, T343)) :- deletec1(0, void, T352).
deletec1(s(T363), tree(s(T362), void, T343), tree(s(T362), T364, T343)) :- qc50(T363, T362, T364).
deletec1(T379, tree(T376, void, T377), tree(T376, void, T380)) :- qc93(T376, T379, T377, T380).
deletec1(s(T399), tree(0, void, T389), tree(0, void, T398)) :- deletec1(s(T399), T389, T398).
deletec1(s(T414), tree(s(T408), void, T389), tree(s(T408), void, T415)) :- ','(lessc31(T408, T414), deletec1(s(T414), T389, T415)).
deletec1(T428, tree(T428, T429, void), T429).
deletec1(T464, tree(T457, T458, void), tree(T457, T465, void)) :- ','(lessc19(T464, T457), deletec1(T464, T458, T465)).
deletec1(T488, tree(T485, T486, void), tree(T485, T486, T489)) :- qc29(T485, T488, T489).
deletec1(0, tree(s(T506), T498, void), tree(s(T506), T507, void)) :- deletec1(0, T498, T507).
deletec1(s(T524), tree(s(T519), T498, void), tree(s(T519), T525, void)) :- ','(lessc19(T524, T519), deletec1(s(T524), T498, T525)).
deletec1(T548, tree(T545, T546, void), tree(T545, T546, T549)) :- qc29(T545, T548, T549).
deletec1(s(T568), tree(0, T558, void), tree(0, T558, T567)) :- deletec1(s(T568), void, T567).
deletec1(s(T582), tree(s(T580), T558, void), tree(s(T580), T558, T583)) :- qc64(T580, T582, T583).
deletec1(T591, tree(T591, T592, tree(T606, void, T607)), tree(T606, T592, T607)).
deletec1(T591, tree(T591, T592, tree(T632, T633, T634)), tree(T638, T592, tree(T632, T639, T637))) :- delminc78(T633, T638, T639).
deletec1(T673, tree(T665, T666, T676), tree(T665, T674, T676)) :- ','(lessc19(T673, T665), deletec1(T673, T666, T674)).
deletec1(T707, tree(T699, T710, T701), tree(T699, T710, T708)) :- ','(lessc31(T699, T707), deletec1(T707, T701, T708)).
deletec1(0, tree(s(T738), T729, T730), tree(s(T738), T739, T730)) :- deletec1(0, T729, T739).
deletec1(s(T756), tree(s(T751), T729, T759), tree(s(T751), T757, T759)) :- ','(lessc19(T756, T751), deletec1(s(T756), T729, T757)).
deletec1(T788, tree(T780, T791, T782), tree(T780, T791, T789)) :- ','(lessc31(T780, T788), deletec1(T788, T782, T789)).
deletec1(s(T826), tree(0, T815, T816), tree(0, T815, T825)) :- deletec1(s(T826), T816, T825).
deletec1(s(T841), tree(s(T835), T844, T816), tree(s(T835), T844, T842)) :- ','(lessc31(T835, T841), deletec1(s(T841), T816, T842)).
lessc19(0, s(T45)).
lessc19(s(T52), s(T51)) :- lessc19(T52, T51).
lessc31(0, s(T83)).
lessc31(s(T88), s(T90)) :- lessc31(T88, T90).
qc29(T69, T75, T76) :- ','(lessc31(T69, T75), deletec1(T75, void, T76)).
delminc78(tree(T259, void, T260), T259, T260).
delminc78(tree(T273, T274, T275), T279, tree(T273, T280, T278)) :- delminc78(T274, T279, T280).
qc17(T37, T31, T38) :- ','(lessc19(T37, T31), deletec1(T37, void, T38)).
qc50(T128, T123, T129) :- ','(lessc19(T128, T123), deletec1(s(T128), void, T129)).
qc93(T318, T325, T319, T326) :- ','(lessc31(T318, T325), deletec1(T325, T319, T326)).
qc64(T178, T184, T185) :- ','(lessc31(T178, T184), deletec1(s(T184), void, T185)).

Afs:

delete1(x1, x2, x3) = delete1(x2)

(3) TriplesToPiDPProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
delete1_in: (f,b,f) (b,b,f)
p17_in: (f,b,f) (b,b,f)
less19_in: (f,b) (b,b)
lessc19_in: (f,b) (b,b)
p29_in: (b,b,f) (b,f,f)
less31_in: (b,b) (b,f)
lessc31_in: (b,b) (b,f)
p50_in: (b,b,f) (f,b,f)
p64_in: (b,b,f) (b,f,f)
delmin78_in: (b,f,f)
p93_in: (b,b,b,f) (b,f,b,f)
Transforming TRIPLES into the following Term Rewriting System:
Pi DP problem:
The TRS P consists of the following rules:

DELETE1_IN_AGA(T33, tree(T31, void, void), tree(T31, T34, void)) → U19_AGA(T33, T31, T34, p17_in_aga(T33, T31, T34))
DELETE1_IN_AGA(T33, tree(T31, void, void), tree(T31, T34, void)) → P17_IN_AGA(T33, T31, T34)
P17_IN_AGA(T33, T31, T34) → U7_AGA(T33, T31, T34, less19_in_ag(T33, T31))
P17_IN_AGA(T33, T31, T34) → LESS19_IN_AG(T33, T31)
LESS19_IN_AG(s(T52), s(T51)) → U1_AG(T52, T51, less19_in_ag(T52, T51))
LESS19_IN_AG(s(T52), s(T51)) → LESS19_IN_AG(T52, T51)
P17_IN_AGA(T37, T31, T38) → U8_AGA(T37, T31, T38, lessc19_in_ag(T37, T31))
U8_AGA(T37, T31, T38, lessc19_out_ag(T37, T31)) → U9_AGA(T37, T31, T38, delete1_in_gga(T37, void, T38))
U8_AGA(T37, T31, T38, lessc19_out_ag(T37, T31)) → DELETE1_IN_GGA(T37, void, T38)
DELETE1_IN_GGA(T33, tree(T31, void, void), tree(T31, T34, void)) → U19_GGA(T33, T31, T34, p17_in_gga(T33, T31, T34))
DELETE1_IN_GGA(T33, tree(T31, void, void), tree(T31, T34, void)) → P17_IN_GGA(T33, T31, T34)
P17_IN_GGA(T33, T31, T34) → U7_GGA(T33, T31, T34, less19_in_gg(T33, T31))
P17_IN_GGA(T33, T31, T34) → LESS19_IN_GG(T33, T31)
LESS19_IN_GG(s(T52), s(T51)) → U1_GG(T52, T51, less19_in_gg(T52, T51))
LESS19_IN_GG(s(T52), s(T51)) → LESS19_IN_GG(T52, T51)
P17_IN_GGA(T37, T31, T38) → U8_GGA(T37, T31, T38, lessc19_in_gg(T37, T31))
U8_GGA(T37, T31, T38, lessc19_out_gg(T37, T31)) → U9_GGA(T37, T31, T38, delete1_in_gga(T37, void, T38))
U8_GGA(T37, T31, T38, lessc19_out_gg(T37, T31)) → DELETE1_IN_GGA(T37, void, T38)
DELETE1_IN_GGA(T71, tree(T69, void, void), tree(T69, void, T72)) → U20_GGA(T71, T69, T72, p29_in_gga(T69, T71, T72))
DELETE1_IN_GGA(T71, tree(T69, void, void), tree(T69, void, T72)) → P29_IN_GGA(T69, T71, T72)
P29_IN_GGA(T69, T71, T72) → U3_GGA(T69, T71, T72, less31_in_gg(T69, T71))
P29_IN_GGA(T69, T71, T72) → LESS31_IN_GG(T69, T71)
LESS31_IN_GG(s(T88), s(T90)) → U2_GG(T88, T90, less31_in_gg(T88, T90))
LESS31_IN_GG(s(T88), s(T90)) → LESS31_IN_GG(T88, T90)
P29_IN_GGA(T69, T75, T76) → U4_GGA(T69, T75, T76, lessc31_in_gg(T69, T75))
U4_GGA(T69, T75, T76, lessc31_out_gg(T69, T75)) → U5_GGA(T69, T75, T76, delete1_in_gga(T75, void, T76))
U4_GGA(T69, T75, T76, lessc31_out_gg(T69, T75)) → DELETE1_IN_GGA(T75, void, T76)
DELETE1_IN_GGA(0, tree(s(T112), void, void), tree(s(T112), T113, void)) → U21_GGA(T112, T113, delete1_in_gga(0, void, T113))
DELETE1_IN_GGA(0, tree(s(T112), void, void), tree(s(T112), T113, void)) → DELETE1_IN_GGA(0, void, T113)
DELETE1_IN_GGA(s(T124), tree(s(T123), void, void), tree(s(T123), T125, void)) → U22_GGA(T124, T123, T125, p50_in_gga(T124, T123, T125))
DELETE1_IN_GGA(s(T124), tree(s(T123), void, void), tree(s(T123), T125, void)) → P50_IN_GGA(T124, T123, T125)
P50_IN_GGA(T124, T123, T125) → U10_GGA(T124, T123, T125, less19_in_gg(T124, T123))
P50_IN_GGA(T124, T123, T125) → LESS19_IN_GG(T124, T123)
P50_IN_GGA(T128, T123, T129) → U11_GGA(T128, T123, T129, lessc19_in_gg(T128, T123))
U11_GGA(T128, T123, T129, lessc19_out_gg(T128, T123)) → U12_GGA(T128, T123, T129, delete1_in_gga(s(T128), void, T129))
U11_GGA(T128, T123, T129, lessc19_out_gg(T128, T123)) → DELETE1_IN_GGA(s(T128), void, T129)
DELETE1_IN_GGA(T148, tree(T146, void, void), tree(T146, void, T149)) → U23_GGA(T148, T146, T149, p29_in_gga(T146, T148, T149))
DELETE1_IN_GGA(s(T166), tree(0, void, void), tree(0, void, T165)) → U24_GGA(T166, T165, delete1_in_gga(s(T166), void, T165))
DELETE1_IN_GGA(s(T166), tree(0, void, void), tree(0, void, T165)) → DELETE1_IN_GGA(s(T166), void, T165)
DELETE1_IN_GGA(s(T180), tree(s(T178), void, void), tree(s(T178), void, T181)) → U25_GGA(T180, T178, T181, p64_in_gga(T178, T180, T181))
DELETE1_IN_GGA(s(T180), tree(s(T178), void, void), tree(s(T178), void, T181)) → P64_IN_GGA(T178, T180, T181)
P64_IN_GGA(T178, T180, T181) → U16_GGA(T178, T180, T181, less31_in_gg(T178, T180))
P64_IN_GGA(T178, T180, T181) → LESS31_IN_GG(T178, T180)
P64_IN_GGA(T178, T184, T185) → U17_GGA(T178, T184, T185, lessc31_in_gg(T178, T184))
U17_GGA(T178, T184, T185, lessc31_out_gg(T178, T184)) → U18_GGA(T178, T184, T185, delete1_in_gga(s(T184), void, T185))
U17_GGA(T178, T184, T185, lessc31_out_gg(T178, T184)) → DELETE1_IN_GGA(s(T184), void, T185)
DELETE1_IN_GGA(T199, tree(T199, void, tree(T239, T240, T241)), tree(T245, void, tree(T239, T246, T244))) → U26_GGA(T199, T239, T240, T241, T245, T246, T244, delmin78_in_gaa(T240, T245, T246))
DELETE1_IN_GGA(T199, tree(T199, void, tree(T239, T240, T241)), tree(T245, void, tree(T239, T246, T244))) → DELMIN78_IN_GAA(T240, T245, T246)
DELMIN78_IN_GAA(tree(T273, T274, T275), T279, tree(T273, T280, T278)) → U6_GAA(T273, T274, T275, T279, T280, T278, delmin78_in_gaa(T274, T279, T280))
DELMIN78_IN_GAA(tree(T273, T274, T275), T279, tree(T273, T280, T278)) → DELMIN78_IN_GAA(T274, T279, T280)
DELETE1_IN_GGA(T305, tree(T302, void, T303), tree(T302, T306, T303)) → U27_GGA(T305, T302, T303, T306, p17_in_gga(T305, T302, T306))
DELETE1_IN_GGA(T305, tree(T302, void, T303), tree(T302, T306, T303)) → P17_IN_GGA(T305, T302, T306)
DELETE1_IN_GGA(T321, tree(T318, void, T319), tree(T318, void, T322)) → U28_GGA(T321, T318, T319, T322, p93_in_ggga(T318, T321, T319, T322))
DELETE1_IN_GGA(T321, tree(T318, void, T319), tree(T318, void, T322)) → P93_IN_GGGA(T318, T321, T319, T322)
P93_IN_GGGA(T318, T321, T319, T322) → U13_GGGA(T318, T321, T319, T322, less31_in_gg(T318, T321))
P93_IN_GGGA(T318, T321, T319, T322) → LESS31_IN_GG(T318, T321)
P93_IN_GGGA(T318, T325, T319, T326) → U14_GGGA(T318, T325, T319, T326, lessc31_in_gg(T318, T325))
U14_GGGA(T318, T325, T319, T326, lessc31_out_gg(T318, T325)) → U15_GGGA(T318, T325, T319, T326, delete1_in_gga(T325, T319, T326))
U14_GGGA(T318, T325, T319, T326, lessc31_out_gg(T318, T325)) → DELETE1_IN_GGA(T325, T319, T326)
DELETE1_IN_GGA(0, tree(s(T351), void, T343), tree(s(T351), T352, T343)) → U29_GGA(T351, T343, T352, delete1_in_gga(0, void, T352))
DELETE1_IN_GGA(0, tree(s(T351), void, T343), tree(s(T351), T352, T343)) → DELETE1_IN_GGA(0, void, T352)
DELETE1_IN_GGA(s(T363), tree(s(T362), void, T343), tree(s(T362), T364, T343)) → U30_GGA(T363, T362, T343, T364, p50_in_gga(T363, T362, T364))
DELETE1_IN_GGA(s(T363), tree(s(T362), void, T343), tree(s(T362), T364, T343)) → P50_IN_GGA(T363, T362, T364)
DELETE1_IN_GGA(T379, tree(T376, void, T377), tree(T376, void, T380)) → U31_GGA(T379, T376, T377, T380, p93_in_ggga(T376, T379, T377, T380))
DELETE1_IN_GGA(s(T399), tree(0, void, T389), tree(0, void, T398)) → U32_GGA(T399, T389, T398, delete1_in_gga(s(T399), T389, T398))
DELETE1_IN_GGA(s(T399), tree(0, void, T389), tree(0, void, T398)) → DELETE1_IN_GGA(s(T399), T389, T398)
DELETE1_IN_GGA(s(T410), tree(s(T408), void, T389), tree(s(T408), void, T411)) → U33_GGA(T410, T408, T389, T411, less31_in_gg(T408, T410))
DELETE1_IN_GGA(s(T410), tree(s(T408), void, T389), tree(s(T408), void, T411)) → LESS31_IN_GG(T408, T410)
DELETE1_IN_GGA(s(T414), tree(s(T408), void, T389), tree(s(T408), void, T415)) → U34_GGA(T414, T408, T389, T415, lessc31_in_gg(T408, T414))
U34_GGA(T414, T408, T389, T415, lessc31_out_gg(T408, T414)) → U35_GGA(T414, T408, T389, T415, delete1_in_gga(s(T414), T389, T415))
U34_GGA(T414, T408, T389, T415, lessc31_out_gg(T408, T414)) → DELETE1_IN_GGA(s(T414), T389, T415)
DELETE1_IN_GGA(T460, tree(T457, T458, void), tree(T457, T461, void)) → U36_GGA(T460, T457, T458, T461, less19_in_gg(T460, T457))
DELETE1_IN_GGA(T460, tree(T457, T458, void), tree(T457, T461, void)) → LESS19_IN_GG(T460, T457)
DELETE1_IN_GGA(T464, tree(T457, T458, void), tree(T457, T465, void)) → U37_GGA(T464, T457, T458, T465, lessc19_in_gg(T464, T457))
U37_GGA(T464, T457, T458, T465, lessc19_out_gg(T464, T457)) → U38_GGA(T464, T457, T458, T465, delete1_in_gga(T464, T458, T465))
U37_GGA(T464, T457, T458, T465, lessc19_out_gg(T464, T457)) → DELETE1_IN_GGA(T464, T458, T465)
DELETE1_IN_GGA(T488, tree(T485, T486, void), tree(T485, T486, T489)) → U39_GGA(T488, T485, T486, T489, p29_in_gga(T485, T488, T489))
DELETE1_IN_GGA(T488, tree(T485, T486, void), tree(T485, T486, T489)) → P29_IN_GGA(T485, T488, T489)
DELETE1_IN_GGA(0, tree(s(T506), T498, void), tree(s(T506), T507, void)) → U40_GGA(T506, T498, T507, delete1_in_gga(0, T498, T507))
DELETE1_IN_GGA(0, tree(s(T506), T498, void), tree(s(T506), T507, void)) → DELETE1_IN_GGA(0, T498, T507)
DELETE1_IN_GGA(s(T520), tree(s(T519), T498, void), tree(s(T519), T521, void)) → U41_GGA(T520, T519, T498, T521, less19_in_gg(T520, T519))
DELETE1_IN_GGA(s(T520), tree(s(T519), T498, void), tree(s(T519), T521, void)) → LESS19_IN_GG(T520, T519)
DELETE1_IN_GGA(s(T524), tree(s(T519), T498, void), tree(s(T519), T525, void)) → U42_GGA(T524, T519, T498, T525, lessc19_in_gg(T524, T519))
U42_GGA(T524, T519, T498, T525, lessc19_out_gg(T524, T519)) → U43_GGA(T524, T519, T498, T525, delete1_in_gga(s(T524), T498, T525))
U42_GGA(T524, T519, T498, T525, lessc19_out_gg(T524, T519)) → DELETE1_IN_GGA(s(T524), T498, T525)
DELETE1_IN_GGA(T548, tree(T545, T546, void), tree(T545, T546, T549)) → U44_GGA(T548, T545, T546, T549, p29_in_gga(T545, T548, T549))
DELETE1_IN_GGA(s(T568), tree(0, T558, void), tree(0, T558, T567)) → U45_GGA(T568, T558, T567, delete1_in_gga(s(T568), void, T567))
DELETE1_IN_GGA(s(T568), tree(0, T558, void), tree(0, T558, T567)) → DELETE1_IN_GGA(s(T568), void, T567)
DELETE1_IN_GGA(s(T582), tree(s(T580), T558, void), tree(s(T580), T558, T583)) → U46_GGA(T582, T580, T558, T583, p64_in_gga(T580, T582, T583))
DELETE1_IN_GGA(s(T582), tree(s(T580), T558, void), tree(s(T580), T558, T583)) → P64_IN_GGA(T580, T582, T583)
DELETE1_IN_GGA(T591, tree(T591, T592, tree(T632, T633, T634)), tree(T638, T592, tree(T632, T639, T637))) → U47_GGA(T591, T592, T632, T633, T634, T638, T639, T637, delmin78_in_gaa(T633, T638, T639))
DELETE1_IN_GGA(T591, tree(T591, T592, tree(T632, T633, T634)), tree(T638, T592, tree(T632, T639, T637))) → DELMIN78_IN_GAA(T633, T638, T639)
DELETE1_IN_GGA(T669, tree(T665, T666, T667), tree(T665, T670, T667)) → U48_GGA(T669, T665, T666, T667, T670, less19_in_gg(T669, T665))
DELETE1_IN_GGA(T669, tree(T665, T666, T667), tree(T665, T670, T667)) → LESS19_IN_GG(T669, T665)
DELETE1_IN_GGA(T673, tree(T665, T666, T676), tree(T665, T674, T676)) → U49_GGA(T673, T665, T666, T676, T674, lessc19_in_gg(T673, T665))
U49_GGA(T673, T665, T666, T676, T674, lessc19_out_gg(T673, T665)) → U50_GGA(T673, T665, T666, T676, T674, delete1_in_gga(T673, T666, T674))
U49_GGA(T673, T665, T666, T676, T674, lessc19_out_gg(T673, T665)) → DELETE1_IN_GGA(T673, T666, T674)
DELETE1_IN_GGA(T703, tree(T699, T700, T701), tree(T699, T700, T704)) → U51_GGA(T703, T699, T700, T701, T704, less31_in_gg(T699, T703))
DELETE1_IN_GGA(T703, tree(T699, T700, T701), tree(T699, T700, T704)) → LESS31_IN_GG(T699, T703)
DELETE1_IN_GGA(T707, tree(T699, T710, T701), tree(T699, T710, T708)) → U52_GGA(T707, T699, T710, T701, T708, lessc31_in_gg(T699, T707))
U52_GGA(T707, T699, T710, T701, T708, lessc31_out_gg(T699, T707)) → U53_GGA(T707, T699, T710, T701, T708, delete1_in_gga(T707, T701, T708))
U52_GGA(T707, T699, T710, T701, T708, lessc31_out_gg(T699, T707)) → DELETE1_IN_GGA(T707, T701, T708)
DELETE1_IN_GGA(0, tree(s(T738), T729, T730), tree(s(T738), T739, T730)) → U54_GGA(T738, T729, T730, T739, delete1_in_gga(0, T729, T739))
DELETE1_IN_GGA(0, tree(s(T738), T729, T730), tree(s(T738), T739, T730)) → DELETE1_IN_GGA(0, T729, T739)
DELETE1_IN_GGA(s(T752), tree(s(T751), T729, T730), tree(s(T751), T753, T730)) → U55_GGA(T752, T751, T729, T730, T753, less19_in_gg(T752, T751))
DELETE1_IN_GGA(s(T752), tree(s(T751), T729, T730), tree(s(T751), T753, T730)) → LESS19_IN_GG(T752, T751)
DELETE1_IN_GGA(s(T756), tree(s(T751), T729, T759), tree(s(T751), T757, T759)) → U56_GGA(T756, T751, T729, T759, T757, lessc19_in_gg(T756, T751))
U56_GGA(T756, T751, T729, T759, T757, lessc19_out_gg(T756, T751)) → U57_GGA(T756, T751, T729, T759, T757, delete1_in_gga(s(T756), T729, T757))
U56_GGA(T756, T751, T729, T759, T757, lessc19_out_gg(T756, T751)) → DELETE1_IN_GGA(s(T756), T729, T757)
DELETE1_IN_GGA(T784, tree(T780, T781, T782), tree(T780, T781, T785)) → U58_GGA(T784, T780, T781, T782, T785, less31_in_gg(T780, T784))
DELETE1_IN_GGA(T788, tree(T780, T791, T782), tree(T780, T791, T789)) → U59_GGA(T788, T780, T791, T782, T789, lessc31_in_gg(T780, T788))
U59_GGA(T788, T780, T791, T782, T789, lessc31_out_gg(T780, T788)) → U60_GGA(T788, T780, T791, T782, T789, delete1_in_gga(T788, T782, T789))
U59_GGA(T788, T780, T791, T782, T789, lessc31_out_gg(T780, T788)) → DELETE1_IN_GGA(T788, T782, T789)
DELETE1_IN_GGA(s(T826), tree(0, T815, T816), tree(0, T815, T825)) → U61_GGA(T826, T815, T816, T825, delete1_in_gga(s(T826), T816, T825))
DELETE1_IN_GGA(s(T826), tree(0, T815, T816), tree(0, T815, T825)) → DELETE1_IN_GGA(s(T826), T816, T825)
DELETE1_IN_GGA(s(T837), tree(s(T835), T815, T816), tree(s(T835), T815, T838)) → U62_GGA(T837, T835, T815, T816, T838, less31_in_gg(T835, T837))
DELETE1_IN_GGA(s(T837), tree(s(T835), T815, T816), tree(s(T835), T815, T838)) → LESS31_IN_GG(T835, T837)
DELETE1_IN_GGA(s(T841), tree(s(T835), T844, T816), tree(s(T835), T844, T842)) → U63_GGA(T841, T835, T844, T816, T842, lessc31_in_gg(T835, T841))
U63_GGA(T841, T835, T844, T816, T842, lessc31_out_gg(T835, T841)) → U64_GGA(T841, T835, T844, T816, T842, delete1_in_gga(s(T841), T816, T842))
U63_GGA(T841, T835, T844, T816, T842, lessc31_out_gg(T835, T841)) → DELETE1_IN_GGA(s(T841), T816, T842)
DELETE1_IN_AGA(T71, tree(T69, void, void), tree(T69, void, T72)) → U20_AGA(T71, T69, T72, p29_in_gaa(T69, T71, T72))
DELETE1_IN_AGA(T71, tree(T69, void, void), tree(T69, void, T72)) → P29_IN_GAA(T69, T71, T72)
P29_IN_GAA(T69, T71, T72) → U3_GAA(T69, T71, T72, less31_in_ga(T69, T71))
P29_IN_GAA(T69, T71, T72) → LESS31_IN_GA(T69, T71)
LESS31_IN_GA(s(T88), s(T90)) → U2_GA(T88, T90, less31_in_ga(T88, T90))
LESS31_IN_GA(s(T88), s(T90)) → LESS31_IN_GA(T88, T90)
P29_IN_GAA(T69, T75, T76) → U4_GAA(T69, T75, T76, lessc31_in_ga(T69, T75))
U4_GAA(T69, T75, T76, lessc31_out_ga(T69, T75)) → U5_GAA(T69, T75, T76, delete1_in_aga(T75, void, T76))
U4_GAA(T69, T75, T76, lessc31_out_ga(T69, T75)) → DELETE1_IN_AGA(T75, void, T76)
DELETE1_IN_AGA(0, tree(s(T112), void, void), tree(s(T112), T113, void)) → U21_AGA(T112, T113, delete1_in_gga(0, void, T113))
DELETE1_IN_AGA(0, tree(s(T112), void, void), tree(s(T112), T113, void)) → DELETE1_IN_GGA(0, void, T113)
DELETE1_IN_AGA(s(T124), tree(s(T123), void, void), tree(s(T123), T125, void)) → U22_AGA(T124, T123, T125, p50_in_aga(T124, T123, T125))
DELETE1_IN_AGA(s(T124), tree(s(T123), void, void), tree(s(T123), T125, void)) → P50_IN_AGA(T124, T123, T125)
P50_IN_AGA(T124, T123, T125) → U10_AGA(T124, T123, T125, less19_in_ag(T124, T123))
P50_IN_AGA(T124, T123, T125) → LESS19_IN_AG(T124, T123)
P50_IN_AGA(T128, T123, T129) → U11_AGA(T128, T123, T129, lessc19_in_ag(T128, T123))
U11_AGA(T128, T123, T129, lessc19_out_ag(T128, T123)) → U12_AGA(T128, T123, T129, delete1_in_gga(s(T128), void, T129))
U11_AGA(T128, T123, T129, lessc19_out_ag(T128, T123)) → DELETE1_IN_GGA(s(T128), void, T129)
DELETE1_IN_AGA(T148, tree(T146, void, void), tree(T146, void, T149)) → U23_AGA(T148, T146, T149, p29_in_gaa(T146, T148, T149))
DELETE1_IN_AGA(s(T166), tree(0, void, void), tree(0, void, T165)) → U24_AGA(T166, T165, delete1_in_aga(s(T166), void, T165))
DELETE1_IN_AGA(s(T166), tree(0, void, void), tree(0, void, T165)) → DELETE1_IN_AGA(s(T166), void, T165)
DELETE1_IN_AGA(s(T180), tree(s(T178), void, void), tree(s(T178), void, T181)) → U25_AGA(T180, T178, T181, p64_in_gaa(T178, T180, T181))
DELETE1_IN_AGA(s(T180), tree(s(T178), void, void), tree(s(T178), void, T181)) → P64_IN_GAA(T178, T180, T181)
P64_IN_GAA(T178, T180, T181) → U16_GAA(T178, T180, T181, less31_in_ga(T178, T180))
P64_IN_GAA(T178, T180, T181) → LESS31_IN_GA(T178, T180)
P64_IN_GAA(T178, T184, T185) → U17_GAA(T178, T184, T185, lessc31_in_ga(T178, T184))
U17_GAA(T178, T184, T185, lessc31_out_ga(T178, T184)) → U18_GAA(T178, T184, T185, delete1_in_aga(s(T184), void, T185))
U17_GAA(T178, T184, T185, lessc31_out_ga(T178, T184)) → DELETE1_IN_AGA(s(T184), void, T185)
DELETE1_IN_AGA(T199, tree(T199, void, tree(T239, T240, T241)), tree(T245, void, tree(T239, T246, T244))) → U26_AGA(T199, T239, T240, T241, T245, T246, T244, delmin78_in_gaa(T240, T245, T246))
DELETE1_IN_AGA(T199, tree(T199, void, tree(T239, T240, T241)), tree(T245, void, tree(T239, T246, T244))) → DELMIN78_IN_GAA(T240, T245, T246)
DELETE1_IN_AGA(T305, tree(T302, void, T303), tree(T302, T306, T303)) → U27_AGA(T305, T302, T303, T306, p17_in_aga(T305, T302, T306))
DELETE1_IN_AGA(T305, tree(T302, void, T303), tree(T302, T306, T303)) → P17_IN_AGA(T305, T302, T306)
DELETE1_IN_AGA(T321, tree(T318, void, T319), tree(T318, void, T322)) → U28_AGA(T321, T318, T319, T322, p93_in_gaga(T318, T321, T319, T322))
DELETE1_IN_AGA(T321, tree(T318, void, T319), tree(T318, void, T322)) → P93_IN_GAGA(T318, T321, T319, T322)
P93_IN_GAGA(T318, T321, T319, T322) → U13_GAGA(T318, T321, T319, T322, less31_in_ga(T318, T321))
P93_IN_GAGA(T318, T321, T319, T322) → LESS31_IN_GA(T318, T321)
P93_IN_GAGA(T318, T325, T319, T326) → U14_GAGA(T318, T325, T319, T326, lessc31_in_ga(T318, T325))
U14_GAGA(T318, T325, T319, T326, lessc31_out_ga(T318, T325)) → U15_GAGA(T318, T325, T319, T326, delete1_in_aga(T325, T319, T326))
U14_GAGA(T318, T325, T319, T326, lessc31_out_ga(T318, T325)) → DELETE1_IN_AGA(T325, T319, T326)
DELETE1_IN_AGA(0, tree(s(T351), void, T343), tree(s(T351), T352, T343)) → U29_AGA(T351, T343, T352, delete1_in_gga(0, void, T352))
DELETE1_IN_AGA(0, tree(s(T351), void, T343), tree(s(T351), T352, T343)) → DELETE1_IN_GGA(0, void, T352)
DELETE1_IN_AGA(s(T363), tree(s(T362), void, T343), tree(s(T362), T364, T343)) → U30_AGA(T363, T362, T343, T364, p50_in_aga(T363, T362, T364))
DELETE1_IN_AGA(s(T363), tree(s(T362), void, T343), tree(s(T362), T364, T343)) → P50_IN_AGA(T363, T362, T364)
DELETE1_IN_AGA(T379, tree(T376, void, T377), tree(T376, void, T380)) → U31_AGA(T379, T376, T377, T380, p93_in_gaga(T376, T379, T377, T380))
DELETE1_IN_AGA(s(T399), tree(0, void, T389), tree(0, void, T398)) → U32_AGA(T399, T389, T398, delete1_in_aga(s(T399), T389, T398))
DELETE1_IN_AGA(s(T399), tree(0, void, T389), tree(0, void, T398)) → DELETE1_IN_AGA(s(T399), T389, T398)
DELETE1_IN_AGA(s(T410), tree(s(T408), void, T389), tree(s(T408), void, T411)) → U33_AGA(T410, T408, T389, T411, less31_in_ga(T408, T410))
DELETE1_IN_AGA(s(T410), tree(s(T408), void, T389), tree(s(T408), void, T411)) → LESS31_IN_GA(T408, T410)
DELETE1_IN_AGA(s(T414), tree(s(T408), void, T389), tree(s(T408), void, T415)) → U34_AGA(T414, T408, T389, T415, lessc31_in_ga(T408, T414))
U34_AGA(T414, T408, T389, T415, lessc31_out_ga(T408, T414)) → U35_AGA(T414, T408, T389, T415, delete1_in_aga(s(T414), T389, T415))
U34_AGA(T414, T408, T389, T415, lessc31_out_ga(T408, T414)) → DELETE1_IN_AGA(s(T414), T389, T415)
DELETE1_IN_AGA(T460, tree(T457, T458, void), tree(T457, T461, void)) → U36_AGA(T460, T457, T458, T461, less19_in_ag(T460, T457))
DELETE1_IN_AGA(T460, tree(T457, T458, void), tree(T457, T461, void)) → LESS19_IN_AG(T460, T457)
DELETE1_IN_AGA(T464, tree(T457, T458, void), tree(T457, T465, void)) → U37_AGA(T464, T457, T458, T465, lessc19_in_ag(T464, T457))
U37_AGA(T464, T457, T458, T465, lessc19_out_ag(T464, T457)) → U38_AGA(T464, T457, T458, T465, delete1_in_gga(T464, T458, T465))
U37_AGA(T464, T457, T458, T465, lessc19_out_ag(T464, T457)) → DELETE1_IN_GGA(T464, T458, T465)
DELETE1_IN_AGA(T488, tree(T485, T486, void), tree(T485, T486, T489)) → U39_AGA(T488, T485, T486, T489, p29_in_gaa(T485, T488, T489))
DELETE1_IN_AGA(T488, tree(T485, T486, void), tree(T485, T486, T489)) → P29_IN_GAA(T485, T488, T489)
DELETE1_IN_AGA(0, tree(s(T506), T498, void), tree(s(T506), T507, void)) → U40_AGA(T506, T498, T507, delete1_in_gga(0, T498, T507))
DELETE1_IN_AGA(0, tree(s(T506), T498, void), tree(s(T506), T507, void)) → DELETE1_IN_GGA(0, T498, T507)
DELETE1_IN_AGA(s(T520), tree(s(T519), T498, void), tree(s(T519), T521, void)) → U41_AGA(T520, T519, T498, T521, less19_in_ag(T520, T519))
DELETE1_IN_AGA(s(T520), tree(s(T519), T498, void), tree(s(T519), T521, void)) → LESS19_IN_AG(T520, T519)
DELETE1_IN_AGA(s(T524), tree(s(T519), T498, void), tree(s(T519), T525, void)) → U42_AGA(T524, T519, T498, T525, lessc19_in_ag(T524, T519))
U42_AGA(T524, T519, T498, T525, lessc19_out_ag(T524, T519)) → U43_AGA(T524, T519, T498, T525, delete1_in_gga(s(T524), T498, T525))
U42_AGA(T524, T519, T498, T525, lessc19_out_ag(T524, T519)) → DELETE1_IN_GGA(s(T524), T498, T525)
DELETE1_IN_AGA(T548, tree(T545, T546, void), tree(T545, T546, T549)) → U44_AGA(T548, T545, T546, T549, p29_in_gaa(T545, T548, T549))
DELETE1_IN_AGA(s(T568), tree(0, T558, void), tree(0, T558, T567)) → U45_AGA(T568, T558, T567, delete1_in_aga(s(T568), void, T567))
DELETE1_IN_AGA(s(T568), tree(0, T558, void), tree(0, T558, T567)) → DELETE1_IN_AGA(s(T568), void, T567)
DELETE1_IN_AGA(s(T582), tree(s(T580), T558, void), tree(s(T580), T558, T583)) → U46_AGA(T582, T580, T558, T583, p64_in_gaa(T580, T582, T583))
DELETE1_IN_AGA(s(T582), tree(s(T580), T558, void), tree(s(T580), T558, T583)) → P64_IN_GAA(T580, T582, T583)
DELETE1_IN_AGA(T591, tree(T591, T592, tree(T632, T633, T634)), tree(T638, T592, tree(T632, T639, T637))) → U47_AGA(T591, T592, T632, T633, T634, T638, T639, T637, delmin78_in_gaa(T633, T638, T639))
DELETE1_IN_AGA(T591, tree(T591, T592, tree(T632, T633, T634)), tree(T638, T592, tree(T632, T639, T637))) → DELMIN78_IN_GAA(T633, T638, T639)
DELETE1_IN_AGA(T669, tree(T665, T666, T667), tree(T665, T670, T667)) → U48_AGA(T669, T665, T666, T667, T670, less19_in_ag(T669, T665))
DELETE1_IN_AGA(T669, tree(T665, T666, T667), tree(T665, T670, T667)) → LESS19_IN_AG(T669, T665)
DELETE1_IN_AGA(T673, tree(T665, T666, T676), tree(T665, T674, T676)) → U49_AGA(T673, T665, T666, T676, T674, lessc19_in_ag(T673, T665))
U49_AGA(T673, T665, T666, T676, T674, lessc19_out_ag(T673, T665)) → U50_AGA(T673, T665, T666, T676, T674, delete1_in_gga(T673, T666, T674))
U49_AGA(T673, T665, T666, T676, T674, lessc19_out_ag(T673, T665)) → DELETE1_IN_GGA(T673, T666, T674)
DELETE1_IN_AGA(T703, tree(T699, T700, T701), tree(T699, T700, T704)) → U51_AGA(T703, T699, T700, T701, T704, less31_in_ga(T699, T703))
DELETE1_IN_AGA(T703, tree(T699, T700, T701), tree(T699, T700, T704)) → LESS31_IN_GA(T699, T703)
DELETE1_IN_AGA(T707, tree(T699, T710, T701), tree(T699, T710, T708)) → U52_AGA(T707, T699, T710, T701, T708, lessc31_in_ga(T699, T707))
U52_AGA(T707, T699, T710, T701, T708, lessc31_out_ga(T699, T707)) → U53_AGA(T707, T699, T710, T701, T708, delete1_in_aga(T707, T701, T708))
U52_AGA(T707, T699, T710, T701, T708, lessc31_out_ga(T699, T707)) → DELETE1_IN_AGA(T707, T701, T708)
DELETE1_IN_AGA(0, tree(s(T738), T729, T730), tree(s(T738), T739, T730)) → U54_AGA(T738, T729, T730, T739, delete1_in_gga(0, T729, T739))
DELETE1_IN_AGA(0, tree(s(T738), T729, T730), tree(s(T738), T739, T730)) → DELETE1_IN_GGA(0, T729, T739)
DELETE1_IN_AGA(s(T752), tree(s(T751), T729, T730), tree(s(T751), T753, T730)) → U55_AGA(T752, T751, T729, T730, T753, less19_in_ag(T752, T751))
DELETE1_IN_AGA(s(T752), tree(s(T751), T729, T730), tree(s(T751), T753, T730)) → LESS19_IN_AG(T752, T751)
DELETE1_IN_AGA(s(T756), tree(s(T751), T729, T759), tree(s(T751), T757, T759)) → U56_AGA(T756, T751, T729, T759, T757, lessc19_in_ag(T756, T751))
U56_AGA(T756, T751, T729, T759, T757, lessc19_out_ag(T756, T751)) → U57_AGA(T756, T751, T729, T759, T757, delete1_in_gga(s(T756), T729, T757))
U56_AGA(T756, T751, T729, T759, T757, lessc19_out_ag(T756, T751)) → DELETE1_IN_GGA(s(T756), T729, T757)
DELETE1_IN_AGA(T784, tree(T780, T781, T782), tree(T780, T781, T785)) → U58_AGA(T784, T780, T781, T782, T785, less31_in_ga(T780, T784))
DELETE1_IN_AGA(T788, tree(T780, T791, T782), tree(T780, T791, T789)) → U59_AGA(T788, T780, T791, T782, T789, lessc31_in_ga(T780, T788))
U59_AGA(T788, T780, T791, T782, T789, lessc31_out_ga(T780, T788)) → U60_AGA(T788, T780, T791, T782, T789, delete1_in_aga(T788, T782, T789))
U59_AGA(T788, T780, T791, T782, T789, lessc31_out_ga(T780, T788)) → DELETE1_IN_AGA(T788, T782, T789)
DELETE1_IN_AGA(s(T826), tree(0, T815, T816), tree(0, T815, T825)) → U61_AGA(T826, T815, T816, T825, delete1_in_aga(s(T826), T816, T825))
DELETE1_IN_AGA(s(T826), tree(0, T815, T816), tree(0, T815, T825)) → DELETE1_IN_AGA(s(T826), T816, T825)
DELETE1_IN_AGA(s(T837), tree(s(T835), T815, T816), tree(s(T835), T815, T838)) → U62_AGA(T837, T835, T815, T816, T838, less31_in_ga(T835, T837))
DELETE1_IN_AGA(s(T837), tree(s(T835), T815, T816), tree(s(T835), T815, T838)) → LESS31_IN_GA(T835, T837)
DELETE1_IN_AGA(s(T841), tree(s(T835), T844, T816), tree(s(T835), T844, T842)) → U63_AGA(T841, T835, T844, T816, T842, lessc31_in_ga(T835, T841))
U63_AGA(T841, T835, T844, T816, T842, lessc31_out_ga(T835, T841)) → U64_AGA(T841, T835, T844, T816, T842, delete1_in_aga(s(T841), T816, T842))
U63_AGA(T841, T835, T844, T816, T842, lessc31_out_ga(T835, T841)) → DELETE1_IN_AGA(s(T841), T816, T842)

The TRS R consists of the following rules:

lessc19_in_ag(0, s(T45)) → lessc19_out_ag(0, s(T45))
lessc19_in_ag(s(T52), s(T51)) → U104_ag(T52, T51, lessc19_in_ag(T52, T51))
U104_ag(T52, T51, lessc19_out_ag(T52, T51)) → lessc19_out_ag(s(T52), s(T51))
lessc19_in_gg(0, s(T45)) → lessc19_out_gg(0, s(T45))
lessc19_in_gg(s(T52), s(T51)) → U104_gg(T52, T51, lessc19_in_gg(T52, T51))
U104_gg(T52, T51, lessc19_out_gg(T52, T51)) → lessc19_out_gg(s(T52), s(T51))
lessc31_in_gg(0, s(T83)) → lessc31_out_gg(0, s(T83))
lessc31_in_gg(s(T88), s(T90)) → U105_gg(T88, T90, lessc31_in_gg(T88, T90))
U105_gg(T88, T90, lessc31_out_gg(T88, T90)) → lessc31_out_gg(s(T88), s(T90))
lessc31_in_ga(0, s(T83)) → lessc31_out_ga(0, s(T83))
lessc31_in_ga(s(T88), s(T90)) → U105_ga(T88, T90, lessc31_in_ga(T88, T90))
U105_ga(T88, T90, lessc31_out_ga(T88, T90)) → lessc31_out_ga(s(T88), s(T90))

The argument filtering Pi contains the following mapping:
delete1_in_aga(x1, x2, x3) = delete1_in_aga(x2)
tree(x1, x2, x3) = tree(x1, x2, x3)
void = void
p17_in_aga(x1, x2, x3) = p17_in_aga(x2)
less19_in_ag(x1, x2) = less19_in_ag(x2)
s(x1) = s(x1)
lessc19_in_ag(x1, x2) = lessc19_in_ag(x2)
lessc19_out_ag(x1, x2) = lessc19_out_ag(x1, x2)
U104_ag(x1, x2, x3) = U104_ag(x2, x3)
delete1_in_gga(x1, x2, x3) = delete1_in_gga(x1, x2)
p17_in_gga(x1, x2, x3) = p17_in_gga(x1, x2)
less19_in_gg(x1, x2) = less19_in_gg(x1, x2)
lessc19_in_gg(x1, x2) = lessc19_in_gg(x1, x2)
0 = 0
lessc19_out_gg(x1, x2) = lessc19_out_gg(x1, x2)
U104_gg(x1, x2, x3) = U104_gg(x1, x2, x3)
p29_in_gga(x1, x2, x3) = p29_in_gga(x1, x2)
less31_in_gg(x1, x2) = less31_in_gg(x1, x2)
lessc31_in_gg(x1, x2) = lessc31_in_gg(x1, x2)
lessc31_out_gg(x1, x2) = lessc31_out_gg(x1, x2)
U105_gg(x1, x2, x3) = U105_gg(x1, x2, x3)
p50_in_gga(x1, x2, x3) = p50_in_gga(x1, x2)
p64_in_gga(x1, x2, x3) = p64_in_gga(x1, x2)
delmin78_in_gaa(x1, x2, x3) = delmin78_in_gaa(x1)
p93_in_ggga(x1, x2, x3, x4) = p93_in_ggga(x1, x2, x3)
p29_in_gaa(x1, x2, x3) = p29_in_gaa(x1)
less31_in_ga(x1, x2) = less31_in_ga(x1)
lessc31_in_ga(x1, x2) = lessc31_in_ga(x1)
lessc31_out_ga(x1, x2) = lessc31_out_ga(x1)
U105_ga(x1, x2, x3) = U105_ga(x1, x3)
p50_in_aga(x1, x2, x3) = p50_in_aga(x2)
p64_in_gaa(x1, x2, x3) = p64_in_gaa(x1)
p93_in_gaga(x1, x2, x3, x4) = p93_in_gaga(x1, x3)
DELETE1_IN_AGA(x1, x2, x3) = DELETE1_IN_AGA(x2)
U19_AGA(x1, x2, x3, x4) = U19_AGA(x2, x4)
P17_IN_AGA(x1, x2, x3) = P17_IN_AGA(x2)
U7_AGA(x1, x2, x3, x4) = U7_AGA(x2, x4)
LESS19_IN_AG(x1, x2) = LESS19_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)
DELETE1_IN_GGA(x1, x2, x3) = DELETE1_IN_GGA(x1, x2)
U19_GGA(x1, x2, x3, x4) = U19_GGA(x1, x2, x4)
P17_IN_GGA(x1, x2, x3) = P17_IN_GGA(x1, x2)
U7_GGA(x1, x2, x3, x4) = U7_GGA(x1, x2, x4)
LESS19_IN_GG(x1, x2) = LESS19_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)
U20_GGA(x1, x2, x3, x4) = U20_GGA'(x1, x2, x4)
P29_IN_GGA(x1, x2, x3) = P29_IN_GGA(x1, x2)
U3_GGA(x1, x2, x3, x4) = U3_GGA(x1, x2, x4)
LESS31_IN_GG(x1, x2) = LESS31_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)
U21_GGA(x1, x2, x3) = U21_GGA(x1, x3)
U22_GGA(x1, x2, x3, x4) = U22_GGA(x1, x2, x4)
P50_IN_GGA(x1, x2, x3) = P50_IN_GGA(x1, x2)
U10_GGA(x1, x2, x3, x4) = U10_GGA(x1, x2, x4)
U11_GGA(x1, x2, x3, x4) = U11_GGA(x1, x2, x4)
U12_GGA(x1, x2, x3, x4) = U12_GGA(x1, x2, x4)
U23_GGA(x1, x2, x3, x4) = U23_GGA(x1, x2, x4)
U24_GGA(x1, x2, x3) = U24_GGA(x1, x3)
U25_GGA(x1, x2, x3, x4) = U25_GGA(x1, x2, x4)
P64_IN_GGA(x1, x2, x3) = P64_IN_GGA(x1, x2)
U16_GGA(x1, x2, x3, x4) = U16_GGA(x1, x2, x4)
U17_GGA(x1, x2, x3, x4) = U17_GGA(x1, x2, x4)
U18_GGA(x1, x2, x3, x4) = U18_GGA(x1, x2, x4)
U26_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U26_GGA(x1, x2, x3, x4, x8)
DELMIN78_IN_GAA(x1, x2, x3) = DELMIN78_IN_GAA(x1)
U6_GAA(x1, x2, x3, x4, x5, x6, x7) = U6_GAA(x1, x2, x3, x7)
U27_GGA(x1, x2, x3, x4, x5) = U27_GGA(x1, x2, x3, x5)
U28_GGA(x1, x2, x3, x4, x5) = U28_GGA(x1, x2, x3, x5)
P93_IN_GGGA(x1, x2, x3, x4) = P93_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)
U29_GGA(x1, x2, x3, x4) = U29_GGA(x1, x2, x4)
U30_GGA(x1, x2, x3, x4, x5) = U30_GGA(x1, x2, x3, x5)
U31_GGA(x1, x2, x3, x4, x5) = U31_GGA'(x1, x2, x3, x5)
U32_GGA(x1, x2, x3, x4) = U32_GGA(x1, x2, x4)
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, x5) = U35_GGA(x1, x2, x3, x5)
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) = U40_GGA(x1, x2, x4)
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, x5) = U43_GGA(x1, x2, x3, x5)
U44_GGA(x1, x2, x3, x4, x5) = U44_GGA(x1, x2, x3, x5)
U45_GGA(x1, x2, x3, x4) = U45_GGA(x1, x2, x4)
U46_GGA(x1, x2, x3, x4, x5) = U46_GGA(x1, x2, x3, x5)
U47_GGA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U47_GGA(x1, x2, x3, x4, x5, x9)
U48_GGA(x1, x2, x3, x4, x5, x6) = U48_GGA(x1, x2, x3, x4, x6)
U49_GGA(x1, x2, x3, x4, x5, x6) = U49_GGA(x1, x2, x3, x4, x6)
U50_GGA(x1, x2, x3, x4, x5, x6) = U50_GGA(x1, x2, x3, x4, x6)
U51_GGA(x1, x2, x3, x4, x5, x6) = U51_GGA(x1, x2, x3, x4, x6)
U52_GGA(x1, x2, x3, x4, x5, x6) = U52_GGA(x1, x2, x3, x4, x6)
U53_GGA(x1, x2, x3, x4, x5, x6) = U53_GGA(x1, x2, x3, x4, x6)
U54_GGA(x1, x2, x3, x4, x5) = U54_GGA(x1, x2, x3, x5)
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)
U57_GGA(x1, x2, x3, x4, x5, x6) = U57_GGA(x1, x2, x3, x4, x6)
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) = U61_GGA(x1, x2, x3, x5)
U62_GGA(x1, x2, x3, x4, x5, x6) = U62_GGA(x1, x2, x3, x4, x6)
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)
U20_AGA(x1, x2, x3, x4) = U20_AGA'(x2, x4)
P29_IN_GAA(x1, x2, x3) = P29_IN_GAA(x1)
U3_GAA(x1, x2, x3, x4) = U3_GAA(x1, x4)
LESS31_IN_GA(x1, x2) = LESS31_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)
U21_AGA(x1, x2, x3) = U21_AGA(x1, x3)
U22_AGA(x1, x2, x3, x4) = U22_AGA(x2, x4)
P50_IN_AGA(x1, x2, x3) = P50_IN_AGA(x2)
U10_AGA(x1, x2, x3, x4) = U10_AGA(x2, x4)
U11_AGA(x1, x2, x3, x4) = U11_AGA(x2, x4)
U12_AGA(x1, x2, x3, x4) = U12_AGA(x1, x2, x4)
U23_AGA(x1, x2, x3, x4) = U23_AGA(x2, x4)
U24_AGA(x1, x2, x3) = U24_AGA(x3)
U25_AGA(x1, x2, x3, x4) = U25_AGA'(x2, x4)
P64_IN_GAA(x1, x2, x3) = P64_IN_GAA(x1)
U16_GAA(x1, x2, x3, x4) = U16_GAA(x1, x4)
U17_GAA(x1, x2, x3, x4) = U17_GAA(x1, x4)
U18_GAA(x1, x2, x3, x4) = U18_GAA(x1, x4)
U26_AGA(x1, x2, x3, x4, x5, x6, x7, x8) = U26_AGA(x1, x2, x3, x4, x8)
U27_AGA(x1, x2, x3, x4, x5) = U27_AGA(x2, x3, x5)
U28_AGA(x1, x2, x3, x4, x5) = U28_AGA(x2, x3, x5)
P93_IN_GAGA(x1, x2, x3, x4) = P93_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)
U29_AGA(x1, x2, x3, x4) = U29_AGA'(x1, x2, x4)
U30_AGA(x1, x2, x3, x4, x5) = U30_AGA(x2, x3, x5)
U31_AGA(x1, x2, x3, x4, x5) = U31_AGA(x2, x3, x5)
U32_AGA(x1, x2, x3, x4) = U32_AGA(x2, x4)
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, x5) = U35_AGA(x2, x3, x5)
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(x1, x2, x3, x5)
U39_AGA(x1, x2, x3, x4, x5) = U39_AGA(x2, x3, x5)
U40_AGA(x1, x2, x3, x4) = U40_AGA(x1, x2, x4)
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, x5) = U43_AGA(x1, x2, x3, x5)
U44_AGA(x1, x2, x3, x4, x5) = U44_AGA(x2, x3, x5)
U45_AGA(x1, x2, x3, x4) = U45_AGA(x2, x4)
U46_AGA(x1, x2, x3, x4, x5) = U46_AGA(x2, x3, x5)
U47_AGA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U47_AGA(x1, x2, x3, x4, x5, x9)
U48_AGA(x1, x2, x3, x4, x5, x6) = U48_AGA(x2, x3, x4, x6)
U49_AGA(x1, x2, x3, x4, x5, x6) = U49_AGA(x2, x3, x4, x6)
U50_AGA(x1, x2, x3, x4, x5, x6) = U50_AGA(x1, x2, x3, x4, x6)
U51_AGA(x1, x2, x3, x4, x5, x6) = U51_AGA(x2, x3, x4, x6)
U52_AGA(x1, x2, x3, x4, x5, x6) = U52_AGA(x2, x3, x4, x6)
U53_AGA(x1, x2, x3, x4, x5, x6) = U53_AGA(x2, x3, x4, x6)
U54_AGA(x1, x2, x3, x4, x5) = U54_AGA(x1, x2, x3, x5)
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)
U57_AGA(x1, x2, x3, x4, x5, x6) = U57_AGA(x1, x2, x3, x4, x6)
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) = U61_AGA(x2, x3, x5)
U62_AGA(x1, x2, x3, x4, x5, x6) = U62_AGA(x2, x3, x4, x6)
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)

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

Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES

(4) Obligation:

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

DELETE1_IN_AGA(T33, tree(T31, void, void), tree(T31, T34, void)) → U19_AGA(T33, T31, T34, p17_in_aga(T33, T31, T34))
DELETE1_IN_AGA(T33, tree(T31, void, void), tree(T31, T34, void)) → P17_IN_AGA(T33, T31, T34)
P17_IN_AGA(T33, T31, T34) → U7_AGA(T33, T31, T34, less19_in_ag(T33, T31))
P17_IN_AGA(T33, T31, T34) → LESS19_IN_AG(T33, T31)
LESS19_IN_AG(s(T52), s(T51)) → U1_AG(T52, T51, less19_in_ag(T52, T51))
LESS19_IN_AG(s(T52), s(T51)) → LESS19_IN_AG(T52, T51)
P17_IN_AGA(T37, T31, T38) → U8_AGA(T37, T31, T38, lessc19_in_ag(T37, T31))
U8_AGA(T37, T31, T38, lessc19_out_ag(T37, T31)) → U9_AGA(T37, T31, T38, delete1_in_gga(T37, void, T38))
U8_AGA(T37, T31, T38, lessc19_out_ag(T37, T31)) → DELETE1_IN_GGA(T37, void, T38)
DELETE1_IN_GGA(T33, tree(T31, void, void), tree(T31, T34, void)) → U19_GGA(T33, T31, T34, p17_in_gga(T33, T31, T34))
DELETE1_IN_GGA(T33, tree(T31, void, void), tree(T31, T34, void)) → P17_IN_GGA(T33, T31, T34)
P17_IN_GGA(T33, T31, T34) → U7_GGA(T33, T31, T34, less19_in_gg(T33, T31))
P17_IN_GGA(T33, T31, T34) → LESS19_IN_GG(T33, T31)
LESS19_IN_GG(s(T52), s(T51)) → U1_GG(T52, T51, less19_in_gg(T52, T51))
LESS19_IN_GG(s(T52), s(T51)) → LESS19_IN_GG(T52, T51)
P17_IN_GGA(T37, T31, T38) → U8_GGA(T37, T31, T38, lessc19_in_gg(T37, T31))
U8_GGA(T37, T31, T38, lessc19_out_gg(T37, T31)) → U9_GGA(T37, T31, T38, delete1_in_gga(T37, void, T38))
U8_GGA(T37, T31, T38, lessc19_out_gg(T37, T31)) → DELETE1_IN_GGA(T37, void, T38)
DELETE1_IN_GGA(T71, tree(T69, void, void), tree(T69, void, T72)) → U20_GGA(T71, T69, T72, p29_in_gga(T69, T71, T72))
DELETE1_IN_GGA(T71, tree(T69, void, void), tree(T69, void, T72)) → P29_IN_GGA(T69, T71, T72)
P29_IN_GGA(T69, T71, T72) → U3_GGA(T69, T71, T72, less31_in_gg(T69, T71))
P29_IN_GGA(T69, T71, T72) → LESS31_IN_GG(T69, T71)
LESS31_IN_GG(s(T88), s(T90)) → U2_GG(T88, T90, less31_in_gg(T88, T90))
LESS31_IN_GG(s(T88), s(T90)) → LESS31_IN_GG(T88, T90)
P29_IN_GGA(T69, T75, T76) → U4_GGA(T69, T75, T76, lessc31_in_gg(T69, T75))
U4_GGA(T69, T75, T76, lessc31_out_gg(T69, T75)) → U5_GGA(T69, T75, T76, delete1_in_gga(T75, void, T76))
U4_GGA(T69, T75, T76, lessc31_out_gg(T69, T75)) → DELETE1_IN_GGA(T75, void, T76)
DELETE1_IN_GGA(0, tree(s(T112), void, void), tree(s(T112), T113, void)) → U21_GGA(T112, T113, delete1_in_gga(0, void, T113))
DELETE1_IN_GGA(0, tree(s(T112), void, void), tree(s(T112), T113, void)) → DELETE1_IN_GGA(0, void, T113)
DELETE1_IN_GGA(s(T124), tree(s(T123), void, void), tree(s(T123), T125, void)) → U22_GGA(T124, T123, T125, p50_in_gga(T124, T123, T125))
DELETE1_IN_GGA(s(T124), tree(s(T123), void, void), tree(s(T123), T125, void)) → P50_IN_GGA(T124, T123, T125)
P50_IN_GGA(T124, T123, T125) → U10_GGA(T124, T123, T125, less19_in_gg(T124, T123))
P50_IN_GGA(T124, T123, T125) → LESS19_IN_GG(T124, T123)
P50_IN_GGA(T128, T123, T129) → U11_GGA(T128, T123, T129, lessc19_in_gg(T128, T123))
U11_GGA(T128, T123, T129, lessc19_out_gg(T128, T123)) → U12_GGA(T128, T123, T129, delete1_in_gga(s(T128), void, T129))
U11_GGA(T128, T123, T129, lessc19_out_gg(T128, T123)) → DELETE1_IN_GGA(s(T128), void, T129)
DELETE1_IN_GGA(T148, tree(T146, void, void), tree(T146, void, T149)) → U23_GGA(T148, T146, T149, p29_in_gga(T146, T148, T149))
DELETE1_IN_GGA(s(T166), tree(0, void, void), tree(0, void, T165)) → U24_GGA(T166, T165, delete1_in_gga(s(T166), void, T165))
DELETE1_IN_GGA(s(T166), tree(0, void, void), tree(0, void, T165)) → DELETE1_IN_GGA(s(T166), void, T165)
DELETE1_IN_GGA(s(T180), tree(s(T178), void, void), tree(s(T178), void, T181)) → U25_GGA(T180, T178, T181, p64_in_gga(T178, T180, T181))
DELETE1_IN_GGA(s(T180), tree(s(T178), void, void), tree(s(T178), void, T181)) → P64_IN_GGA(T178, T180, T181)
P64_IN_GGA(T178, T180, T181) → U16_GGA(T178, T180, T181, less31_in_gg(T178, T180))
P64_IN_GGA(T178, T180, T181) → LESS31_IN_GG(T178, T180)
P64_IN_GGA(T178, T184, T185) → U17_GGA(T178, T184, T185, lessc31_in_gg(T178, T184))
U17_GGA(T178, T184, T185, lessc31_out_gg(T178, T184)) → U18_GGA(T178, T184, T185, delete1_in_gga(s(T184), void, T185))
U17_GGA(T178, T184, T185, lessc31_out_gg(T178, T184)) → DELETE1_IN_GGA(s(T184), void, T185)
DELETE1_IN_GGA(T199, tree(T199, void, tree(T239, T240, T241)), tree(T245, void, tree(T239, T246, T244))) → U26_GGA(T199, T239, T240, T241, T245, T246, T244, delmin78_in_gaa(T240, T245, T246))
DELETE1_IN_GGA(T199, tree(T199, void, tree(T239, T240, T241)), tree(T245, void, tree(T239, T246, T244))) → DELMIN78_IN_GAA(T240, T245, T246)
DELMIN78_IN_GAA(tree(T273, T274, T275), T279, tree(T273, T280, T278)) → U6_GAA(T273, T274, T275, T279, T280, T278, delmin78_in_gaa(T274, T279, T280))
DELMIN78_IN_GAA(tree(T273, T274, T275), T279, tree(T273, T280, T278)) → DELMIN78_IN_GAA(T274, T279, T280)
DELETE1_IN_GGA(T305, tree(T302, void, T303), tree(T302, T306, T303)) → U27_GGA(T305, T302, T303, T306, p17_in_gga(T305, T302, T306))
DELETE1_IN_GGA(T305, tree(T302, void, T303), tree(T302, T306, T303)) → P17_IN_GGA(T305, T302, T306)
DELETE1_IN_GGA(T321, tree(T318, void, T319), tree(T318, void, T322)) → U28_GGA(T321, T318, T319, T322, p93_in_ggga(T318, T321, T319, T322))
DELETE1_IN_GGA(T321, tree(T318, void, T319), tree(T318, void, T322)) → P93_IN_GGGA(T318, T321, T319, T322)
P93_IN_GGGA(T318, T321, T319, T322) → U13_GGGA(T318, T321, T319, T322, less31_in_gg(T318, T321))
P93_IN_GGGA(T318, T321, T319, T322) → LESS31_IN_GG(T318, T321)
P93_IN_GGGA(T318, T325, T319, T326) → U14_GGGA(T318, T325, T319, T326, lessc31_in_gg(T318, T325))
U14_GGGA(T318, T325, T319, T326, lessc31_out_gg(T318, T325)) → U15_GGGA(T318, T325, T319, T326, delete1_in_gga(T325, T319, T326))
U14_GGGA(T318, T325, T319, T326, lessc31_out_gg(T318, T325)) → DELETE1_IN_GGA(T325, T319, T326)
DELETE1_IN_GGA(0, tree(s(T351), void, T343), tree(s(T351), T352, T343)) → U29_GGA(T351, T343, T352, delete1_in_gga(0, void, T352))
DELETE1_IN_GGA(0, tree(s(T351), void, T343), tree(s(T351), T352, T343)) → DELETE1_IN_GGA(0, void, T352)
DELETE1_IN_GGA(s(T363), tree(s(T362), void, T343), tree(s(T362), T364, T343)) → U30_GGA(T363, T362, T343, T364, p50_in_gga(T363, T362, T364))
DELETE1_IN_GGA(s(T363), tree(s(T362), void, T343), tree(s(T362), T364, T343)) → P50_IN_GGA(T363, T362, T364)
DELETE1_IN_GGA(T379, tree(T376, void, T377), tree(T376, void, T380)) → U31_GGA(T379, T376, T377, T380, p93_in_ggga(T376, T379, T377, T380))
DELETE1_IN_GGA(s(T399), tree(0, void, T389), tree(0, void, T398)) → U32_GGA(T399, T389, T398, delete1_in_gga(s(T399), T389, T398))
DELETE1_IN_GGA(s(T399), tree(0, void, T389), tree(0, void, T398)) → DELETE1_IN_GGA(s(T399), T389, T398)
DELETE1_IN_GGA(s(T410), tree(s(T408), void, T389), tree(s(T408), void, T411)) → U33_GGA(T410, T408, T389, T411, less31_in_gg(T408, T410))
DELETE1_IN_GGA(s(T410), tree(s(T408), void, T389), tree(s(T408), void, T411)) → LESS31_IN_GG(T408, T410)
DELETE1_IN_GGA(s(T414), tree(s(T408), void, T389), tree(s(T408), void, T415)) → U34_GGA(T414, T408, T389, T415, lessc31_in_gg(T408, T414))
U34_GGA(T414, T408, T389, T415, lessc31_out_gg(T408, T414)) → U35_GGA(T414, T408, T389, T415, delete1_in_gga(s(T414), T389, T415))
U34_GGA(T414, T408, T389, T415, lessc31_out_gg(T408, T414)) → DELETE1_IN_GGA(s(T414), T389, T415)
DELETE1_IN_GGA(T460, tree(T457, T458, void), tree(T457, T461, void)) → U36_GGA(T460, T457, T458, T461, less19_in_gg(T460, T457))
DELETE1_IN_GGA(T460, tree(T457, T458, void), tree(T457, T461, void)) → LESS19_IN_GG(T460, T457)
DELETE1_IN_GGA(T464, tree(T457, T458, void), tree(T457, T465, void)) → U37_GGA(T464, T457, T458, T465, lessc19_in_gg(T464, T457))
U37_GGA(T464, T457, T458, T465, lessc19_out_gg(T464, T457)) → U38_GGA(T464, T457, T458, T465, delete1_in_gga(T464, T458, T465))
U37_GGA(T464, T457, T458, T465, lessc19_out_gg(T464, T457)) → DELETE1_IN_GGA(T464, T458, T465)
DELETE1_IN_GGA(T488, tree(T485, T486, void), tree(T485, T486, T489)) → U39_GGA(T488, T485, T486, T489, p29_in_gga(T485, T488, T489))
DELETE1_IN_GGA(T488, tree(T485, T486, void), tree(T485, T486, T489)) → P29_IN_GGA(T485, T488, T489)
DELETE1_IN_GGA(0, tree(s(T506), T498, void), tree(s(T506), T507, void)) → U40_GGA(T506, T498, T507, delete1_in_gga(0, T498, T507))
DELETE1_IN_GGA(0, tree(s(T506), T498, void), tree(s(T506), T507, void)) → DELETE1_IN_GGA(0, T498, T507)
DELETE1_IN_GGA(s(T520), tree(s(T519), T498, void), tree(s(T519), T521, void)) → U41_GGA(T520, T519, T498, T521, less19_in_gg(T520, T519))
DELETE1_IN_GGA(s(T520), tree(s(T519), T498, void), tree(s(T519), T521, void)) → LESS19_IN_GG(T520, T519)
DELETE1_IN_GGA(s(T524), tree(s(T519), T498, void), tree(s(T519), T525, void)) → U42_GGA(T524, T519, T498, T525, lessc19_in_gg(T524, T519))
U42_GGA(T524, T519, T498, T525, lessc19_out_gg(T524, T519)) → U43_GGA(T524, T519, T498, T525, delete1_in_gga(s(T524), T498, T525))
U42_GGA(T524, T519, T498, T525, lessc19_out_gg(T524, T519)) → DELETE1_IN_GGA(s(T524), T498, T525)
DELETE1_IN_GGA(T548, tree(T545, T546, void), tree(T545, T546, T549)) → U44_GGA(T548, T545, T546, T549, p29_in_gga(T545, T548, T549))
DELETE1_IN_GGA(s(T568), tree(0, T558, void), tree(0, T558, T567)) → U45_GGA(T568, T558, T567, delete1_in_gga(s(T568), void, T567))
DELETE1_IN_GGA(s(T568), tree(0, T558, void), tree(0, T558, T567)) → DELETE1_IN_GGA(s(T568), void, T567)
DELETE1_IN_GGA(s(T582), tree(s(T580), T558, void), tree(s(T580), T558, T583)) → U46_GGA(T582, T580, T558, T583, p64_in_gga(T580, T582, T583))
DELETE1_IN_GGA(s(T582), tree(s(T580), T558, void), tree(s(T580), T558, T583)) → P64_IN_GGA(T580, T582, T583)
DELETE1_IN_GGA(T591, tree(T591, T592, tree(T632, T633, T634)), tree(T638, T592, tree(T632, T639, T637))) → U47_GGA(T591, T592, T632, T633, T634, T638, T639, T637, delmin78_in_gaa(T633, T638, T639))
DELETE1_IN_GGA(T591, tree(T591, T592, tree(T632, T633, T634)), tree(T638, T592, tree(T632, T639, T637))) → DELMIN78_IN_GAA(T633, T638, T639)
DELETE1_IN_GGA(T669, tree(T665, T666, T667), tree(T665, T670, T667)) → U48_GGA(T669, T665, T666, T667, T670, less19_in_gg(T669, T665))
DELETE1_IN_GGA(T669, tree(T665, T666, T667), tree(T665, T670, T667)) → LESS19_IN_GG(T669, T665)
DELETE1_IN_GGA(T673, tree(T665, T666, T676), tree(T665, T674, T676)) → U49_GGA(T673, T665, T666, T676, T674, lessc19_in_gg(T673, T665))
U49_GGA(T673, T665, T666, T676, T674, lessc19_out_gg(T673, T665)) → U50_GGA(T673, T665, T666, T676, T674, delete1_in_gga(T673, T666, T674))
U49_GGA(T673, T665, T666, T676, T674, lessc19_out_gg(T673, T665)) → DELETE1_IN_GGA(T673, T666, T674)
DELETE1_IN_GGA(T703, tree(T699, T700, T701), tree(T699, T700, T704)) → U51_GGA(T703, T699, T700, T701, T704, less31_in_gg(T699, T703))
DELETE1_IN_GGA(T703, tree(T699, T700, T701), tree(T699, T700, T704)) → LESS31_IN_GG(T699, T703)
DELETE1_IN_GGA(T707, tree(T699, T710, T701), tree(T699, T710, T708)) → U52_GGA(T707, T699, T710, T701, T708, lessc31_in_gg(T699, T707))
U52_GGA(T707, T699, T710, T701, T708, lessc31_out_gg(T699, T707)) → U53_GGA(T707, T699, T710, T701, T708, delete1_in_gga(T707, T701, T708))
U52_GGA(T707, T699, T710, T701, T708, lessc31_out_gg(T699, T707)) → DELETE1_IN_GGA(T707, T701, T708)
DELETE1_IN_GGA(0, tree(s(T738), T729, T730), tree(s(T738), T739, T730)) → U54_GGA(T738, T729, T730, T739, delete1_in_gga(0, T729, T739))
DELETE1_IN_GGA(0, tree(s(T738), T729, T730), tree(s(T738), T739, T730)) → DELETE1_IN_GGA(0, T729, T739)
DELETE1_IN_GGA(s(T752), tree(s(T751), T729, T730), tree(s(T751), T753, T730)) → U55_GGA(T752, T751, T729, T730, T753, less19_in_gg(T752, T751))
DELETE1_IN_GGA(s(T752), tree(s(T751), T729, T730), tree(s(T751), T753, T730)) → LESS19_IN_GG(T752, T751)
DELETE1_IN_GGA(s(T756), tree(s(T751), T729, T759), tree(s(T751), T757, T759)) → U56_GGA(T756, T751, T729, T759, T757, lessc19_in_gg(T756, T751))
U56_GGA(T756, T751, T729, T759, T757, lessc19_out_gg(T756, T751)) → U57_GGA(T756, T751, T729, T759, T757, delete1_in_gga(s(T756), T729, T757))
U56_GGA(T756, T751, T729, T759, T757, lessc19_out_gg(T756, T751)) → DELETE1_IN_GGA(s(T756), T729, T757)
DELETE1_IN_GGA(T784, tree(T780, T781, T782), tree(T780, T781, T785)) → U58_GGA(T784, T780, T781, T782, T785, less31_in_gg(T780, T784))
DELETE1_IN_GGA(T788, tree(T780, T791, T782), tree(T780, T791, T789)) → U59_GGA(T788, T780, T791, T782, T789, lessc31_in_gg(T780, T788))
U59_GGA(T788, T780, T791, T782, T789, lessc31_out_gg(T780, T788)) → U60_GGA(T788, T780, T791, T782, T789, delete1_in_gga(T788, T782, T789))
U59_GGA(T788, T780, T791, T782, T789, lessc31_out_gg(T780, T788)) → DELETE1_IN_GGA(T788, T782, T789)
DELETE1_IN_GGA(s(T826), tree(0, T815, T816), tree(0, T815, T825)) → U61_GGA(T826, T815, T816, T825, delete1_in_gga(s(T826), T816, T825))
DELETE1_IN_GGA(s(T826), tree(0, T815, T816), tree(0, T815, T825)) → DELETE1_IN_GGA(s(T826), T816, T825)
DELETE1_IN_GGA(s(T837), tree(s(T835), T815, T816), tree(s(T835), T815, T838)) → U62_GGA(T837, T835, T815, T816, T838, less31_in_gg(T835, T837))
DELETE1_IN_GGA(s(T837), tree(s(T835), T815, T816), tree(s(T835), T815, T838)) → LESS31_IN_GG(T835, T837)
DELETE1_IN_GGA(s(T841), tree(s(T835), T844, T816), tree(s(T835), T844, T842)) → U63_GGA(T841, T835, T844, T816, T842, lessc31_in_gg(T835, T841))
U63_GGA(T841, T835, T844, T816, T842, lessc31_out_gg(T835, T841)) → U64_GGA(T841, T835, T844, T816, T842, delete1_in_gga(s(T841), T816, T842))
U63_GGA(T841, T835, T844, T816, T842, lessc31_out_gg(T835, T841)) → DELETE1_IN_GGA(s(T841), T816, T842)
DELETE1_IN_AGA(T71, tree(T69, void, void), tree(T69, void, T72)) → U20_AGA(T71, T69, T72, p29_in_gaa(T69, T71, T72))
DELETE1_IN_AGA(T71, tree(T69, void, void), tree(T69, void, T72)) → P29_IN_GAA(T69, T71, T72)
P29_IN_GAA(T69, T71, T72) → U3_GAA(T69, T71, T72, less31_in_ga(T69, T71))
P29_IN_GAA(T69, T71, T72) → LESS31_IN_GA(T69, T71)
LESS31_IN_GA(s(T88), s(T90)) → U2_GA(T88, T90, less31_in_ga(T88, T90))
LESS31_IN_GA(s(T88), s(T90)) → LESS31_IN_GA(T88, T90)
P29_IN_GAA(T69, T75, T76) → U4_GAA(T69, T75, T76, lessc31_in_ga(T69, T75))
U4_GAA(T69, T75, T76, lessc31_out_ga(T69, T75)) → U5_GAA(T69, T75, T76, delete1_in_aga(T75, void, T76))
U4_GAA(T69, T75, T76, lessc31_out_ga(T69, T75)) → DELETE1_IN_AGA(T75, void, T76)
DELETE1_IN_AGA(0, tree(s(T112), void, void), tree(s(T112), T113, void)) → U21_AGA(T112, T113, delete1_in_gga(0, void, T113))
DELETE1_IN_AGA(0, tree(s(T112), void, void), tree(s(T112), T113, void)) → DELETE1_IN_GGA(0, void, T113)
DELETE1_IN_AGA(s(T124), tree(s(T123), void, void), tree(s(T123), T125, void)) → U22_AGA(T124, T123, T125, p50_in_aga(T124, T123, T125))
DELETE1_IN_AGA(s(T124), tree(s(T123), void, void), tree(s(T123), T125, void)) → P50_IN_AGA(T124, T123, T125)
P50_IN_AGA(T124, T123, T125) → U10_AGA(T124, T123, T125, less19_in_ag(T124, T123))
P50_IN_AGA(T124, T123, T125) → LESS19_IN_AG(T124, T123)
P50_IN_AGA(T128, T123, T129) → U11_AGA(T128, T123, T129, lessc19_in_ag(T128, T123))
U11_AGA(T128, T123, T129, lessc19_out_ag(T128, T123)) → U12_AGA(T128, T123, T129, delete1_in_gga(s(T128), void, T129))
U11_AGA(T128, T123, T129, lessc19_out_ag(T128, T123)) → DELETE1_IN_GGA(s(T128), void, T129)
DELETE1_IN_AGA(T148, tree(T146, void, void), tree(T146, void, T149)) → U23_AGA(T148, T146, T149, p29_in_gaa(T146, T148, T149))
DELETE1_IN_AGA(s(T166), tree(0, void, void), tree(0, void, T165)) → U24_AGA(T166, T165, delete1_in_aga(s(T166), void, T165))
DELETE1_IN_AGA(s(T166), tree(0, void, void), tree(0, void, T165)) → DELETE1_IN_AGA(s(T166), void, T165)
DELETE1_IN_AGA(s(T180), tree(s(T178), void, void), tree(s(T178), void, T181)) → U25_AGA(T180, T178, T181, p64_in_gaa(T178, T180, T181))
DELETE1_IN_AGA(s(T180), tree(s(T178), void, void), tree(s(T178), void, T181)) → P64_IN_GAA(T178, T180, T181)
P64_IN_GAA(T178, T180, T181) → U16_GAA(T178, T180, T181, less31_in_ga(T178, T180))
P64_IN_GAA(T178, T180, T181) → LESS31_IN_GA(T178, T180)
P64_IN_GAA(T178, T184, T185) → U17_GAA(T178, T184, T185, lessc31_in_ga(T178, T184))
U17_GAA(T178, T184, T185, lessc31_out_ga(T178, T184)) → U18_GAA(T178, T184, T185, delete1_in_aga(s(T184), void, T185))
U17_GAA(T178, T184, T185, lessc31_out_ga(T178, T184)) → DELETE1_IN_AGA(s(T184), void, T185)
DELETE1_IN_AGA(T199, tree(T199, void, tree(T239, T240, T241)), tree(T245, void, tree(T239, T246, T244))) → U26_AGA(T199, T239, T240, T241, T245, T246, T244, delmin78_in_gaa(T240, T245, T246))
DELETE1_IN_AGA(T199, tree(T199, void, tree(T239, T240, T241)), tree(T245, void, tree(T239, T246, T244))) → DELMIN78_IN_GAA(T240, T245, T246)
DELETE1_IN_AGA(T305, tree(T302, void, T303), tree(T302, T306, T303)) → U27_AGA(T305, T302, T303, T306, p17_in_aga(T305, T302, T306))
DELETE1_IN_AGA(T305, tree(T302, void, T303), tree(T302, T306, T303)) → P17_IN_AGA(T305, T302, T306)
DELETE1_IN_AGA(T321, tree(T318, void, T319), tree(T318, void, T322)) → U28_AGA(T321, T318, T319, T322, p93_in_gaga(T318, T321, T319, T322))
DELETE1_IN_AGA(T321, tree(T318, void, T319), tree(T318, void, T322)) → P93_IN_GAGA(T318, T321, T319, T322)
P93_IN_GAGA(T318, T321, T319, T322) → U13_GAGA(T318, T321, T319, T322, less31_in_ga(T318, T321))
P93_IN_GAGA(T318, T321, T319, T322) → LESS31_IN_GA(T318, T321)
P93_IN_GAGA(T318, T325, T319, T326) → U14_GAGA(T318, T325, T319, T326, lessc31_in_ga(T318, T325))
U14_GAGA(T318, T325, T319, T326, lessc31_out_ga(T318, T325)) → U15_GAGA(T318, T325, T319, T326, delete1_in_aga(T325, T319, T326))
U14_GAGA(T318, T325, T319, T326, lessc31_out_ga(T318, T325)) → DELETE1_IN_AGA(T325, T319, T326)
DELETE1_IN_AGA(0, tree(s(T351), void, T343), tree(s(T351), T352, T343)) → U29_AGA(T351, T343, T352, delete1_in_gga(0, void, T352))
DELETE1_IN_AGA(0, tree(s(T351), void, T343), tree(s(T351), T352, T343)) → DELETE1_IN_GGA(0, void, T352)
DELETE1_IN_AGA(s(T363), tree(s(T362), void, T343), tree(s(T362), T364, T343)) → U30_AGA(T363, T362, T343, T364, p50_in_aga(T363, T362, T364))
DELETE1_IN_AGA(s(T363), tree(s(T362), void, T343), tree(s(T362), T364, T343)) → P50_IN_AGA(T363, T362, T364)
DELETE1_IN_AGA(T379, tree(T376, void, T377), tree(T376, void, T380)) → U31_AGA(T379, T376, T377, T380, p93_in_gaga(T376, T379, T377, T380))
DELETE1_IN_AGA(s(T399), tree(0, void, T389), tree(0, void, T398)) → U32_AGA(T399, T389, T398, delete1_in_aga(s(T399), T389, T398))
DELETE1_IN_AGA(s(T399), tree(0, void, T389), tree(0, void, T398)) → DELETE1_IN_AGA(s(T399), T389, T398)
DELETE1_IN_AGA(s(T410), tree(s(T408), void, T389), tree(s(T408), void, T411)) → U33_AGA(T410, T408, T389, T411, less31_in_ga(T408, T410))
DELETE1_IN_AGA(s(T410), tree(s(T408), void, T389), tree(s(T408), void, T411)) → LESS31_IN_GA(T408, T410)
DELETE1_IN_AGA(s(T414), tree(s(T408), void, T389), tree(s(T408), void, T415)) → U34_AGA(T414, T408, T389, T415, lessc31_in_ga(T408, T414))
U34_AGA(T414, T408, T389, T415, lessc31_out_ga(T408, T414)) → U35_AGA(T414, T408, T389, T415, delete1_in_aga(s(T414), T389, T415))
U34_AGA(T414, T408, T389, T415, lessc31_out_ga(T408, T414)) → DELETE1_IN_AGA(s(T414), T389, T415)
DELETE1_IN_AGA(T460, tree(T457, T458, void), tree(T457, T461, void)) → U36_AGA(T460, T457, T458, T461, less19_in_ag(T460, T457))
DELETE1_IN_AGA(T460, tree(T457, T458, void), tree(T457, T461, void)) → LESS19_IN_AG(T460, T457)
DELETE1_IN_AGA(T464, tree(T457, T458, void), tree(T457, T465, void)) → U37_AGA(T464, T457, T458, T465, lessc19_in_ag(T464, T457))
U37_AGA(T464, T457, T458, T465, lessc19_out_ag(T464, T457)) → U38_AGA(T464, T457, T458, T465, delete1_in_gga(T464, T458, T465))
U37_AGA(T464, T457, T458, T465, lessc19_out_ag(T464, T457)) → DELETE1_IN_GGA(T464, T458, T465)
DELETE1_IN_AGA(T488, tree(T485, T486, void), tree(T485, T486, T489)) → U39_AGA(T488, T485, T486, T489, p29_in_gaa(T485, T488, T489))
DELETE1_IN_AGA(T488, tree(T485, T486, void), tree(T485, T486, T489)) → P29_IN_GAA(T485, T488, T489)
DELETE1_IN_AGA(0, tree(s(T506), T498, void), tree(s(T506), T507, void)) → U40_AGA(T506, T498, T507, delete1_in_gga(0, T498, T507))
DELETE1_IN_AGA(0, tree(s(T506), T498, void), tree(s(T506), T507, void)) → DELETE1_IN_GGA(0, T498, T507)
DELETE1_IN_AGA(s(T520), tree(s(T519), T498, void), tree(s(T519), T521, void)) → U41_AGA(T520, T519, T498, T521, less19_in_ag(T520, T519))
DELETE1_IN_AGA(s(T520), tree(s(T519), T498, void), tree(s(T519), T521, void)) → LESS19_IN_AG(T520, T519)
DELETE1_IN_AGA(s(T524), tree(s(T519), T498, void), tree(s(T519), T525, void)) → U42_AGA(T524, T519, T498, T525, lessc19_in_ag(T524, T519))
U42_AGA(T524, T519, T498, T525, lessc19_out_ag(T524, T519)) → U43_AGA(T524, T519, T498, T525, delete1_in_gga(s(T524), T498, T525))
U42_AGA(T524, T519, T498, T525, lessc19_out_ag(T524, T519)) → DELETE1_IN_GGA(s(T524), T498, T525)
DELETE1_IN_AGA(T548, tree(T545, T546, void), tree(T545, T546, T549)) → U44_AGA(T548, T545, T546, T549, p29_in_gaa(T545, T548, T549))
DELETE1_IN_AGA(s(T568), tree(0, T558, void), tree(0, T558, T567)) → U45_AGA(T568, T558, T567, delete1_in_aga(s(T568), void, T567))
DELETE1_IN_AGA(s(T568), tree(0, T558, void), tree(0, T558, T567)) → DELETE1_IN_AGA(s(T568), void, T567)
DELETE1_IN_AGA(s(T582), tree(s(T580), T558, void), tree(s(T580), T558, T583)) → U46_AGA(T582, T580, T558, T583, p64_in_gaa(T580, T582, T583))
DELETE1_IN_AGA(s(T582), tree(s(T580), T558, void), tree(s(T580), T558, T583)) → P64_IN_GAA(T580, T582, T583)
DELETE1_IN_AGA(T591, tree(T591, T592, tree(T632, T633, T634)), tree(T638, T592, tree(T632, T639, T637))) → U47_AGA(T591, T592, T632, T633, T634, T638, T639, T637, delmin78_in_gaa(T633, T638, T639))
DELETE1_IN_AGA(T591, tree(T591, T592, tree(T632, T633, T634)), tree(T638, T592, tree(T632, T639, T637))) → DELMIN78_IN_GAA(T633, T638, T639)
DELETE1_IN_AGA(T669, tree(T665, T666, T667), tree(T665, T670, T667)) → U48_AGA(T669, T665, T666, T667, T670, less19_in_ag(T669, T665))
DELETE1_IN_AGA(T669, tree(T665, T666, T667), tree(T665, T670, T667)) → LESS19_IN_AG(T669, T665)
DELETE1_IN_AGA(T673, tree(T665, T666, T676), tree(T665, T674, T676)) → U49_AGA(T673, T665, T666, T676, T674, lessc19_in_ag(T673, T665))
U49_AGA(T673, T665, T666, T676, T674, lessc19_out_ag(T673, T665)) → U50_AGA(T673, T665, T666, T676, T674, delete1_in_gga(T673, T666, T674))
U49_AGA(T673, T665, T666, T676, T674, lessc19_out_ag(T673, T665)) → DELETE1_IN_GGA(T673, T666, T674)
DELETE1_IN_AGA(T703, tree(T699, T700, T701), tree(T699, T700, T704)) → U51_AGA(T703, T699, T700, T701, T704, less31_in_ga(T699, T703))
DELETE1_IN_AGA(T703, tree(T699, T700, T701), tree(T699, T700, T704)) → LESS31_IN_GA(T699, T703)
DELETE1_IN_AGA(T707, tree(T699, T710, T701), tree(T699, T710, T708)) → U52_AGA(T707, T699, T710, T701, T708, lessc31_in_ga(T699, T707))
U52_AGA(T707, T699, T710, T701, T708, lessc31_out_ga(T699, T707)) → U53_AGA(T707, T699, T710, T701, T708, delete1_in_aga(T707, T701, T708))
U52_AGA(T707, T699, T710, T701, T708, lessc31_out_ga(T699, T707)) → DELETE1_IN_AGA(T707, T701, T708)
DELETE1_IN_AGA(0, tree(s(T738), T729, T730), tree(s(T738), T739, T730)) → U54_AGA(T738, T729, T730, T739, delete1_in_gga(0, T729, T739))
DELETE1_IN_AGA(0, tree(s(T738), T729, T730), tree(s(T738), T739, T730)) → DELETE1_IN_GGA(0, T729, T739)
DELETE1_IN_AGA(s(T752), tree(s(T751), T729, T730), tree(s(T751), T753, T730)) → U55_AGA(T752, T751, T729, T730, T753, less19_in_ag(T752, T751))
DELETE1_IN_AGA(s(T752), tree(s(T751), T729, T730), tree(s(T751), T753, T730)) → LESS19_IN_AG(T752, T751)
DELETE1_IN_AGA(s(T756), tree(s(T751), T729, T759), tree(s(T751), T757, T759)) → U56_AGA(T756, T751, T729, T759, T757, lessc19_in_ag(T756, T751))
U56_AGA(T756, T751, T729, T759, T757, lessc19_out_ag(T756, T751)) → U57_AGA(T756, T751, T729, T759, T757, delete1_in_gga(s(T756), T729, T757))
U56_AGA(T756, T751, T729, T759, T757, lessc19_out_ag(T756, T751)) → DELETE1_IN_GGA(s(T756), T729, T757)
DELETE1_IN_AGA(T784, tree(T780, T781, T782), tree(T780, T781, T785)) → U58_AGA(T784, T780, T781, T782, T785, less31_in_ga(T780, T784))
DELETE1_IN_AGA(T788, tree(T780, T791, T782), tree(T780, T791, T789)) → U59_AGA(T788, T780, T791, T782, T789, lessc31_in_ga(T780, T788))
U59_AGA(T788, T780, T791, T782, T789, lessc31_out_ga(T780, T788)) → U60_AGA(T788, T780, T791, T782, T789, delete1_in_aga(T788, T782, T789))
U59_AGA(T788, T780, T791, T782, T789, lessc31_out_ga(T780, T788)) → DELETE1_IN_AGA(T788, T782, T789)
DELETE1_IN_AGA(s(T826), tree(0, T815, T816), tree(0, T815, T825)) → U61_AGA(T826, T815, T816, T825, delete1_in_aga(s(T826), T816, T825))
DELETE1_IN_AGA(s(T826), tree(0, T815, T816), tree(0, T815, T825)) → DELETE1_IN_AGA(s(T826), T816, T825)
DELETE1_IN_AGA(s(T837), tree(s(T835), T815, T816), tree(s(T835), T815, T838)) → U62_AGA(T837, T835, T815, T816, T838, less31_in_ga(T835, T837))
DELETE1_IN_AGA(s(T837), tree(s(T835), T815, T816), tree(s(T835), T815, T838)) → LESS31_IN_GA(T835, T837)
DELETE1_IN_AGA(s(T841), tree(s(T835), T844, T816), tree(s(T835), T844, T842)) → U63_AGA(T841, T835, T844, T816, T842, lessc31_in_ga(T835, T841))
U63_AGA(T841, T835, T844, T816, T842, lessc31_out_ga(T835, T841)) → U64_AGA(T841, T835, T844, T816, T842, delete1_in_aga(s(T841), T816, T842))
U63_AGA(T841, T835, T844, T816, T842, lessc31_out_ga(T835, T841)) → DELETE1_IN_AGA(s(T841), T816, T842)

The TRS R consists of the following rules:

lessc19_in_ag(0, s(T45)) → lessc19_out_ag(0, s(T45))
lessc19_in_ag(s(T52), s(T51)) → U104_ag(T52, T51, lessc19_in_ag(T52, T51))
U104_ag(T52, T51, lessc19_out_ag(T52, T51)) → lessc19_out_ag(s(T52), s(T51))
lessc19_in_gg(0, s(T45)) → lessc19_out_gg(0, s(T45))
lessc19_in_gg(s(T52), s(T51)) → U104_gg(T52, T51, lessc19_in_gg(T52, T51))
U104_gg(T52, T51, lessc19_out_gg(T52, T51)) → lessc19_out_gg(s(T52), s(T51))
lessc31_in_gg(0, s(T83)) → lessc31_out_gg(0, s(T83))
lessc31_in_gg(s(T88), s(T90)) → U105_gg(T88, T90, lessc31_in_gg(T88, T90))
U105_gg(T88, T90, lessc31_out_gg(T88, T90)) → lessc31_out_gg(s(T88), s(T90))
lessc31_in_ga(0, s(T83)) → lessc31_out_ga(0, s(T83))
lessc31_in_ga(s(T88), s(T90)) → U105_ga(T88, T90, lessc31_in_ga(T88, T90))
U105_ga(T88, T90, lessc31_out_ga(T88, T90)) → lessc31_out_ga(s(T88), s(T90))

The argument filtering Pi contains the following mapping:
delete1_in_aga(x1, x2, x3) = delete1_in_aga(x2)
tree(x1, x2, x3) = tree(x1, x2, x3)
void = void
p17_in_aga(x1, x2, x3) = p17_in_aga(x2)
less19_in_ag(x1, x2) = less19_in_ag(x2)
s(x1) = s(x1)
lessc19_in_ag(x1, x2) = lessc19_in_ag(x2)
lessc19_out_ag(x1, x2) = lessc19_out_ag(x1, x2)
U104_ag(x1, x2, x3) = U104_ag(x2, x3)
delete1_in_gga(x1, x2, x3) = delete1_in_gga(x1, x2)
p17_in_gga(x1, x2, x3) = p17_in_gga(x1, x2)
less19_in_gg(x1, x2) = less19_in_gg(x1, x2)
lessc19_in_gg(x1, x2) = lessc19_in_gg(x1, x2)
0 = 0
lessc19_out_gg(x1, x2) = lessc19_out_gg(x1, x2)
U104_gg(x1, x2, x3) = U104_gg(x1, x2, x3)
p29_in_gga(x1, x2, x3) = p29_in_gga(x1, x2)
less31_in_gg(x1, x2) = less31_in_gg(x1, x2)
lessc31_in_gg(x1, x2) = lessc31_in_gg(x1, x2)
lessc31_out_gg(x1, x2) = lessc31_out_gg(x1, x2)
U105_gg(x1, x2, x3) = U105_gg(x1, x2, x3)
p50_in_gga(x1, x2, x3) = p50_in_gga(x1, x2)
p64_in_gga(x1, x2, x3) = p64_in_gga(x1, x2)
delmin78_in_gaa(x1, x2, x3) = delmin78_in_gaa(x1)
p93_in_ggga(x1, x2, x3, x4) = p93_in_ggga(x1, x2, x3)
p29_in_gaa(x1, x2, x3) = p29_in_gaa(x1)
less31_in_ga(x1, x2) = less31_in_ga(x1)
lessc31_in_ga(x1, x2) = lessc31_in_ga(x1)
lessc31_out_ga(x1, x2) = lessc31_out_ga(x1)
U105_ga(x1, x2, x3) = U105_ga(x1, x3)
p50_in_aga(x1, x2, x3) = p50_in_aga(x2)
p64_in_gaa(x1, x2, x3) = p64_in_gaa(x1)
p93_in_gaga(x1, x2, x3, x4) = p93_in_gaga(x1, x3)
DELETE1_IN_AGA(x1, x2, x3) = DELETE1_IN_AGA(x2)
U19_AGA(x1, x2, x3, x4) = U19_AGA(x2, x4)
P17_IN_AGA(x1, x2, x3) = P17_IN_AGA(x2)
U7_AGA(x1, x2, x3, x4) = U7_AGA(x2, x4)
LESS19_IN_AG(x1, x2) = LESS19_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)
DELETE1_IN_GGA(x1, x2, x3) = DELETE1_IN_GGA(x1, x2)
U19_GGA(x1, x2, x3, x4) = U19_GGA(x1, x2, x4)
P17_IN_GGA(x1, x2, x3) = P17_IN_GGA(x1, x2)
U7_GGA(x1, x2, x3, x4) = U7_GGA(x1, x2, x4)
LESS19_IN_GG(x1, x2) = LESS19_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)
U20_GGA(x1, x2, x3, x4) = U20_GGA(x1, x2, x4)
P29_IN_GGA(x1, x2, x3) = P29_IN_GGA(x1, x2)
U3_GGA(x1, x2, x3, x4) = U3_GGA(x1, x2, x4)
LESS31_IN_GG(x1, x2) = LESS31_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)
U21_GGA(x1, x2, x3) = U21_GGA(x1, x3)
U22_GGA(x1, x2, x3, x4) = U22_GGA(x1, x2, x4)
P50_IN_GGA(x1, x2, x3) = P50_IN_GGA(x1, x2)
U10_GGA(x1, x2, x3, x4) = U10_GGA(x1, x2, x4)
U11_GGA(x1, x2, x3, x4) = U11_GGA(x1, x2, x4)
U12_GGA(x1, x2, x3, x4) = U12_GGA(x1, x2, x4)
U23_GGA(x1, x2, x3, x4) = U23_GGA(x1, x2, x4)
U24_GGA(x1, x2, x3) = U24_GGA(x1, x3)
U25_GGA(x1, x2, x3, x4) = U25_GGA(x1, x2, x4)
P64_IN_GGA(x1, x2, x3) = P64_IN_GGA(x1, x2)
U16_GGA(x1, x2, x3, x4) = U16_GGA(x1, x2, x4)
U17_GGA(x1, x2, x3, x4) = U17_GGA(x1, x2, x4)
U18_GGA(x1, x2, x3, x4) = U18_GGA(x1, x2, x4)
U26_GGA(x1, x2, x3, x4, x5, x6, x7, x8) = U26_GGA(x1, x2, x3, x4, x8)
DELMIN78_IN_GAA(x1, x2, x3) = DELMIN78_IN_GAA(x1)
U6_GAA(x1, x2, x3, x4, x5, x6, x7) = U6_GAA(x1, x2, x3, x7)
U27_GGA(x1, x2, x3, x4, x5) = U27_GGA(x1, x2, x3, x5)
U28_GGA(x1, x2, x3, x4, x5) = U28_GGA(x1, x2, x3, x5)
P93_IN_GGGA(x1, x2, x3, x4) = P93_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)
U29_GGA(x1, x2, x3, x4) = U29_GGA(x1, x2, x4)
U30_GGA(x1, x2, x3, x4, x5) = U30_GGA(x1, x2, x3, x5)
U31_GGA(x1, x2, x3, x4, x5) = U31_GGA(x1, x2, x3, x5)
U32_GGA(x1, x2, x3, x4) = U32_GGA(x1, x2, x4)
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, x5) = U35_GGA(x1, x2, x3, x5)
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) = U40_GGA(x1, x2, x4)
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, x5) = U43_GGA(x1, x2, x3, x5)
U44_GGA(x1, x2, x3, x4, x5) = U44_GGA(x1, x2, x3, x5)
U45_GGA(x1, x2, x3, x4) = U45_GGA'(x1, x2, x4)
U46_GGA(x1, x2, x3, x4, x5) = U46_GGA(x1, x2, x3, x5)
U47_GGA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U47_GGA(x1, x2, x3, x4, x5, x9)
U48_GGA(x1, x2, x3, x4, x5, x6) = U48_GGA(x1, x2, x3, x4, x6)
U49_GGA(x1, x2, x3, x4, x5, x6) = U49_GGA(x1, x2, x3, x4, x6)
U50_GGA(x1, x2, x3, x4, x5, x6) = U50_GGA(x1, x2, x3, x4, x6)
U51_GGA(x1, x2, x3, x4, x5, x6) = U51_GGA(x1, x2, x3, x4, x6)
U52_GGA(x1, x2, x3, x4, x5, x6) = U52_GGA(x1, x2, x3, x4, x6)
U53_GGA(x1, x2, x3, x4, x5, x6) = U53_GGA(x1, x2, x3, x4, x6)
U54_GGA(x1, x2, x3, x4, x5) = U54_GGA(x1, x2, x3, x5)
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)
U57_GGA(x1, x2, x3, x4, x5, x6) = U57_GGA(x1, x2, x3, x4, x6)
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) = U61_GGA(x1, x2, x3, x5)
U62_GGA(x1, x2, x3, x4, x5, x6) = U62_GGA(x1, x2, x3, x4, x6)
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)
U20_AGA(x1, x2, x3, x4) = U20_AGA(x2, x4)
P29_IN_GAA(x1, x2, x3) = P29_IN_GAA(x1)
U3_GAA(x1, x2, x3, x4) = U3_GAA(x1, x4)
LESS31_IN_GA(x1, x2) = LESS31_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)
U21_AGA(x1, x2, x3) = U21_AGA(x1, x3)
U22_AGA(x1, x2, x3, x4) = U22_AGA(x2, x4)
P50_IN_AGA(x1, x2, x3) = P50_IN_AGA(x2)
U10_AGA(x1, x2, x3, x4) = U10_AGA(x2, x4)
U11_AGA(x1, x2, x3, x4) = U11_AGA'(x2, x4)
U12_AGA(x1, x2, x3, x4) = U12_AGA(x1, x2, x4)
U23_AGA(x1, x2, x3, x4) = U23_AGA(x2, x4)
U24_AGA(x1, x2, x3) = U24_AGA(x3)
U25_AGA(x1, x2, x3, x4) = U25_AGA(x2, x4)
P64_IN_GAA(x1, x2, x3) = P64_IN_GAA(x1)
U16_GAA(x1, x2, x3, x4) = U16_GAA(x1, x4)
U17_GAA(x1, x2, x3, x4) = U17_GAA(x1, x4)
U18_GAA(x1, x2, x3, x4) = U18_GAA(x1, x4)
U26_AGA(x1, x2, x3, x4, x5, x6, x7, x8) = U26_AGA(x1, x2, x3, x4, x8)
U27_AGA(x1, x2, x3, x4, x5) = U27_AGA(x2, x3, x5)
U28_AGA(x1, x2, x3, x4, x5) = U28_AGA'(x2, x3, x5)
P93_IN_GAGA(x1, x2, x3, x4) = P93_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)
U29_AGA(x1, x2, x3, x4) = U29_AGA(x1, x2, x4)
U30_AGA(x1, x2, x3, x4, x5) = U30_AGA(x2, x3, x5)
U31_AGA(x1, x2, x3, x4, x5) = U31_AGA(x2, x3, x5)
U32_AGA(x1, x2, x3, x4) = U32_AGA(x2, x4)
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, x5) = U35_AGA(x2, x3, x5)
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(x1, x2, x3, x5)
U39_AGA(x1, x2, x3, x4, x5) = U39_AGA(x2, x3, x5)
U40_AGA(x1, x2, x3, x4) = U40_AGA(x1, x2, x4)
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, x5) = U43_AGA(x1, x2, x3, x5)
U44_AGA(x1, x2, x3, x4, x5) = U44_AGA(x2, x3, x5)
U45_AGA(x1, x2, x3, x4) = U45_AGA(x2, x4)
U46_AGA(x1, x2, x3, x4, x5) = U46_AGA(x2, x3, x5)
U47_AGA(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U47_AGA(x1, x2, x3, x4, x5, x9)
U48_AGA(x1, x2, x3, x4, x5, x6) = U48_AGA(x2, x3, x4, x6)
U49_AGA(x1, x2, x3, x4, x5, x6) = U49_AGA(x2, x3, x4, x6)
U50_AGA(x1, x2, x3, x4, x5, x6) = U50_AGA'(x1, x2, x3, x4, x6)
U51_AGA(x1, x2, x3, x4, x5, x6) = U51_AGA(x2, x3, x4, x6)
U52_AGA(x1, x2, x3, x4, x5, x6) = U52_AGA(x2, x3, x4, x6)
U53_AGA(x1, x2, x3, x4, x5, x6) = U53_AGA(x2, x3, x4, x6)
U54_AGA(x1, x2, x3, x4, x5) = U54_AGA(x1, x2, x3, x5)
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)
U57_AGA(x1, x2, x3, x4, x5, x6) = U57_AGA(x1, x2, x3, x4, x6)
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) = U61_AGA(x2, x3, x5)
U62_AGA(x1, x2, x3, x4, x5, x6) = U62_AGA(x2, x3, x4, x6)
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)

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

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 7 SCCs with 179 less nodes.

(6) Complex Obligation (AND)

(7) Obligation:

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

LESS31_IN_GA(s(T88), s(T90)) → LESS31_IN_GA(T88, T90)

The TRS R consists of the following rules:

lessc19_in_ag(0, s(T45)) → lessc19_out_ag(0, s(T45))
lessc19_in_ag(s(T52), s(T51)) → U104_ag(T52, T51, lessc19_in_ag(T52, T51))
U104_ag(T52, T51, lessc19_out_ag(T52, T51)) → lessc19_out_ag(s(T52), s(T51))
lessc19_in_gg(0, s(T45)) → lessc19_out_gg(0, s(T45))
lessc19_in_gg(s(T52), s(T51)) → U104_gg(T52, T51, lessc19_in_gg(T52, T51))
U104_gg(T52, T51, lessc19_out_gg(T52, T51)) → lessc19_out_gg(s(T52), s(T51))
lessc31_in_gg(0, s(T83)) → lessc31_out_gg(0, s(T83))
lessc31_in_gg(s(T88), s(T90)) → U105_gg(T88, T90, lessc31_in_gg(T88, T90))
U105_gg(T88, T90, lessc31_out_gg(T88, T90)) → lessc31_out_gg(s(T88), s(T90))
lessc31_in_ga(0, s(T83)) → lessc31_out_ga(0, s(T83))
lessc31_in_ga(s(T88), s(T90)) → U105_ga(T88, T90, lessc31_in_ga(T88, T90))
U105_ga(T88, T90, lessc31_out_ga(T88, T90)) → lessc31_out_ga(s(T88), s(T90))

The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
lessc19_in_ag(x1, x2) = lessc19_in_ag(x2)
lessc19_out_ag(x1, x2) = lessc19_out_ag(x1, x2)
U104_ag(x1, x2, x3) = U104_ag(x2, x3)
lessc19_in_gg(x1, x2) = lessc19_in_gg(x1, x2)
0 = 0
lessc19_out_gg(x1, x2) = lessc19_out_gg(x1, x2)
U104_gg(x1, x2, x3) = U104_gg(x1, x2, x3)
lessc31_in_gg(x1, x2) = lessc31_in_gg(x1, x2)
lessc31_out_gg(x1, x2) = lessc31_out_gg(x1, x2)
U105_gg(x1, x2, x3) = U105_gg(x1, x2, x3)
lessc31_in_ga(x1, x2) = lessc31_in_ga(x1)
lessc31_out_ga(x1, x2) = lessc31_out_ga(x1)
U105_ga(x1, x2, x3) = U105_ga(x1, x3)
LESS31_IN_GA(x1, x2) = LESS31_IN_GA(x1)

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

(8) UsableRulesProof (EQUIVALENT transformation)

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

(9) Obligation:

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

LESS31_IN_GA(s(T88), s(T90)) → LESS31_IN_GA(T88, T90)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
LESS31_IN_GA(x1, x2) = LESS31_IN_GA(x1)

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

(10) PiDPToQDPProof (SOUND transformation)

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

(11) Obligation:

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

LESS31_IN_GA(s(T88)) → LESS31_IN_GA(T88)

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

(12) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

LESS31_IN_GA(s(T88)) → LESS31_IN_GA(T88)
The graph contains the following edges 1 > 1

(13) YES

(14) Obligation:

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

DELMIN78_IN_GAA(tree(T273, T274, T275), T279, tree(T273, T280, T278)) → DELMIN78_IN_GAA(T274, T279, T280)

The TRS R consists of the following rules:

lessc19_in_ag(0, s(T45)) → lessc19_out_ag(0, s(T45))
lessc19_in_ag(s(T52), s(T51)) → U104_ag(T52, T51, lessc19_in_ag(T52, T51))
U104_ag(T52, T51, lessc19_out_ag(T52, T51)) → lessc19_out_ag(s(T52), s(T51))
lessc19_in_gg(0, s(T45)) → lessc19_out_gg(0, s(T45))
lessc19_in_gg(s(T52), s(T51)) → U104_gg(T52, T51, lessc19_in_gg(T52, T51))
U104_gg(T52, T51, lessc19_out_gg(T52, T51)) → lessc19_out_gg(s(T52), s(T51))
lessc31_in_gg(0, s(T83)) → lessc31_out_gg(0, s(T83))
lessc31_in_gg(s(T88), s(T90)) → U105_gg(T88, T90, lessc31_in_gg(T88, T90))
U105_gg(T88, T90, lessc31_out_gg(T88, T90)) → lessc31_out_gg(s(T88), s(T90))
lessc31_in_ga(0, s(T83)) → lessc31_out_ga(0, s(T83))
lessc31_in_ga(s(T88), s(T90)) → U105_ga(T88, T90, lessc31_in_ga(T88, T90))
U105_ga(T88, T90, lessc31_out_ga(T88, T90)) → lessc31_out_ga(s(T88), s(T90))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
s(x1) = s(x1)
lessc19_in_ag(x1, x2) = lessc19_in_ag(x2)
lessc19_out_ag(x1, x2) = lessc19_out_ag(x1, x2)
U104_ag(x1, x2, x3) = U104_ag(x2, x3)
lessc19_in_gg(x1, x2) = lessc19_in_gg(x1, x2)
0 = 0
lessc19_out_gg(x1, x2) = lessc19_out_gg(x1, x2)
U104_gg(x1, x2, x3) = U104_gg(x1, x2, x3)
lessc31_in_gg(x1, x2) = lessc31_in_gg(x1, x2)
lessc31_out_gg(x1, x2) = lessc31_out_gg(x1, x2)
U105_gg(x1, x2, x3) = U105_gg(x1, x2, x3)
lessc31_in_ga(x1, x2) = lessc31_in_ga(x1)
lessc31_out_ga(x1, x2) = lessc31_out_ga(x1)
U105_ga(x1, x2, x3) = U105_ga(x1, x3)
DELMIN78_IN_GAA(x1, x2, x3) = DELMIN78_IN_GAA(x1)

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

(15) UsableRulesProof (EQUIVALENT transformation)

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

(16) Obligation:

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

DELMIN78_IN_GAA(tree(T273, T274, T275), T279, tree(T273, T280, T278)) → DELMIN78_IN_GAA(T274, T279, T280)

R is empty.
The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
DELMIN78_IN_GAA(x1, x2, x3) = DELMIN78_IN_GAA(x1)

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

(17) PiDPToQDPProof (SOUND transformation)

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

(18) Obligation:

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

DELMIN78_IN_GAA(tree(T273, T274, T275)) → DELMIN78_IN_GAA(T274)

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

(19) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

DELMIN78_IN_GAA(tree(T273, T274, T275)) → DELMIN78_IN_GAA(T274)
The graph contains the following edges 1 > 1

(20) YES

(21) Obligation:

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

LESS31_IN_GG(s(T88), s(T90)) → LESS31_IN_GG(T88, T90)

The TRS R consists of the following rules:

lessc19_in_ag(0, s(T45)) → lessc19_out_ag(0, s(T45))
lessc19_in_ag(s(T52), s(T51)) → U104_ag(T52, T51, lessc19_in_ag(T52, T51))
U104_ag(T52, T51, lessc19_out_ag(T52, T51)) → lessc19_out_ag(s(T52), s(T51))
lessc19_in_gg(0, s(T45)) → lessc19_out_gg(0, s(T45))
lessc19_in_gg(s(T52), s(T51)) → U104_gg(T52, T51, lessc19_in_gg(T52, T51))
U104_gg(T52, T51, lessc19_out_gg(T52, T51)) → lessc19_out_gg(s(T52), s(T51))
lessc31_in_gg(0, s(T83)) → lessc31_out_gg(0, s(T83))
lessc31_in_gg(s(T88), s(T90)) → U105_gg(T88, T90, lessc31_in_gg(T88, T90))
U105_gg(T88, T90, lessc31_out_gg(T88, T90)) → lessc31_out_gg(s(T88), s(T90))
lessc31_in_ga(0, s(T83)) → lessc31_out_ga(0, s(T83))
lessc31_in_ga(s(T88), s(T90)) → U105_ga(T88, T90, lessc31_in_ga(T88, T90))
U105_ga(T88, T90, lessc31_out_ga(T88, T90)) → lessc31_out_ga(s(T88), s(T90))

The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
lessc19_in_ag(x1, x2) = lessc19_in_ag(x2)
lessc19_out_ag(x1, x2) = lessc19_out_ag(x1, x2)
U104_ag(x1, x2, x3) = U104_ag(x2, x3)
lessc19_in_gg(x1, x2) = lessc19_in_gg(x1, x2)
0 = 0
lessc19_out_gg(x1, x2) = lessc19_out_gg(x1, x2)
U104_gg(x1, x2, x3) = U104_gg(x1, x2, x3)
lessc31_in_gg(x1, x2) = lessc31_in_gg(x1, x2)
lessc31_out_gg(x1, x2) = lessc31_out_gg(x1, x2)
U105_gg(x1, x2, x3) = U105_gg(x1, x2, x3)
lessc31_in_ga(x1, x2) = lessc31_in_ga(x1)
lessc31_out_ga(x1, x2) = lessc31_out_ga(x1)
U105_ga(x1, x2, x3) = U105_ga(x1, x3)
LESS31_IN_GG(x1, x2) = LESS31_IN_GG(x1, x2)

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

(22) UsableRulesProof (EQUIVALENT transformation)

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

(23) Obligation:

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

LESS31_IN_GG(s(T88), s(T90)) → LESS31_IN_GG(T88, T90)

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

(24) PiDPToQDPProof (EQUIVALENT transformation)

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

(25) Obligation:

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

LESS31_IN_GG(s(T88), s(T90)) → LESS31_IN_GG(T88, T90)

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

(26) 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:

LESS31_IN_GG(s(T88), s(T90)) → LESS31_IN_GG(T88, T90)
The graph contains the following edges 1 > 1, 2 > 2

(27) YES

(28) Obligation:

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

LESS19_IN_GG(s(T52), s(T51)) → LESS19_IN_GG(T52, T51)

The TRS R consists of the following rules:

lessc19_in_ag(0, s(T45)) → lessc19_out_ag(0, s(T45))
lessc19_in_ag(s(T52), s(T51)) → U104_ag(T52, T51, lessc19_in_ag(T52, T51))
U104_ag(T52, T51, lessc19_out_ag(T52, T51)) → lessc19_out_ag(s(T52), s(T51))
lessc19_in_gg(0, s(T45)) → lessc19_out_gg(0, s(T45))
lessc19_in_gg(s(T52), s(T51)) → U104_gg(T52, T51, lessc19_in_gg(T52, T51))
U104_gg(T52, T51, lessc19_out_gg(T52, T51)) → lessc19_out_gg(s(T52), s(T51))
lessc31_in_gg(0, s(T83)) → lessc31_out_gg(0, s(T83))
lessc31_in_gg(s(T88), s(T90)) → U105_gg(T88, T90, lessc31_in_gg(T88, T90))
U105_gg(T88, T90, lessc31_out_gg(T88, T90)) → lessc31_out_gg(s(T88), s(T90))
lessc31_in_ga(0, s(T83)) → lessc31_out_ga(0, s(T83))
lessc31_in_ga(s(T88), s(T90)) → U105_ga(T88, T90, lessc31_in_ga(T88, T90))
U105_ga(T88, T90, lessc31_out_ga(T88, T90)) → lessc31_out_ga(s(T88), s(T90))

The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
lessc19_in_ag(x1, x2) = lessc19_in_ag(x2)
lessc19_out_ag(x1, x2) = lessc19_out_ag(x1, x2)
U104_ag(x1, x2, x3) = U104_ag(x2, x3)
lessc19_in_gg(x1, x2) = lessc19_in_gg(x1, x2)
0 = 0
lessc19_out_gg(x1, x2) = lessc19_out_gg(x1, x2)
U104_gg(x1, x2, x3) = U104_gg(x1, x2, x3)
lessc31_in_gg(x1, x2) = lessc31_in_gg(x1, x2)
lessc31_out_gg(x1, x2) = lessc31_out_gg(x1, x2)
U105_gg(x1, x2, x3) = U105_gg(x1, x2, x3)
lessc31_in_ga(x1, x2) = lessc31_in_ga(x1)
lessc31_out_ga(x1, x2) = lessc31_out_ga(x1)
U105_ga(x1, x2, x3) = U105_ga(x1, x3)
LESS19_IN_GG(x1, x2) = LESS19_IN_GG(x1, x2)

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

(29) UsableRulesProof (EQUIVALENT transformation)

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

(30) Obligation:

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

LESS19_IN_GG(s(T52), s(T51)) → LESS19_IN_GG(T52, T51)

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

(31) PiDPToQDPProof (EQUIVALENT transformation)

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

(32) Obligation:

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

LESS19_IN_GG(s(T52), s(T51)) → LESS19_IN_GG(T52, T51)

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

(33) 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:

LESS19_IN_GG(s(T52), s(T51)) → LESS19_IN_GG(T52, T51)
The graph contains the following edges 1 > 1, 2 > 2

(34) YES

(35) Obligation:

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

DELETE1_IN_GGA(T321, tree(T318, void, T319), tree(T318, void, T322)) → P93_IN_GGGA(T318, T321, T319, T322)
P93_IN_GGGA(T318, T325, T319, T326) → U14_GGGA(T318, T325, T319, T326, lessc31_in_gg(T318, T325))
U14_GGGA(T318, T325, T319, T326, lessc31_out_gg(T318, T325)) → DELETE1_IN_GGA(T325, T319, T326)
DELETE1_IN_GGA(s(T399), tree(0, void, T389), tree(0, void, T398)) → DELETE1_IN_GGA(s(T399), T389, T398)
DELETE1_IN_GGA(s(T414), tree(s(T408), void, T389), tree(s(T408), void, T415)) → U34_GGA(T414, T408, T389, T415, lessc31_in_gg(T408, T414))
U34_GGA(T414, T408, T389, T415, lessc31_out_gg(T408, T414)) → DELETE1_IN_GGA(s(T414), T389, T415)
DELETE1_IN_GGA(T464, tree(T457, T458, void), tree(T457, T465, void)) → U37_GGA(T464, T457, T458, T465, lessc19_in_gg(T464, T457))
U37_GGA(T464, T457, T458, T465, lessc19_out_gg(T464, T457)) → DELETE1_IN_GGA(T464, T458, T465)
DELETE1_IN_GGA(0, tree(s(T506), T498, void), tree(s(T506), T507, void)) → DELETE1_IN_GGA(0, T498, T507)
DELETE1_IN_GGA(T673, tree(T665, T666, T676), tree(T665, T674, T676)) → U49_GGA(T673, T665, T666, T676, T674, lessc19_in_gg(T673, T665))
U49_GGA(T673, T665, T666, T676, T674, lessc19_out_gg(T673, T665)) → DELETE1_IN_GGA(T673, T666, T674)
DELETE1_IN_GGA(s(T524), tree(s(T519), T498, void), tree(s(T519), T525, void)) → U42_GGA(T524, T519, T498, T525, lessc19_in_gg(T524, T519))
U42_GGA(T524, T519, T498, T525, lessc19_out_gg(T524, T519)) → DELETE1_IN_GGA(s(T524), T498, T525)
DELETE1_IN_GGA(T707, tree(T699, T710, T701), tree(T699, T710, T708)) → U52_GGA(T707, T699, T710, T701, T708, lessc31_in_gg(T699, T707))
U52_GGA(T707, T699, T710, T701, T708, lessc31_out_gg(T699, T707)) → DELETE1_IN_GGA(T707, T701, T708)
DELETE1_IN_GGA(0, tree(s(T738), T729, T730), tree(s(T738), T739, T730)) → DELETE1_IN_GGA(0, T729, T739)
DELETE1_IN_GGA(T788, tree(T780, T791, T782), tree(T780, T791, T789)) → U59_GGA(T788, T780, T791, T782, T789, lessc31_in_gg(T780, T788))
U59_GGA(T788, T780, T791, T782, T789, lessc31_out_gg(T780, T788)) → DELETE1_IN_GGA(T788, T782, T789)
DELETE1_IN_GGA(s(T756), tree(s(T751), T729, T759), tree(s(T751), T757, T759)) → U56_GGA(T756, T751, T729, T759, T757, lessc19_in_gg(T756, T751))
U56_GGA(T756, T751, T729, T759, T757, lessc19_out_gg(T756, T751)) → DELETE1_IN_GGA(s(T756), T729, T757)
DELETE1_IN_GGA(s(T826), tree(0, T815, T816), tree(0, T815, T825)) → DELETE1_IN_GGA(s(T826), T816, T825)
DELETE1_IN_GGA(s(T841), tree(s(T835), T844, T816), tree(s(T835), T844, T842)) → U63_GGA(T841, T835, T844, T816, T842, lessc31_in_gg(T835, T841))
U63_GGA(T841, T835, T844, T816, T842, lessc31_out_gg(T835, T841)) → DELETE1_IN_GGA(s(T841), T816, T842)

The TRS R consists of the following rules:

lessc19_in_ag(0, s(T45)) → lessc19_out_ag(0, s(T45))
lessc19_in_ag(s(T52), s(T51)) → U104_ag(T52, T51, lessc19_in_ag(T52, T51))
U104_ag(T52, T51, lessc19_out_ag(T52, T51)) → lessc19_out_ag(s(T52), s(T51))
lessc19_in_gg(0, s(T45)) → lessc19_out_gg(0, s(T45))
lessc19_in_gg(s(T52), s(T51)) → U104_gg(T52, T51, lessc19_in_gg(T52, T51))
U104_gg(T52, T51, lessc19_out_gg(T52, T51)) → lessc19_out_gg(s(T52), s(T51))
lessc31_in_gg(0, s(T83)) → lessc31_out_gg(0, s(T83))
lessc31_in_gg(s(T88), s(T90)) → U105_gg(T88, T90, lessc31_in_gg(T88, T90))
U105_gg(T88, T90, lessc31_out_gg(T88, T90)) → lessc31_out_gg(s(T88), s(T90))
lessc31_in_ga(0, s(T83)) → lessc31_out_ga(0, s(T83))
lessc31_in_ga(s(T88), s(T90)) → U105_ga(T88, T90, lessc31_in_ga(T88, T90))
U105_ga(T88, T90, lessc31_out_ga(T88, T90)) → lessc31_out_ga(s(T88), s(T90))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
void = void
s(x1) = s(x1)
lessc19_in_ag(x1, x2) = lessc19_in_ag(x2)
lessc19_out_ag(x1, x2) = lessc19_out_ag(x1, x2)
U104_ag(x1, x2, x3) = U104_ag(x2, x3)
lessc19_in_gg(x1, x2) = lessc19_in_gg(x1, x2)
0 = 0
lessc19_out_gg(x1, x2) = lessc19_out_gg(x1, x2)
U104_gg(x1, x2, x3) = U104_gg(x1, x2, x3)
lessc31_in_gg(x1, x2) = lessc31_in_gg(x1, x2)
lessc31_out_gg(x1, x2) = lessc31_out_gg(x1, x2)
U105_gg(x1, x2, x3) = U105_gg(x1, x2, x3)
lessc31_in_ga(x1, x2) = lessc31_in_ga(x1)
lessc31_out_ga(x1, x2) = lessc31_out_ga(x1)
U105_ga(x1, x2, x3) = U105_ga(x1, x3)
DELETE1_IN_GGA(x1, x2, x3) = DELETE1_IN_GGA(x1, x2)
P93_IN_GGGA(x1, x2, x3, x4) = P93_IN_GGGA(x1, x2, x3)
U14_GGGA(x1, x2, x3, x4, x5) = U14_GGGA(x1, x2, x3, x5)
U34_GGA(x1, x2, x3, x4, x5) = U34_GGA(x1, x2, x3, x5)
U37_GGA(x1, x2, x3, x4, x5) = U37_GGA(x1, x2, x3, x5)
U42_GGA(x1, x2, x3, x4, x5) = U42_GGA(x1, x2, x3, x5)
U49_GGA(x1, x2, x3, x4, x5, x6) = U49_GGA(x1, x2, x3, x4, x6)
U52_GGA(x1, x2, x3, x4, x5, x6) = U52_GGA(x1, x2, x3, x4, x6)
U56_GGA(x1, x2, x3, x4, x5, x6) = U56_GGA(x1, x2, x3, x4, x6)
U59_GGA(x1, x2, x3, x4, x5, x6) = U59_GGA(x1, x2, x3, x4, x6)
U63_GGA(x1, x2, x3, x4, x5, x6) = U63_GGA(x1, x2, x3, x4, x6)

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

(36) UsableRulesProof (EQUIVALENT transformation)

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

(37) Obligation:

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

DELETE1_IN_GGA(T321, tree(T318, void, T319), tree(T318, void, T322)) → P93_IN_GGGA(T318, T321, T319, T322)
P93_IN_GGGA(T318, T325, T319, T326) → U14_GGGA(T318, T325, T319, T326, lessc31_in_gg(T318, T325))
U14_GGGA(T318, T325, T319, T326, lessc31_out_gg(T318, T325)) → DELETE1_IN_GGA(T325, T319, T326)
DELETE1_IN_GGA(s(T399), tree(0, void, T389), tree(0, void, T398)) → DELETE1_IN_GGA(s(T399), T389, T398)
DELETE1_IN_GGA(s(T414), tree(s(T408), void, T389), tree(s(T408), void, T415)) → U34_GGA(T414, T408, T389, T415, lessc31_in_gg(T408, T414))
U34_GGA(T414, T408, T389, T415, lessc31_out_gg(T408, T414)) → DELETE1_IN_GGA(s(T414), T389, T415)
DELETE1_IN_GGA(T464, tree(T457, T458, void), tree(T457, T465, void)) → U37_GGA(T464, T457, T458, T465, lessc19_in_gg(T464, T457))
U37_GGA(T464, T457, T458, T465, lessc19_out_gg(T464, T457)) → DELETE1_IN_GGA(T464, T458, T465)
DELETE1_IN_GGA(0, tree(s(T506), T498, void), tree(s(T506), T507, void)) → DELETE1_IN_GGA(0, T498, T507)
DELETE1_IN_GGA(T673, tree(T665, T666, T676), tree(T665, T674, T676)) → U49_GGA(T673, T665, T666, T676, T674, lessc19_in_gg(T673, T665))
U49_GGA(T673, T665, T666, T676, T674, lessc19_out_gg(T673, T665)) → DELETE1_IN_GGA(T673, T666, T674)
DELETE1_IN_GGA(s(T524), tree(s(T519), T498, void), tree(s(T519), T525, void)) → U42_GGA(T524, T519, T498, T525, lessc19_in_gg(T524, T519))
U42_GGA(T524, T519, T498, T525, lessc19_out_gg(T524, T519)) → DELETE1_IN_GGA(s(T524), T498, T525)
DELETE1_IN_GGA(T707, tree(T699, T710, T701), tree(T699, T710, T708)) → U52_GGA(T707, T699, T710, T701, T708, lessc31_in_gg(T699, T707))
U52_GGA(T707, T699, T710, T701, T708, lessc31_out_gg(T699, T707)) → DELETE1_IN_GGA(T707, T701, T708)
DELETE1_IN_GGA(0, tree(s(T738), T729, T730), tree(s(T738), T739, T730)) → DELETE1_IN_GGA(0, T729, T739)
DELETE1_IN_GGA(T788, tree(T780, T791, T782), tree(T780, T791, T789)) → U59_GGA(T788, T780, T791, T782, T789, lessc31_in_gg(T780, T788))
U59_GGA(T788, T780, T791, T782, T789, lessc31_out_gg(T780, T788)) → DELETE1_IN_GGA(T788, T782, T789)
DELETE1_IN_GGA(s(T756), tree(s(T751), T729, T759), tree(s(T751), T757, T759)) → U56_GGA(T756, T751, T729, T759, T757, lessc19_in_gg(T756, T751))
U56_GGA(T756, T751, T729, T759, T757, lessc19_out_gg(T756, T751)) → DELETE1_IN_GGA(s(T756), T729, T757)
DELETE1_IN_GGA(s(T826), tree(0, T815, T816), tree(0, T815, T825)) → DELETE1_IN_GGA(s(T826), T816, T825)
DELETE1_IN_GGA(s(T841), tree(s(T835), T844, T816), tree(s(T835), T844, T842)) → U63_GGA(T841, T835, T844, T816, T842, lessc31_in_gg(T835, T841))
U63_GGA(T841, T835, T844, T816, T842, lessc31_out_gg(T835, T841)) → DELETE1_IN_GGA(s(T841), T816, T842)

The TRS R consists of the following rules:

lessc31_in_gg(0, s(T83)) → lessc31_out_gg(0, s(T83))
lessc31_in_gg(s(T88), s(T90)) → U105_gg(T88, T90, lessc31_in_gg(T88, T90))
lessc19_in_gg(0, s(T45)) → lessc19_out_gg(0, s(T45))
lessc19_in_gg(s(T52), s(T51)) → U104_gg(T52, T51, lessc19_in_gg(T52, T51))
U105_gg(T88, T90, lessc31_out_gg(T88, T90)) → lessc31_out_gg(s(T88), s(T90))
U104_gg(T52, T51, lessc19_out_gg(T52, T51)) → lessc19_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)
lessc19_in_gg(x1, x2) = lessc19_in_gg(x1, x2)
0 = 0
lessc19_out_gg(x1, x2) = lessc19_out_gg(x1, x2)
U104_gg(x1, x2, x3) = U104_gg(x1, x2, x3)
lessc31_in_gg(x1, x2) = lessc31_in_gg(x1, x2)
lessc31_out_gg(x1, x2) = lessc31_out_gg(x1, x2)
U105_gg(x1, x2, x3) = U105_gg(x1, x2, x3)
DELETE1_IN_GGA(x1, x2, x3) = DELETE1_IN_GGA(x1, x2)
P93_IN_GGGA(x1, x2, x3, x4) = P93_IN_GGGA(x1, x2, x3)
U14_GGGA(x1, x2, x3, x4, x5) = U14_GGGA(x1, x2, x3, x5)
U34_GGA(x1, x2, x3, x4, x5) = U34_GGA(x1, x2, x3, x5)
U37_GGA(x1, x2, x3, x4, x5) = U37_GGA(x1, x2, x3, x5)
U42_GGA(x1, x2, x3, x4, x5) = U42_GGA(x1, x2, x3, x5)
U49_GGA(x1, x2, x3, x4, x5, x6) = U49_GGA(x1, x2, x3, x4, x6)
U52_GGA(x1, x2, x3, x4, x5, x6) = U52_GGA(x1, x2, x3, x4, x6)
U56_GGA(x1, x2, x3, x4, x5, x6) = U56_GGA(x1, x2, x3, x4, x6)
U59_GGA(x1, x2, x3, x4, x5, x6) = U59_GGA(x1, x2, x3, x4, x6)
U63_GGA(x1, x2, x3, x4, x5, x6) = U63_GGA(x1, x2, x3, x4, x6)

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

(38) PiDPToQDPProof (SOUND transformation)

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

(39) Obligation:

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

DELETE1_IN_GGA(T321, tree(T318, void, T319)) → P93_IN_GGGA(T318, T321, T319)
P93_IN_GGGA(T318, T325, T319) → U14_GGGA(T318, T325, T319, lessc31_in_gg(T318, T325))
U14_GGGA(T318, T325, T319, lessc31_out_gg(T318, T325)) → DELETE1_IN_GGA(T325, T319)
DELETE1_IN_GGA(s(T399), tree(0, void, T389)) → DELETE1_IN_GGA(s(T399), T389)
DELETE1_IN_GGA(s(T414), tree(s(T408), void, T389)) → U34_GGA(T414, T408, T389, lessc31_in_gg(T408, T414))
U34_GGA(T414, T408, T389, lessc31_out_gg(T408, T414)) → DELETE1_IN_GGA(s(T414), T389)
DELETE1_IN_GGA(T464, tree(T457, T458, void)) → U37_GGA(T464, T457, T458, lessc19_in_gg(T464, T457))
U37_GGA(T464, T457, T458, lessc19_out_gg(T464, T457)) → DELETE1_IN_GGA(T464, T458)
DELETE1_IN_GGA(0, tree(s(T506), T498, void)) → DELETE1_IN_GGA(0, T498)
DELETE1_IN_GGA(T673, tree(T665, T666, T676)) → U49_GGA(T673, T665, T666, T676, lessc19_in_gg(T673, T665))
U49_GGA(T673, T665, T666, T676, lessc19_out_gg(T673, T665)) → DELETE1_IN_GGA(T673, T666)
DELETE1_IN_GGA(s(T524), tree(s(T519), T498, void)) → U42_GGA(T524, T519, T498, lessc19_in_gg(T524, T519))
U42_GGA(T524, T519, T498, lessc19_out_gg(T524, T519)) → DELETE1_IN_GGA(s(T524), T498)
DELETE1_IN_GGA(T707, tree(T699, T710, T701)) → U52_GGA(T707, T699, T710, T701, lessc31_in_gg(T699, T707))
U52_GGA(T707, T699, T710, T701, lessc31_out_gg(T699, T707)) → DELETE1_IN_GGA(T707, T701)
DELETE1_IN_GGA(0, tree(s(T738), T729, T730)) → DELETE1_IN_GGA(0, T729)
DELETE1_IN_GGA(T788, tree(T780, T791, T782)) → U59_GGA(T788, T780, T791, T782, lessc31_in_gg(T780, T788))
U59_GGA(T788, T780, T791, T782, lessc31_out_gg(T780, T788)) → DELETE1_IN_GGA(T788, T782)
DELETE1_IN_GGA(s(T756), tree(s(T751), T729, T759)) → U56_GGA(T756, T751, T729, T759, lessc19_in_gg(T756, T751))
U56_GGA(T756, T751, T729, T759, lessc19_out_gg(T756, T751)) → DELETE1_IN_GGA(s(T756), T729)
DELETE1_IN_GGA(s(T826), tree(0, T815, T816)) → DELETE1_IN_GGA(s(T826), T816)
DELETE1_IN_GGA(s(T841), tree(s(T835), T844, T816)) → U63_GGA(T841, T835, T844, T816, lessc31_in_gg(T835, T841))
U63_GGA(T841, T835, T844, T816, lessc31_out_gg(T835, T841)) → DELETE1_IN_GGA(s(T841), T816)

The TRS R consists of the following rules:

lessc31_in_gg(0, s(T83)) → lessc31_out_gg(0, s(T83))
lessc31_in_gg(s(T88), s(T90)) → U105_gg(T88, T90, lessc31_in_gg(T88, T90))
lessc19_in_gg(0, s(T45)) → lessc19_out_gg(0, s(T45))
lessc19_in_gg(s(T52), s(T51)) → U104_gg(T52, T51, lessc19_in_gg(T52, T51))
U105_gg(T88, T90, lessc31_out_gg(T88, T90)) → lessc31_out_gg(s(T88), s(T90))
U104_gg(T52, T51, lessc19_out_gg(T52, T51)) → lessc19_out_gg(s(T52), s(T51))

The set Q consists of the following terms:

lessc31_in_gg(x0, x1)
lessc19_in_gg(x0, x1)
U105_gg(x0, x1, x2)
U104_gg(x0, x1, x2)

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

(40) 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:

P93_IN_GGGA(T318, T325, T319) → U14_GGGA(T318, T325, T319, lessc31_in_gg(T318, T325))
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
U14_GGGA(T318, T325, T319, lessc31_out_gg(T318, T325)) → DELETE1_IN_GGA(T325, T319)
The graph contains the following edges 2 >= 1, 4 > 1, 3 >= 2
DELETE1_IN_GGA(T321, tree(T318, void, T319)) → P93_IN_GGGA(T318, T321, T319)
The graph contains the following edges 2 > 1, 1 >= 2, 2 > 3
U34_GGA(T414, T408, T389, lessc31_out_gg(T408, T414)) → DELETE1_IN_GGA(s(T414), T389)
The graph contains the following edges 3 >= 2
DELETE1_IN_GGA(s(T414), tree(s(T408), void, T389)) → U34_GGA(T414, T408, T389, lessc31_in_gg(T408, T414))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3
U37_GGA(T464, T457, T458, lessc19_out_gg(T464, T457)) → DELETE1_IN_GGA(T464, T458)
The graph contains the following edges 1 >= 1, 4 > 1, 3 >= 2
DELETE1_IN_GGA(T464, tree(T457, T458, void)) → U37_GGA(T464, T457, T458, lessc19_in_gg(T464, T457))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
U49_GGA(T673, T665, T666, T676, lessc19_out_gg(T673, T665)) → DELETE1_IN_GGA(T673, T666)
The graph contains the following edges 1 >= 1, 5 > 1, 3 >= 2
DELETE1_IN_GGA(T673, tree(T665, T666, T676)) → U49_GGA(T673, T665, T666, T676, lessc19_in_gg(T673, T665))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4
U42_GGA(T524, T519, T498, lessc19_out_gg(T524, T519)) → DELETE1_IN_GGA(s(T524), T498)
The graph contains the following edges 3 >= 2
DELETE1_IN_GGA(s(T524), tree(s(T519), T498, void)) → U42_GGA(T524, T519, T498, lessc19_in_gg(T524, T519))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3
U52_GGA(T707, T699, T710, T701, lessc31_out_gg(T699, T707)) → DELETE1_IN_GGA(T707, T701)
The graph contains the following edges 1 >= 1, 5 > 1, 4 >= 2
U59_GGA(T788, T780, T791, T782, lessc31_out_gg(T780, T788)) → DELETE1_IN_GGA(T788, T782)
The graph contains the following edges 1 >= 1, 5 > 1, 4 >= 2
DELETE1_IN_GGA(T707, tree(T699, T710, T701)) → U52_GGA(T707, T699, T710, T701, lessc31_in_gg(T699, T707))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4
DELETE1_IN_GGA(T788, tree(T780, T791, T782)) → U59_GGA(T788, T780, T791, T782, lessc31_in_gg(T780, T788))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4
U56_GGA(T756, T751, T729, T759, lessc19_out_gg(T756, T751)) → DELETE1_IN_GGA(s(T756), T729)
The graph contains the following edges 3 >= 2
U63_GGA(T841, T835, T844, T816, lessc31_out_gg(T835, T841)) → DELETE1_IN_GGA(s(T841), T816)
The graph contains the following edges 4 >= 2
DELETE1_IN_GGA(s(T756), tree(s(T751), T729, T759)) → U56_GGA(T756, T751, T729, T759, lessc19_in_gg(T756, T751))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4
DELETE1_IN_GGA(s(T841), tree(s(T835), T844, T816)) → U63_GGA(T841, T835, T844, T816, lessc31_in_gg(T835, T841))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4
DELETE1_IN_GGA(s(T399), tree(0, void, T389)) → DELETE1_IN_GGA(s(T399), T389)
The graph contains the following edges 1 >= 1, 2 > 2
DELETE1_IN_GGA(s(T826), tree(0, T815, T816)) → DELETE1_IN_GGA(s(T826), T816)
The graph contains the following edges 1 >= 1, 2 > 2
DELETE1_IN_GGA(0, tree(s(T506), T498, void)) → DELETE1_IN_GGA(0, T498)
The graph contains the following edges 1 >= 1, 2 > 2
DELETE1_IN_GGA(0, tree(s(T738), T729, T730)) → DELETE1_IN_GGA(0, T729)
The graph contains the following edges 1 >= 1, 2 > 2

(41) YES

(42) Obligation:

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

LESS19_IN_AG(s(T52), s(T51)) → LESS19_IN_AG(T52, T51)

The TRS R consists of the following rules:

lessc19_in_ag(0, s(T45)) → lessc19_out_ag(0, s(T45))
lessc19_in_ag(s(T52), s(T51)) → U104_ag(T52, T51, lessc19_in_ag(T52, T51))
U104_ag(T52, T51, lessc19_out_ag(T52, T51)) → lessc19_out_ag(s(T52), s(T51))
lessc19_in_gg(0, s(T45)) → lessc19_out_gg(0, s(T45))
lessc19_in_gg(s(T52), s(T51)) → U104_gg(T52, T51, lessc19_in_gg(T52, T51))
U104_gg(T52, T51, lessc19_out_gg(T52, T51)) → lessc19_out_gg(s(T52), s(T51))
lessc31_in_gg(0, s(T83)) → lessc31_out_gg(0, s(T83))
lessc31_in_gg(s(T88), s(T90)) → U105_gg(T88, T90, lessc31_in_gg(T88, T90))
U105_gg(T88, T90, lessc31_out_gg(T88, T90)) → lessc31_out_gg(s(T88), s(T90))
lessc31_in_ga(0, s(T83)) → lessc31_out_ga(0, s(T83))
lessc31_in_ga(s(T88), s(T90)) → U105_ga(T88, T90, lessc31_in_ga(T88, T90))
U105_ga(T88, T90, lessc31_out_ga(T88, T90)) → lessc31_out_ga(s(T88), s(T90))

The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
lessc19_in_ag(x1, x2) = lessc19_in_ag(x2)
lessc19_out_ag(x1, x2) = lessc19_out_ag(x1, x2)
U104_ag(x1, x2, x3) = U104_ag(x2, x3)
lessc19_in_gg(x1, x2) = lessc19_in_gg(x1, x2)
0 = 0
lessc19_out_gg(x1, x2) = lessc19_out_gg(x1, x2)
U104_gg(x1, x2, x3) = U104_gg(x1, x2, x3)
lessc31_in_gg(x1, x2) = lessc31_in_gg(x1, x2)
lessc31_out_gg(x1, x2) = lessc31_out_gg(x1, x2)
U105_gg(x1, x2, x3) = U105_gg(x1, x2, x3)
lessc31_in_ga(x1, x2) = lessc31_in_ga(x1)
lessc31_out_ga(x1, x2) = lessc31_out_ga(x1)
U105_ga(x1, x2, x3) = U105_ga(x1, x3)
LESS19_IN_AG(x1, x2) = LESS19_IN_AG(x2)

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

(43) UsableRulesProof (EQUIVALENT transformation)

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

(44) Obligation:

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

LESS19_IN_AG(s(T52), s(T51)) → LESS19_IN_AG(T52, T51)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
LESS19_IN_AG(x1, x2) = LESS19_IN_AG(x2)

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

(45) PiDPToQDPProof (SOUND transformation)

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

(46) Obligation:

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

LESS19_IN_AG(s(T51)) → LESS19_IN_AG(T51)

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

(47) 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:

LESS19_IN_AG(s(T51)) → LESS19_IN_AG(T51)
The graph contains the following edges 1 > 1

(48) YES

(49) Obligation:

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

DELETE1_IN_AGA(T321, tree(T318, void, T319), tree(T318, void, T322)) → P93_IN_GAGA(T318, T321, T319, T322)
P93_IN_GAGA(T318, T325, T319, T326) → U14_GAGA(T318, T325, T319, T326, lessc31_in_ga(T318, T325))
U14_GAGA(T318, T325, T319, T326, lessc31_out_ga(T318, T325)) → DELETE1_IN_AGA(T325, T319, T326)
DELETE1_IN_AGA(s(T399), tree(0, void, T389), tree(0, void, T398)) → DELETE1_IN_AGA(s(T399), T389, T398)
DELETE1_IN_AGA(s(T414), tree(s(T408), void, T389), tree(s(T408), void, T415)) → U34_AGA(T414, T408, T389, T415, lessc31_in_ga(T408, T414))
U34_AGA(T414, T408, T389, T415, lessc31_out_ga(T408, T414)) → DELETE1_IN_AGA(s(T414), T389, T415)
DELETE1_IN_AGA(T707, tree(T699, T710, T701), tree(T699, T710, T708)) → U52_AGA(T707, T699, T710, T701, T708, lessc31_in_ga(T699, T707))
U52_AGA(T707, T699, T710, T701, T708, lessc31_out_ga(T699, T707)) → DELETE1_IN_AGA(T707, T701, T708)
DELETE1_IN_AGA(T788, tree(T780, T791, T782), tree(T780, T791, T789)) → U59_AGA(T788, T780, T791, T782, T789, lessc31_in_ga(T780, T788))
U59_AGA(T788, T780, T791, T782, T789, lessc31_out_ga(T780, T788)) → DELETE1_IN_AGA(T788, T782, T789)
DELETE1_IN_AGA(s(T826), tree(0, T815, T816), tree(0, T815, T825)) → DELETE1_IN_AGA(s(T826), T816, T825)
DELETE1_IN_AGA(s(T841), tree(s(T835), T844, T816), tree(s(T835), T844, T842)) → U63_AGA(T841, T835, T844, T816, T842, lessc31_in_ga(T835, T841))
U63_AGA(T841, T835, T844, T816, T842, lessc31_out_ga(T835, T841)) → DELETE1_IN_AGA(s(T841), T816, T842)

The TRS R consists of the following rules:

lessc19_in_ag(0, s(T45)) → lessc19_out_ag(0, s(T45))
lessc19_in_ag(s(T52), s(T51)) → U104_ag(T52, T51, lessc19_in_ag(T52, T51))
U104_ag(T52, T51, lessc19_out_ag(T52, T51)) → lessc19_out_ag(s(T52), s(T51))
lessc19_in_gg(0, s(T45)) → lessc19_out_gg(0, s(T45))
lessc19_in_gg(s(T52), s(T51)) → U104_gg(T52, T51, lessc19_in_gg(T52, T51))
U104_gg(T52, T51, lessc19_out_gg(T52, T51)) → lessc19_out_gg(s(T52), s(T51))
lessc31_in_gg(0, s(T83)) → lessc31_out_gg(0, s(T83))
lessc31_in_gg(s(T88), s(T90)) → U105_gg(T88, T90, lessc31_in_gg(T88, T90))
U105_gg(T88, T90, lessc31_out_gg(T88, T90)) → lessc31_out_gg(s(T88), s(T90))
lessc31_in_ga(0, s(T83)) → lessc31_out_ga(0, s(T83))
lessc31_in_ga(s(T88), s(T90)) → U105_ga(T88, T90, lessc31_in_ga(T88, T90))
U105_ga(T88, T90, lessc31_out_ga(T88, T90)) → lessc31_out_ga(s(T88), s(T90))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
void = void
s(x1) = s(x1)
lessc19_in_ag(x1, x2) = lessc19_in_ag(x2)
lessc19_out_ag(x1, x2) = lessc19_out_ag(x1, x2)
U104_ag(x1, x2, x3) = U104_ag(x2, x3)
lessc19_in_gg(x1, x2) = lessc19_in_gg(x1, x2)
0 = 0
lessc19_out_gg(x1, x2) = lessc19_out_gg(x1, x2)
U104_gg(x1, x2, x3) = U104_gg(x1, x2, x3)
lessc31_in_gg(x1, x2) = lessc31_in_gg(x1, x2)
lessc31_out_gg(x1, x2) = lessc31_out_gg(x1, x2)
U105_gg(x1, x2, x3) = U105_gg(x1, x2, x3)
lessc31_in_ga(x1, x2) = lessc31_in_ga(x1)
lessc31_out_ga(x1, x2) = lessc31_out_ga(x1)
U105_ga(x1, x2, x3) = U105_ga(x1, x3)
DELETE1_IN_AGA(x1, x2, x3) = DELETE1_IN_AGA(x2)
P93_IN_GAGA(x1, x2, x3, x4) = P93_IN_GAGA(x1, x3)
U14_GAGA(x1, x2, x3, x4, x5) = U14_GAGA(x1, x3, x5)
U34_AGA(x1, x2, x3, x4, x5) = U34_AGA(x2, x3, x5)
U52_AGA(x1, x2, x3, x4, x5, x6) = U52_AGA(x2, x3, x4, x6)
U59_AGA(x1, x2, x3, x4, x5, x6) = U59_AGA(x2, x3, x4, x6)
U63_AGA(x1, x2, x3, x4, x5, x6) = U63_AGA(x2, x3, x4, x6)

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

(50) UsableRulesProof (EQUIVALENT transformation)

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

(51) Obligation:

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

DELETE1_IN_AGA(T321, tree(T318, void, T319), tree(T318, void, T322)) → P93_IN_GAGA(T318, T321, T319, T322)
P93_IN_GAGA(T318, T325, T319, T326) → U14_GAGA(T318, T325, T319, T326, lessc31_in_ga(T318, T325))
U14_GAGA(T318, T325, T319, T326, lessc31_out_ga(T318, T325)) → DELETE1_IN_AGA(T325, T319, T326)
DELETE1_IN_AGA(s(T399), tree(0, void, T389), tree(0, void, T398)) → DELETE1_IN_AGA(s(T399), T389, T398)
DELETE1_IN_AGA(s(T414), tree(s(T408), void, T389), tree(s(T408), void, T415)) → U34_AGA(T414, T408, T389, T415, lessc31_in_ga(T408, T414))
U34_AGA(T414, T408, T389, T415, lessc31_out_ga(T408, T414)) → DELETE1_IN_AGA(s(T414), T389, T415)
DELETE1_IN_AGA(T707, tree(T699, T710, T701), tree(T699, T710, T708)) → U52_AGA(T707, T699, T710, T701, T708, lessc31_in_ga(T699, T707))
U52_AGA(T707, T699, T710, T701, T708, lessc31_out_ga(T699, T707)) → DELETE1_IN_AGA(T707, T701, T708)
DELETE1_IN_AGA(T788, tree(T780, T791, T782), tree(T780, T791, T789)) → U59_AGA(T788, T780, T791, T782, T789, lessc31_in_ga(T780, T788))
U59_AGA(T788, T780, T791, T782, T789, lessc31_out_ga(T780, T788)) → DELETE1_IN_AGA(T788, T782, T789)
DELETE1_IN_AGA(s(T826), tree(0, T815, T816), tree(0, T815, T825)) → DELETE1_IN_AGA(s(T826), T816, T825)
DELETE1_IN_AGA(s(T841), tree(s(T835), T844, T816), tree(s(T835), T844, T842)) → U63_AGA(T841, T835, T844, T816, T842, lessc31_in_ga(T835, T841))
U63_AGA(T841, T835, T844, T816, T842, lessc31_out_ga(T835, T841)) → DELETE1_IN_AGA(s(T841), T816, T842)

The TRS R consists of the following rules:

lessc31_in_ga(0, s(T83)) → lessc31_out_ga(0, s(T83))
lessc31_in_ga(s(T88), s(T90)) → U105_ga(T88, T90, lessc31_in_ga(T88, T90))
U105_ga(T88, T90, lessc31_out_ga(T88, T90)) → lessc31_out_ga(s(T88), s(T90))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
void = void
s(x1) = s(x1)
0 = 0
lessc31_in_ga(x1, x2) = lessc31_in_ga(x1)
lessc31_out_ga(x1, x2) = lessc31_out_ga(x1)
U105_ga(x1, x2, x3) = U105_ga(x1, x3)
DELETE1_IN_AGA(x1, x2, x3) = DELETE1_IN_AGA(x2)
P93_IN_GAGA(x1, x2, x3, x4) = P93_IN_GAGA(x1, x3)
U14_GAGA(x1, x2, x3, x4, x5) = U14_GAGA(x1, x3, x5)
U34_AGA(x1, x2, x3, x4, x5) = U34_AGA(x2, x3, x5)
U52_AGA(x1, x2, x3, x4, x5, x6) = U52_AGA(x2, x3, x4, x6)
U59_AGA(x1, x2, x3, x4, x5, x6) = U59_AGA(x2, x3, x4, x6)
U63_AGA(x1, x2, x3, x4, x5, x6) = U63_AGA(x2, x3, x4, x6)

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

(52) PiDPToQDPProof (SOUND transformation)

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

(53) Obligation:

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

DELETE1_IN_AGA(tree(T318, void, T319)) → P93_IN_GAGA(T318, T319)
P93_IN_GAGA(T318, T319) → U14_GAGA(T318, T319, lessc31_in_ga(T318))
U14_GAGA(T318, T319, lessc31_out_ga(T318)) → DELETE1_IN_AGA(T319)
DELETE1_IN_AGA(tree(0, void, T389)) → DELETE1_IN_AGA(T389)
DELETE1_IN_AGA(tree(s(T408), void, T389)) → U34_AGA(T408, T389, lessc31_in_ga(T408))
U34_AGA(T408, T389, lessc31_out_ga(T408)) → DELETE1_IN_AGA(T389)
DELETE1_IN_AGA(tree(T699, T710, T701)) → U52_AGA(T699, T710, T701, lessc31_in_ga(T699))
U52_AGA(T699, T710, T701, lessc31_out_ga(T699)) → DELETE1_IN_AGA(T701)
DELETE1_IN_AGA(tree(T780, T791, T782)) → U59_AGA(T780, T791, T782, lessc31_in_ga(T780))
U59_AGA(T780, T791, T782, lessc31_out_ga(T780)) → DELETE1_IN_AGA(T782)
DELETE1_IN_AGA(tree(0, T815, T816)) → DELETE1_IN_AGA(T816)
DELETE1_IN_AGA(tree(s(T835), T844, T816)) → U63_AGA(T835, T844, T816, lessc31_in_ga(T835))
U63_AGA(T835, T844, T816, lessc31_out_ga(T835)) → DELETE1_IN_AGA(T816)

The TRS R consists of the following rules:

lessc31_in_ga(0) → lessc31_out_ga(0)
lessc31_in_ga(s(T88)) → U105_ga(T88, lessc31_in_ga(T88))
U105_ga(T88, lessc31_out_ga(T88)) → lessc31_out_ga(s(T88))

The set Q consists of the following terms:

lessc31_in_ga(x0)
U105_ga(x0, x1)

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

(54) 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:

P93_IN_GAGA(T318, T319) → U14_GAGA(T318, T319, lessc31_in_ga(T318))
The graph contains the following edges 1 >= 1, 2 >= 2
U14_GAGA(T318, T319, lessc31_out_ga(T318)) → DELETE1_IN_AGA(T319)
The graph contains the following edges 2 >= 1
DELETE1_IN_AGA(tree(T318, void, T319)) → P93_IN_GAGA(T318, T319)
The graph contains the following edges 1 > 1, 1 > 2
U34_AGA(T408, T389, lessc31_out_ga(T408)) → DELETE1_IN_AGA(T389)
The graph contains the following edges 2 >= 1
DELETE1_IN_AGA(tree(s(T408), void, T389)) → U34_AGA(T408, T389, lessc31_in_ga(T408))
The graph contains the following edges 1 > 1, 1 > 2
U52_AGA(T699, T710, T701, lessc31_out_ga(T699)) → DELETE1_IN_AGA(T701)
The graph contains the following edges 3 >= 1
DELETE1_IN_AGA(tree(T699, T710, T701)) → U52_AGA(T699, T710, T701, lessc31_in_ga(T699))
The graph contains the following edges 1 > 1, 1 > 2, 1 > 3
U59_AGA(T780, T791, T782, lessc31_out_ga(T780)) → DELETE1_IN_AGA(T782)
The graph contains the following edges 3 >= 1
U63_AGA(T835, T844, T816, lessc31_out_ga(T835)) → DELETE1_IN_AGA(T816)
The graph contains the following edges 3 >= 1
DELETE1_IN_AGA(tree(T780, T791, T782)) → U59_AGA(T780, T791, T782, lessc31_in_ga(T780))
The graph contains the following edges 1 > 1, 1 > 2, 1 > 3
DELETE1_IN_AGA(tree(s(T835), T844, T816)) → U63_AGA(T835, T844, T816, lessc31_in_ga(T835))
The graph contains the following edges 1 > 1, 1 > 2, 1 > 3
DELETE1_IN_AGA(tree(0, void, T389)) → DELETE1_IN_AGA(T389)
The graph contains the following edges 1 > 1
DELETE1_IN_AGA(tree(0, T815, T816)) → DELETE1_IN_AGA(T816)
The graph contains the following edges 1 > 1

(0) Obligation:

(1) PrologToDTProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) TriplesToPiDPProof (SOUND transformation)

(4) Obligation:

(5) DependencyGraphProof (EQUIVALENT transformation)

(6) Complex Obligation (AND)

(7) Obligation:

(8) UsableRulesProof (EQUIVALENT transformation)

(9) Obligation:

(10) PiDPToQDPProof (SOUND transformation)

(11) Obligation:

(12) QDPSizeChangeProof (EQUIVALENT transformation)

(13) YES

(14) Obligation:

(15) UsableRulesProof (EQUIVALENT transformation)

(16) Obligation:

(17) PiDPToQDPProof (SOUND transformation)

(18) Obligation:

(19) QDPSizeChangeProof (EQUIVALENT transformation)

(20) YES

(21) Obligation:

(22) UsableRulesProof (EQUIVALENT transformation)

(23) Obligation:

(24) PiDPToQDPProof (EQUIVALENT transformation)

(25) Obligation:

(26) QDPSizeChangeProof (EQUIVALENT transformation)

(27) YES

(28) Obligation:

(29) UsableRulesProof (EQUIVALENT transformation)

(30) Obligation:

(31) PiDPToQDPProof (EQUIVALENT transformation)

(32) Obligation:

(33) QDPSizeChangeProof (EQUIVALENT transformation)

(34) YES

(35) Obligation:

(36) UsableRulesProof (EQUIVALENT transformation)

(37) Obligation:

(38) PiDPToQDPProof (SOUND transformation)

(39) Obligation:

(40) QDPSizeChangeProof (EQUIVALENT transformation)

(41) YES

(42) Obligation:

(43) UsableRulesProof (EQUIVALENT transformation)

(44) Obligation:

(45) PiDPToQDPProof (SOUND transformation)

(46) Obligation:

(47) QDPSizeChangeProof (EQUIVALENT transformation)

(48) YES

(49) Obligation:

(50) UsableRulesProof (EQUIVALENT transformation)

(51) Obligation:

(52) PiDPToQDPProof (SOUND transformation)

(53) Obligation:

(54) QDPSizeChangeProof (EQUIVALENT transformation)

(55) YES