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

(0) Obligation:

Clauses:

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

Query: delete(a,g,a)

(1) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph DT10.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="B: delete(T1, T2, T3)\n\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 0 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: true | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 1 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT2 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 1 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: true | delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\nT7 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: delmin(void, T16, T17) | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT9 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T9, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: delmin(void, T16, T17), SCOPE: 2, CLAUSE: 5 | delmin(void, T16, T17), SCOPE: 2, CLAUSE: 6 | ?_2 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: delmin(void, T16, T17), SCOPE: 2, CLAUSE: 6 | ?_2 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ?_2 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 3\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: delete(T1, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="C: ','(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="A: less(T33, T31)\n\nT31 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="E: 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: delete(T37, void, T38), SCOPE: 4, CLAUSE: 0 | delete(T37, void, T38), SCOPE: 4, CLAUSE: 1 | delete(T37, void, T38), SCOPE: 4, CLAUSE: 2 | delete(T37, void, T38), SCOPE: 4, CLAUSE: 3 | delete(T37, void, T38), SCOPE: 4, CLAUSE: 4\n\nT37 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: delete(T37, void, T38), SCOPE: 4, CLAUSE: 1 | delete(T37, void, T38), SCOPE: 4, CLAUSE: 2 | delete(T37, void, T38), SCOPE: 4, CLAUSE: 3 | delete(T37, void, T38), SCOPE: 4, CLAUSE: 4\n\nT37 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: delete(T37, void, T38), SCOPE: 4, CLAUSE: 2 | delete(T37, void, T38), SCOPE: 4, CLAUSE: 3 | delete(T37, void, T38), SCOPE: 4, CLAUSE: 4\n\nT37 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: delete(T37, void, T38), SCOPE: 4, CLAUSE: 3 | delete(T37, void, T38), SCOPE: 4, CLAUSE: 4\n\nT37 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: delete(T37, void, T38), SCOPE: 4, CLAUSE: 4\n\nT37 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="D: ','(less(T69, T71), delete(T71, void, T72))\n\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="F: less(T69, T71)\n\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: delete(T75, void, T76)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: less(T69, T71), SCOPE: 5, CLAUSE: 7 | less(T69, T71), SCOPE: 5, CLAUSE: 8\n\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: less(T69, T71), SCOPE: 5, CLAUSE: 7\n\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: less(T69, T71), SCOPE: 5, CLAUSE: 8\n\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: less(T88, T90)\n\nT88 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: ','(less(T101, T99), delete(T101, void, T102)) | delete(T1, tree(T99, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT99 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T99, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: delete(T1, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT9 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX136 is free\nX137 is free\nX138 is free\nX139 is free\nX140 is free\ndelete(T1, tree(T9, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, tree(T9, void, void), T3) !=? delete(X136, tree(X137, X138, X139), tree(X137, X140, X139))", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: ','(less(T101, T99), delete(T101, void, T102)), SCOPE: 6, CLAUSE: 7 | ','(less(T101, T99), delete(T101, void, T102)), SCOPE: 6, CLAUSE: 8 | ?_6 | delete(T1, tree(T99, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT99 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T99, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(less(T101, T99), delete(T101, void, T102)), SCOPE: 6, CLAUSE: 7\n\nT99 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T99, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: ','(less(T101, T99), delete(T101, void, T102)), SCOPE: 6, CLAUSE: 8 | ?_6 | delete(T1, tree(T99, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT99 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T99, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: delete(0, void, T108)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: ','(less(T101, T99), delete(T101, void, T102)), SCOPE: 6, CLAUSE: 8\n\nT99 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T99, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: ?_6 | delete(T1, tree(T99, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT99 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T99, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: ','(less(T119, T118), delete(s(T119), void, T120))\n\nT118 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(s(T118), void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: less(T119, T118)\n\nT118 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(s(T118), void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: delete(s(T123), void, T124)\n\nT123 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: delete(T1, tree(T99, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT99 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T99, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(less(T138, T140), delete(T140, void, T141))\n\nT138 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, tree(T138, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: ','(less(T148, T150), delete(T150, void, T151))\n\nT148 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX136 is free\nX137 is free\nX138 is free\nX139 is free\nX140 is free\ndelete(T1, tree(T148, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, tree(T148, void, void), T3) !=? delete(X136, tree(X137, X138, X139), tree(X137, X140, X139))", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: ','(less(T148, T150), delete(T150, void, T151)), SCOPE: 7, CLAUSE: 7 | ','(less(T148, T150), delete(T150, void, T151)), SCOPE: 7, CLAUSE: 8\n\nT148 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX136 is free\nX137 is free\nX138 is free\nX139 is free\nX140 is free\ndelete(T1, tree(T148, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, tree(T148, void, void), T3) !=? delete(X136, tree(X137, X138, X139), tree(X137, X140, X139))", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: ','(less(T148, T150), delete(T150, void, T151)), SCOPE: 7, CLAUSE: 7\n\nT148 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX136 is free\nX137 is free\nX138 is free\nX139 is free\nX140 is free\ndelete(T1, tree(T148, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, tree(T148, void, void), T3) !=? delete(X136, tree(X137, X138, X139), tree(X137, X140, X139))", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: ','(less(T148, T150), delete(T150, void, T151)), SCOPE: 7, CLAUSE: 8\n\nT148 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX136 is free\nX137 is free\nX138 is free\nX139 is free\nX140 is free\ndelete(T1, tree(T148, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, tree(T148, void, void), T3) !=? delete(X136, tree(X137, X138, X139), tree(X137, X140, X139))", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: delete(s(T158), void, T157)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: ','(less(T165, T167), delete(s(T167), void, T168))\n\nT165 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX136 is free\nX137 is free\nX138 is free\nX139 is free\nX140 is free\ndelete(T1, tree(s(T165), void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, tree(s(T165), void, void), T3) !=? delete(X136, tree(X137, X138, X139), tree(X137, X140, X139))", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: less(T165, T167)\n\nT165 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX136 is free\nX137 is free\nX138 is free\nX139 is free\nX140 is free\ndelete(T1, tree(s(T165), void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, tree(s(T165), void, void), T3) !=? delete(X136, tree(X137, X138, X139), tree(X137, X140, X139))", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: delete(s(T171), void, T172)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: delmin(T184, T187, T188) | delete(T1, tree(T183, void, T184), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T183, void, T184), T3), SCOPE: 1, CLAUSE: 4\n\nT183 is ground\nT184 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T183, void, T184), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\nT7 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: delmin(T184, T187, T188), SCOPE: 8, CLAUSE: 5 | delmin(T184, T187, T188), SCOPE: 8, CLAUSE: 6 | ?_8 | delete(T1, tree(T183, void, T184), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T183, void, T184), T3), SCOPE: 1, CLAUSE: 4\n\nT183 is ground\nT184 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T183, void, T184), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: delmin(T184, T187, T188), SCOPE: 8, CLAUSE: 5\n\nT183 is ground\nT184 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T183, void, T184), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: delmin(T184, T187, T188), SCOPE: 8, CLAUSE: 6 | ?_8 | delete(T1, tree(T183, void, T184), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T183, void, T184), T3), SCOPE: 1, CLAUSE: 4\n\nT183 is ground\nT184 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T183, void, T184), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: delmin(T184, T187, T188), SCOPE: 8, CLAUSE: 6\n\nT183 is ground\nT184 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T183, void, T184), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: ?_8 | delete(T1, tree(T183, void, T184), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T183, void, T184), T3), SCOPE: 1, CLAUSE: 4\n\nT183 is ground\nT184 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T183, void, T184), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="G: delmin(T224, T229, T230)\n\nT224 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: delmin(T224, T229, T230), SCOPE: 9, CLAUSE: 5 | delmin(T224, T229, T230), SCOPE: 9, CLAUSE: 6\n\nT224 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: delmin(T224, T229, T230), SCOPE: 9, CLAUSE: 5\n\nT224 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: delmin(T224, T229, T230), SCOPE: 9, CLAUSE: 6\n\nT224 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: delmin(T258, T263, T264)\n\nT258 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: delete(T1, tree(T183, void, T184), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T183, void, T184), T3), SCOPE: 1, CLAUSE: 4\n\nT183 is ground\nT184 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T183, void, T184), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: delete(T1, tree(T183, void, T184), T3), SCOPE: 1, CLAUSE: 3\n\nT183 is ground\nT184 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T183, void, T184), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: delete(T1, tree(T183, void, T184), T3), SCOPE: 1, CLAUSE: 4\n\nT183 is ground\nT184 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T183, void, T184), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: ','(less(T289, T286), delete(T289, void, T290))\n\nT286 is ground\nT287 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T286, void, T287), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="H: ','(less(T302, T305), delete(T305, T303, T306))\n\nT302 is ground\nT303 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T302, void, T303), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: less(T302, T305)\n\nT302 is ground\nT303 is ground\nX10 is free\nX11 is free\ndelete(T1, tree(T302, void, T303), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: delete(T309, T303, T310)\n\nT302 is ground\nT303 is ground\nX10 is free\nX11 is free\ndelete(T311, tree(T302, void, T303), T312) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: ','(less(T327, T324), delete(T327, void, T328)) | delete(T1, tree(T324, void, T325), T3), SCOPE: 1, CLAUSE: 4\n\nT324 is ground\nT325 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\ndelete(T1, tree(T324, void, T325), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T324, void, T325), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: delete(T1, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\nT7 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\nX359 is free\nX360 is free\nX361 is free\nX362 is free\nX363 is free\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))\ndelete(T1, tree(T6, void, T7), T3) !=? delete(X359, tree(X360, X361, X362), tree(X360, X363, X362))", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: ','(less(T327, T324), delete(T327, void, T328)), SCOPE: 10, CLAUSE: 7 | ','(less(T327, T324), delete(T327, void, T328)), SCOPE: 10, CLAUSE: 8 | ?_10 | delete(T1, tree(T324, void, T325), T3), SCOPE: 1, CLAUSE: 4\n\nT324 is ground\nT325 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\ndelete(T1, tree(T324, void, T325), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T324, void, T325), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: ','(less(T327, T324), delete(T327, void, T328)), SCOPE: 10, CLAUSE: 7\n\nT324 is ground\nT325 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\ndelete(T1, tree(T324, void, T325), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T324, void, T325), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: ','(less(T327, T324), delete(T327, void, T328)), SCOPE: 10, CLAUSE: 8 | ?_10 | delete(T1, tree(T324, void, T325), T3), SCOPE: 1, CLAUSE: 4\n\nT324 is ground\nT325 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\ndelete(T1, tree(T324, void, T325), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T324, void, T325), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: delete(0, void, T334)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: ','(less(T327, T324), delete(T327, void, T328)), SCOPE: 10, CLAUSE: 8\n\nT324 is ground\nT325 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\ndelete(T1, tree(T324, void, T325), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T324, void, T325), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ?_10 | delete(T1, tree(T324, void, T325), T3), SCOPE: 1, CLAUSE: 4\n\nT324 is ground\nT325 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\ndelete(T1, tree(T324, void, T325), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T324, void, T325), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: ','(less(T345, T344), delete(s(T345), void, T346))\n\nT325 is ground\nT344 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\ndelete(T1, tree(s(T344), void, T325), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(s(T344), void, T325), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: less(T345, T344)\n\nT325 is ground\nT344 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\ndelete(T1, tree(s(T344), void, T325), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(s(T344), void, T325), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: delete(s(T349), void, T350)\n\nT349 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: delete(T1, tree(T324, void, T325), T3), SCOPE: 1, CLAUSE: 4\n\nT324 is ground\nT325 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\ndelete(T1, tree(T324, void, T325), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T324, void, T325), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: ','(less(T366, T369), delete(T369, T367, T370))\n\nT366 is ground\nT367 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\ndelete(T1, tree(T366, void, T367), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T366, void, T367), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: ','(less(T378, T381), delete(T381, T379, T382))\n\nT378 is ground\nT379 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\nX359 is free\nX360 is free\nX361 is free\nX362 is free\nX363 is free\ndelete(T1, tree(T378, void, T379), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T378, void, T379), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))\ndelete(T1, tree(T378, void, T379), T3) !=? delete(X359, tree(X360, X361, X362), tree(X360, X363, X362))", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: ','(less(T378, T381), delete(T381, T379, T382)), SCOPE: 11, CLAUSE: 7 | ','(less(T378, T381), delete(T381, T379, T382)), SCOPE: 11, CLAUSE: 8\n\nT378 is ground\nT379 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\nX359 is free\nX360 is free\nX361 is free\nX362 is free\nX363 is free\ndelete(T1, tree(T378, void, T379), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T378, void, T379), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))\ndelete(T1, tree(T378, void, T379), T3) !=? delete(X359, tree(X360, X361, X362), tree(X360, X363, X362))", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: ','(less(T378, T381), delete(T381, T379, T382)), SCOPE: 11, CLAUSE: 7\n\nT378 is ground\nT379 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\nX359 is free\nX360 is free\nX361 is free\nX362 is free\nX363 is free\ndelete(T1, tree(T378, void, T379), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T378, void, T379), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))\ndelete(T1, tree(T378, void, T379), T3) !=? delete(X359, tree(X360, X361, X362), tree(X360, X363, X362))", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: ','(less(T378, T381), delete(T381, T379, T382)), SCOPE: 11, CLAUSE: 8\n\nT378 is ground\nT379 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\nX359 is free\nX360 is free\nX361 is free\nX362 is free\nX363 is free\ndelete(T1, tree(T378, void, T379), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(T378, void, T379), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))\ndelete(T1, tree(T378, void, T379), T3) !=? delete(X359, tree(X360, X361, X362), tree(X360, X363, X362))", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: delete(s(T389), T379, T388)\n\nT379 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\nX359 is free\nX360 is free\nX361 is free\nX362 is free\nX363 is free\ndelete(T1, tree(0, void, T379), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(0, void, T379), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))\ndelete(T1, tree(0, void, T379), T3) !=? delete(X359, tree(X360, X361, X362), tree(X360, X363, X362))", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: ','(less(T398, T400), delete(s(T400), T379, T401))\n\nT379 is ground\nT398 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\nX359 is free\nX360 is free\nX361 is free\nX362 is free\nX363 is free\ndelete(T1, tree(s(T398), void, T379), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(s(T398), void, T379), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))\ndelete(T1, tree(s(T398), void, T379), T3) !=? delete(X359, tree(X360, X361, X362), tree(X360, X363, X362))", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: less(T398, T400)\n\nT379 is ground\nT398 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\nX359 is free\nX360 is free\nX361 is free\nX362 is free\nX363 is free\ndelete(T1, tree(s(T398), void, T379), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, tree(s(T398), void, T379), T3) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))\ndelete(T1, tree(s(T398), void, T379), T3) !=? delete(X359, tree(X360, X361, X362), tree(X360, X363, X362))", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: delete(s(T404), T379, T405)\n\nT379 is ground\nT398 is ground\nX10 is free\nX11 is free\nX223 is free\nX224 is free\nX225 is free\nX226 is free\nX227 is free\nX359 is free\nX360 is free\nX361 is free\nX362 is free\nX363 is free\ndelete(T406, tree(s(T398), void, T379), T407) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T406, tree(s(T398), void, T379), T407) !=? delete(X223, tree(X223, X224, X225), tree(X226, X224, X227))\ndelete(T406, tree(s(T398), void, T379), T407) !=? delete(X359, tree(X360, X361, X362), tree(X360, X363, X362))", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: true | delete(T1, tree(T416, T417, void), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T416, T417, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T416, T417, void), T3), SCOPE: 1, CLAUSE: 4\n\nT416 is ground\nT417 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T416, T417, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT2 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: delete(T1, tree(T416, T417, void), T3), SCOPE: 1, CLAUSE: 2 | delete(T1, tree(T416, T417, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T416, T417, void), T3), SCOPE: 1, CLAUSE: 4\n\nT416 is ground\nT417 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T416, T417, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: delmin(void, T426, T427) | delete(T1, tree(T422, T423, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T422, T423, void), T3), SCOPE: 1, CLAUSE: 4\n\nT422 is ground\nT423 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T422, T423, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: delete(T1, tree(T416, T417, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T416, T417, void), T3), SCOPE: 1, CLAUSE: 4\n\nT416 is ground\nT417 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\ndelete(T1, tree(T416, T417, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T416, T417, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: delmin(void, T426, T427), SCOPE: 12, CLAUSE: 5 | delmin(void, T426, T427), SCOPE: 12, CLAUSE: 6 | ?_12 | delete(T1, tree(T422, T423, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T422, T423, void), T3), SCOPE: 1, CLAUSE: 4\n\nT422 is ground\nT423 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T422, T423, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: delmin(void, T426, T427), SCOPE: 12, CLAUSE: 6 | ?_12 | delete(T1, tree(T422, T423, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T422, T423, void), T3), SCOPE: 1, CLAUSE: 4\n\nT422 is ground\nT423 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T422, T423, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: ?_12 | delete(T1, tree(T422, T423, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T422, T423, void), T3), SCOPE: 1, CLAUSE: 4\n\nT422 is ground\nT423 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T422, T423, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: delete(T1, tree(T422, T423, void), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T422, T423, void), T3), SCOPE: 1, CLAUSE: 4\n\nT422 is ground\nT423 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T422, T423, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: delete(T1, tree(T422, T423, void), T3), SCOPE: 1, CLAUSE: 3\n\nT422 is ground\nT423 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T422, T423, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: delete(T1, tree(T422, T423, void), T3), SCOPE: 1, CLAUSE: 4\n\nT422 is ground\nT423 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T422, T423, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: ','(less(T448, T445), delete(T448, T446, T449))\n\nT445 is ground\nT446 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T445, T446, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: less(T448, T445)\n\nT445 is ground\nT446 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T445, T446, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: delete(T452, T446, T453)\n\nT445 is ground\nT446 is ground\nT452 is ground\nX6 is free\nX7 is free\ndelete(T454, tree(T445, T446, void), T455) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: delete(T452, T446, T453), SCOPE: 13, CLAUSE: 0 | delete(T452, T446, T453), SCOPE: 13, CLAUSE: 1 | delete(T452, T446, T453), SCOPE: 13, CLAUSE: 2 | delete(T452, T446, T453), SCOPE: 13, CLAUSE: 3 | delete(T452, T446, T453), SCOPE: 13, CLAUSE: 4\n\nT445 is ground\nT446 is ground\nT452 is ground\nX6 is free\nX7 is free\ndelete(T454, tree(T445, T446, void), T455) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: delete(T452, T446, T453), SCOPE: 13, CLAUSE: 0\n\nT445 is ground\nT446 is ground\nT452 is ground\nX6 is free\nX7 is free\ndelete(T454, tree(T445, T446, void), T455) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: delete(T452, T446, T453), SCOPE: 13, CLAUSE: 1 | delete(T452, T446, T453), SCOPE: 13, CLAUSE: 2 | delete(T452, T446, T453), SCOPE: 13, CLAUSE: 3 | delete(T452, T446, T453), SCOPE: 13, CLAUSE: 4\n\nT445 is ground\nT446 is ground\nT452 is ground\nX6 is free\nX7 is free\ndelete(T454, tree(T445, T446, void), T455) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: delete(T452, T446, T453), SCOPE: 13, CLAUSE: 1\n\nT445 is ground\nT446 is ground\nT452 is ground\nX6 is free\nX7 is free\ndelete(T454, tree(T445, T446, void), T455) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: delete(T452, T446, T453), SCOPE: 13, CLAUSE: 2 | delete(T452, T446, T453), SCOPE: 13, CLAUSE: 3 | delete(T452, T446, T453), SCOPE: 13, CLAUSE: 4\n\nT445 is ground\nT446 is ground\nT452 is ground\nX6 is free\nX7 is free\ndelete(T454, tree(T445, T446, void), T455) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: delete(T452, T446, T453), SCOPE: 13, CLAUSE: 2\n\nT445 is ground\nT446 is ground\nT452 is ground\nX6 is free\nX7 is free\ndelete(T454, tree(T445, T446, void), T455) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: delete(T452, T446, T453), SCOPE: 13, CLAUSE: 3 | delete(T452, T446, T453), SCOPE: 13, CLAUSE: 4\n\nT445 is ground\nT446 is ground\nT452 is ground\nX6 is free\nX7 is free\ndelete(T454, tree(T445, T446, void), T455) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: delmin(T504, T507, T508)\n\nT504 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: delete(T452, T446, T453), SCOPE: 13, CLAUSE: 3\n\nT445 is ground\nT446 is ground\nT452 is ground\nX6 is free\nX7 is free\ndelete(T454, tree(T445, T446, void), T455) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: delete(T452, T446, T453), SCOPE: 13, CLAUSE: 4\n\nT445 is ground\nT446 is ground\nT452 is ground\nX6 is free\nX7 is free\ndelete(T454, tree(T445, T446, void), T455) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="I: ','(less(T533, T534), delete(T533, T535, T538))\n\nT533 is ground\nT534 is ground\nT535 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="M: less(T533, T534)\n\nT533 is ground\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="K: delete(T533, T535, T538)\n\nT533 is ground\nT535 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: less(T533, T534), SCOPE: 14, CLAUSE: 7 | less(T533, T534), SCOPE: 14, CLAUSE: 8\n\nT533 is ground\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: less(T533, T534), SCOPE: 14, CLAUSE: 7\n\nT533 is ground\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: less(T533, T534), SCOPE: 14, CLAUSE: 8\n\nT533 is ground\nT534 is ground", 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: less(T552, T553)\n\nT552 is ground\nT553 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: delete(T533, T535, T538), SCOPE: 15, CLAUSE: 0 | delete(T533, T535, T538), SCOPE: 15, CLAUSE: 1 | delete(T533, T535, T538), SCOPE: 15, CLAUSE: 2 | delete(T533, T535, T538), SCOPE: 15, CLAUSE: 3 | delete(T533, T535, T538), SCOPE: 15, CLAUSE: 4\n\nT533 is ground\nT535 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: delete(T533, T535, T538), SCOPE: 15, CLAUSE: 0\n\nT533 is ground\nT535 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: delete(T533, T535, T538), SCOPE: 15, CLAUSE: 1 | delete(T533, T535, T538), SCOPE: 15, CLAUSE: 2 | delete(T533, T535, T538), SCOPE: 15, CLAUSE: 3 | delete(T533, T535, T538), SCOPE: 15, CLAUSE: 4\n\nT533 is ground\nT535 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: delete(T533, T535, T538), SCOPE: 15, CLAUSE: 1\n\nT533 is ground\nT535 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: delete(T533, T535, T538), SCOPE: 15, CLAUSE: 2 | delete(T533, T535, T538), SCOPE: 15, CLAUSE: 3 | delete(T533, T535, T538), SCOPE: 15, CLAUSE: 4\n\nT533 is ground\nT535 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: delete(T533, T535, T538), SCOPE: 15, CLAUSE: 2\n\nT533 is ground\nT535 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: delete(T533, T535, T538), SCOPE: 15, CLAUSE: 3 | delete(T533, T535, T538), SCOPE: 15, CLAUSE: 4\n\nT533 is ground\nT535 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: delmin(T602, T605, T606)\n\nT602 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: delete(T533, T535, T538), SCOPE: 15, CLAUSE: 3\n\nT533 is ground\nT535 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: delete(T533, T535, T538), SCOPE: 15, CLAUSE: 4\n\nT533 is ground\nT535 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: ','(less(T631, T632), delete(T631, T633, T636))\n\nT631 is ground\nT632 is ground\nT633 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="J: ','(less(T650, T649), delete(T649, T652, T654))\n\nT649 is ground\nT650 is ground\nT652 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: less(T650, T649)\n\nT649 is ground\nT650 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: delete(T649, T652, T654)\n\nT649 is ground\nT652 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: ','(less(T674, T673), delete(T673, T676, T678))\n\nT673 is ground\nT674 is ground\nT676 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: ','(less(T690, T693), delete(T693, void, T694))\n\nT690 is ground\nT691 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T690, T691, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: ','(less(T705, T702), delete(T705, T703, T706)) | delete(T1, tree(T702, T703, void), T3), SCOPE: 1, CLAUSE: 4\n\nT702 is ground\nT703 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\ndelete(T1, tree(T702, T703, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T702, T703, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: delete(T1, tree(T416, T417, void), T3), SCOPE: 1, CLAUSE: 4\n\nT416 is ground\nT417 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\nX729 is free\nX730 is free\nX731 is free\nX732 is free\nX733 is free\ndelete(T1, tree(T416, T417, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T416, T417, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))\ndelete(T1, tree(T416, T417, void), T3) !=? delete(X729, tree(X730, X731, X732), tree(X730, X733, X732))", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: ','(less(T705, T702), delete(T705, T703, T706)), SCOPE: 16, CLAUSE: 7 | ','(less(T705, T702), delete(T705, T703, T706)), SCOPE: 16, CLAUSE: 8 | ?_16 | delete(T1, tree(T702, T703, void), T3), SCOPE: 1, CLAUSE: 4\n\nT702 is ground\nT703 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\ndelete(T1, tree(T702, T703, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T702, T703, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: ','(less(T705, T702), delete(T705, T703, T706)), SCOPE: 16, CLAUSE: 7\n\nT702 is ground\nT703 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\ndelete(T1, tree(T702, T703, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T702, T703, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: ','(less(T705, T702), delete(T705, T703, T706)), SCOPE: 16, CLAUSE: 8 | ?_16 | delete(T1, tree(T702, T703, void), T3), SCOPE: 1, CLAUSE: 4\n\nT702 is ground\nT703 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\ndelete(T1, tree(T702, T703, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T702, T703, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: delete(0, T703, T712)\n\nT703 is ground\nT711 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\ndelete(T1, tree(s(T711), T703, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T711), T703, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: ','(less(T705, T702), delete(T705, T703, T706)), SCOPE: 16, CLAUSE: 8\n\nT702 is ground\nT703 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\ndelete(T1, tree(T702, T703, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T702, T703, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: ?_16 | delete(T1, tree(T702, T703, void), T3), SCOPE: 1, CLAUSE: 4\n\nT702 is ground\nT703 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\ndelete(T1, tree(T702, T703, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T702, T703, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: ','(less(T725, T724), delete(s(T725), T703, T726))\n\nT703 is ground\nT724 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\ndelete(T1, tree(s(T724), T703, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T724), T703, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: less(T725, T724)\n\nT703 is ground\nT724 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\ndelete(T1, tree(s(T724), T703, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T724), T703, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: delete(s(T729), T703, T730)\n\nT703 is ground\nT724 is ground\nT729 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\ndelete(T731, tree(s(T724), T703, void), T732) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T731, tree(s(T724), T703, void), T732) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: delete(T1, tree(T702, T703, void), T3), SCOPE: 1, CLAUSE: 4\n\nT702 is ground\nT703 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\ndelete(T1, tree(T702, T703, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T702, T703, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: ','(less(T748, T751), delete(T751, void, T752))\n\nT748 is ground\nT749 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\ndelete(T1, tree(T748, T749, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T748, T749, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: ','(less(T760, T763), delete(T763, void, T764))\n\nT760 is ground\nT761 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\nX729 is free\nX730 is free\nX731 is free\nX732 is free\nX733 is free\ndelete(T1, tree(T760, T761, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T760, T761, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))\ndelete(T1, tree(T760, T761, void), T3) !=? delete(X729, tree(X730, X731, X732), tree(X730, X733, X732))", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: ','(less(T760, T763), delete(T763, void, T764)), SCOPE: 17, CLAUSE: 7 | ','(less(T760, T763), delete(T763, void, T764)), SCOPE: 17, CLAUSE: 8\n\nT760 is ground\nT761 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\nX729 is free\nX730 is free\nX731 is free\nX732 is free\nX733 is free\ndelete(T1, tree(T760, T761, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T760, T761, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))\ndelete(T1, tree(T760, T761, void), T3) !=? delete(X729, tree(X730, X731, X732), tree(X730, X733, X732))", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: ','(less(T760, T763), delete(T763, void, T764)), SCOPE: 17, CLAUSE: 7\n\nT760 is ground\nT761 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\nX729 is free\nX730 is free\nX731 is free\nX732 is free\nX733 is free\ndelete(T1, tree(T760, T761, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T760, T761, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))\ndelete(T1, tree(T760, T761, void), T3) !=? delete(X729, tree(X730, X731, X732), tree(X730, X733, X732))", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: ','(less(T760, T763), delete(T763, void, T764)), SCOPE: 17, CLAUSE: 8\n\nT760 is ground\nT761 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\nX729 is free\nX730 is free\nX731 is free\nX732 is free\nX733 is free\ndelete(T1, tree(T760, T761, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T760, T761, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))\ndelete(T1, tree(T760, T761, void), T3) !=? delete(X729, tree(X730, X731, X732), tree(X730, X733, X732))", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: delete(s(T771), void, T770)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: ','(less(T778, T780), delete(s(T780), void, T781))\n\nT761 is ground\nT778 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\nX729 is free\nX730 is free\nX731 is free\nX732 is free\nX733 is free\ndelete(T1, tree(s(T778), T761, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T778), T761, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))\ndelete(T1, tree(s(T778), T761, void), T3) !=? delete(X729, tree(X730, X731, X732), tree(X730, X733, X732))", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: less(T778, T780)\n\nT761 is ground\nT778 is ground\nX6 is free\nX7 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\nX729 is free\nX730 is free\nX731 is free\nX732 is free\nX733 is free\ndelete(T1, tree(s(T778), T761, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T778), T761, void), T3) !=? delete(X450, tree(X450, X451, X452), tree(X453, X451, X454))\ndelete(T1, tree(s(T778), T761, void), T3) !=? delete(X729, tree(X730, X731, X732), tree(X730, X733, X732))", fontsize=16, style=filled, fillcolor=lightyellow];
227 [label="227: delete(s(T784), void, T785)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
228 [label="228: delmin(T799, T802, T803) | delete(T1, tree(T797, T798, T799), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T797, T798, T799), T3), SCOPE: 1, CLAUSE: 4\n\nT797 is ground\nT798 is ground\nT799 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
229 [label="229: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT2 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, T2, T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="230: delmin(T799, T802, T803), SCOPE: 18, CLAUSE: 5 | delmin(T799, T802, T803), SCOPE: 18, CLAUSE: 6 | ?_18 | delete(T1, tree(T797, T798, T799), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T797, T798, T799), T3), SCOPE: 1, CLAUSE: 4\n\nT797 is ground\nT798 is ground\nT799 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
231 [label="231: delmin(T799, T802, T803), SCOPE: 18, CLAUSE: 5\n\nT797 is ground\nT798 is ground\nT799 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
232 [label="232: delmin(T799, T802, T803), SCOPE: 18, CLAUSE: 6 | ?_18 | delete(T1, tree(T797, T798, T799), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T797, T798, T799), T3), SCOPE: 1, CLAUSE: 4\n\nT797 is ground\nT798 is ground\nT799 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
233 [label="233: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
234 [label="234: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
235 [label="235: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
236 [label="236: delmin(T799, T802, T803), SCOPE: 18, CLAUSE: 6\n\nT797 is ground\nT798 is ground\nT799 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
237 [label="237: ?_18 | delete(T1, tree(T797, T798, T799), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T797, T798, T799), T3), SCOPE: 1, CLAUSE: 4\n\nT797 is ground\nT798 is ground\nT799 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
238 [label="238: delmin(T839, T844, T845)\n\nT797 is ground\nT798 is ground\nT838 is ground\nT839 is ground\nT840 is ground\nX6 is free\nX7 is free\ndelete(T1, tree(T797, T798, tree(T838, T839, T840)), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
239 [label="239: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
240 [label="240: delete(T1, tree(T797, T798, T799), T3), SCOPE: 1, CLAUSE: 3 | delete(T1, tree(T797, T798, T799), T3), SCOPE: 1, CLAUSE: 4\n\nT797 is ground\nT798 is ground\nT799 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
241 [label="241: delete(T1, tree(T797, T798, T799), T3), SCOPE: 1, CLAUSE: 3\n\nT797 is ground\nT798 is ground\nT799 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
242 [label="242: delete(T1, tree(T797, T798, T799), T3), SCOPE: 1, CLAUSE: 4\n\nT797 is ground\nT798 is ground\nT799 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T797, T798, T799), T3) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
243 [label="243: ','(less(T875, T871), delete(T875, T872, T876))\n\nT871 is ground\nT872 is ground\nT873 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T1, tree(T871, T872, T873), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T871, T872, T873), T3) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
244 [label="244: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
245 [label="245: less(T875, T871)\n\nT871 is ground\nT872 is ground\nT873 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T1, tree(T871, T872, T873), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T871, T872, T873), T3) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
246 [label="246: delete(T879, T872, T880)\n\nT871 is ground\nT872 is ground\nT873 is ground\nT879 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T881, tree(T871, T872, T873), T882) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T881, tree(T871, T872, T873), T882) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
247 [label="L: ','(less(T900, T904), delete(T904, T902, T905))\n\nT900 is ground\nT901 is ground\nT902 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T1, tree(T900, T901, T902), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T900, T901, T902), T3) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
248 [label="248: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
249 [label="249: less(T900, T904)\n\nT900 is ground\nT901 is ground\nT902 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T1, tree(T900, T901, T902), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T900, T901, T902), T3) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
250 [label="250: delete(T908, T902, T909)\n\nT900 is ground\nT901 is ground\nT902 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\ndelete(T910, tree(T900, T901, T902), T911) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T910, tree(T900, T901, T902), T911) !=? delete(X443, tree(X443, X444, void), X444)", fontsize=16, style=filled, fillcolor=lightyellow];
251 [label="251: ','(less(T928, T924), delete(T928, T925, T929)) | delete(T1, tree(T924, T925, T926), T3), SCOPE: 1, CLAUSE: 4\n\nT924 is ground\nT925 is ground\nT926 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))", fontsize=16, style=filled, fillcolor=lightyellow];
252 [label="252: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT2 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\nX926 is free\nX927 is free\nX928 is free\nX929 is free\nX930 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, T2, T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))\ndelete(T1, T2, T3) !=? delete(X926, tree(X927, X928, X929), tree(X927, X930, X929))", fontsize=16, style=filled, fillcolor=lightyellow];
253 [label="253: ','(less(T928, T924), delete(T928, T925, T929)), SCOPE: 19, CLAUSE: 7 | ','(less(T928, T924), delete(T928, T925, T929)), SCOPE: 19, CLAUSE: 8 | ?_19 | delete(T1, tree(T924, T925, T926), T3), SCOPE: 1, CLAUSE: 4\n\nT924 is ground\nT925 is ground\nT926 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))", fontsize=16, style=filled, fillcolor=lightyellow];
254 [label="254: ','(less(T928, T924), delete(T928, T925, T929)), SCOPE: 19, CLAUSE: 7\n\nT924 is ground\nT925 is ground\nT926 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))", fontsize=16, style=filled, fillcolor=lightyellow];
255 [label="255: ','(less(T928, T924), delete(T928, T925, T929)), SCOPE: 19, CLAUSE: 8 | ?_19 | delete(T1, tree(T924, T925, T926), T3), SCOPE: 1, CLAUSE: 4\n\nT924 is ground\nT925 is ground\nT926 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))", fontsize=16, style=filled, fillcolor=lightyellow];
256 [label="256: delete(0, T925, T935)\n\nT925 is ground\nT926 is ground\nT934 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\ndelete(T1, tree(s(T934), T925, T926), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T934), T925, T926), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(s(T934), T925, T926), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))", fontsize=16, style=filled, fillcolor=lightyellow];
257 [label="257: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
258 [label="258: ','(less(T928, T924), delete(T928, T925, T929)), SCOPE: 19, CLAUSE: 8\n\nT924 is ground\nT925 is ground\nT926 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))", fontsize=16, style=filled, fillcolor=lightyellow];
259 [label="259: ?_19 | delete(T1, tree(T924, T925, T926), T3), SCOPE: 1, CLAUSE: 4\n\nT924 is ground\nT925 is ground\nT926 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))", fontsize=16, style=filled, fillcolor=lightyellow];
260 [label="260: ','(less(T948, T947), delete(s(T948), T925, T949))\n\nT925 is ground\nT926 is ground\nT947 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\ndelete(T1, tree(s(T947), T925, T926), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T947), T925, T926), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(s(T947), T925, T926), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))", fontsize=16, style=filled, fillcolor=lightyellow];
261 [label="261: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
262 [label="262: less(T948, T947)\n\nT925 is ground\nT926 is ground\nT947 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\ndelete(T1, tree(s(T947), T925, T926), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T947), T925, T926), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(s(T947), T925, T926), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))", fontsize=16, style=filled, fillcolor=lightyellow];
263 [label="263: delete(s(T952), T925, T953)\n\nT925 is ground\nT926 is ground\nT947 is ground\nT952 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\ndelete(T954, tree(s(T947), T925, T926), T955) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T954, tree(s(T947), T925, T926), T955) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T954, tree(s(T947), T925, T926), T955) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))", fontsize=16, style=filled, fillcolor=lightyellow];
264 [label="264: delete(T1, tree(T924, T925, T926), T3), SCOPE: 1, CLAUSE: 4\n\nT924 is ground\nT925 is ground\nT926 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(T924, T925, T926), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))", fontsize=16, style=filled, fillcolor=lightyellow];
265 [label="265: ','(less(T973, T977), delete(T977, T975, T978))\n\nT973 is ground\nT974 is ground\nT975 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\ndelete(T1, tree(T973, T974, T975), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T973, T974, T975), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(T973, T974, T975), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))", fontsize=16, style=filled, fillcolor=lightyellow];
266 [label="266: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
267 [label="267: ','(less(T987, T991), delete(T991, T989, T992))\n\nT987 is ground\nT988 is ground\nT989 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\nX926 is free\nX927 is free\nX928 is free\nX929 is free\nX930 is free\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X926, tree(X927, X928, X929), tree(X927, X930, X929))", fontsize=16, style=filled, fillcolor=lightyellow];
268 [label="268: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
269 [label="269: ','(less(T987, T991), delete(T991, T989, T992)), SCOPE: 20, CLAUSE: 7 | ','(less(T987, T991), delete(T991, T989, T992)), SCOPE: 20, CLAUSE: 8\n\nT987 is ground\nT988 is ground\nT989 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\nX926 is free\nX927 is free\nX928 is free\nX929 is free\nX930 is free\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X926, tree(X927, X928, X929), tree(X927, X930, X929))", fontsize=16, style=filled, fillcolor=lightyellow];
270 [label="270: ','(less(T987, T991), delete(T991, T989, T992)), SCOPE: 20, CLAUSE: 7\n\nT987 is ground\nT988 is ground\nT989 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\nX926 is free\nX927 is free\nX928 is free\nX929 is free\nX930 is free\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X926, tree(X927, X928, X929), tree(X927, X930, X929))", fontsize=16, style=filled, fillcolor=lightyellow];
271 [label="271: ','(less(T987, T991), delete(T991, T989, T992)), SCOPE: 20, CLAUSE: 8\n\nT987 is ground\nT988 is ground\nT989 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\nX926 is free\nX927 is free\nX928 is free\nX929 is free\nX930 is free\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))\ndelete(T1, tree(T987, T988, T989), T3) !=? delete(X926, tree(X927, X928, X929), tree(X927, X930, X929))", fontsize=16, style=filled, fillcolor=lightyellow];
272 [label="272: delete(s(T999), T989, T998)\n\nT988 is ground\nT989 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\nX926 is free\nX927 is free\nX928 is free\nX929 is free\nX930 is free\ndelete(T1, tree(0, T988, T989), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(0, T988, T989), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(0, T988, T989), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))\ndelete(T1, tree(0, T988, T989), T3) !=? delete(X926, tree(X927, X928, X929), tree(X927, X930, X929))", fontsize=16, style=filled, fillcolor=lightyellow];
273 [label="273: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
274 [label="274: ','(less(T1008, T1010), delete(s(T1010), T989, T1011))\n\nT988 is ground\nT989 is ground\nT1008 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\nX926 is free\nX927 is free\nX928 is free\nX929 is free\nX930 is free\ndelete(T1, tree(s(T1008), T988, T989), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T1008), T988, T989), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(s(T1008), T988, T989), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))\ndelete(T1, tree(s(T1008), T988, T989), T3) !=? delete(X926, tree(X927, X928, X929), tree(X927, X930, X929))", fontsize=16, style=filled, fillcolor=lightyellow];
275 [label="275: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
276 [label="276: less(T1008, T1010)\n\nT988 is ground\nT989 is ground\nT1008 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\nX926 is free\nX927 is free\nX928 is free\nX929 is free\nX930 is free\ndelete(T1, tree(s(T1008), T988, T989), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, tree(s(T1008), T988, T989), T3) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1, tree(s(T1008), T988, T989), T3) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))\ndelete(T1, tree(s(T1008), T988, T989), T3) !=? delete(X926, tree(X927, X928, X929), tree(X927, X930, X929))", fontsize=16, style=filled, fillcolor=lightyellow];
277 [label="277: delete(s(T1014), T989, T1015)\n\nT988 is ground\nT989 is ground\nT1008 is ground\nX6 is free\nX7 is free\nX443 is free\nX444 is free\nX816 is free\nX817 is free\nX818 is free\nX819 is free\nX820 is free\nX926 is free\nX927 is free\nX928 is free\nX929 is free\nX930 is free\ndelete(T1016, tree(s(T1008), T988, T989), T1017) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1016, tree(s(T1008), T988, T989), T1017) !=? delete(X443, tree(X443, X444, void), X444)\ndelete(T1016, tree(s(T1008), T988, T989), T1017) !=? delete(X816, tree(X816, X817, X818), tree(X819, X817, X820))\ndelete(T1016, tree(s(T1008), T988, T989), T1017) !=? delete(X926, tree(X927, X928, X929), tree(X927, X930, X929))", fontsize=16, style=filled, fillcolor=lightyellow];
278 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 278 [arrowhead = none ];
278 -> 2;

279 [label="EVAL with clause\ndelete(X6, tree(X6, void, X7), X7).\nand substitutionT1 -> T6,\nX6 -> T6,\nX7 -> T7,\nT2 -> tree(T6, void, T7),\nT3 -> T7", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 279 [arrowhead = none ];
279 -> 3;

280 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2 -> 280 [arrowhead = none ];
280 -> 4;

281 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 281 [arrowhead = none ];
281 -> 5;

282 [label="EVAL with clause\ndelete(X443, tree(X443, X444, void), X444).\nand substitutionT1 -> T416,\nX443 -> T416,\nX444 -> T417,\nT2 -> tree(T416, T417, void),\nT3 -> T417", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 282 [arrowhead = none ];
282 -> 130;

283 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 283 [arrowhead = none ];
283 -> 131;

284 [label="EVAL with clause\ndelete(X10, tree(X10, X11, void), X11).\nand substitutionT1 -> T9,\nX10 -> T9,\nT6 -> T9,\nX11 -> void,\nT7 -> void,\nT3 -> void", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 284 [arrowhead = none ];
284 -> 6;

285 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 285 [arrowhead = none ];
285 -> 7;

286 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 286 [arrowhead = none ];
286 -> 8;

287 [label="EVAL with clause\ndelete(X223, tree(X223, X224, X225), tree(X226, X224, X227)) :- delmin(X225, X226, X227).\nand substitutionT1 -> T183,\nX223 -> T183,\nT6 -> T183,\nX224 -> void,\nT7 -> T184,\nX225 -> T184,\nX226 -> T187,\nX227 -> T188,\nT3 -> tree(T187, void, T188),\nT185 -> T187,\nT186 -> T188", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 287 [arrowhead = none ];
287 -> 74;

288 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 288 [arrowhead = none ];
288 -> 75;

289 [label="EVAL with clause\ndelete(X17, tree(X17, X18, X19), tree(X20, X18, X21)) :- delmin(X19, X20, X21).\nand substitutionT1 -> T13,\nX17 -> T13,\nT9 -> T13,\nX18 -> void,\nX19 -> void,\nX20 -> T16,\nX21 -> T17,\nT3 -> tree(T16, void, T17),\nT14 -> T16,\nT15 -> T17", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 289 [arrowhead = none ];
289 -> 9;

290 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 290 [arrowhead = none ];
290 -> 10;

291 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 291 [arrowhead = none ];
291 -> 11;

292 [label="EVAL with clause\ndelete(X136, tree(X137, X138, X139), tree(X137, X140, X139)) :- ','(less(X136, X137), delete(X136, X138, X140)).\nand substitutionT1 -> T101,\nX136 -> T101,\nT9 -> T99,\nX137 -> T99,\nX138 -> void,\nX139 -> void,\nX140 -> T102,\nT3 -> tree(T99, T102, void),\nT98 -> T101,\nT100 -> T102", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 292 [arrowhead = none ];
292 -> 47;

293 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
10 -> 293 [arrowhead = none ];
293 -> 48;

294 [label="BACKTRACK\nfor clause: delmin(tree(Y, void, Right), Y, Right)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 294 [arrowhead = none ];
294 -> 12;

295 [label="BACKTRACK\nfor clause: delmin(tree(X, Left, X1), Y, tree(X, Left1, X2)) :- delmin(Left, Y, Left1)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 295 [arrowhead = none ];
295 -> 13;

296 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
13 -> 296 [arrowhead = none ];
296 -> 14;

297 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 297 [arrowhead = none ];
297 -> 15;

298 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 298 [arrowhead = none ];
298 -> 16;

299 [label="EVAL with clause\ndelete(X50, tree(X51, X52, X53), tree(X51, X54, X53)) :- ','(less(X50, X51), delete(X50, X52, X54)).\nand substitutionT1 -> T33,\nX50 -> T33,\nT13 -> T31,\nX51 -> T31,\nX52 -> void,\nX53 -> void,\nX54 -> T34,\nT3 -> tree(T31, T34, void),\nT30 -> T33,\nT32 -> T34", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 299 [arrowhead = none ];
299 -> 17;

300 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
15 -> 300 [arrowhead = none ];
300 -> 18;

301 [label="EVAL with clause\ndelete(X105, tree(X106, X107, X108), tree(X106, X107, X109)) :- ','(less(X106, X105), delete(X105, X108, X109)).\nand substitutionT1 -> T71,\nX105 -> T71,\nT13 -> T69,\nX106 -> T69,\nX107 -> void,\nX108 -> void,\nX109 -> T72,\nT3 -> tree(T69, void, T72),\nT68 -> T71,\nT70 -> T72", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 301 [arrowhead = none ];
301 -> 35;

302 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 302 [arrowhead = none ];
302 -> 36;

303 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
17 -> 303 [arrowhead = none ];
303 -> 19;

304 [label="SPLIT 2\nnew knowledge:\nT37 is ground\nT31 is ground\nreplacements:T33 -> T37,\nT34 -> T38", fontsize=14, style = filled, fillcolor = violet];
17 -> 304 [arrowhead = none ];
304 -> 20;

305 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
19 -> 305 [arrowhead = none ];
305 -> 21;

306 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
20 -> 306 [arrowhead = none ];
306 -> 29;

307 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 307 [arrowhead = none ];
307 -> 22;

308 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 308 [arrowhead = none ];
308 -> 23;

309 [label="EVAL with clause\nless(0, s(X63)).\nand substitutionT33 -> 0,\nX63 -> T45,\nT31 -> s(T45)", fontsize=14, style = filled, fillcolor = lightblue];
22 -> 309 [arrowhead = none ];
309 -> 24;

310 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
22 -> 310 [arrowhead = none ];
310 -> 25;

311 [label="EVAL with clause\nless(s(X68), s(X69)) :- less(X68, X69).\nand substitutionX68 -> T52,\nT33 -> s(T52),\nX69 -> T51,\nT31 -> s(T51),\nT50 -> T52", fontsize=14, style = filled, fillcolor = lightblue];
23 -> 311 [arrowhead = none ];
311 -> 27;

312 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
23 -> 312 [arrowhead = none ];
312 -> 28;

313 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
24 -> 313 [arrowhead = none ];
313 -> 26;

314 [label="INSTANCE with matching:\nT33 -> T52\nT31 -> T51", fontsize=14, style = filled, fillcolor = lightgrey];
27 -> 314 [arrowhead = none , style=dashed];
314 -> 19[style=dashed];

315 [label="BACKTRACK\nfor clause: delete(X, tree(X, void, Right), Right)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
29 -> 315 [arrowhead = none ];
315 -> 30;

316 [label="BACKTRACK\nfor clause: delete(X, tree(X, Left, void), Left)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 316 [arrowhead = none ];
316 -> 31;

317 [label="BACKTRACK\nfor clause: delete(X, tree(X, Left, Right), tree(Y, Left, Right1)) :- delmin(Right, Y, Right1)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
31 -> 317 [arrowhead = none ];
317 -> 32;

318 [label="BACKTRACK\nfor clause: delete(X, tree(Y, Left, Right), tree(Y, Left1, Right)) :- ','(less(X, Y), delete(X, Left, Left1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
32 -> 318 [arrowhead = none ];
318 -> 33;

319 [label="BACKTRACK\nfor clause: delete(X, tree(Y, Left, Right), tree(Y, Left, Right1)) :- ','(less(Y, X), delete(X, Right, Right1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
33 -> 319 [arrowhead = none ];
319 -> 34;

320 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
35 -> 320 [arrowhead = none ];
320 -> 37;

321 [label="SPLIT 2\nnew knowledge:\nT69 is ground\nreplacements:T71 -> T75,\nT72 -> T76", fontsize=14, style = filled, fillcolor = violet];
35 -> 321 [arrowhead = none ];
321 -> 38;

322 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
37 -> 322 [arrowhead = none ];
322 -> 39;

323 [label="INSTANCE with matching:\nT1 -> T75\nT2 -> void\nT3 -> T76", fontsize=14, style = filled, fillcolor = lightgrey];
38 -> 323 [arrowhead = none , style=dashed];
323 -> 1[style=dashed];

324 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
39 -> 324 [arrowhead = none ];
324 -> 40;

325 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
39 -> 325 [arrowhead = none ];
325 -> 41;

326 [label="EVAL with clause\nless(0, s(X118)).\nand substitutionT69 -> 0,\nX118 -> T83,\nT71 -> s(T83)", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 326 [arrowhead = none ];
326 -> 42;

327 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
40 -> 327 [arrowhead = none ];
327 -> 43;

328 [label="EVAL with clause\nless(s(X123), s(X124)) :- less(X123, X124).\nand substitutionX123 -> T88,\nT69 -> s(T88),\nX124 -> T90,\nT71 -> s(T90),\nT89 -> T90", fontsize=14, style = filled, fillcolor = lightblue];
41 -> 328 [arrowhead = none ];
328 -> 45;

329 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 329 [arrowhead = none ];
329 -> 46;

330 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
42 -> 330 [arrowhead = none ];
330 -> 44;

331 [label="INSTANCE with matching:\nT69 -> T88\nT71 -> T90", fontsize=14, style = filled, fillcolor = lightgrey];
45 -> 331 [arrowhead = none , style=dashed];
331 -> 37[style=dashed];

332 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
47 -> 332 [arrowhead = none ];
332 -> 49;

333 [label="EVAL with clause\ndelete(X190, tree(X191, X192, X193), tree(X191, X192, X194)) :- ','(less(X191, X190), delete(X190, X193, X194)).\nand substitutionT1 -> T150,\nX190 -> T150,\nT9 -> T148,\nX191 -> T148,\nX192 -> void,\nX193 -> void,\nX194 -> T151,\nT3 -> tree(T148, void, T151),\nT147 -> T150,\nT149 -> T151", fontsize=14, style = filled, fillcolor = lightblue];
48 -> 333 [arrowhead = none ];
333 -> 63;

334 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
48 -> 334 [arrowhead = none ];
334 -> 64;

335 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
49 -> 335 [arrowhead = none ];
335 -> 50;

336 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
49 -> 336 [arrowhead = none ];
336 -> 51;

337 [label="EVAL with clause\nless(0, s(X145)).\nand substitutionT101 -> 0,\nX145 -> T107,\nT99 -> s(T107),\nT102 -> T108", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 337 [arrowhead = none ];
337 -> 52;

338 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
50 -> 338 [arrowhead = none ];
338 -> 53;

339 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
51 -> 339 [arrowhead = none ];
339 -> 54;

340 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
51 -> 340 [arrowhead = none ];
340 -> 55;

341 [label="INSTANCE with matching:\nT37 -> 0\nT38 -> T108", fontsize=14, style = filled, fillcolor = lightgrey];
52 -> 341 [arrowhead = none , style=dashed];
341 -> 20[style=dashed];

342 [label="EVAL with clause\nless(s(X158), s(X159)) :- less(X158, X159).\nand substitutionX158 -> T119,\nT101 -> s(T119),\nX159 -> T118,\nT99 -> s(T118),\nT117 -> T119,\nT102 -> T120", fontsize=14, style = filled, fillcolor = lightblue];
54 -> 342 [arrowhead = none ];
342 -> 56;

343 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
54 -> 343 [arrowhead = none ];
343 -> 57;

344 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
55 -> 344 [arrowhead = none ];
344 -> 60;

345 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
56 -> 345 [arrowhead = none ];
345 -> 58;

346 [label="SPLIT 2\nnew knowledge:\nT123 is ground\nT118 is ground\nreplacements:T119 -> T123,\nT120 -> T124,\nT1 -> T125,\nT3 -> T126", fontsize=14, style = filled, fillcolor = violet];
56 -> 346 [arrowhead = none ];
346 -> 59;

347 [label="INSTANCE with matching:\nT33 -> T119\nT31 -> T118", fontsize=14, style = filled, fillcolor = lightgrey];
58 -> 347 [arrowhead = none , style=dashed];
347 -> 19[style=dashed];

348 [label="INSTANCE with matching:\nT37 -> s(T123)\nT38 -> T124", fontsize=14, style = filled, fillcolor = lightgrey];
59 -> 348 [arrowhead = none , style=dashed];
348 -> 20[style=dashed];

349 [label="EVAL with clause\ndelete(X178, tree(X179, X180, X181), tree(X179, X180, X182)) :- ','(less(X179, X178), delete(X178, X181, X182)).\nand substitutionT1 -> T140,\nX178 -> T140,\nT99 -> T138,\nX179 -> T138,\nX180 -> void,\nX181 -> void,\nX182 -> T141,\nT3 -> tree(T138, void, T141),\nT137 -> T140,\nT139 -> T141", fontsize=14, style = filled, fillcolor = lightblue];
60 -> 349 [arrowhead = none ];
349 -> 61;

350 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
60 -> 350 [arrowhead = none ];
350 -> 62;

351 [label="INSTANCE with matching:\nT69 -> T138\nT71 -> T140\nT72 -> T141", fontsize=14, style = filled, fillcolor = lightgrey];
61 -> 351 [arrowhead = none , style=dashed];
351 -> 35[style=dashed];

352 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
63 -> 352 [arrowhead = none ];
352 -> 65;

353 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
65 -> 353 [arrowhead = none ];
353 -> 66;

354 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
65 -> 354 [arrowhead = none ];
354 -> 67;

355 [label="EVAL with clause\nless(0, s(X199)).\nand substitutionT148 -> 0,\nX199 -> T158,\nT150 -> s(T158),\nT151 -> T157,\nT156 -> T158", fontsize=14, style = filled, fillcolor = lightblue];
66 -> 355 [arrowhead = none ];
355 -> 68;

356 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
66 -> 356 [arrowhead = none ];
356 -> 69;

357 [label="EVAL with clause\nless(s(X208), s(X209)) :- less(X208, X209).\nand substitutionX208 -> T165,\nT148 -> s(T165),\nX209 -> T167,\nT150 -> s(T167),\nT166 -> T167,\nT151 -> T168", fontsize=14, style = filled, fillcolor = lightblue];
67 -> 357 [arrowhead = none ];
357 -> 70;

358 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
67 -> 358 [arrowhead = none ];
358 -> 71;

359 [label="INSTANCE with matching:\nT1 -> s(T158)\nT2 -> void\nT3 -> T157", fontsize=14, style = filled, fillcolor = lightgrey];
68 -> 359 [arrowhead = none , style=dashed];
359 -> 1[style=dashed];

360 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
70 -> 360 [arrowhead = none ];
360 -> 72;

361 [label="SPLIT 2\nnew knowledge:\nT165 is ground\nreplacements:T167 -> T171,\nT168 -> T172,\nT1 -> T173,\nT3 -> T174", fontsize=14, style = filled, fillcolor = violet];
70 -> 361 [arrowhead = none ];
361 -> 73;

362 [label="INSTANCE with matching:\nT69 -> T165\nT71 -> T167", fontsize=14, style = filled, fillcolor = lightgrey];
72 -> 362 [arrowhead = none , style=dashed];
362 -> 37[style=dashed];

363 [label="INSTANCE with matching:\nT1 -> s(T171)\nT2 -> void\nT3 -> T172", fontsize=14, style = filled, fillcolor = lightgrey];
73 -> 363 [arrowhead = none , style=dashed];
363 -> 1[style=dashed];

364 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
74 -> 364 [arrowhead = none ];
364 -> 76;

365 [label="EVAL with clause\ndelete(X359, tree(X360, X361, X362), tree(X360, X363, X362)) :- ','(less(X359, X360), delete(X359, X361, X363)).\nand substitutionT1 -> T327,\nX359 -> T327,\nT6 -> T324,\nX360 -> T324,\nX361 -> void,\nT7 -> T325,\nX362 -> T325,\nX363 -> T328,\nT3 -> tree(T324, T328, T325),\nT323 -> T327,\nT326 -> T328", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 365 [arrowhead = none ];
365 -> 103;

366 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
75 -> 366 [arrowhead = none ];
366 -> 104;

367 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
76 -> 367 [arrowhead = none ];
367 -> 77;

368 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
76 -> 368 [arrowhead = none ];
368 -> 78;

369 [label="EVAL with clause\ndelmin(tree(X236, void, X237), X236, X237).\nand substitutionX236 -> T197,\nX237 -> T198,\nT184 -> tree(T197, void, T198),\nT187 -> T197,\nT188 -> T198", fontsize=14, style = filled, fillcolor = lightblue];
77 -> 369 [arrowhead = none ];
369 -> 79;

370 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
77 -> 370 [arrowhead = none ];
370 -> 80;

371 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
78 -> 371 [arrowhead = none ];
371 -> 82;

372 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
78 -> 372 [arrowhead = none ];
372 -> 83;

373 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
79 -> 373 [arrowhead = none ];
373 -> 81;

374 [label="EVAL with clause\ndelmin(tree(X262, X263, X264), X265, tree(X262, X266, X267)) :- delmin(X263, X265, X266).\nand substitutionX262 -> T223,\nX263 -> T224,\nX264 -> T225,\nT184 -> tree(T223, T224, T225),\nT187 -> T229,\nX265 -> T229,\nX266 -> T230,\nX267 -> T228,\nT188 -> tree(T223, T230, T228),\nT226 -> T229,\nT227 -> T230", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 374 [arrowhead = none ];
374 -> 84;

375 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
82 -> 375 [arrowhead = none ];
375 -> 85;

376 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
83 -> 376 [arrowhead = none ];
376 -> 94;

377 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
84 -> 377 [arrowhead = none ];
377 -> 86;

378 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
86 -> 378 [arrowhead = none ];
378 -> 87;

379 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
86 -> 379 [arrowhead = none ];
379 -> 88;

380 [label="EVAL with clause\ndelmin(tree(X280, void, X281), X280, X281).\nand substitutionX280 -> T243,\nX281 -> T244,\nT224 -> tree(T243, void, T244),\nT229 -> T243,\nT230 -> T244", fontsize=14, style = filled, fillcolor = lightblue];
87 -> 380 [arrowhead = none ];
380 -> 89;

381 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
87 -> 381 [arrowhead = none ];
381 -> 90;

382 [label="EVAL with clause\ndelmin(tree(X294, X295, X296), X297, tree(X294, X298, X299)) :- delmin(X295, X297, X298).\nand substitutionX294 -> T257,\nX295 -> T258,\nX296 -> T259,\nT224 -> tree(T257, T258, T259),\nT229 -> T263,\nX297 -> T263,\nX298 -> T264,\nX299 -> T262,\nT230 -> tree(T257, T264, T262),\nT260 -> T263,\nT261 -> T264", fontsize=14, style = filled, fillcolor = lightblue];
88 -> 382 [arrowhead = none ];
382 -> 92;

383 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
88 -> 383 [arrowhead = none ];
383 -> 93;

384 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
89 -> 384 [arrowhead = none ];
384 -> 91;

385 [label="INSTANCE with matching:\nT224 -> T258\nT229 -> T263\nT230 -> T264", fontsize=14, style = filled, fillcolor = lightgrey];
92 -> 385 [arrowhead = none , style=dashed];
385 -> 84[style=dashed];

386 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
94 -> 386 [arrowhead = none ];
386 -> 95;

387 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
94 -> 387 [arrowhead = none ];
387 -> 96;

388 [label="EVAL with clause\ndelete(X324, tree(X325, X326, X327), tree(X325, X328, X327)) :- ','(less(X324, X325), delete(X324, X326, X328)).\nand substitutionT1 -> T289,\nX324 -> T289,\nT183 -> T286,\nX325 -> T286,\nX326 -> void,\nT184 -> T287,\nX327 -> T287,\nX328 -> T290,\nT3 -> tree(T286, T290, T287),\nT285 -> T289,\nT288 -> T290", fontsize=14, style = filled, fillcolor = lightblue];
95 -> 388 [arrowhead = none ];
388 -> 97;

389 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
95 -> 389 [arrowhead = none ];
389 -> 98;

390 [label="EVAL with clause\ndelete(X341, tree(X342, X343, X344), tree(X342, X343, X345)) :- ','(less(X342, X341), delete(X341, X344, X345)).\nand substitutionT1 -> T305,\nX341 -> T305,\nT183 -> T302,\nX342 -> T302,\nX343 -> void,\nT184 -> T303,\nX344 -> T303,\nX345 -> T306,\nT3 -> tree(T302, void, T306),\nT301 -> T305,\nT304 -> T306", fontsize=14, style = filled, fillcolor = lightblue];
96 -> 390 [arrowhead = none ];
390 -> 99;

391 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
96 -> 391 [arrowhead = none ];
391 -> 100;

392 [label="INSTANCE with matching:\nT33 -> T289\nT31 -> T286\nT34 -> T290", fontsize=14, style = filled, fillcolor = lightgrey];
97 -> 392 [arrowhead = none , style=dashed];
392 -> 17[style=dashed];

393 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
99 -> 393 [arrowhead = none ];
393 -> 101;

394 [label="SPLIT 2\nnew knowledge:\nT302 is ground\nreplacements:T305 -> T309,\nT306 -> T310,\nT1 -> T311,\nT3 -> T312", fontsize=14, style = filled, fillcolor = violet];
99 -> 394 [arrowhead = none ];
394 -> 102;

395 [label="INSTANCE with matching:\nT69 -> T302\nT71 -> T305", fontsize=14, style = filled, fillcolor = lightgrey];
101 -> 395 [arrowhead = none , style=dashed];
395 -> 37[style=dashed];

396 [label="INSTANCE with matching:\nT1 -> T309\nT2 -> T303\nT3 -> T310", fontsize=14, style = filled, fillcolor = lightgrey];
102 -> 396 [arrowhead = none , style=dashed];
396 -> 1[style=dashed];

397 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
103 -> 397 [arrowhead = none ];
397 -> 105;

398 [label="EVAL with clause\ndelete(X413, tree(X414, X415, X416), tree(X414, X415, X417)) :- ','(less(X414, X413), delete(X413, X416, X417)).\nand substitutionT1 -> T381,\nX413 -> T381,\nT6 -> T378,\nX414 -> T378,\nX415 -> void,\nT7 -> T379,\nX416 -> T379,\nX417 -> T382,\nT3 -> tree(T378, void, T382),\nT377 -> T381,\nT380 -> T382", fontsize=14, style = filled, fillcolor = lightblue];
104 -> 398 [arrowhead = none ];
398 -> 119;

399 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
104 -> 399 [arrowhead = none ];
399 -> 120;

400 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
105 -> 400 [arrowhead = none ];
400 -> 106;

401 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
105 -> 401 [arrowhead = none ];
401 -> 107;

402 [label="EVAL with clause\nless(0, s(X368)).\nand substitutionT327 -> 0,\nX368 -> T333,\nT324 -> s(T333),\nT328 -> T334", fontsize=14, style = filled, fillcolor = lightblue];
106 -> 402 [arrowhead = none ];
402 -> 108;

403 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
106 -> 403 [arrowhead = none ];
403 -> 109;

404 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
107 -> 404 [arrowhead = none ];
404 -> 110;

405 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
107 -> 405 [arrowhead = none ];
405 -> 111;

406 [label="INSTANCE with matching:\nT37 -> 0\nT38 -> T334", fontsize=14, style = filled, fillcolor = lightgrey];
108 -> 406 [arrowhead = none , style=dashed];
406 -> 20[style=dashed];

407 [label="EVAL with clause\nless(s(X381), s(X382)) :- less(X381, X382).\nand substitutionX381 -> T345,\nT327 -> s(T345),\nX382 -> T344,\nT324 -> s(T344),\nT343 -> T345,\nT328 -> T346", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 407 [arrowhead = none ];
407 -> 112;

408 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
110 -> 408 [arrowhead = none ];
408 -> 113;

409 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
111 -> 409 [arrowhead = none ];
409 -> 116;

410 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
112 -> 410 [arrowhead = none ];
410 -> 114;

411 [label="SPLIT 2\nnew knowledge:\nT349 is ground\nT344 is ground\nreplacements:T345 -> T349,\nT346 -> T350,\nT1 -> T351,\nT3 -> T352", fontsize=14, style = filled, fillcolor = violet];
112 -> 411 [arrowhead = none ];
411 -> 115;

412 [label="INSTANCE with matching:\nT33 -> T345\nT31 -> T344", fontsize=14, style = filled, fillcolor = lightgrey];
114 -> 412 [arrowhead = none , style=dashed];
412 -> 19[style=dashed];

413 [label="INSTANCE with matching:\nT37 -> s(T349)\nT38 -> T350", fontsize=14, style = filled, fillcolor = lightgrey];
115 -> 413 [arrowhead = none , style=dashed];
413 -> 20[style=dashed];

414 [label="EVAL with clause\ndelete(X401, tree(X402, X403, X404), tree(X402, X403, X405)) :- ','(less(X402, X401), delete(X401, X404, X405)).\nand substitutionT1 -> T369,\nX401 -> T369,\nT324 -> T366,\nX402 -> T366,\nX403 -> void,\nT325 -> T367,\nX404 -> T367,\nX405 -> T370,\nT3 -> tree(T366, void, T370),\nT365 -> T369,\nT368 -> T370", fontsize=14, style = filled, fillcolor = lightblue];
116 -> 414 [arrowhead = none ];
414 -> 117;

415 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
116 -> 415 [arrowhead = none ];
415 -> 118;

416 [label="INSTANCE with matching:\nT302 -> T366\nT305 -> T369\nT303 -> T367\nT306 -> T370", fontsize=14, style = filled, fillcolor = lightgrey];
117 -> 416 [arrowhead = none , style=dashed];
416 -> 99[style=dashed];

417 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
119 -> 417 [arrowhead = none ];
417 -> 121;

418 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
121 -> 418 [arrowhead = none ];
418 -> 122;

419 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
121 -> 419 [arrowhead = none ];
419 -> 123;

420 [label="EVAL with clause\nless(0, s(X422)).\nand substitutionT378 -> 0,\nX422 -> T389,\nT381 -> s(T389),\nT382 -> T388,\nT387 -> T389", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 420 [arrowhead = none ];
420 -> 124;

421 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
122 -> 421 [arrowhead = none ];
421 -> 125;

422 [label="EVAL with clause\nless(s(X431), s(X432)) :- less(X431, X432).\nand substitutionX431 -> T398,\nT378 -> s(T398),\nX432 -> T400,\nT381 -> s(T400),\nT399 -> T400,\nT382 -> T401", fontsize=14, style = filled, fillcolor = lightblue];
123 -> 422 [arrowhead = none ];
422 -> 126;

423 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
123 -> 423 [arrowhead = none ];
423 -> 127;

424 [label="INSTANCE with matching:\nT1 -> s(T389)\nT2 -> T379\nT3 -> T388", fontsize=14, style = filled, fillcolor = lightgrey];
124 -> 424 [arrowhead = none , style=dashed];
424 -> 1[style=dashed];

425 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
126 -> 425 [arrowhead = none ];
425 -> 128;

426 [label="SPLIT 2\nnew knowledge:\nT398 is ground\nreplacements:T400 -> T404,\nT401 -> T405,\nT1 -> T406,\nT3 -> T407", fontsize=14, style = filled, fillcolor = violet];
126 -> 426 [arrowhead = none ];
426 -> 129;

427 [label="INSTANCE with matching:\nT69 -> T398\nT71 -> T400", fontsize=14, style = filled, fillcolor = lightgrey];
128 -> 427 [arrowhead = none , style=dashed];
427 -> 37[style=dashed];

428 [label="INSTANCE with matching:\nT1 -> s(T404)\nT2 -> T379\nT3 -> T405", fontsize=14, style = filled, fillcolor = lightgrey];
129 -> 428 [arrowhead = none , style=dashed];
428 -> 1[style=dashed];

429 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
130 -> 429 [arrowhead = none ];
429 -> 132;

430 [label="EVAL with clause\ndelete(X816, tree(X816, X817, X818), tree(X819, X817, X820)) :- delmin(X818, X819, X820).\nand substitutionT1 -> T797,\nX816 -> T797,\nX817 -> T798,\nX818 -> T799,\nT2 -> tree(T797, T798, T799),\nX819 -> T802,\nX820 -> T803,\nT3 -> tree(T802, T798, T803),\nT800 -> T802,\nT801 -> T803", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 430 [arrowhead = none ];
430 -> 228;

431 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
131 -> 431 [arrowhead = none ];
431 -> 229;

432 [label="EVAL with clause\ndelete(X450, tree(X450, X451, X452), tree(X453, X451, X454)) :- delmin(X452, X453, X454).\nand substitutionT1 -> T422,\nX450 -> T422,\nT416 -> T422,\nT417 -> T423,\nX451 -> T423,\nX452 -> void,\nX453 -> T426,\nX454 -> T427,\nT3 -> tree(T426, T423, T427),\nT424 -> T426,\nT425 -> T427", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 432 [arrowhead = none ];
432 -> 133;

433 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
132 -> 433 [arrowhead = none ];
433 -> 134;

434 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
133 -> 434 [arrowhead = none ];
434 -> 135;

435 [label="EVAL with clause\ndelete(X729, tree(X730, X731, X732), tree(X730, X733, X732)) :- ','(less(X729, X730), delete(X729, X731, X733)).\nand substitutionT1 -> T705,\nX729 -> T705,\nT416 -> T702,\nX730 -> T702,\nT417 -> T703,\nX731 -> T703,\nX732 -> void,\nX733 -> T706,\nT3 -> tree(T702, T706, void),\nT701 -> T705,\nT704 -> T706", fontsize=14, style = filled, fillcolor = lightblue];
134 -> 435 [arrowhead = none ];
435 -> 201;

436 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
134 -> 436 [arrowhead = none ];
436 -> 202;

437 [label="BACKTRACK\nfor clause: delmin(tree(Y, void, Right), Y, Right)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
135 -> 437 [arrowhead = none ];
437 -> 136;

438 [label="BACKTRACK\nfor clause: delmin(tree(X, Left, X1), Y, tree(X, Left1, X2)) :- delmin(Left, Y, Left1)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
136 -> 438 [arrowhead = none ];
438 -> 137;

439 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
137 -> 439 [arrowhead = none ];
439 -> 138;

440 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
138 -> 440 [arrowhead = none ];
440 -> 139;

441 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
138 -> 441 [arrowhead = none ];
441 -> 140;

442 [label="EVAL with clause\ndelete(X483, tree(X484, X485, X486), tree(X484, X487, X486)) :- ','(less(X483, X484), delete(X483, X485, X487)).\nand substitutionT1 -> T448,\nX483 -> T448,\nT422 -> T445,\nX484 -> T445,\nT423 -> T446,\nX485 -> T446,\nX486 -> void,\nX487 -> T449,\nT3 -> tree(T445, T449, void),\nT444 -> T448,\nT447 -> T449", fontsize=14, style = filled, fillcolor = lightblue];
139 -> 442 [arrowhead = none ];
442 -> 141;

443 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
139 -> 443 [arrowhead = none ];
443 -> 142;

444 [label="EVAL with clause\ndelete(X717, tree(X718, X719, X720), tree(X718, X719, X721)) :- ','(less(X718, X717), delete(X717, X720, X721)).\nand substitutionT1 -> T693,\nX717 -> T693,\nT422 -> T690,\nX718 -> T690,\nT423 -> T691,\nX719 -> T691,\nX720 -> void,\nX721 -> T694,\nT3 -> tree(T690, T691, T694),\nT689 -> T693,\nT692 -> T694", fontsize=14, style = filled, fillcolor = lightblue];
140 -> 444 [arrowhead = none ];
444 -> 199;

445 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
140 -> 445 [arrowhead = none ];
445 -> 200;

446 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
141 -> 446 [arrowhead = none ];
446 -> 143;

447 [label="SPLIT 2\nnew knowledge:\nT452 is ground\nT445 is ground\nreplacements:T448 -> T452,\nT449 -> T453,\nT1 -> T454,\nT3 -> T455", fontsize=14, style = filled, fillcolor = violet];
141 -> 447 [arrowhead = none ];
447 -> 144;

448 [label="INSTANCE with matching:\nT33 -> T448\nT31 -> T445", fontsize=14, style = filled, fillcolor = lightgrey];
143 -> 448 [arrowhead = none , style=dashed];
448 -> 19[style=dashed];

449 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
144 -> 449 [arrowhead = none ];
449 -> 145;

450 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
145 -> 450 [arrowhead = none ];
450 -> 146;

451 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
145 -> 451 [arrowhead = none ];
451 -> 147;

452 [label="EVAL with clause\ndelete(X504, tree(X504, void, X505), X505).\nand substitutionT452 -> T470,\nX504 -> T470,\nX505 -> T471,\nT446 -> tree(T470, void, T471),\nT453 -> T471", fontsize=14, style = filled, fillcolor = lightblue];
146 -> 452 [arrowhead = none ];
452 -> 148;

453 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
146 -> 453 [arrowhead = none ];
453 -> 149;

454 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
147 -> 454 [arrowhead = none ];
454 -> 151;

455 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
147 -> 455 [arrowhead = none ];
455 -> 152;

456 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
148 -> 456 [arrowhead = none ];
456 -> 150;

457 [label="EVAL with clause\ndelete(X514, tree(X514, X515, void), X515).\nand substitutionT452 -> T480,\nX514 -> T480,\nX515 -> T481,\nT446 -> tree(T480, T481, void),\nT453 -> T481", fontsize=14, style = filled, fillcolor = lightblue];
151 -> 457 [arrowhead = none ];
457 -> 153;

458 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
151 -> 458 [arrowhead = none ];
458 -> 154;

459 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
152 -> 459 [arrowhead = none ];
459 -> 156;

460 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
152 -> 460 [arrowhead = none ];
460 -> 157;

461 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
153 -> 461 [arrowhead = none ];
461 -> 155;

462 [label="EVAL with clause\ndelete(X536, tree(X536, X537, X538), tree(X539, X537, X540)) :- delmin(X538, X539, X540).\nand substitutionT452 -> T502,\nX536 -> T502,\nX537 -> T503,\nX538 -> T504,\nT446 -> tree(T502, T503, T504),\nX539 -> T507,\nX540 -> T508,\nT453 -> tree(T507, T503, T508),\nT505 -> T507,\nT506 -> T508", fontsize=14, style = filled, fillcolor = lightblue];
156 -> 462 [arrowhead = none ];
462 -> 158;

463 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
156 -> 463 [arrowhead = none ];
463 -> 159;

464 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
157 -> 464 [arrowhead = none ];
464 -> 160;

465 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
157 -> 465 [arrowhead = none ];
465 -> 161;

466 [label="INSTANCE with matching:\nT224 -> T504\nT229 -> T507\nT230 -> T508", fontsize=14, style = filled, fillcolor = lightgrey];
158 -> 466 [arrowhead = none , style=dashed];
466 -> 84[style=dashed];

467 [label="EVAL with clause\ndelete(X565, tree(X566, X567, X568), tree(X566, X569, X568)) :- ','(less(X565, X566), delete(X565, X567, X569)).\nand substitutionT452 -> T533,\nX565 -> T533,\nX566 -> T534,\nX567 -> T535,\nX568 -> T536,\nT446 -> tree(T534, T535, T536),\nX569 -> T538,\nT453 -> tree(T534, T538, T536),\nT537 -> T538", fontsize=14, style = filled, fillcolor = lightblue];
160 -> 467 [arrowhead = none ];
467 -> 162;

468 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
160 -> 468 [arrowhead = none ];
468 -> 163;

469 [label="EVAL with clause\ndelete(X700, tree(X701, X702, X703), tree(X701, X702, X704)) :- ','(less(X701, X700), delete(X700, X703, X704)).\nand substitutionT452 -> T673,\nX700 -> T673,\nX701 -> T674,\nX702 -> T675,\nX703 -> T676,\nT446 -> tree(T674, T675, T676),\nX704 -> T678,\nT453 -> tree(T674, T675, T678),\nT677 -> T678", fontsize=14, style = filled, fillcolor = lightblue];
161 -> 469 [arrowhead = none ];
469 -> 197;

470 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
161 -> 470 [arrowhead = none ];
470 -> 198;

471 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
162 -> 471 [arrowhead = none ];
471 -> 164;

472 [label="SPLIT 2\nnew knowledge:\nT533 is ground\nT534 is ground", fontsize=14, style = filled, fillcolor = violet];
162 -> 472 [arrowhead = none ];
472 -> 165;

473 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
164 -> 473 [arrowhead = none ];
473 -> 166;

474 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
165 -> 474 [arrowhead = none ];
474 -> 174;

475 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
166 -> 475 [arrowhead = none ];
475 -> 167;

476 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
166 -> 476 [arrowhead = none ];
476 -> 168;

477 [label="EVAL with clause\nless(0, s(X578)).\nand substitutionT533 -> 0,\nX578 -> T547,\nT534 -> s(T547)", fontsize=14, style = filled, fillcolor = lightblue];
167 -> 477 [arrowhead = none ];
477 -> 169;

478 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
167 -> 478 [arrowhead = none ];
478 -> 170;

479 [label="EVAL with clause\nless(s(X583), s(X584)) :- less(X583, X584).\nand substitutionX583 -> T552,\nT533 -> s(T552),\nX584 -> T553,\nT534 -> s(T553)", fontsize=14, style = filled, fillcolor = lightblue];
168 -> 479 [arrowhead = none ];
479 -> 172;

480 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
168 -> 480 [arrowhead = none ];
480 -> 173;

481 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
169 -> 481 [arrowhead = none ];
481 -> 171;

482 [label="INSTANCE with matching:\nT533 -> T552\nT534 -> T553", fontsize=14, style = filled, fillcolor = lightgrey];
172 -> 482 [arrowhead = none , style=dashed];
482 -> 164[style=dashed];

483 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
174 -> 483 [arrowhead = none ];
483 -> 175;

484 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
174 -> 484 [arrowhead = none ];
484 -> 176;

485 [label="EVAL with clause\ndelete(X599, tree(X599, void, X600), X600).\nand substitutionT533 -> T568,\nX599 -> T568,\nX600 -> T569,\nT535 -> tree(T568, void, T569),\nT538 -> T569", fontsize=14, style = filled, fillcolor = lightblue];
175 -> 485 [arrowhead = none ];
485 -> 177;

486 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
175 -> 486 [arrowhead = none ];
486 -> 178;

487 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
176 -> 487 [arrowhead = none ];
487 -> 180;

488 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
176 -> 488 [arrowhead = none ];
488 -> 181;

489 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
177 -> 489 [arrowhead = none ];
489 -> 179;

490 [label="EVAL with clause\ndelete(X609, tree(X609, X610, void), X610).\nand substitutionT533 -> T578,\nX609 -> T578,\nX610 -> T579,\nT535 -> tree(T578, T579, void),\nT538 -> T579", fontsize=14, style = filled, fillcolor = lightblue];
180 -> 490 [arrowhead = none ];
490 -> 182;

491 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
180 -> 491 [arrowhead = none ];
491 -> 183;

492 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
181 -> 492 [arrowhead = none ];
492 -> 185;

493 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
181 -> 493 [arrowhead = none ];
493 -> 186;

494 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
182 -> 494 [arrowhead = none ];
494 -> 184;

495 [label="EVAL with clause\ndelete(X631, tree(X631, X632, X633), tree(X634, X632, X635)) :- delmin(X633, X634, X635).\nand substitutionT533 -> T600,\nX631 -> T600,\nX632 -> T601,\nX633 -> T602,\nT535 -> tree(T600, T601, T602),\nX634 -> T605,\nX635 -> T606,\nT538 -> tree(T605, T601, T606),\nT603 -> T605,\nT604 -> T606", fontsize=14, style = filled, fillcolor = lightblue];
185 -> 495 [arrowhead = none ];
495 -> 187;

496 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
185 -> 496 [arrowhead = none ];
496 -> 188;

497 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
186 -> 497 [arrowhead = none ];
497 -> 189;

498 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
186 -> 498 [arrowhead = none ];
498 -> 190;

499 [label="INSTANCE with matching:\nT224 -> T602\nT229 -> T605\nT230 -> T606", fontsize=14, style = filled, fillcolor = lightgrey];
187 -> 499 [arrowhead = none , style=dashed];
499 -> 84[style=dashed];

500 [label="EVAL with clause\ndelete(X660, tree(X661, X662, X663), tree(X661, X664, X663)) :- ','(less(X660, X661), delete(X660, X662, X664)).\nand substitutionT533 -> T631,\nX660 -> T631,\nX661 -> T632,\nX662 -> T633,\nX663 -> T634,\nT535 -> tree(T632, T633, T634),\nX664 -> T636,\nT538 -> tree(T632, T636, T634),\nT635 -> T636", fontsize=14, style = filled, fillcolor = lightblue];
189 -> 500 [arrowhead = none ];
500 -> 191;

501 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
189 -> 501 [arrowhead = none ];
501 -> 192;

502 [label="EVAL with clause\ndelete(X677, tree(X678, X679, X680), tree(X678, X679, X681)) :- ','(less(X678, X677), delete(X677, X680, X681)).\nand substitutionT533 -> T649,\nX677 -> T649,\nX678 -> T650,\nX679 -> T651,\nX680 -> T652,\nT535 -> tree(T650, T651, T652),\nX681 -> T654,\nT538 -> tree(T650, T651, T654),\nT653 -> T654", fontsize=14, style = filled, fillcolor = lightblue];
190 -> 502 [arrowhead = none ];
502 -> 193;

503 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
190 -> 503 [arrowhead = none ];
503 -> 194;

504 [label="INSTANCE with matching:\nT533 -> T631\nT534 -> T632\nT535 -> T633\nT538 -> T636", fontsize=14, style = filled, fillcolor = lightgrey];
191 -> 504 [arrowhead = none , style=dashed];
504 -> 162[style=dashed];

505 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
193 -> 505 [arrowhead = none ];
505 -> 195;

506 [label="SPLIT 2\nnew knowledge:\nT650 is ground\nT649 is ground", fontsize=14, style = filled, fillcolor = violet];
193 -> 506 [arrowhead = none ];
506 -> 196;

507 [label="INSTANCE with matching:\nT533 -> T650\nT534 -> T649", fontsize=14, style = filled, fillcolor = lightgrey];
195 -> 507 [arrowhead = none , style=dashed];
507 -> 164[style=dashed];

508 [label="INSTANCE with matching:\nT533 -> T649\nT535 -> T652\nT538 -> T654", fontsize=14, style = filled, fillcolor = lightgrey];
196 -> 508 [arrowhead = none , style=dashed];
508 -> 165[style=dashed];

509 [label="INSTANCE with matching:\nT650 -> T674\nT649 -> T673\nT652 -> T676\nT654 -> T678", fontsize=14, style = filled, fillcolor = lightgrey];
197 -> 509 [arrowhead = none , style=dashed];
509 -> 193[style=dashed];

510 [label="INSTANCE with matching:\nT69 -> T690\nT71 -> T693\nT72 -> T694", fontsize=14, style = filled, fillcolor = lightgrey];
199 -> 510 [arrowhead = none , style=dashed];
510 -> 35[style=dashed];

511 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
201 -> 511 [arrowhead = none ];
511 -> 203;

512 [label="EVAL with clause\ndelete(X783, tree(X784, X785, X786), tree(X784, X785, X787)) :- ','(less(X784, X783), delete(X783, X786, X787)).\nand substitutionT1 -> T763,\nX783 -> T763,\nT416 -> T760,\nX784 -> T760,\nT417 -> T761,\nX785 -> T761,\nX786 -> void,\nX787 -> T764,\nT3 -> tree(T760, T761, T764),\nT759 -> T763,\nT762 -> T764", fontsize=14, style = filled, fillcolor = lightblue];
202 -> 512 [arrowhead = none ];
512 -> 217;

513 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
202 -> 513 [arrowhead = none ];
513 -> 218;

514 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
203 -> 514 [arrowhead = none ];
514 -> 204;

515 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
203 -> 515 [arrowhead = none ];
515 -> 205;

516 [label="EVAL with clause\nless(0, s(X738)).\nand substitutionT705 -> 0,\nX738 -> T711,\nT702 -> s(T711),\nT706 -> T712", fontsize=14, style = filled, fillcolor = lightblue];
204 -> 516 [arrowhead = none ];
516 -> 206;

517 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
204 -> 517 [arrowhead = none ];
517 -> 207;

518 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
205 -> 518 [arrowhead = none ];
518 -> 208;

519 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
205 -> 519 [arrowhead = none ];
519 -> 209;

520 [label="INSTANCE with matching:\nT533 -> 0\nT535 -> T703\nT538 -> T712", fontsize=14, style = filled, fillcolor = lightgrey];
206 -> 520 [arrowhead = none , style=dashed];
520 -> 165[style=dashed];

521 [label="EVAL with clause\nless(s(X751), s(X752)) :- less(X751, X752).\nand substitutionX751 -> T725,\nT705 -> s(T725),\nX752 -> T724,\nT702 -> s(T724),\nT723 -> T725,\nT706 -> T726", fontsize=14, style = filled, fillcolor = lightblue];
208 -> 521 [arrowhead = none ];
521 -> 210;

522 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
208 -> 522 [arrowhead = none ];
522 -> 211;

523 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
209 -> 523 [arrowhead = none ];
523 -> 214;

524 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
210 -> 524 [arrowhead = none ];
524 -> 212;

525 [label="SPLIT 2\nnew knowledge:\nT729 is ground\nT724 is ground\nreplacements:T725 -> T729,\nT726 -> T730,\nT1 -> T731,\nT3 -> T732", fontsize=14, style = filled, fillcolor = violet];
210 -> 525 [arrowhead = none ];
525 -> 213;

526 [label="INSTANCE with matching:\nT33 -> T725\nT31 -> T724", fontsize=14, style = filled, fillcolor = lightgrey];
212 -> 526 [arrowhead = none , style=dashed];
526 -> 19[style=dashed];

527 [label="INSTANCE with matching:\nT533 -> s(T729)\nT535 -> T703\nT538 -> T730", fontsize=14, style = filled, fillcolor = lightgrey];
213 -> 527 [arrowhead = none , style=dashed];
527 -> 165[style=dashed];

528 [label="EVAL with clause\ndelete(X771, tree(X772, X773, X774), tree(X772, X773, X775)) :- ','(less(X772, X771), delete(X771, X774, X775)).\nand substitutionT1 -> T751,\nX771 -> T751,\nT702 -> T748,\nX772 -> T748,\nT703 -> T749,\nX773 -> T749,\nX774 -> void,\nX775 -> T752,\nT3 -> tree(T748, T749, T752),\nT747 -> T751,\nT750 -> T752", fontsize=14, style = filled, fillcolor = lightblue];
214 -> 528 [arrowhead = none ];
528 -> 215;

529 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
214 -> 529 [arrowhead = none ];
529 -> 216;

530 [label="INSTANCE with matching:\nT69 -> T748\nT71 -> T751\nT72 -> T752", fontsize=14, style = filled, fillcolor = lightgrey];
215 -> 530 [arrowhead = none , style=dashed];
530 -> 35[style=dashed];

531 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
217 -> 531 [arrowhead = none ];
531 -> 219;

532 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
219 -> 532 [arrowhead = none ];
532 -> 220;

533 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
219 -> 533 [arrowhead = none ];
533 -> 221;

534 [label="EVAL with clause\nless(0, s(X792)).\nand substitutionT760 -> 0,\nX792 -> T771,\nT763 -> s(T771),\nT764 -> T770,\nT769 -> T771", fontsize=14, style = filled, fillcolor = lightblue];
220 -> 534 [arrowhead = none ];
534 -> 222;

535 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
220 -> 535 [arrowhead = none ];
535 -> 223;

536 [label="EVAL with clause\nless(s(X801), s(X802)) :- less(X801, X802).\nand substitutionX801 -> T778,\nT760 -> s(T778),\nX802 -> T780,\nT763 -> s(T780),\nT779 -> T780,\nT764 -> T781", fontsize=14, style = filled, fillcolor = lightblue];
221 -> 536 [arrowhead = none ];
536 -> 224;

537 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
221 -> 537 [arrowhead = none ];
537 -> 225;

538 [label="INSTANCE with matching:\nT1 -> s(T771)\nT2 -> void\nT3 -> T770", fontsize=14, style = filled, fillcolor = lightgrey];
222 -> 538 [arrowhead = none , style=dashed];
538 -> 1[style=dashed];

539 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
224 -> 539 [arrowhead = none ];
539 -> 226;

540 [label="SPLIT 2\nnew knowledge:\nT778 is ground\nreplacements:T780 -> T784,\nT781 -> T785,\nT1 -> T786,\nT3 -> T787", fontsize=14, style = filled, fillcolor = violet];
224 -> 540 [arrowhead = none ];
540 -> 227;

541 [label="INSTANCE with matching:\nT69 -> T778\nT71 -> T780", fontsize=14, style = filled, fillcolor = lightgrey];
226 -> 541 [arrowhead = none , style=dashed];
541 -> 37[style=dashed];

542 [label="INSTANCE with matching:\nT1 -> s(T784)\nT2 -> void\nT3 -> T785", fontsize=14, style = filled, fillcolor = lightgrey];
227 -> 542 [arrowhead = none , style=dashed];
542 -> 1[style=dashed];

543 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
228 -> 543 [arrowhead = none ];
543 -> 230;

544 [label="EVAL with clause\ndelete(X926, tree(X927, X928, X929), tree(X927, X930, X929)) :- ','(less(X926, X927), delete(X926, X928, X930)).\nand substitutionT1 -> T928,\nX926 -> T928,\nX927 -> T924,\nX928 -> T925,\nX929 -> T926,\nT2 -> tree(T924, T925, T926),\nX930 -> T929,\nT3 -> tree(T924, T929, T926),\nT923 -> T928,\nT927 -> T929", fontsize=14, style = filled, fillcolor = lightblue];
229 -> 544 [arrowhead = none ];
544 -> 251;

545 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
229 -> 545 [arrowhead = none ];
545 -> 252;

546 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
230 -> 546 [arrowhead = none ];
546 -> 231;

547 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
230 -> 547 [arrowhead = none ];
547 -> 232;

548 [label="EVAL with clause\ndelmin(tree(X829, void, X830), X829, X830).\nand substitutionX829 -> T812,\nX830 -> T813,\nT799 -> tree(T812, void, T813),\nT802 -> T812,\nT803 -> T813", fontsize=14, style = filled, fillcolor = lightblue];
231 -> 548 [arrowhead = none ];
548 -> 233;

549 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
231 -> 549 [arrowhead = none ];
549 -> 234;

550 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
232 -> 550 [arrowhead = none ];
550 -> 236;

551 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
232 -> 551 [arrowhead = none ];
551 -> 237;

552 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
233 -> 552 [arrowhead = none ];
552 -> 235;

553 [label="EVAL with clause\ndelmin(tree(X855, X856, X857), X858, tree(X855, X859, X860)) :- delmin(X856, X858, X859).\nand substitutionX855 -> T838,\nX856 -> T839,\nX857 -> T840,\nT799 -> tree(T838, T839, T840),\nT802 -> T844,\nX858 -> T844,\nX859 -> T845,\nX860 -> T843,\nT803 -> tree(T838, T845, T843),\nT841 -> T844,\nT842 -> T845", fontsize=14, style = filled, fillcolor = lightblue];
236 -> 553 [arrowhead = none ];
553 -> 238;

554 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
236 -> 554 [arrowhead = none ];
554 -> 239;

555 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
237 -> 555 [arrowhead = none ];
555 -> 240;

556 [label="INSTANCE with matching:\nT224 -> T839\nT229 -> T844\nT230 -> T845", fontsize=14, style = filled, fillcolor = lightgrey];
238 -> 556 [arrowhead = none , style=dashed];
556 -> 84[style=dashed];

557 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
240 -> 557 [arrowhead = none ];
557 -> 241;

558 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
240 -> 558 [arrowhead = none ];
558 -> 242;

559 [label="EVAL with clause\ndelete(X885, tree(X886, X887, X888), tree(X886, X889, X888)) :- ','(less(X885, X886), delete(X885, X887, X889)).\nand substitutionT1 -> T875,\nX885 -> T875,\nT797 -> T871,\nX886 -> T871,\nT798 -> T872,\nX887 -> T872,\nT799 -> T873,\nX888 -> T873,\nX889 -> T876,\nT3 -> tree(T871, T876, T873),\nT870 -> T875,\nT874 -> T876", fontsize=14, style = filled, fillcolor = lightblue];
241 -> 559 [arrowhead = none ];
559 -> 243;

560 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
241 -> 560 [arrowhead = none ];
560 -> 244;

561 [label="EVAL with clause\ndelete(X908, tree(X909, X910, X911), tree(X909, X910, X912)) :- ','(less(X909, X908), delete(X908, X911, X912)).\nand substitutionT1 -> T904,\nX908 -> T904,\nT797 -> T900,\nX909 -> T900,\nT798 -> T901,\nX910 -> T901,\nT799 -> T902,\nX911 -> T902,\nX912 -> T905,\nT3 -> tree(T900, T901, T905),\nT899 -> T904,\nT903 -> T905", fontsize=14, style = filled, fillcolor = lightblue];
242 -> 561 [arrowhead = none ];
561 -> 247;

562 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
242 -> 562 [arrowhead = none ];
562 -> 248;

563 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
243 -> 563 [arrowhead = none ];
563 -> 245;

564 [label="SPLIT 2\nnew knowledge:\nT879 is ground\nT871 is ground\nreplacements:T875 -> T879,\nT876 -> T880,\nT1 -> T881,\nT3 -> T882", fontsize=14, style = filled, fillcolor = violet];
243 -> 564 [arrowhead = none ];
564 -> 246;

565 [label="INSTANCE with matching:\nT33 -> T875\nT31 -> T871", fontsize=14, style = filled, fillcolor = lightgrey];
245 -> 565 [arrowhead = none , style=dashed];
565 -> 19[style=dashed];

566 [label="INSTANCE with matching:\nT533 -> T879\nT535 -> T872\nT538 -> T880", fontsize=14, style = filled, fillcolor = lightgrey];
246 -> 566 [arrowhead = none , style=dashed];
566 -> 165[style=dashed];

567 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
247 -> 567 [arrowhead = none ];
567 -> 249;

568 [label="SPLIT 2\nnew knowledge:\nT900 is ground\nreplacements:T904 -> T908,\nT905 -> T909,\nT1 -> T910,\nT3 -> T911", fontsize=14, style = filled, fillcolor = violet];
247 -> 568 [arrowhead = none ];
568 -> 250;

569 [label="INSTANCE with matching:\nT69 -> T900\nT71 -> T904", fontsize=14, style = filled, fillcolor = lightgrey];
249 -> 569 [arrowhead = none , style=dashed];
569 -> 37[style=dashed];

570 [label="INSTANCE with matching:\nT1 -> T908\nT2 -> T902\nT3 -> T909", fontsize=14, style = filled, fillcolor = lightgrey];
250 -> 570 [arrowhead = none , style=dashed];
570 -> 1[style=dashed];

571 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
251 -> 571 [arrowhead = none ];
571 -> 253;

572 [label="EVAL with clause\ndelete(X980, tree(X981, X982, X983), tree(X981, X982, X984)) :- ','(less(X981, X980), delete(X980, X983, X984)).\nand substitutionT1 -> T991,\nX980 -> T991,\nX981 -> T987,\nX982 -> T988,\nX983 -> T989,\nT2 -> tree(T987, T988, T989),\nX984 -> T992,\nT3 -> tree(T987, T988, T992),\nT986 -> T991,\nT990 -> T992", fontsize=14, style = filled, fillcolor = lightblue];
252 -> 572 [arrowhead = none ];
572 -> 267;

573 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
252 -> 573 [arrowhead = none ];
573 -> 268;

574 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
253 -> 574 [arrowhead = none ];
574 -> 254;

575 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
253 -> 575 [arrowhead = none ];
575 -> 255;

576 [label="EVAL with clause\nless(0, s(X935)).\nand substitutionT928 -> 0,\nX935 -> T934,\nT924 -> s(T934),\nT929 -> T935", fontsize=14, style = filled, fillcolor = lightblue];
254 -> 576 [arrowhead = none ];
576 -> 256;

577 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
254 -> 577 [arrowhead = none ];
577 -> 257;

578 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
255 -> 578 [arrowhead = none ];
578 -> 258;

579 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
255 -> 579 [arrowhead = none ];
579 -> 259;

580 [label="INSTANCE with matching:\nT533 -> 0\nT535 -> T925\nT538 -> T935", fontsize=14, style = filled, fillcolor = lightgrey];
256 -> 580 [arrowhead = none , style=dashed];
580 -> 165[style=dashed];

581 [label="EVAL with clause\nless(s(X948), s(X949)) :- less(X948, X949).\nand substitutionX948 -> T948,\nT928 -> s(T948),\nX949 -> T947,\nT924 -> s(T947),\nT946 -> T948,\nT929 -> T949", fontsize=14, style = filled, fillcolor = lightblue];
258 -> 581 [arrowhead = none ];
581 -> 260;

582 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
258 -> 582 [arrowhead = none ];
582 -> 261;

583 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
259 -> 583 [arrowhead = none ];
583 -> 264;

584 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
260 -> 584 [arrowhead = none ];
584 -> 262;

585 [label="SPLIT 2\nnew knowledge:\nT952 is ground\nT947 is ground\nreplacements:T948 -> T952,\nT949 -> T953,\nT1 -> T954,\nT3 -> T955", fontsize=14, style = filled, fillcolor = violet];
260 -> 585 [arrowhead = none ];
585 -> 263;

586 [label="INSTANCE with matching:\nT33 -> T948\nT31 -> T947", fontsize=14, style = filled, fillcolor = lightgrey];
262 -> 586 [arrowhead = none , style=dashed];
586 -> 19[style=dashed];

587 [label="INSTANCE with matching:\nT533 -> s(T952)\nT535 -> T925\nT538 -> T953", fontsize=14, style = filled, fillcolor = lightgrey];
263 -> 587 [arrowhead = none , style=dashed];
587 -> 165[style=dashed];

588 [label="EVAL with clause\ndelete(X968, tree(X969, X970, X971), tree(X969, X970, X972)) :- ','(less(X969, X968), delete(X968, X971, X972)).\nand substitutionT1 -> T977,\nX968 -> T977,\nT924 -> T973,\nX969 -> T973,\nT925 -> T974,\nX970 -> T974,\nT926 -> T975,\nX971 -> T975,\nX972 -> T978,\nT3 -> tree(T973, T974, T978),\nT972 -> T977,\nT976 -> T978", fontsize=14, style = filled, fillcolor = lightblue];
264 -> 588 [arrowhead = none ];
588 -> 265;

589 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
264 -> 589 [arrowhead = none ];
589 -> 266;

590 [label="INSTANCE with matching:\nT900 -> T973\nT904 -> T977\nT902 -> T975\nT905 -> T978\nT901 -> T974", fontsize=14, style = filled, fillcolor = lightgrey];
265 -> 590 [arrowhead = none , style=dashed];
590 -> 247[style=dashed];

591 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
267 -> 591 [arrowhead = none ];
591 -> 269;

592 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
269 -> 592 [arrowhead = none ];
592 -> 270;

593 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
269 -> 593 [arrowhead = none ];
593 -> 271;

594 [label="EVAL with clause\nless(0, s(X989)).\nand substitutionT987 -> 0,\nX989 -> T999,\nT991 -> s(T999),\nT992 -> T998,\nT997 -> T999", fontsize=14, style = filled, fillcolor = lightblue];
270 -> 594 [arrowhead = none ];
594 -> 272;

595 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
270 -> 595 [arrowhead = none ];
595 -> 273;

596 [label="EVAL with clause\nless(s(X998), s(X999)) :- less(X998, X999).\nand substitutionX998 -> T1008,\nT987 -> s(T1008),\nX999 -> T1010,\nT991 -> s(T1010),\nT1009 -> T1010,\nT992 -> T1011", fontsize=14, style = filled, fillcolor = lightblue];
271 -> 596 [arrowhead = none ];
596 -> 274;

597 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
271 -> 597 [arrowhead = none ];
597 -> 275;

598 [label="INSTANCE with matching:\nT1 -> s(T999)\nT2 -> T989\nT3 -> T998", fontsize=14, style = filled, fillcolor = lightgrey];
272 -> 598 [arrowhead = none , style=dashed];
598 -> 1[style=dashed];

599 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
274 -> 599 [arrowhead = none ];
599 -> 276;

600 [label="SPLIT 2\nnew knowledge:\nT1008 is ground\nreplacements:T1010 -> T1014,\nT1011 -> T1015,\nT1 -> T1016,\nT3 -> T1017", fontsize=14, style = filled, fillcolor = violet];
274 -> 600 [arrowhead = none ];
600 -> 277;

601 [label="INSTANCE with matching:\nT69 -> T1008\nT71 -> T1010", fontsize=14, style = filled, fillcolor = lightgrey];
276 -> 601 [arrowhead = none , style=dashed];
601 -> 37[style=dashed];

602 [label="INSTANCE with matching:\nT1 -> s(T1014)\nT2 -> T989\nT3 -> T1015", fontsize=14, style = filled, fillcolor = lightgrey];
277 -> 602 [arrowhead = none , style=dashed];
602 -> 1[style=dashed];

}

(2) Obligation:

Triples:

lessA(s(X1), s(X2)) :- lessA(X1, X2).
lessF(s(X1), s(X2)) :- lessF(X1, X2).
pD(X1, X2, X3) :- lessF(X1, X2).
pD(X1, X2, X3) :- ','(lesscF(X1, X2), deleteB(X2, void, X3)).
delminG(tree(X1, X2, X3), X4, tree(X1, X5, X6)) :- delminG(X2, X4, X5).
pC(X1, X2, X3) :- lessA(X1, X2).
pC(X1, X2, X3) :- ','(lesscA(X1, X2), deleteE(X1, X3)).
pH(X1, X2, X3, X4) :- lessF(X1, X2).
pH(X1, X2, X3, X4) :- ','(lesscF(X1, X2), deleteB(X2, X3, X4)).
lessM(s(X1), s(X2)) :- lessM(X1, X2).
pI(X1, X2, X3, X4) :- lessM(X1, X2).
pI(X1, X2, X3, X4) :- ','(lesscM(X1, X2), deleteK(X1, X3, X4)).
deleteK(X1, tree(X1, X2, X3), tree(X4, X2, X5)) :- delminG(X3, X4, X5).
deleteK(X1, tree(X2, X3, X4), tree(X2, X5, X4)) :- pI(X1, X2, X3, X5).
deleteK(X1, tree(X2, X3, X4), tree(X2, X3, X5)) :- pJ(X2, X1, X4, X5).
pJ(X1, X2, X3, X4) :- lessM(X1, X2).
pJ(X1, X2, X3, X4) :- ','(lesscM(X1, X2), deleteK(X2, X3, X4)).
pL(X1, X2, X3, X4) :- lessF(X1, X2).
pL(X1, X2, X3, X4) :- ','(lesscF(X1, X2), deleteB(X2, X3, X4)).
deleteB(X1, tree(X2, void, void), tree(X2, X3, void)) :- pC(X1, X2, X3).
deleteB(X1, tree(X2, void, void), tree(X2, void, X3)) :- pD(X2, X1, X3).
deleteB(0, tree(s(X1), void, void), tree(s(X1), X2, void)) :- deleteE(0, X2).
deleteB(s(X1), tree(s(X2), void, void), tree(s(X2), X3, void)) :- lessA(X1, X2).
deleteB(s(X1), tree(s(X2), void, void), tree(s(X2), X3, void)) :- ','(lesscA(X1, X2), deleteE(s(X1), X3)).
deleteB(X1, tree(X2, void, void), tree(X2, void, X3)) :- pD(X2, X1, X3).
deleteB(s(X1), tree(0, void, void), tree(0, void, X2)) :- deleteB(s(X1), void, X2).
deleteB(s(X1), tree(s(X2), void, void), tree(s(X2), void, X3)) :- lessF(X2, X1).
deleteB(s(X1), tree(s(X2), void, void), tree(s(X2), void, X3)) :- ','(lesscF(X2, X1), deleteB(s(X1), void, X3)).
deleteB(X1, tree(X1, void, tree(X2, X3, X4)), tree(X5, void, tree(X2, X6, X7))) :- delminG(X3, X5, X6).
deleteB(X1, tree(X2, void, X3), tree(X2, X4, X3)) :- pC(X1, X2, X4).
deleteB(X1, tree(X2, void, X3), tree(X2, void, X4)) :- pH(X2, X1, X3, X4).
deleteB(0, tree(s(X1), void, X2), tree(s(X1), X3, X2)) :- deleteE(0, X3).
deleteB(s(X1), tree(s(X2), void, X3), tree(s(X2), X4, X3)) :- lessA(X1, X2).
deleteB(s(X1), tree(s(X2), void, X3), tree(s(X2), X4, X3)) :- ','(lesscA(X1, X2), deleteE(s(X1), X4)).
deleteB(X1, tree(X2, void, X3), tree(X2, void, X4)) :- pH(X2, X1, X3, X4).
deleteB(s(X1), tree(0, void, X2), tree(0, void, X3)) :- deleteB(s(X1), X2, X3).
deleteB(s(X1), tree(s(X2), void, X3), tree(s(X2), void, X4)) :- lessF(X2, X1).
deleteB(s(X1), tree(s(X2), void, X3), tree(s(X2), void, X4)) :- ','(lesscF(X2, X1), deleteB(s(X1), X3, X4)).
deleteB(X1, tree(X2, X3, void), tree(X2, X4, void)) :- lessA(X1, X2).
deleteB(X1, tree(X2, tree(X1, X3, X4), void), tree(X2, tree(X5, X3, X6), void)) :- ','(lesscA(X1, X2), delminG(X4, X5, X6)).
deleteB(X1, tree(X2, tree(X3, X4, X5), void), tree(X2, tree(X3, X6, X5), void)) :- ','(lesscA(X1, X2), pI(X1, X3, X4, X6)).
deleteB(X1, tree(X2, tree(X3, X4, X5), void), tree(X2, tree(X3, X4, X6), void)) :- ','(lesscA(X1, X2), pJ(X3, X1, X5, X6)).
deleteB(X1, tree(X2, X3, void), tree(X2, X3, X4)) :- pD(X2, X1, X4).
deleteB(0, tree(s(X1), X2, void), tree(s(X1), X3, void)) :- deleteK(0, X2, X3).
deleteB(s(X1), tree(s(X2), X3, void), tree(s(X2), X4, void)) :- lessA(X1, X2).
deleteB(s(X1), tree(s(X2), X3, void), tree(s(X2), X4, void)) :- ','(lesscA(X1, X2), deleteK(s(X1), X3, X4)).
deleteB(X1, tree(X2, X3, void), tree(X2, X3, X4)) :- pD(X2, X1, X4).
deleteB(s(X1), tree(0, X2, void), tree(0, X2, X3)) :- deleteB(s(X1), void, X3).
deleteB(s(X1), tree(s(X2), X3, void), tree(s(X2), X3, X4)) :- lessF(X2, X1).
deleteB(s(X1), tree(s(X2), X3, void), tree(s(X2), X3, X4)) :- ','(lesscF(X2, X1), deleteB(s(X1), void, X4)).
deleteB(X1, tree(X1, X2, tree(X3, X4, X5)), tree(X6, X2, tree(X3, X7, X8))) :- delminG(X4, X6, X7).
deleteB(X1, tree(X2, X3, X4), tree(X2, X5, X4)) :- lessA(X1, X2).
deleteB(X1, tree(X2, X3, X4), tree(X2, X5, X4)) :- ','(lesscA(X1, X2), deleteK(X1, X3, X5)).
deleteB(X1, tree(X2, X3, X4), tree(X2, X3, X5)) :- pL(X2, X1, X4, X5).
deleteB(0, tree(s(X1), X2, X3), tree(s(X1), X4, X3)) :- deleteK(0, X2, X4).
deleteB(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) :- lessA(X1, X2).
deleteB(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) :- ','(lesscA(X1, X2), deleteK(s(X1), X3, X5)).
deleteB(X1, tree(X2, X3, X4), tree(X2, X3, X5)) :- pL(X2, X1, X4, X5).
deleteB(s(X1), tree(0, X2, X3), tree(0, X2, X4)) :- deleteB(s(X1), X3, X4).
deleteB(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) :- lessF(X2, X1).
deleteB(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) :- ','(lesscF(X2, X1), deleteB(s(X1), X4, X5)).

Clauses:

lesscA(0, s(X1)).
lesscA(s(X1), s(X2)) :- lesscA(X1, X2).
deletecB(X1, tree(X1, void, X2), X2).
deletecB(X1, tree(X1, void, void), void).
deletecB(X1, tree(X2, void, void), tree(X2, X3, void)) :- qcC(X1, X2, X3).
deletecB(X1, tree(X2, void, void), tree(X2, void, X3)) :- qcD(X2, X1, X3).
deletecB(0, tree(s(X1), void, void), tree(s(X1), X2, void)) :- deletecE(0, X2).
deletecB(s(X1), tree(s(X2), void, void), tree(s(X2), X3, void)) :- ','(lesscA(X1, X2), deletecE(s(X1), X3)).
deletecB(X1, tree(X2, void, void), tree(X2, void, X3)) :- qcD(X2, X1, X3).
deletecB(s(X1), tree(0, void, void), tree(0, void, X2)) :- deletecB(s(X1), void, X2).
deletecB(s(X1), tree(s(X2), void, void), tree(s(X2), void, X3)) :- ','(lesscF(X2, X1), deletecB(s(X1), void, X3)).
deletecB(X1, tree(X1, void, tree(X2, void, X3)), tree(X2, void, X3)).
deletecB(X1, tree(X1, void, tree(X2, X3, X4)), tree(X5, void, tree(X2, X6, X7))) :- delmincG(X3, X5, X6).
deletecB(X1, tree(X2, void, X3), tree(X2, X4, X3)) :- qcC(X1, X2, X4).
deletecB(X1, tree(X2, void, X3), tree(X2, void, X4)) :- qcH(X2, X1, X3, X4).
deletecB(0, tree(s(X1), void, X2), tree(s(X1), X3, X2)) :- deletecE(0, X3).
deletecB(s(X1), tree(s(X2), void, X3), tree(s(X2), X4, X3)) :- ','(lesscA(X1, X2), deletecE(s(X1), X4)).
deletecB(X1, tree(X2, void, X3), tree(X2, void, X4)) :- qcH(X2, X1, X3, X4).
deletecB(s(X1), tree(0, void, X2), tree(0, void, X3)) :- deletecB(s(X1), X2, X3).
deletecB(s(X1), tree(s(X2), void, X3), tree(s(X2), void, X4)) :- ','(lesscF(X2, X1), deletecB(s(X1), X3, X4)).
deletecB(X1, tree(X1, X2, void), X2).
deletecB(X1, tree(X2, tree(X1, void, X3), void), tree(X2, X3, void)) :- lesscA(X1, X2).
deletecB(X1, tree(X2, tree(X1, X3, void), void), tree(X2, X3, void)) :- lesscA(X1, X2).
deletecB(X1, tree(X2, tree(X1, X3, X4), void), tree(X2, tree(X5, X3, X6), void)) :- ','(lesscA(X1, X2), delmincG(X4, X5, X6)).
deletecB(X1, tree(X2, tree(X3, X4, X5), void), tree(X2, tree(X3, X6, X5), void)) :- ','(lesscA(X1, X2), qcI(X1, X3, X4, X6)).
deletecB(X1, tree(X2, tree(X3, X4, X5), void), tree(X2, tree(X3, X4, X6), void)) :- ','(lesscA(X1, X2), qcJ(X3, X1, X5, X6)).
deletecB(X1, tree(X2, X3, void), tree(X2, X3, X4)) :- qcD(X2, X1, X4).
deletecB(0, tree(s(X1), X2, void), tree(s(X1), X3, void)) :- deletecK(0, X2, X3).
deletecB(s(X1), tree(s(X2), X3, void), tree(s(X2), X4, void)) :- ','(lesscA(X1, X2), deletecK(s(X1), X3, X4)).
deletecB(X1, tree(X2, X3, void), tree(X2, X3, X4)) :- qcD(X2, X1, X4).
deletecB(s(X1), tree(0, X2, void), tree(0, X2, X3)) :- deletecB(s(X1), void, X3).
deletecB(s(X1), tree(s(X2), X3, void), tree(s(X2), X3, X4)) :- ','(lesscF(X2, X1), deletecB(s(X1), void, X4)).
deletecB(X1, tree(X1, X2, tree(X3, void, X4)), tree(X3, X2, X4)).
deletecB(X1, tree(X1, X2, tree(X3, X4, X5)), tree(X6, X2, tree(X3, X7, X8))) :- delmincG(X4, X6, X7).
deletecB(X1, tree(X2, X3, X4), tree(X2, X5, X4)) :- ','(lesscA(X1, X2), deletecK(X1, X3, X5)).
deletecB(X1, tree(X2, X3, X4), tree(X2, X3, X5)) :- qcL(X2, X1, X4, X5).
deletecB(0, tree(s(X1), X2, X3), tree(s(X1), X4, X3)) :- deletecK(0, X2, X4).
deletecB(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) :- ','(lesscA(X1, X2), deletecK(s(X1), X3, X5)).
deletecB(X1, tree(X2, X3, X4), tree(X2, X3, X5)) :- qcL(X2, X1, X4, X5).
deletecB(s(X1), tree(0, X2, X3), tree(0, X2, X4)) :- deletecB(s(X1), X3, X4).
deletecB(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) :- ','(lesscF(X2, X1), deletecB(s(X1), X4, X5)).
lesscF(0, s(X1)).
lesscF(s(X1), s(X2)) :- lesscF(X1, X2).
qcD(X1, X2, X3) :- ','(lesscF(X1, X2), deletecB(X2, void, X3)).
delmincG(tree(X1, void, X2), X1, X2).
delmincG(tree(X1, X2, X3), X4, tree(X1, X5, X6)) :- delmincG(X2, X4, X5).
qcC(X1, X2, X3) :- ','(lesscA(X1, X2), deletecE(X1, X3)).
qcH(X1, X2, X3, X4) :- ','(lesscF(X1, X2), deletecB(X2, X3, X4)).
lesscM(0, s(X1)).
lesscM(s(X1), s(X2)) :- lesscM(X1, X2).
qcI(X1, X2, X3, X4) :- ','(lesscM(X1, X2), deletecK(X1, X3, X4)).
deletecK(X1, tree(X1, void, X2), X2).
deletecK(X1, tree(X1, X2, void), X2).
deletecK(X1, tree(X1, X2, X3), tree(X4, X2, X5)) :- delmincG(X3, X4, X5).
deletecK(X1, tree(X2, X3, X4), tree(X2, X5, X4)) :- qcI(X1, X2, X3, X5).
deletecK(X1, tree(X2, X3, X4), tree(X2, X3, X5)) :- qcJ(X2, X1, X4, X5).
qcJ(X1, X2, X3, X4) :- ','(lesscM(X1, X2), deletecK(X2, X3, X4)).
qcL(X1, X2, X3, X4) :- ','(lesscF(X1, X2), deletecB(X2, X3, X4)).

Afs:

deleteB(x1, x2, x3)  =  deleteB(x2)

(3) UndefinedPredicateInTriplesTransformerProof (SOUND transformation)

Deleted triples and predicates having undefined goals [DT09].

(4) Obligation:

Triples:

lessA(s(X1), s(X2)) :- lessA(X1, X2).
lessF(s(X1), s(X2)) :- lessF(X1, X2).
pD(X1, X2, X3) :- lessF(X1, X2).
pD(X1, X2, X3) :- ','(lesscF(X1, X2), deleteB(X2, void, X3)).
delminG(tree(X1, X2, X3), X4, tree(X1, X5, X6)) :- delminG(X2, X4, X5).
pC(X1, X2, X3) :- lessA(X1, X2).
pH(X1, X2, X3, X4) :- lessF(X1, X2).
pH(X1, X2, X3, X4) :- ','(lesscF(X1, X2), deleteB(X2, X3, X4)).
lessM(s(X1), s(X2)) :- lessM(X1, X2).
pI(X1, X2, X3, X4) :- lessM(X1, X2).
pI(X1, X2, X3, X4) :- ','(lesscM(X1, X2), deleteK(X1, X3, X4)).
deleteK(X1, tree(X1, X2, X3), tree(X4, X2, X5)) :- delminG(X3, X4, X5).
deleteK(X1, tree(X2, X3, X4), tree(X2, X5, X4)) :- pI(X1, X2, X3, X5).
deleteK(X1, tree(X2, X3, X4), tree(X2, X3, X5)) :- pJ(X2, X1, X4, X5).
pJ(X1, X2, X3, X4) :- lessM(X1, X2).
pJ(X1, X2, X3, X4) :- ','(lesscM(X1, X2), deleteK(X2, X3, X4)).
pL(X1, X2, X3, X4) :- lessF(X1, X2).
pL(X1, X2, X3, X4) :- ','(lesscF(X1, X2), deleteB(X2, X3, X4)).
deleteB(X1, tree(X2, void, void), tree(X2, X3, void)) :- pC(X1, X2, X3).
deleteB(X1, tree(X2, void, void), tree(X2, void, X3)) :- pD(X2, X1, X3).
deleteB(s(X1), tree(s(X2), void, void), tree(s(X2), X3, void)) :- lessA(X1, X2).
deleteB(X1, tree(X2, void, void), tree(X2, void, X3)) :- pD(X2, X1, X3).
deleteB(s(X1), tree(0, void, void), tree(0, void, X2)) :- deleteB(s(X1), void, X2).
deleteB(s(X1), tree(s(X2), void, void), tree(s(X2), void, X3)) :- lessF(X2, X1).
deleteB(s(X1), tree(s(X2), void, void), tree(s(X2), void, X3)) :- ','(lesscF(X2, X1), deleteB(s(X1), void, X3)).
deleteB(X1, tree(X1, void, tree(X2, X3, X4)), tree(X5, void, tree(X2, X6, X7))) :- delminG(X3, X5, X6).
deleteB(X1, tree(X2, void, X3), tree(X2, X4, X3)) :- pC(X1, X2, X4).
deleteB(X1, tree(X2, void, X3), tree(X2, void, X4)) :- pH(X2, X1, X3, X4).
deleteB(s(X1), tree(s(X2), void, X3), tree(s(X2), X4, X3)) :- lessA(X1, X2).
deleteB(X1, tree(X2, void, X3), tree(X2, void, X4)) :- pH(X2, X1, X3, X4).
deleteB(s(X1), tree(0, void, X2), tree(0, void, X3)) :- deleteB(s(X1), X2, X3).
deleteB(s(X1), tree(s(X2), void, X3), tree(s(X2), void, X4)) :- lessF(X2, X1).
deleteB(s(X1), tree(s(X2), void, X3), tree(s(X2), void, X4)) :- ','(lesscF(X2, X1), deleteB(s(X1), X3, X4)).
deleteB(X1, tree(X2, X3, void), tree(X2, X4, void)) :- lessA(X1, X2).
deleteB(X1, tree(X2, tree(X1, X3, X4), void), tree(X2, tree(X5, X3, X6), void)) :- ','(lesscA(X1, X2), delminG(X4, X5, X6)).
deleteB(X1, tree(X2, tree(X3, X4, X5), void), tree(X2, tree(X3, X6, X5), void)) :- ','(lesscA(X1, X2), pI(X1, X3, X4, X6)).
deleteB(X1, tree(X2, tree(X3, X4, X5), void), tree(X2, tree(X3, X4, X6), void)) :- ','(lesscA(X1, X2), pJ(X3, X1, X5, X6)).
deleteB(X1, tree(X2, X3, void), tree(X2, X3, X4)) :- pD(X2, X1, X4).
deleteB(0, tree(s(X1), X2, void), tree(s(X1), X3, void)) :- deleteK(0, X2, X3).
deleteB(s(X1), tree(s(X2), X3, void), tree(s(X2), X4, void)) :- lessA(X1, X2).
deleteB(s(X1), tree(s(X2), X3, void), tree(s(X2), X4, void)) :- ','(lesscA(X1, X2), deleteK(s(X1), X3, X4)).
deleteB(X1, tree(X2, X3, void), tree(X2, X3, X4)) :- pD(X2, X1, X4).
deleteB(s(X1), tree(0, X2, void), tree(0, X2, X3)) :- deleteB(s(X1), void, X3).
deleteB(s(X1), tree(s(X2), X3, void), tree(s(X2), X3, X4)) :- lessF(X2, X1).
deleteB(s(X1), tree(s(X2), X3, void), tree(s(X2), X3, X4)) :- ','(lesscF(X2, X1), deleteB(s(X1), void, X4)).
deleteB(X1, tree(X1, X2, tree(X3, X4, X5)), tree(X6, X2, tree(X3, X7, X8))) :- delminG(X4, X6, X7).
deleteB(X1, tree(X2, X3, X4), tree(X2, X5, X4)) :- lessA(X1, X2).
deleteB(X1, tree(X2, X3, X4), tree(X2, X5, X4)) :- ','(lesscA(X1, X2), deleteK(X1, X3, X5)).
deleteB(X1, tree(X2, X3, X4), tree(X2, X3, X5)) :- pL(X2, X1, X4, X5).
deleteB(0, tree(s(X1), X2, X3), tree(s(X1), X4, X3)) :- deleteK(0, X2, X4).
deleteB(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) :- lessA(X1, X2).
deleteB(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) :- ','(lesscA(X1, X2), deleteK(s(X1), X3, X5)).
deleteB(X1, tree(X2, X3, X4), tree(X2, X3, X5)) :- pL(X2, X1, X4, X5).
deleteB(s(X1), tree(0, X2, X3), tree(0, X2, X4)) :- deleteB(s(X1), X3, X4).
deleteB(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) :- lessF(X2, X1).
deleteB(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) :- ','(lesscF(X2, X1), deleteB(s(X1), X4, X5)).

Clauses:

lesscA(0, s(X1)).
lesscA(s(X1), s(X2)) :- lesscA(X1, X2).
deletecB(X1, tree(X1, void, X2), X2).
deletecB(X1, tree(X1, void, void), void).
deletecB(X1, tree(X2, void, void), tree(X2, void, X3)) :- qcD(X2, X1, X3).
deletecB(X1, tree(X2, void, void), tree(X2, void, X3)) :- qcD(X2, X1, X3).
deletecB(s(X1), tree(0, void, void), tree(0, void, X2)) :- deletecB(s(X1), void, X2).
deletecB(s(X1), tree(s(X2), void, void), tree(s(X2), void, X3)) :- ','(lesscF(X2, X1), deletecB(s(X1), void, X3)).
deletecB(X1, tree(X1, void, tree(X2, void, X3)), tree(X2, void, X3)).
deletecB(X1, tree(X1, void, tree(X2, X3, X4)), tree(X5, void, tree(X2, X6, X7))) :- delmincG(X3, X5, X6).
deletecB(X1, tree(X2, void, X3), tree(X2, void, X4)) :- qcH(X2, X1, X3, X4).
deletecB(X1, tree(X2, void, X3), tree(X2, void, X4)) :- qcH(X2, X1, X3, X4).
deletecB(s(X1), tree(0, void, X2), tree(0, void, X3)) :- deletecB(s(X1), X2, X3).
deletecB(s(X1), tree(s(X2), void, X3), tree(s(X2), void, X4)) :- ','(lesscF(X2, X1), deletecB(s(X1), X3, X4)).
deletecB(X1, tree(X1, X2, void), X2).
deletecB(X1, tree(X2, tree(X1, void, X3), void), tree(X2, X3, void)) :- lesscA(X1, X2).
deletecB(X1, tree(X2, tree(X1, X3, void), void), tree(X2, X3, void)) :- lesscA(X1, X2).
deletecB(X1, tree(X2, tree(X1, X3, X4), void), tree(X2, tree(X5, X3, X6), void)) :- ','(lesscA(X1, X2), delmincG(X4, X5, X6)).
deletecB(X1, tree(X2, tree(X3, X4, X5), void), tree(X2, tree(X3, X6, X5), void)) :- ','(lesscA(X1, X2), qcI(X1, X3, X4, X6)).
deletecB(X1, tree(X2, tree(X3, X4, X5), void), tree(X2, tree(X3, X4, X6), void)) :- ','(lesscA(X1, X2), qcJ(X3, X1, X5, X6)).
deletecB(X1, tree(X2, X3, void), tree(X2, X3, X4)) :- qcD(X2, X1, X4).
deletecB(0, tree(s(X1), X2, void), tree(s(X1), X3, void)) :- deletecK(0, X2, X3).
deletecB(s(X1), tree(s(X2), X3, void), tree(s(X2), X4, void)) :- ','(lesscA(X1, X2), deletecK(s(X1), X3, X4)).
deletecB(X1, tree(X2, X3, void), tree(X2, X3, X4)) :- qcD(X2, X1, X4).
deletecB(s(X1), tree(0, X2, void), tree(0, X2, X3)) :- deletecB(s(X1), void, X3).
deletecB(s(X1), tree(s(X2), X3, void), tree(s(X2), X3, X4)) :- ','(lesscF(X2, X1), deletecB(s(X1), void, X4)).
deletecB(X1, tree(X1, X2, tree(X3, void, X4)), tree(X3, X2, X4)).
deletecB(X1, tree(X1, X2, tree(X3, X4, X5)), tree(X6, X2, tree(X3, X7, X8))) :- delmincG(X4, X6, X7).
deletecB(X1, tree(X2, X3, X4), tree(X2, X5, X4)) :- ','(lesscA(X1, X2), deletecK(X1, X3, X5)).
deletecB(X1, tree(X2, X3, X4), tree(X2, X3, X5)) :- qcL(X2, X1, X4, X5).
deletecB(0, tree(s(X1), X2, X3), tree(s(X1), X4, X3)) :- deletecK(0, X2, X4).
deletecB(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) :- ','(lesscA(X1, X2), deletecK(s(X1), X3, X5)).
deletecB(X1, tree(X2, X3, X4), tree(X2, X3, X5)) :- qcL(X2, X1, X4, X5).
deletecB(s(X1), tree(0, X2, X3), tree(0, X2, X4)) :- deletecB(s(X1), X3, X4).
deletecB(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) :- ','(lesscF(X2, X1), deletecB(s(X1), X4, X5)).
lesscF(0, s(X1)).
lesscF(s(X1), s(X2)) :- lesscF(X1, X2).
qcD(X1, X2, X3) :- ','(lesscF(X1, X2), deletecB(X2, void, X3)).
delmincG(tree(X1, void, X2), X1, X2).
delmincG(tree(X1, X2, X3), X4, tree(X1, X5, X6)) :- delmincG(X2, X4, X5).
qcH(X1, X2, X3, X4) :- ','(lesscF(X1, X2), deletecB(X2, X3, X4)).
lesscM(0, s(X1)).
lesscM(s(X1), s(X2)) :- lesscM(X1, X2).
qcI(X1, X2, X3, X4) :- ','(lesscM(X1, X2), deletecK(X1, X3, X4)).
deletecK(X1, tree(X1, void, X2), X2).
deletecK(X1, tree(X1, X2, void), X2).
deletecK(X1, tree(X1, X2, X3), tree(X4, X2, X5)) :- delmincG(X3, X4, X5).
deletecK(X1, tree(X2, X3, X4), tree(X2, X5, X4)) :- qcI(X1, X2, X3, X5).
deletecK(X1, tree(X2, X3, X4), tree(X2, X3, X5)) :- qcJ(X2, X1, X4, X5).
qcJ(X1, X2, X3, X4) :- ','(lesscM(X1, X2), deletecK(X2, X3, X4)).
qcL(X1, X2, X3, X4) :- ','(lesscF(X1, X2), deletecB(X2, X3, X4)).

Afs:

deleteB(x1, x2, x3)  =  deleteB(x2)

(5) TriplesToPiDPProof (SOUND transformation)

We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes:
deleteB_in: (f,b,f)
pC_in: (f,b,f)
lessA_in: (f,b)
pD_in: (b,f,f)
lessF_in: (b,f)
lesscF_in: (b,f)
delminG_in: (b,f,f)
pH_in: (b,f,b,f)
lesscA_in: (b,b) (f,b)
pI_in: (b,b,b,f)
lessM_in: (b,b)
lesscM_in: (b,b)
deleteK_in: (b,b,f)
pJ_in: (b,b,b,f)
pL_in: (b,f,b,f)
Transforming TRIPLES into the following Term Rewriting System:
Pi DP problem:
The TRS P consists of the following rules:

DELETEB_IN_AGA(X1, tree(X2, void, void), tree(X2, X3, void)) → U24_AGA(X1, X2, X3, pC_in_aga(X1, X2, X3))
DELETEB_IN_AGA(X1, tree(X2, void, void), tree(X2, X3, void)) → PC_IN_AGA(X1, X2, X3)
PC_IN_AGA(X1, X2, X3) → U7_AGA(X1, X2, X3, lessA_in_ag(X1, X2))
PC_IN_AGA(X1, X2, X3) → LESSA_IN_AG(X1, X2)
LESSA_IN_AG(s(X1), s(X2)) → U1_AG(X1, X2, lessA_in_ag(X1, X2))
LESSA_IN_AG(s(X1), s(X2)) → LESSA_IN_AG(X1, X2)
DELETEB_IN_AGA(X1, tree(X2, void, void), tree(X2, void, X3)) → U25_AGA(X1, X2, X3, pD_in_gaa(X2, X1, X3))
DELETEB_IN_AGA(X1, tree(X2, void, void), tree(X2, void, X3)) → PD_IN_GAA(X2, X1, X3)
PD_IN_GAA(X1, X2, X3) → U3_GAA(X1, X2, X3, lessF_in_ga(X1, X2))
PD_IN_GAA(X1, X2, X3) → LESSF_IN_GA(X1, X2)
LESSF_IN_GA(s(X1), s(X2)) → U2_GA(X1, X2, lessF_in_ga(X1, X2))
LESSF_IN_GA(s(X1), s(X2)) → LESSF_IN_GA(X1, X2)
PD_IN_GAA(X1, X2, X3) → U4_GAA(X1, X2, X3, lesscF_in_ga(X1, X2))
U4_GAA(X1, X2, X3, lesscF_out_ga(X1, X2)) → U5_GAA(X1, X2, X3, deleteB_in_aga(X2, void, X3))
U4_GAA(X1, X2, X3, lesscF_out_ga(X1, X2)) → DELETEB_IN_AGA(X2, void, X3)
DELETEB_IN_AGA(s(X1), tree(s(X2), void, void), tree(s(X2), X3, void)) → U26_AGA(X1, X2, X3, lessA_in_ag(X1, X2))
DELETEB_IN_AGA(s(X1), tree(s(X2), void, void), tree(s(X2), X3, void)) → LESSA_IN_AG(X1, X2)
DELETEB_IN_AGA(s(X1), tree(0, void, void), tree(0, void, X2)) → U27_AGA(X1, X2, deleteB_in_aga(s(X1), void, X2))
DELETEB_IN_AGA(s(X1), tree(0, void, void), tree(0, void, X2)) → DELETEB_IN_AGA(s(X1), void, X2)
DELETEB_IN_AGA(s(X1), tree(s(X2), void, void), tree(s(X2), void, X3)) → U28_AGA(X1, X2, X3, lessF_in_ga(X2, X1))
DELETEB_IN_AGA(s(X1), tree(s(X2), void, void), tree(s(X2), void, X3)) → LESSF_IN_GA(X2, X1)
DELETEB_IN_AGA(s(X1), tree(s(X2), void, void), tree(s(X2), void, X3)) → U29_AGA(X1, X2, X3, lesscF_in_ga(X2, X1))
U29_AGA(X1, X2, X3, lesscF_out_ga(X2, X1)) → U30_AGA(X1, X2, X3, deleteB_in_aga(s(X1), void, X3))
U29_AGA(X1, X2, X3, lesscF_out_ga(X2, X1)) → DELETEB_IN_AGA(s(X1), void, X3)
DELETEB_IN_AGA(X1, tree(X1, void, tree(X2, X3, X4)), tree(X5, void, tree(X2, X6, X7))) → U31_AGA(X1, X2, X3, X4, X5, X6, X7, delminG_in_gaa(X3, X5, X6))
DELETEB_IN_AGA(X1, tree(X1, void, tree(X2, X3, X4)), tree(X5, void, tree(X2, X6, X7))) → DELMING_IN_GAA(X3, X5, X6)
DELMING_IN_GAA(tree(X1, X2, X3), X4, tree(X1, X5, X6)) → U6_GAA(X1, X2, X3, X4, X5, X6, delminG_in_gaa(X2, X4, X5))
DELMING_IN_GAA(tree(X1, X2, X3), X4, tree(X1, X5, X6)) → DELMING_IN_GAA(X2, X4, X5)
DELETEB_IN_AGA(X1, tree(X2, void, X3), tree(X2, X4, X3)) → U32_AGA(X1, X2, X3, X4, pC_in_aga(X1, X2, X4))
DELETEB_IN_AGA(X1, tree(X2, void, X3), tree(X2, X4, X3)) → PC_IN_AGA(X1, X2, X4)
DELETEB_IN_AGA(X1, tree(X2, void, X3), tree(X2, void, X4)) → U33_AGA(X1, X2, X3, X4, pH_in_gaga(X2, X1, X3, X4))
DELETEB_IN_AGA(X1, tree(X2, void, X3), tree(X2, void, X4)) → PH_IN_GAGA(X2, X1, X3, X4)
PH_IN_GAGA(X1, X2, X3, X4) → U8_GAGA(X1, X2, X3, X4, lessF_in_ga(X1, X2))
PH_IN_GAGA(X1, X2, X3, X4) → LESSF_IN_GA(X1, X2)
PH_IN_GAGA(X1, X2, X3, X4) → U9_GAGA(X1, X2, X3, X4, lesscF_in_ga(X1, X2))
U9_GAGA(X1, X2, X3, X4, lesscF_out_ga(X1, X2)) → U10_GAGA(X1, X2, X3, X4, deleteB_in_aga(X2, X3, X4))
U9_GAGA(X1, X2, X3, X4, lesscF_out_ga(X1, X2)) → DELETEB_IN_AGA(X2, X3, X4)
DELETEB_IN_AGA(s(X1), tree(s(X2), void, X3), tree(s(X2), X4, X3)) → U34_AGA(X1, X2, X3, X4, lessA_in_ag(X1, X2))
DELETEB_IN_AGA(s(X1), tree(s(X2), void, X3), tree(s(X2), X4, X3)) → LESSA_IN_AG(X1, X2)
DELETEB_IN_AGA(s(X1), tree(0, void, X2), tree(0, void, X3)) → U35_AGA(X1, X2, X3, deleteB_in_aga(s(X1), X2, X3))
DELETEB_IN_AGA(s(X1), tree(0, void, X2), tree(0, void, X3)) → DELETEB_IN_AGA(s(X1), X2, X3)
DELETEB_IN_AGA(s(X1), tree(s(X2), void, X3), tree(s(X2), void, X4)) → U36_AGA(X1, X2, X3, X4, lessF_in_ga(X2, X1))
DELETEB_IN_AGA(s(X1), tree(s(X2), void, X3), tree(s(X2), void, X4)) → LESSF_IN_GA(X2, X1)
DELETEB_IN_AGA(s(X1), tree(s(X2), void, X3), tree(s(X2), void, X4)) → U37_AGA(X1, X2, X3, X4, lesscF_in_ga(X2, X1))
U37_AGA(X1, X2, X3, X4, lesscF_out_ga(X2, X1)) → U38_AGA(X1, X2, X3, X4, deleteB_in_aga(s(X1), X3, X4))
U37_AGA(X1, X2, X3, X4, lesscF_out_ga(X2, X1)) → DELETEB_IN_AGA(s(X1), X3, X4)
DELETEB_IN_AGA(X1, tree(X2, X3, void), tree(X2, X4, void)) → U39_AGA(X1, X2, X3, X4, lessA_in_ag(X1, X2))
DELETEB_IN_AGA(X1, tree(X2, X3, void), tree(X2, X4, void)) → LESSA_IN_AG(X1, X2)
DELETEB_IN_AGA(X1, tree(X2, tree(X1, X3, X4), void), tree(X2, tree(X5, X3, X6), void)) → U40_AGA(X1, X2, X3, X4, X5, X6, lesscA_in_gg(X1, X2))
U40_AGA(X1, X2, X3, X4, X5, X6, lesscA_out_gg(X1, X2)) → U41_AGA(X1, X2, X3, X4, X5, X6, delminG_in_gaa(X4, X5, X6))
U40_AGA(X1, X2, X3, X4, X5, X6, lesscA_out_gg(X1, X2)) → DELMING_IN_GAA(X4, X5, X6)
DELETEB_IN_AGA(X1, tree(X2, tree(X3, X4, X5), void), tree(X2, tree(X3, X6, X5), void)) → U42_AGA(X1, X2, X3, X4, X5, X6, lesscA_in_ag(X1, X2))
U42_AGA(X1, X2, X3, X4, X5, X6, lesscA_out_ag(X1, X2)) → U43_AGA(X1, X2, X3, X4, X5, X6, pI_in_ggga(X1, X3, X4, X6))
U42_AGA(X1, X2, X3, X4, X5, X6, lesscA_out_ag(X1, X2)) → PI_IN_GGGA(X1, X3, X4, X6)
PI_IN_GGGA(X1, X2, X3, X4) → U12_GGGA(X1, X2, X3, X4, lessM_in_gg(X1, X2))
PI_IN_GGGA(X1, X2, X3, X4) → LESSM_IN_GG(X1, X2)
LESSM_IN_GG(s(X1), s(X2)) → U11_GG(X1, X2, lessM_in_gg(X1, X2))
LESSM_IN_GG(s(X1), s(X2)) → LESSM_IN_GG(X1, X2)
PI_IN_GGGA(X1, X2, X3, X4) → U13_GGGA(X1, X2, X3, X4, lesscM_in_gg(X1, X2))
U13_GGGA(X1, X2, X3, X4, lesscM_out_gg(X1, X2)) → U14_GGGA(X1, X2, X3, X4, deleteK_in_gga(X1, X3, X4))
U13_GGGA(X1, X2, X3, X4, lesscM_out_gg(X1, X2)) → DELETEK_IN_GGA(X1, X3, X4)
DELETEK_IN_GGA(X1, tree(X1, X2, X3), tree(X4, X2, X5)) → U15_GGA(X1, X2, X3, X4, X5, delminG_in_gaa(X3, X4, X5))
DELETEK_IN_GGA(X1, tree(X1, X2, X3), tree(X4, X2, X5)) → DELMING_IN_GAA(X3, X4, X5)
DELETEK_IN_GGA(X1, tree(X2, X3, X4), tree(X2, X5, X4)) → U16_GGA(X1, X2, X3, X4, X5, pI_in_ggga(X1, X2, X3, X5))
DELETEK_IN_GGA(X1, tree(X2, X3, X4), tree(X2, X5, X4)) → PI_IN_GGGA(X1, X2, X3, X5)
DELETEK_IN_GGA(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → U17_GGA(X1, X2, X3, X4, X5, pJ_in_ggga(X2, X1, X4, X5))
DELETEK_IN_GGA(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → PJ_IN_GGGA(X2, X1, X4, X5)
PJ_IN_GGGA(X1, X2, X3, X4) → U18_GGGA(X1, X2, X3, X4, lessM_in_gg(X1, X2))
PJ_IN_GGGA(X1, X2, X3, X4) → LESSM_IN_GG(X1, X2)
PJ_IN_GGGA(X1, X2, X3, X4) → U19_GGGA(X1, X2, X3, X4, lesscM_in_gg(X1, X2))
U19_GGGA(X1, X2, X3, X4, lesscM_out_gg(X1, X2)) → U20_GGGA(X1, X2, X3, X4, deleteK_in_gga(X2, X3, X4))
U19_GGGA(X1, X2, X3, X4, lesscM_out_gg(X1, X2)) → DELETEK_IN_GGA(X2, X3, X4)
DELETEB_IN_AGA(X1, tree(X2, tree(X3, X4, X5), void), tree(X2, tree(X3, X4, X6), void)) → U44_AGA(X1, X2, X3, X4, X5, X6, lesscA_in_ag(X1, X2))
U44_AGA(X1, X2, X3, X4, X5, X6, lesscA_out_ag(X1, X2)) → U45_AGA(X1, X2, X3, X4, X5, X6, pJ_in_ggga(X3, X1, X5, X6))
U44_AGA(X1, X2, X3, X4, X5, X6, lesscA_out_ag(X1, X2)) → PJ_IN_GGGA(X3, X1, X5, X6)
DELETEB_IN_AGA(X1, tree(X2, X3, void), tree(X2, X3, X4)) → U46_AGA(X1, X2, X3, X4, pD_in_gaa(X2, X1, X4))
DELETEB_IN_AGA(X1, tree(X2, X3, void), tree(X2, X3, X4)) → PD_IN_GAA(X2, X1, X4)
DELETEB_IN_AGA(0, tree(s(X1), X2, void), tree(s(X1), X3, void)) → U47_AGA(X1, X2, X3, deleteK_in_gga(0, X2, X3))
DELETEB_IN_AGA(0, tree(s(X1), X2, void), tree(s(X1), X3, void)) → DELETEK_IN_GGA(0, X2, X3)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, void), tree(s(X2), X4, void)) → U48_AGA(X1, X2, X3, X4, lessA_in_ag(X1, X2))
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, void), tree(s(X2), X4, void)) → LESSA_IN_AG(X1, X2)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, void), tree(s(X2), X4, void)) → U49_AGA(X1, X2, X3, X4, lesscA_in_ag(X1, X2))
U49_AGA(X1, X2, X3, X4, lesscA_out_ag(X1, X2)) → U50_AGA(X1, X2, X3, X4, deleteK_in_gga(s(X1), X3, X4))
U49_AGA(X1, X2, X3, X4, lesscA_out_ag(X1, X2)) → DELETEK_IN_GGA(s(X1), X3, X4)
DELETEB_IN_AGA(s(X1), tree(0, X2, void), tree(0, X2, X3)) → U51_AGA(X1, X2, X3, deleteB_in_aga(s(X1), void, X3))
DELETEB_IN_AGA(s(X1), tree(0, X2, void), tree(0, X2, X3)) → DELETEB_IN_AGA(s(X1), void, X3)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, void), tree(s(X2), X3, X4)) → U52_AGA(X1, X2, X3, X4, lessF_in_ga(X2, X1))
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, void), tree(s(X2), X3, X4)) → LESSF_IN_GA(X2, X1)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, void), tree(s(X2), X3, X4)) → U53_AGA(X1, X2, X3, X4, lesscF_in_ga(X2, X1))
U53_AGA(X1, X2, X3, X4, lesscF_out_ga(X2, X1)) → U54_AGA(X1, X2, X3, X4, deleteB_in_aga(s(X1), void, X4))
U53_AGA(X1, X2, X3, X4, lesscF_out_ga(X2, X1)) → DELETEB_IN_AGA(s(X1), void, X4)
DELETEB_IN_AGA(X1, tree(X1, X2, tree(X3, X4, X5)), tree(X6, X2, tree(X3, X7, X8))) → U55_AGA(X1, X2, X3, X4, X5, X6, X7, X8, delminG_in_gaa(X4, X6, X7))
DELETEB_IN_AGA(X1, tree(X1, X2, tree(X3, X4, X5)), tree(X6, X2, tree(X3, X7, X8))) → DELMING_IN_GAA(X4, X6, X7)
DELETEB_IN_AGA(X1, tree(X2, X3, X4), tree(X2, X5, X4)) → U56_AGA(X1, X2, X3, X4, X5, lessA_in_ag(X1, X2))
DELETEB_IN_AGA(X1, tree(X2, X3, X4), tree(X2, X5, X4)) → LESSA_IN_AG(X1, X2)
DELETEB_IN_AGA(X1, tree(X2, X3, X4), tree(X2, X5, X4)) → U57_AGA(X1, X2, X3, X4, X5, lesscA_in_ag(X1, X2))
U57_AGA(X1, X2, X3, X4, X5, lesscA_out_ag(X1, X2)) → U58_AGA(X1, X2, X3, X4, X5, deleteK_in_gga(X1, X3, X5))
U57_AGA(X1, X2, X3, X4, X5, lesscA_out_ag(X1, X2)) → DELETEK_IN_GGA(X1, X3, X5)
DELETEB_IN_AGA(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → U59_AGA(X1, X2, X3, X4, X5, pL_in_gaga(X2, X1, X4, X5))
DELETEB_IN_AGA(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → PL_IN_GAGA(X2, X1, X4, X5)
PL_IN_GAGA(X1, X2, X3, X4) → U21_GAGA(X1, X2, X3, X4, lessF_in_ga(X1, X2))
PL_IN_GAGA(X1, X2, X3, X4) → LESSF_IN_GA(X1, X2)
PL_IN_GAGA(X1, X2, X3, X4) → U22_GAGA(X1, X2, X3, X4, lesscF_in_ga(X1, X2))
U22_GAGA(X1, X2, X3, X4, lesscF_out_ga(X1, X2)) → U23_GAGA(X1, X2, X3, X4, deleteB_in_aga(X2, X3, X4))
U22_GAGA(X1, X2, X3, X4, lesscF_out_ga(X1, X2)) → DELETEB_IN_AGA(X2, X3, X4)
DELETEB_IN_AGA(0, tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → U60_AGA(X1, X2, X3, X4, deleteK_in_gga(0, X2, X4))
DELETEB_IN_AGA(0, tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → DELETEK_IN_GGA(0, X2, X4)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) → U61_AGA(X1, X2, X3, X4, X5, lessA_in_ag(X1, X2))
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) → LESSA_IN_AG(X1, X2)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) → U62_AGA(X1, X2, X3, X4, X5, lesscA_in_ag(X1, X2))
U62_AGA(X1, X2, X3, X4, X5, lesscA_out_ag(X1, X2)) → U63_AGA(X1, X2, X3, X4, X5, deleteK_in_gga(s(X1), X3, X5))
U62_AGA(X1, X2, X3, X4, X5, lesscA_out_ag(X1, X2)) → DELETEK_IN_GGA(s(X1), X3, X5)
DELETEB_IN_AGA(s(X1), tree(0, X2, X3), tree(0, X2, X4)) → U64_AGA(X1, X2, X3, X4, deleteB_in_aga(s(X1), X3, X4))
DELETEB_IN_AGA(s(X1), tree(0, X2, X3), tree(0, X2, X4)) → DELETEB_IN_AGA(s(X1), X3, X4)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) → U65_AGA(X1, X2, X3, X4, X5, lessF_in_ga(X2, X1))
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) → LESSF_IN_GA(X2, X1)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) → U66_AGA(X1, X2, X3, X4, X5, lesscF_in_ga(X2, X1))
U66_AGA(X1, X2, X3, X4, X5, lesscF_out_ga(X2, X1)) → U67_AGA(X1, X2, X3, X4, X5, deleteB_in_aga(s(X1), X4, X5))
U66_AGA(X1, X2, X3, X4, X5, lesscF_out_ga(X2, X1)) → DELETEB_IN_AGA(s(X1), X4, X5)

The TRS R consists of the following rules:

lesscF_in_ga(0, s(X1)) → lesscF_out_ga(0, s(X1))
lesscF_in_ga(s(X1), s(X2)) → U104_ga(X1, X2, lesscF_in_ga(X1, X2))
U104_ga(X1, X2, lesscF_out_ga(X1, X2)) → lesscF_out_ga(s(X1), s(X2))
lesscA_in_gg(0, s(X1)) → lesscA_out_gg(0, s(X1))
lesscA_in_gg(s(X1), s(X2)) → U69_gg(X1, X2, lesscA_in_gg(X1, X2))
U69_gg(X1, X2, lesscA_out_gg(X1, X2)) → lesscA_out_gg(s(X1), s(X2))
lesscA_in_ag(0, s(X1)) → lesscA_out_ag(0, s(X1))
lesscA_in_ag(s(X1), s(X2)) → U69_ag(X1, X2, lesscA_in_ag(X1, X2))
U69_ag(X1, X2, lesscA_out_ag(X1, X2)) → lesscA_out_ag(s(X1), s(X2))
lesscM_in_gg(0, s(X1)) → lesscM_out_gg(0, s(X1))
lesscM_in_gg(s(X1), s(X2)) → U110_gg(X1, X2, lesscM_in_gg(X1, X2))
U110_gg(X1, X2, lesscM_out_gg(X1, X2)) → lesscM_out_gg(s(X1), s(X2))

The argument filtering Pi contains the following mapping:
deleteB_in_aga(x1, x2, x3)  =  deleteB_in_aga(x2)
tree(x1, x2, x3)  =  tree(x1, x2, x3)
void  =  void
pC_in_aga(x1, x2, x3)  =  pC_in_aga(x2)
lessA_in_ag(x1, x2)  =  lessA_in_ag(x2)
s(x1)  =  s(x1)
pD_in_gaa(x1, x2, x3)  =  pD_in_gaa(x1)
lessF_in_ga(x1, x2)  =  lessF_in_ga(x1)
lesscF_in_ga(x1, x2)  =  lesscF_in_ga(x1)
0  =  0
lesscF_out_ga(x1, x2)  =  lesscF_out_ga(x1)
U104_ga(x1, x2, x3)  =  U104_ga(x1, x3)
delminG_in_gaa(x1, x2, x3)  =  delminG_in_gaa(x1)
pH_in_gaga(x1, x2, x3, x4)  =  pH_in_gaga(x1, x3)
lesscA_in_gg(x1, x2)  =  lesscA_in_gg(x1, x2)
lesscA_out_gg(x1, x2)  =  lesscA_out_gg(x1, x2)
U69_gg(x1, x2, x3)  =  U69_gg(x1, x2, x3)
lesscA_in_ag(x1, x2)  =  lesscA_in_ag(x2)
lesscA_out_ag(x1, x2)  =  lesscA_out_ag(x1, x2)
U69_ag(x1, x2, x3)  =  U69_ag(x2, x3)
pI_in_ggga(x1, x2, x3, x4)  =  pI_in_ggga(x1, x2, x3)
lessM_in_gg(x1, x2)  =  lessM_in_gg(x1, x2)
lesscM_in_gg(x1, x2)  =  lesscM_in_gg(x1, x2)
lesscM_out_gg(x1, x2)  =  lesscM_out_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
deleteK_in_gga(x1, x2, x3)  =  deleteK_in_gga(x1, x2)
pJ_in_ggga(x1, x2, x3, x4)  =  pJ_in_ggga(x1, x2, x3)
pL_in_gaga(x1, x2, x3, x4)  =  pL_in_gaga(x1, x3)
DELETEB_IN_AGA(x1, x2, x3)  =  DELETEB_IN_AGA(x2)
U24_AGA(x1, x2, x3, x4)  =  U24_AGA(x2, x4)
PC_IN_AGA(x1, x2, x3)  =  PC_IN_AGA(x2)
U7_AGA(x1, x2, x3, x4)  =  U7_AGA(x2, x4)
LESSA_IN_AG(x1, x2)  =  LESSA_IN_AG(x2)
U1_AG(x1, x2, x3)  =  U1_AG(x2, x3)
U25_AGA(x1, x2, x3, x4)  =  U25_AGA(x2, x4)
PD_IN_GAA(x1, x2, x3)  =  PD_IN_GAA(x1)
U3_GAA(x1, x2, x3, x4)  =  U3_GAA(x1, x4)
LESSF_IN_GA(x1, x2)  =  LESSF_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)
U26_AGA(x1, x2, x3, x4)  =  U26_AGA(x2, x4)
U27_AGA(x1, x2, x3)  =  U27_AGA(x3)
U28_AGA(x1, x2, x3, x4)  =  U28_AGA(x2, x4)
U29_AGA(x1, x2, x3, x4)  =  U29_AGA(x2, x4)
U30_AGA(x1, x2, x3, x4)  =  U30_AGA(x2, x4)
U31_AGA(x1, x2, x3, x4, x5, x6, x7, x8)  =  U31_AGA(x1, x2, x3, x4, x8)
DELMING_IN_GAA(x1, x2, x3)  =  DELMING_IN_GAA(x1)
U6_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U6_GAA(x1, x2, x3, x7)
U32_AGA(x1, x2, x3, x4, x5)  =  U32_AGA(x2, x3, x5)
U33_AGA(x1, x2, x3, x4, x5)  =  U33_AGA(x2, x3, x5)
PH_IN_GAGA(x1, x2, x3, x4)  =  PH_IN_GAGA(x1, x3)
U8_GAGA(x1, x2, x3, x4, x5)  =  U8_GAGA(x1, x3, x5)
U9_GAGA(x1, x2, x3, x4, x5)  =  U9_GAGA(x1, x3, x5)
U10_GAGA(x1, x2, x3, x4, x5)  =  U10_GAGA(x1, x3, x5)
U34_AGA(x1, x2, x3, x4, x5)  =  U34_AGA(x2, x3, x5)
U35_AGA(x1, x2, x3, x4)  =  U35_AGA(x2, x4)
U36_AGA(x1, x2, x3, x4, x5)  =  U36_AGA(x2, x3, x5)
U37_AGA(x1, x2, x3, x4, x5)  =  U37_AGA(x2, x3, x5)
U38_AGA(x1, x2, x3, x4, x5)  =  U38_AGA(x2, x3, x5)
U39_AGA(x1, x2, x3, x4, x5)  =  U39_AGA(x2, x3, x5)
U40_AGA(x1, x2, x3, x4, x5, x6, x7)  =  U40_AGA(x1, x2, x3, x4, x7)
U41_AGA(x1, x2, x3, x4, x5, x6, x7)  =  U41_AGA(x1, x2, x3, x4, x7)
U42_AGA(x1, x2, x3, x4, x5, x6, x7)  =  U42_AGA(x2, x3, x4, x5, x7)
U43_AGA(x1, x2, x3, x4, x5, x6, x7)  =  U43_AGA(x1, x2, x3, x4, x5, x7)
PI_IN_GGGA(x1, x2, x3, x4)  =  PI_IN_GGGA(x1, x2, x3)
U12_GGGA(x1, x2, x3, x4, x5)  =  U12_GGGA(x1, x2, x3, x5)
LESSM_IN_GG(x1, x2)  =  LESSM_IN_GG(x1, x2)
U11_GG(x1, x2, x3)  =  U11_GG(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)
DELETEK_IN_GGA(x1, x2, x3)  =  DELETEK_IN_GGA(x1, x2)
U15_GGA(x1, x2, x3, x4, x5, x6)  =  U15_GGA(x1, x2, x3, x6)
U16_GGA(x1, x2, x3, x4, x5, x6)  =  U16_GGA(x1, x2, x3, x4, x6)
U17_GGA(x1, x2, x3, x4, x5, x6)  =  U17_GGA(x1, x2, x3, x4, x6)
PJ_IN_GGGA(x1, x2, x3, x4)  =  PJ_IN_GGGA(x1, x2, x3)
U18_GGGA(x1, x2, x3, x4, x5)  =  U18_GGGA(x1, x2, x3, x5)
U19_GGGA(x1, x2, x3, x4, x5)  =  U19_GGGA(x1, x2, x3, x5)
U20_GGGA(x1, x2, x3, x4, x5)  =  U20_GGGA(x1, x2, x3, x5)
U44_AGA(x1, x2, x3, x4, x5, x6, x7)  =  U44_AGA(x2, x3, x4, x5, x7)
U45_AGA(x1, x2, x3, x4, x5, x6, x7)  =  U45_AGA(x1, x2, x3, x4, x5, x7)
U46_AGA(x1, x2, x3, x4, x5)  =  U46_AGA(x2, x3, x5)
U47_AGA(x1, x2, x3, x4)  =  U47_AGA(x1, x2, x4)
U48_AGA(x1, x2, x3, x4, x5)  =  U48_AGA(x2, x3, x5)
U49_AGA(x1, x2, x3, x4, x5)  =  U49_AGA(x2, x3, x5)
U50_AGA(x1, x2, x3, x4, x5)  =  U50_AGA(x1, x2, x3, x5)
U51_AGA(x1, x2, x3, x4)  =  U51_AGA(x2, x4)
U52_AGA(x1, x2, x3, x4, x5)  =  U52_AGA(x2, x3, x5)
U53_AGA(x1, x2, x3, x4, x5)  =  U53_AGA(x2, x3, x5)
U54_AGA(x1, x2, x3, x4, x5)  =  U54_AGA(x2, x3, x5)
U55_AGA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U55_AGA(x1, x2, x3, x4, x5, x9)
U56_AGA(x1, x2, x3, x4, x5, x6)  =  U56_AGA(x2, x3, x4, x6)
U57_AGA(x1, x2, x3, x4, x5, x6)  =  U57_AGA(x2, x3, x4, x6)
U58_AGA(x1, x2, x3, x4, x5, x6)  =  U58_AGA(x1, x2, x3, x4, x6)
U59_AGA(x1, x2, x3, x4, x5, x6)  =  U59_AGA(x2, x3, x4, x6)
PL_IN_GAGA(x1, x2, x3, x4)  =  PL_IN_GAGA(x1, x3)
U21_GAGA(x1, x2, x3, x4, x5)  =  U21_GAGA(x1, x3, x5)
U22_GAGA(x1, x2, x3, x4, x5)  =  U22_GAGA(x1, x3, x5)
U23_GAGA(x1, x2, x3, x4, x5)  =  U23_GAGA(x1, x3, x5)
U60_AGA(x1, x2, x3, x4, x5)  =  U60_AGA(x1, x2, x3, x5)
U61_AGA(x1, x2, x3, x4, x5, x6)  =  U61_AGA(x2, x3, x4, x6)
U62_AGA(x1, x2, x3, x4, x5, x6)  =  U62_AGA(x2, x3, x4, x6)
U63_AGA(x1, x2, x3, x4, x5, x6)  =  U63_AGA(x1, x2, x3, x4, x6)
U64_AGA(x1, x2, x3, x4, x5)  =  U64_AGA(x2, x3, x5)
U65_AGA(x1, x2, x3, x4, x5, x6)  =  U65_AGA(x2, x3, x4, x6)
U66_AGA(x1, x2, x3, x4, x5, x6)  =  U66_AGA(x2, x3, x4, x6)
U67_AGA(x1, x2, x3, x4, x5, x6)  =  U67_AGA(x2, x3, x4, x6)

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

Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES

(6) Obligation:

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

DELETEB_IN_AGA(X1, tree(X2, void, void), tree(X2, X3, void)) → U24_AGA(X1, X2, X3, pC_in_aga(X1, X2, X3))
DELETEB_IN_AGA(X1, tree(X2, void, void), tree(X2, X3, void)) → PC_IN_AGA(X1, X2, X3)
PC_IN_AGA(X1, X2, X3) → U7_AGA(X1, X2, X3, lessA_in_ag(X1, X2))
PC_IN_AGA(X1, X2, X3) → LESSA_IN_AG(X1, X2)
LESSA_IN_AG(s(X1), s(X2)) → U1_AG(X1, X2, lessA_in_ag(X1, X2))
LESSA_IN_AG(s(X1), s(X2)) → LESSA_IN_AG(X1, X2)
DELETEB_IN_AGA(X1, tree(X2, void, void), tree(X2, void, X3)) → U25_AGA(X1, X2, X3, pD_in_gaa(X2, X1, X3))
DELETEB_IN_AGA(X1, tree(X2, void, void), tree(X2, void, X3)) → PD_IN_GAA(X2, X1, X3)
PD_IN_GAA(X1, X2, X3) → U3_GAA(X1, X2, X3, lessF_in_ga(X1, X2))
PD_IN_GAA(X1, X2, X3) → LESSF_IN_GA(X1, X2)
LESSF_IN_GA(s(X1), s(X2)) → U2_GA(X1, X2, lessF_in_ga(X1, X2))
LESSF_IN_GA(s(X1), s(X2)) → LESSF_IN_GA(X1, X2)
PD_IN_GAA(X1, X2, X3) → U4_GAA(X1, X2, X3, lesscF_in_ga(X1, X2))
U4_GAA(X1, X2, X3, lesscF_out_ga(X1, X2)) → U5_GAA(X1, X2, X3, deleteB_in_aga(X2, void, X3))
U4_GAA(X1, X2, X3, lesscF_out_ga(X1, X2)) → DELETEB_IN_AGA(X2, void, X3)
DELETEB_IN_AGA(s(X1), tree(s(X2), void, void), tree(s(X2), X3, void)) → U26_AGA(X1, X2, X3, lessA_in_ag(X1, X2))
DELETEB_IN_AGA(s(X1), tree(s(X2), void, void), tree(s(X2), X3, void)) → LESSA_IN_AG(X1, X2)
DELETEB_IN_AGA(s(X1), tree(0, void, void), tree(0, void, X2)) → U27_AGA(X1, X2, deleteB_in_aga(s(X1), void, X2))
DELETEB_IN_AGA(s(X1), tree(0, void, void), tree(0, void, X2)) → DELETEB_IN_AGA(s(X1), void, X2)
DELETEB_IN_AGA(s(X1), tree(s(X2), void, void), tree(s(X2), void, X3)) → U28_AGA(X1, X2, X3, lessF_in_ga(X2, X1))
DELETEB_IN_AGA(s(X1), tree(s(X2), void, void), tree(s(X2), void, X3)) → LESSF_IN_GA(X2, X1)
DELETEB_IN_AGA(s(X1), tree(s(X2), void, void), tree(s(X2), void, X3)) → U29_AGA(X1, X2, X3, lesscF_in_ga(X2, X1))
U29_AGA(X1, X2, X3, lesscF_out_ga(X2, X1)) → U30_AGA(X1, X2, X3, deleteB_in_aga(s(X1), void, X3))
U29_AGA(X1, X2, X3, lesscF_out_ga(X2, X1)) → DELETEB_IN_AGA(s(X1), void, X3)
DELETEB_IN_AGA(X1, tree(X1, void, tree(X2, X3, X4)), tree(X5, void, tree(X2, X6, X7))) → U31_AGA(X1, X2, X3, X4, X5, X6, X7, delminG_in_gaa(X3, X5, X6))
DELETEB_IN_AGA(X1, tree(X1, void, tree(X2, X3, X4)), tree(X5, void, tree(X2, X6, X7))) → DELMING_IN_GAA(X3, X5, X6)
DELMING_IN_GAA(tree(X1, X2, X3), X4, tree(X1, X5, X6)) → U6_GAA(X1, X2, X3, X4, X5, X6, delminG_in_gaa(X2, X4, X5))
DELMING_IN_GAA(tree(X1, X2, X3), X4, tree(X1, X5, X6)) → DELMING_IN_GAA(X2, X4, X5)
DELETEB_IN_AGA(X1, tree(X2, void, X3), tree(X2, X4, X3)) → U32_AGA(X1, X2, X3, X4, pC_in_aga(X1, X2, X4))
DELETEB_IN_AGA(X1, tree(X2, void, X3), tree(X2, X4, X3)) → PC_IN_AGA(X1, X2, X4)
DELETEB_IN_AGA(X1, tree(X2, void, X3), tree(X2, void, X4)) → U33_AGA(X1, X2, X3, X4, pH_in_gaga(X2, X1, X3, X4))
DELETEB_IN_AGA(X1, tree(X2, void, X3), tree(X2, void, X4)) → PH_IN_GAGA(X2, X1, X3, X4)
PH_IN_GAGA(X1, X2, X3, X4) → U8_GAGA(X1, X2, X3, X4, lessF_in_ga(X1, X2))
PH_IN_GAGA(X1, X2, X3, X4) → LESSF_IN_GA(X1, X2)
PH_IN_GAGA(X1, X2, X3, X4) → U9_GAGA(X1, X2, X3, X4, lesscF_in_ga(X1, X2))
U9_GAGA(X1, X2, X3, X4, lesscF_out_ga(X1, X2)) → U10_GAGA(X1, X2, X3, X4, deleteB_in_aga(X2, X3, X4))
U9_GAGA(X1, X2, X3, X4, lesscF_out_ga(X1, X2)) → DELETEB_IN_AGA(X2, X3, X4)
DELETEB_IN_AGA(s(X1), tree(s(X2), void, X3), tree(s(X2), X4, X3)) → U34_AGA(X1, X2, X3, X4, lessA_in_ag(X1, X2))
DELETEB_IN_AGA(s(X1), tree(s(X2), void, X3), tree(s(X2), X4, X3)) → LESSA_IN_AG(X1, X2)
DELETEB_IN_AGA(s(X1), tree(0, void, X2), tree(0, void, X3)) → U35_AGA(X1, X2, X3, deleteB_in_aga(s(X1), X2, X3))
DELETEB_IN_AGA(s(X1), tree(0, void, X2), tree(0, void, X3)) → DELETEB_IN_AGA(s(X1), X2, X3)
DELETEB_IN_AGA(s(X1), tree(s(X2), void, X3), tree(s(X2), void, X4)) → U36_AGA(X1, X2, X3, X4, lessF_in_ga(X2, X1))
DELETEB_IN_AGA(s(X1), tree(s(X2), void, X3), tree(s(X2), void, X4)) → LESSF_IN_GA(X2, X1)
DELETEB_IN_AGA(s(X1), tree(s(X2), void, X3), tree(s(X2), void, X4)) → U37_AGA(X1, X2, X3, X4, lesscF_in_ga(X2, X1))
U37_AGA(X1, X2, X3, X4, lesscF_out_ga(X2, X1)) → U38_AGA(X1, X2, X3, X4, deleteB_in_aga(s(X1), X3, X4))
U37_AGA(X1, X2, X3, X4, lesscF_out_ga(X2, X1)) → DELETEB_IN_AGA(s(X1), X3, X4)
DELETEB_IN_AGA(X1, tree(X2, X3, void), tree(X2, X4, void)) → U39_AGA(X1, X2, X3, X4, lessA_in_ag(X1, X2))
DELETEB_IN_AGA(X1, tree(X2, X3, void), tree(X2, X4, void)) → LESSA_IN_AG(X1, X2)
DELETEB_IN_AGA(X1, tree(X2, tree(X1, X3, X4), void), tree(X2, tree(X5, X3, X6), void)) → U40_AGA(X1, X2, X3, X4, X5, X6, lesscA_in_gg(X1, X2))
U40_AGA(X1, X2, X3, X4, X5, X6, lesscA_out_gg(X1, X2)) → U41_AGA(X1, X2, X3, X4, X5, X6, delminG_in_gaa(X4, X5, X6))
U40_AGA(X1, X2, X3, X4, X5, X6, lesscA_out_gg(X1, X2)) → DELMING_IN_GAA(X4, X5, X6)
DELETEB_IN_AGA(X1, tree(X2, tree(X3, X4, X5), void), tree(X2, tree(X3, X6, X5), void)) → U42_AGA(X1, X2, X3, X4, X5, X6, lesscA_in_ag(X1, X2))
U42_AGA(X1, X2, X3, X4, X5, X6, lesscA_out_ag(X1, X2)) → U43_AGA(X1, X2, X3, X4, X5, X6, pI_in_ggga(X1, X3, X4, X6))
U42_AGA(X1, X2, X3, X4, X5, X6, lesscA_out_ag(X1, X2)) → PI_IN_GGGA(X1, X3, X4, X6)
PI_IN_GGGA(X1, X2, X3, X4) → U12_GGGA(X1, X2, X3, X4, lessM_in_gg(X1, X2))
PI_IN_GGGA(X1, X2, X3, X4) → LESSM_IN_GG(X1, X2)
LESSM_IN_GG(s(X1), s(X2)) → U11_GG(X1, X2, lessM_in_gg(X1, X2))
LESSM_IN_GG(s(X1), s(X2)) → LESSM_IN_GG(X1, X2)
PI_IN_GGGA(X1, X2, X3, X4) → U13_GGGA(X1, X2, X3, X4, lesscM_in_gg(X1, X2))
U13_GGGA(X1, X2, X3, X4, lesscM_out_gg(X1, X2)) → U14_GGGA(X1, X2, X3, X4, deleteK_in_gga(X1, X3, X4))
U13_GGGA(X1, X2, X3, X4, lesscM_out_gg(X1, X2)) → DELETEK_IN_GGA(X1, X3, X4)
DELETEK_IN_GGA(X1, tree(X1, X2, X3), tree(X4, X2, X5)) → U15_GGA(X1, X2, X3, X4, X5, delminG_in_gaa(X3, X4, X5))
DELETEK_IN_GGA(X1, tree(X1, X2, X3), tree(X4, X2, X5)) → DELMING_IN_GAA(X3, X4, X5)
DELETEK_IN_GGA(X1, tree(X2, X3, X4), tree(X2, X5, X4)) → U16_GGA(X1, X2, X3, X4, X5, pI_in_ggga(X1, X2, X3, X5))
DELETEK_IN_GGA(X1, tree(X2, X3, X4), tree(X2, X5, X4)) → PI_IN_GGGA(X1, X2, X3, X5)
DELETEK_IN_GGA(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → U17_GGA(X1, X2, X3, X4, X5, pJ_in_ggga(X2, X1, X4, X5))
DELETEK_IN_GGA(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → PJ_IN_GGGA(X2, X1, X4, X5)
PJ_IN_GGGA(X1, X2, X3, X4) → U18_GGGA(X1, X2, X3, X4, lessM_in_gg(X1, X2))
PJ_IN_GGGA(X1, X2, X3, X4) → LESSM_IN_GG(X1, X2)
PJ_IN_GGGA(X1, X2, X3, X4) → U19_GGGA(X1, X2, X3, X4, lesscM_in_gg(X1, X2))
U19_GGGA(X1, X2, X3, X4, lesscM_out_gg(X1, X2)) → U20_GGGA(X1, X2, X3, X4, deleteK_in_gga(X2, X3, X4))
U19_GGGA(X1, X2, X3, X4, lesscM_out_gg(X1, X2)) → DELETEK_IN_GGA(X2, X3, X4)
DELETEB_IN_AGA(X1, tree(X2, tree(X3, X4, X5), void), tree(X2, tree(X3, X4, X6), void)) → U44_AGA(X1, X2, X3, X4, X5, X6, lesscA_in_ag(X1, X2))
U44_AGA(X1, X2, X3, X4, X5, X6, lesscA_out_ag(X1, X2)) → U45_AGA(X1, X2, X3, X4, X5, X6, pJ_in_ggga(X3, X1, X5, X6))
U44_AGA(X1, X2, X3, X4, X5, X6, lesscA_out_ag(X1, X2)) → PJ_IN_GGGA(X3, X1, X5, X6)
DELETEB_IN_AGA(X1, tree(X2, X3, void), tree(X2, X3, X4)) → U46_AGA(X1, X2, X3, X4, pD_in_gaa(X2, X1, X4))
DELETEB_IN_AGA(X1, tree(X2, X3, void), tree(X2, X3, X4)) → PD_IN_GAA(X2, X1, X4)
DELETEB_IN_AGA(0, tree(s(X1), X2, void), tree(s(X1), X3, void)) → U47_AGA(X1, X2, X3, deleteK_in_gga(0, X2, X3))
DELETEB_IN_AGA(0, tree(s(X1), X2, void), tree(s(X1), X3, void)) → DELETEK_IN_GGA(0, X2, X3)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, void), tree(s(X2), X4, void)) → U48_AGA(X1, X2, X3, X4, lessA_in_ag(X1, X2))
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, void), tree(s(X2), X4, void)) → LESSA_IN_AG(X1, X2)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, void), tree(s(X2), X4, void)) → U49_AGA(X1, X2, X3, X4, lesscA_in_ag(X1, X2))
U49_AGA(X1, X2, X3, X4, lesscA_out_ag(X1, X2)) → U50_AGA(X1, X2, X3, X4, deleteK_in_gga(s(X1), X3, X4))
U49_AGA(X1, X2, X3, X4, lesscA_out_ag(X1, X2)) → DELETEK_IN_GGA(s(X1), X3, X4)
DELETEB_IN_AGA(s(X1), tree(0, X2, void), tree(0, X2, X3)) → U51_AGA(X1, X2, X3, deleteB_in_aga(s(X1), void, X3))
DELETEB_IN_AGA(s(X1), tree(0, X2, void), tree(0, X2, X3)) → DELETEB_IN_AGA(s(X1), void, X3)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, void), tree(s(X2), X3, X4)) → U52_AGA(X1, X2, X3, X4, lessF_in_ga(X2, X1))
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, void), tree(s(X2), X3, X4)) → LESSF_IN_GA(X2, X1)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, void), tree(s(X2), X3, X4)) → U53_AGA(X1, X2, X3, X4, lesscF_in_ga(X2, X1))
U53_AGA(X1, X2, X3, X4, lesscF_out_ga(X2, X1)) → U54_AGA(X1, X2, X3, X4, deleteB_in_aga(s(X1), void, X4))
U53_AGA(X1, X2, X3, X4, lesscF_out_ga(X2, X1)) → DELETEB_IN_AGA(s(X1), void, X4)
DELETEB_IN_AGA(X1, tree(X1, X2, tree(X3, X4, X5)), tree(X6, X2, tree(X3, X7, X8))) → U55_AGA(X1, X2, X3, X4, X5, X6, X7, X8, delminG_in_gaa(X4, X6, X7))
DELETEB_IN_AGA(X1, tree(X1, X2, tree(X3, X4, X5)), tree(X6, X2, tree(X3, X7, X8))) → DELMING_IN_GAA(X4, X6, X7)
DELETEB_IN_AGA(X1, tree(X2, X3, X4), tree(X2, X5, X4)) → U56_AGA(X1, X2, X3, X4, X5, lessA_in_ag(X1, X2))
DELETEB_IN_AGA(X1, tree(X2, X3, X4), tree(X2, X5, X4)) → LESSA_IN_AG(X1, X2)
DELETEB_IN_AGA(X1, tree(X2, X3, X4), tree(X2, X5, X4)) → U57_AGA(X1, X2, X3, X4, X5, lesscA_in_ag(X1, X2))
U57_AGA(X1, X2, X3, X4, X5, lesscA_out_ag(X1, X2)) → U58_AGA(X1, X2, X3, X4, X5, deleteK_in_gga(X1, X3, X5))
U57_AGA(X1, X2, X3, X4, X5, lesscA_out_ag(X1, X2)) → DELETEK_IN_GGA(X1, X3, X5)
DELETEB_IN_AGA(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → U59_AGA(X1, X2, X3, X4, X5, pL_in_gaga(X2, X1, X4, X5))
DELETEB_IN_AGA(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → PL_IN_GAGA(X2, X1, X4, X5)
PL_IN_GAGA(X1, X2, X3, X4) → U21_GAGA(X1, X2, X3, X4, lessF_in_ga(X1, X2))
PL_IN_GAGA(X1, X2, X3, X4) → LESSF_IN_GA(X1, X2)
PL_IN_GAGA(X1, X2, X3, X4) → U22_GAGA(X1, X2, X3, X4, lesscF_in_ga(X1, X2))
U22_GAGA(X1, X2, X3, X4, lesscF_out_ga(X1, X2)) → U23_GAGA(X1, X2, X3, X4, deleteB_in_aga(X2, X3, X4))
U22_GAGA(X1, X2, X3, X4, lesscF_out_ga(X1, X2)) → DELETEB_IN_AGA(X2, X3, X4)
DELETEB_IN_AGA(0, tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → U60_AGA(X1, X2, X3, X4, deleteK_in_gga(0, X2, X4))
DELETEB_IN_AGA(0, tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → DELETEK_IN_GGA(0, X2, X4)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) → U61_AGA(X1, X2, X3, X4, X5, lessA_in_ag(X1, X2))
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) → LESSA_IN_AG(X1, X2)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) → U62_AGA(X1, X2, X3, X4, X5, lesscA_in_ag(X1, X2))
U62_AGA(X1, X2, X3, X4, X5, lesscA_out_ag(X1, X2)) → U63_AGA(X1, X2, X3, X4, X5, deleteK_in_gga(s(X1), X3, X5))
U62_AGA(X1, X2, X3, X4, X5, lesscA_out_ag(X1, X2)) → DELETEK_IN_GGA(s(X1), X3, X5)
DELETEB_IN_AGA(s(X1), tree(0, X2, X3), tree(0, X2, X4)) → U64_AGA(X1, X2, X3, X4, deleteB_in_aga(s(X1), X3, X4))
DELETEB_IN_AGA(s(X1), tree(0, X2, X3), tree(0, X2, X4)) → DELETEB_IN_AGA(s(X1), X3, X4)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) → U65_AGA(X1, X2, X3, X4, X5, lessF_in_ga(X2, X1))
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) → LESSF_IN_GA(X2, X1)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) → U66_AGA(X1, X2, X3, X4, X5, lesscF_in_ga(X2, X1))
U66_AGA(X1, X2, X3, X4, X5, lesscF_out_ga(X2, X1)) → U67_AGA(X1, X2, X3, X4, X5, deleteB_in_aga(s(X1), X4, X5))
U66_AGA(X1, X2, X3, X4, X5, lesscF_out_ga(X2, X1)) → DELETEB_IN_AGA(s(X1), X4, X5)

The TRS R consists of the following rules:

lesscF_in_ga(0, s(X1)) → lesscF_out_ga(0, s(X1))
lesscF_in_ga(s(X1), s(X2)) → U104_ga(X1, X2, lesscF_in_ga(X1, X2))
U104_ga(X1, X2, lesscF_out_ga(X1, X2)) → lesscF_out_ga(s(X1), s(X2))
lesscA_in_gg(0, s(X1)) → lesscA_out_gg(0, s(X1))
lesscA_in_gg(s(X1), s(X2)) → U69_gg(X1, X2, lesscA_in_gg(X1, X2))
U69_gg(X1, X2, lesscA_out_gg(X1, X2)) → lesscA_out_gg(s(X1), s(X2))
lesscA_in_ag(0, s(X1)) → lesscA_out_ag(0, s(X1))
lesscA_in_ag(s(X1), s(X2)) → U69_ag(X1, X2, lesscA_in_ag(X1, X2))
U69_ag(X1, X2, lesscA_out_ag(X1, X2)) → lesscA_out_ag(s(X1), s(X2))
lesscM_in_gg(0, s(X1)) → lesscM_out_gg(0, s(X1))
lesscM_in_gg(s(X1), s(X2)) → U110_gg(X1, X2, lesscM_in_gg(X1, X2))
U110_gg(X1, X2, lesscM_out_gg(X1, X2)) → lesscM_out_gg(s(X1), s(X2))

The argument filtering Pi contains the following mapping:
deleteB_in_aga(x1, x2, x3)  =  deleteB_in_aga(x2)
tree(x1, x2, x3)  =  tree(x1, x2, x3)
void  =  void
pC_in_aga(x1, x2, x3)  =  pC_in_aga(x2)
lessA_in_ag(x1, x2)  =  lessA_in_ag(x2)
s(x1)  =  s(x1)
pD_in_gaa(x1, x2, x3)  =  pD_in_gaa(x1)
lessF_in_ga(x1, x2)  =  lessF_in_ga(x1)
lesscF_in_ga(x1, x2)  =  lesscF_in_ga(x1)
0  =  0
lesscF_out_ga(x1, x2)  =  lesscF_out_ga(x1)
U104_ga(x1, x2, x3)  =  U104_ga(x1, x3)
delminG_in_gaa(x1, x2, x3)  =  delminG_in_gaa(x1)
pH_in_gaga(x1, x2, x3, x4)  =  pH_in_gaga(x1, x3)
lesscA_in_gg(x1, x2)  =  lesscA_in_gg(x1, x2)
lesscA_out_gg(x1, x2)  =  lesscA_out_gg(x1, x2)
U69_gg(x1, x2, x3)  =  U69_gg(x1, x2, x3)
lesscA_in_ag(x1, x2)  =  lesscA_in_ag(x2)
lesscA_out_ag(x1, x2)  =  lesscA_out_ag(x1, x2)
U69_ag(x1, x2, x3)  =  U69_ag(x2, x3)
pI_in_ggga(x1, x2, x3, x4)  =  pI_in_ggga(x1, x2, x3)
lessM_in_gg(x1, x2)  =  lessM_in_gg(x1, x2)
lesscM_in_gg(x1, x2)  =  lesscM_in_gg(x1, x2)
lesscM_out_gg(x1, x2)  =  lesscM_out_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
deleteK_in_gga(x1, x2, x3)  =  deleteK_in_gga(x1, x2)
pJ_in_ggga(x1, x2, x3, x4)  =  pJ_in_ggga(x1, x2, x3)
pL_in_gaga(x1, x2, x3, x4)  =  pL_in_gaga(x1, x3)
DELETEB_IN_AGA(x1, x2, x3)  =  DELETEB_IN_AGA(x2)
U24_AGA(x1, x2, x3, x4)  =  U24_AGA(x2, x4)
PC_IN_AGA(x1, x2, x3)  =  PC_IN_AGA(x2)
U7_AGA(x1, x2, x3, x4)  =  U7_AGA(x2, x4)
LESSA_IN_AG(x1, x2)  =  LESSA_IN_AG(x2)
U1_AG(x1, x2, x3)  =  U1_AG(x2, x3)
U25_AGA(x1, x2, x3, x4)  =  U25_AGA(x2, x4)
PD_IN_GAA(x1, x2, x3)  =  PD_IN_GAA(x1)
U3_GAA(x1, x2, x3, x4)  =  U3_GAA(x1, x4)
LESSF_IN_GA(x1, x2)  =  LESSF_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)
U26_AGA(x1, x2, x3, x4)  =  U26_AGA(x2, x4)
U27_AGA(x1, x2, x3)  =  U27_AGA(x3)
U28_AGA(x1, x2, x3, x4)  =  U28_AGA(x2, x4)
U29_AGA(x1, x2, x3, x4)  =  U29_AGA(x2, x4)
U30_AGA(x1, x2, x3, x4)  =  U30_AGA(x2, x4)
U31_AGA(x1, x2, x3, x4, x5, x6, x7, x8)  =  U31_AGA(x1, x2, x3, x4, x8)
DELMING_IN_GAA(x1, x2, x3)  =  DELMING_IN_GAA(x1)
U6_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U6_GAA(x1, x2, x3, x7)
U32_AGA(x1, x2, x3, x4, x5)  =  U32_AGA(x2, x3, x5)
U33_AGA(x1, x2, x3, x4, x5)  =  U33_AGA(x2, x3, x5)
PH_IN_GAGA(x1, x2, x3, x4)  =  PH_IN_GAGA(x1, x3)
U8_GAGA(x1, x2, x3, x4, x5)  =  U8_GAGA(x1, x3, x5)
U9_GAGA(x1, x2, x3, x4, x5)  =  U9_GAGA(x1, x3, x5)
U10_GAGA(x1, x2, x3, x4, x5)  =  U10_GAGA(x1, x3, x5)
U34_AGA(x1, x2, x3, x4, x5)  =  U34_AGA(x2, x3, x5)
U35_AGA(x1, x2, x3, x4)  =  U35_AGA(x2, x4)
U36_AGA(x1, x2, x3, x4, x5)  =  U36_AGA(x2, x3, x5)
U37_AGA(x1, x2, x3, x4, x5)  =  U37_AGA(x2, x3, x5)
U38_AGA(x1, x2, x3, x4, x5)  =  U38_AGA(x2, x3, x5)
U39_AGA(x1, x2, x3, x4, x5)  =  U39_AGA(x2, x3, x5)
U40_AGA(x1, x2, x3, x4, x5, x6, x7)  =  U40_AGA(x1, x2, x3, x4, x7)
U41_AGA(x1, x2, x3, x4, x5, x6, x7)  =  U41_AGA(x1, x2, x3, x4, x7)
U42_AGA(x1, x2, x3, x4, x5, x6, x7)  =  U42_AGA(x2, x3, x4, x5, x7)
U43_AGA(x1, x2, x3, x4, x5, x6, x7)  =  U43_AGA(x1, x2, x3, x4, x5, x7)
PI_IN_GGGA(x1, x2, x3, x4)  =  PI_IN_GGGA(x1, x2, x3)
U12_GGGA(x1, x2, x3, x4, x5)  =  U12_GGGA(x1, x2, x3, x5)
LESSM_IN_GG(x1, x2)  =  LESSM_IN_GG(x1, x2)
U11_GG(x1, x2, x3)  =  U11_GG(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)
DELETEK_IN_GGA(x1, x2, x3)  =  DELETEK_IN_GGA(x1, x2)
U15_GGA(x1, x2, x3, x4, x5, x6)  =  U15_GGA(x1, x2, x3, x6)
U16_GGA(x1, x2, x3, x4, x5, x6)  =  U16_GGA(x1, x2, x3, x4, x6)
U17_GGA(x1, x2, x3, x4, x5, x6)  =  U17_GGA(x1, x2, x3, x4, x6)
PJ_IN_GGGA(x1, x2, x3, x4)  =  PJ_IN_GGGA(x1, x2, x3)
U18_GGGA(x1, x2, x3, x4, x5)  =  U18_GGGA(x1, x2, x3, x5)
U19_GGGA(x1, x2, x3, x4, x5)  =  U19_GGGA(x1, x2, x3, x5)
U20_GGGA(x1, x2, x3, x4, x5)  =  U20_GGGA(x1, x2, x3, x5)
U44_AGA(x1, x2, x3, x4, x5, x6, x7)  =  U44_AGA(x2, x3, x4, x5, x7)
U45_AGA(x1, x2, x3, x4, x5, x6, x7)  =  U45_AGA(x1, x2, x3, x4, x5, x7)
U46_AGA(x1, x2, x3, x4, x5)  =  U46_AGA(x2, x3, x5)
U47_AGA(x1, x2, x3, x4)  =  U47_AGA(x1, x2, x4)
U48_AGA(x1, x2, x3, x4, x5)  =  U48_AGA(x2, x3, x5)
U49_AGA(x1, x2, x3, x4, x5)  =  U49_AGA(x2, x3, x5)
U50_AGA(x1, x2, x3, x4, x5)  =  U50_AGA(x1, x2, x3, x5)
U51_AGA(x1, x2, x3, x4)  =  U51_AGA(x2, x4)
U52_AGA(x1, x2, x3, x4, x5)  =  U52_AGA(x2, x3, x5)
U53_AGA(x1, x2, x3, x4, x5)  =  U53_AGA(x2, x3, x5)
U54_AGA(x1, x2, x3, x4, x5)  =  U54_AGA(x2, x3, x5)
U55_AGA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U55_AGA(x1, x2, x3, x4, x5, x9)
U56_AGA(x1, x2, x3, x4, x5, x6)  =  U56_AGA(x2, x3, x4, x6)
U57_AGA(x1, x2, x3, x4, x5, x6)  =  U57_AGA(x2, x3, x4, x6)
U58_AGA(x1, x2, x3, x4, x5, x6)  =  U58_AGA(x1, x2, x3, x4, x6)
U59_AGA(x1, x2, x3, x4, x5, x6)  =  U59_AGA(x2, x3, x4, x6)
PL_IN_GAGA(x1, x2, x3, x4)  =  PL_IN_GAGA(x1, x3)
U21_GAGA(x1, x2, x3, x4, x5)  =  U21_GAGA(x1, x3, x5)
U22_GAGA(x1, x2, x3, x4, x5)  =  U22_GAGA(x1, x3, x5)
U23_GAGA(x1, x2, x3, x4, x5)  =  U23_GAGA(x1, x3, x5)
U60_AGA(x1, x2, x3, x4, x5)  =  U60_AGA(x1, x2, x3, x5)
U61_AGA(x1, x2, x3, x4, x5, x6)  =  U61_AGA(x2, x3, x4, x6)
U62_AGA(x1, x2, x3, x4, x5, x6)  =  U62_AGA(x2, x3, x4, x6)
U63_AGA(x1, x2, x3, x4, x5, x6)  =  U63_AGA(x1, x2, x3, x4, x6)
U64_AGA(x1, x2, x3, x4, x5)  =  U64_AGA(x2, x3, x5)
U65_AGA(x1, x2, x3, x4, x5, x6)  =  U65_AGA(x2, x3, x4, x6)
U66_AGA(x1, x2, x3, x4, x5, x6)  =  U66_AGA(x2, x3, x4, x6)
U67_AGA(x1, x2, x3, x4, x5, x6)  =  U67_AGA(x2, x3, x4, x6)

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

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 6 SCCs with 97 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

LESSM_IN_GG(s(X1), s(X2)) → LESSM_IN_GG(X1, X2)

The TRS R consists of the following rules:

lesscF_in_ga(0, s(X1)) → lesscF_out_ga(0, s(X1))
lesscF_in_ga(s(X1), s(X2)) → U104_ga(X1, X2, lesscF_in_ga(X1, X2))
U104_ga(X1, X2, lesscF_out_ga(X1, X2)) → lesscF_out_ga(s(X1), s(X2))
lesscA_in_gg(0, s(X1)) → lesscA_out_gg(0, s(X1))
lesscA_in_gg(s(X1), s(X2)) → U69_gg(X1, X2, lesscA_in_gg(X1, X2))
U69_gg(X1, X2, lesscA_out_gg(X1, X2)) → lesscA_out_gg(s(X1), s(X2))
lesscA_in_ag(0, s(X1)) → lesscA_out_ag(0, s(X1))
lesscA_in_ag(s(X1), s(X2)) → U69_ag(X1, X2, lesscA_in_ag(X1, X2))
U69_ag(X1, X2, lesscA_out_ag(X1, X2)) → lesscA_out_ag(s(X1), s(X2))
lesscM_in_gg(0, s(X1)) → lesscM_out_gg(0, s(X1))
lesscM_in_gg(s(X1), s(X2)) → U110_gg(X1, X2, lesscM_in_gg(X1, X2))
U110_gg(X1, X2, lesscM_out_gg(X1, X2)) → lesscM_out_gg(s(X1), s(X2))

The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
lesscF_in_ga(x1, x2)  =  lesscF_in_ga(x1)
0  =  0
lesscF_out_ga(x1, x2)  =  lesscF_out_ga(x1)
U104_ga(x1, x2, x3)  =  U104_ga(x1, x3)
lesscA_in_gg(x1, x2)  =  lesscA_in_gg(x1, x2)
lesscA_out_gg(x1, x2)  =  lesscA_out_gg(x1, x2)
U69_gg(x1, x2, x3)  =  U69_gg(x1, x2, x3)
lesscA_in_ag(x1, x2)  =  lesscA_in_ag(x2)
lesscA_out_ag(x1, x2)  =  lesscA_out_ag(x1, x2)
U69_ag(x1, x2, x3)  =  U69_ag(x2, x3)
lesscM_in_gg(x1, x2)  =  lesscM_in_gg(x1, x2)
lesscM_out_gg(x1, x2)  =  lesscM_out_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
LESSM_IN_GG(x1, x2)  =  LESSM_IN_GG(x1, x2)

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

(10) UsableRulesProof (EQUIVALENT transformation)

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

(11) Obligation:

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

LESSM_IN_GG(s(X1), s(X2)) → LESSM_IN_GG(X1, X2)

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

(12) PiDPToQDPProof (EQUIVALENT transformation)

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

(13) Obligation:

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

LESSM_IN_GG(s(X1), s(X2)) → LESSM_IN_GG(X1, X2)

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

(14) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• LESSM_IN_GG(s(X1), s(X2)) → LESSM_IN_GG(X1, X2)
  The graph contains the following edges 1 > 1, 2 > 2

(15) YES

(16) Obligation:

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

DELMING_IN_GAA(tree(X1, X2, X3), X4, tree(X1, X5, X6)) → DELMING_IN_GAA(X2, X4, X5)

The TRS R consists of the following rules:

lesscF_in_ga(0, s(X1)) → lesscF_out_ga(0, s(X1))
lesscF_in_ga(s(X1), s(X2)) → U104_ga(X1, X2, lesscF_in_ga(X1, X2))
U104_ga(X1, X2, lesscF_out_ga(X1, X2)) → lesscF_out_ga(s(X1), s(X2))
lesscA_in_gg(0, s(X1)) → lesscA_out_gg(0, s(X1))
lesscA_in_gg(s(X1), s(X2)) → U69_gg(X1, X2, lesscA_in_gg(X1, X2))
U69_gg(X1, X2, lesscA_out_gg(X1, X2)) → lesscA_out_gg(s(X1), s(X2))
lesscA_in_ag(0, s(X1)) → lesscA_out_ag(0, s(X1))
lesscA_in_ag(s(X1), s(X2)) → U69_ag(X1, X2, lesscA_in_ag(X1, X2))
U69_ag(X1, X2, lesscA_out_ag(X1, X2)) → lesscA_out_ag(s(X1), s(X2))
lesscM_in_gg(0, s(X1)) → lesscM_out_gg(0, s(X1))
lesscM_in_gg(s(X1), s(X2)) → U110_gg(X1, X2, lesscM_in_gg(X1, X2))
U110_gg(X1, X2, lesscM_out_gg(X1, X2)) → lesscM_out_gg(s(X1), s(X2))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3)  =  tree(x1, x2, x3)
s(x1)  =  s(x1)
lesscF_in_ga(x1, x2)  =  lesscF_in_ga(x1)
0  =  0
lesscF_out_ga(x1, x2)  =  lesscF_out_ga(x1)
U104_ga(x1, x2, x3)  =  U104_ga(x1, x3)
lesscA_in_gg(x1, x2)  =  lesscA_in_gg(x1, x2)
lesscA_out_gg(x1, x2)  =  lesscA_out_gg(x1, x2)
U69_gg(x1, x2, x3)  =  U69_gg(x1, x2, x3)
lesscA_in_ag(x1, x2)  =  lesscA_in_ag(x2)
lesscA_out_ag(x1, x2)  =  lesscA_out_ag(x1, x2)
U69_ag(x1, x2, x3)  =  U69_ag(x2, x3)
lesscM_in_gg(x1, x2)  =  lesscM_in_gg(x1, x2)
lesscM_out_gg(x1, x2)  =  lesscM_out_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
DELMING_IN_GAA(x1, x2, x3)  =  DELMING_IN_GAA(x1)

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

(17) UsableRulesProof (EQUIVALENT transformation)

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

(18) Obligation:

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

DELMING_IN_GAA(tree(X1, X2, X3), X4, tree(X1, X5, X6)) → DELMING_IN_GAA(X2, X4, X5)

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

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

(19) PiDPToQDPProof (SOUND transformation)

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

(20) Obligation:

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

DELMING_IN_GAA(tree(X1, X2, X3)) → DELMING_IN_GAA(X2)

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

(21) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• DELMING_IN_GAA(tree(X1, X2, X3)) → DELMING_IN_GAA(X2)
  The graph contains the following edges 1 > 1

(22) YES

(23) Obligation:

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

DELETEK_IN_GGA(X1, tree(X2, X3, X4), tree(X2, X5, X4)) → PI_IN_GGGA(X1, X2, X3, X5)
PI_IN_GGGA(X1, X2, X3, X4) → U13_GGGA(X1, X2, X3, X4, lesscM_in_gg(X1, X2))
U13_GGGA(X1, X2, X3, X4, lesscM_out_gg(X1, X2)) → DELETEK_IN_GGA(X1, X3, X4)
DELETEK_IN_GGA(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → PJ_IN_GGGA(X2, X1, X4, X5)
PJ_IN_GGGA(X1, X2, X3, X4) → U19_GGGA(X1, X2, X3, X4, lesscM_in_gg(X1, X2))
U19_GGGA(X1, X2, X3, X4, lesscM_out_gg(X1, X2)) → DELETEK_IN_GGA(X2, X3, X4)

The TRS R consists of the following rules:

lesscF_in_ga(0, s(X1)) → lesscF_out_ga(0, s(X1))
lesscF_in_ga(s(X1), s(X2)) → U104_ga(X1, X2, lesscF_in_ga(X1, X2))
U104_ga(X1, X2, lesscF_out_ga(X1, X2)) → lesscF_out_ga(s(X1), s(X2))
lesscA_in_gg(0, s(X1)) → lesscA_out_gg(0, s(X1))
lesscA_in_gg(s(X1), s(X2)) → U69_gg(X1, X2, lesscA_in_gg(X1, X2))
U69_gg(X1, X2, lesscA_out_gg(X1, X2)) → lesscA_out_gg(s(X1), s(X2))
lesscA_in_ag(0, s(X1)) → lesscA_out_ag(0, s(X1))
lesscA_in_ag(s(X1), s(X2)) → U69_ag(X1, X2, lesscA_in_ag(X1, X2))
U69_ag(X1, X2, lesscA_out_ag(X1, X2)) → lesscA_out_ag(s(X1), s(X2))
lesscM_in_gg(0, s(X1)) → lesscM_out_gg(0, s(X1))
lesscM_in_gg(s(X1), s(X2)) → U110_gg(X1, X2, lesscM_in_gg(X1, X2))
U110_gg(X1, X2, lesscM_out_gg(X1, X2)) → lesscM_out_gg(s(X1), s(X2))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3)  =  tree(x1, x2, x3)
s(x1)  =  s(x1)
lesscF_in_ga(x1, x2)  =  lesscF_in_ga(x1)
0  =  0
lesscF_out_ga(x1, x2)  =  lesscF_out_ga(x1)
U104_ga(x1, x2, x3)  =  U104_ga(x1, x3)
lesscA_in_gg(x1, x2)  =  lesscA_in_gg(x1, x2)
lesscA_out_gg(x1, x2)  =  lesscA_out_gg(x1, x2)
U69_gg(x1, x2, x3)  =  U69_gg(x1, x2, x3)
lesscA_in_ag(x1, x2)  =  lesscA_in_ag(x2)
lesscA_out_ag(x1, x2)  =  lesscA_out_ag(x1, x2)
U69_ag(x1, x2, x3)  =  U69_ag(x2, x3)
lesscM_in_gg(x1, x2)  =  lesscM_in_gg(x1, x2)
lesscM_out_gg(x1, x2)  =  lesscM_out_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
PI_IN_GGGA(x1, x2, x3, x4)  =  PI_IN_GGGA(x1, x2, x3)
U13_GGGA(x1, x2, x3, x4, x5)  =  U13_GGGA(x1, x2, x3, x5)
DELETEK_IN_GGA(x1, x2, x3)  =  DELETEK_IN_GGA(x1, x2)
PJ_IN_GGGA(x1, x2, x3, x4)  =  PJ_IN_GGGA(x1, x2, x3)
U19_GGGA(x1, x2, x3, x4, x5)  =  U19_GGGA(x1, x2, x3, x5)

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

(24) UsableRulesProof (EQUIVALENT transformation)

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

(25) Obligation:

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

DELETEK_IN_GGA(X1, tree(X2, X3, X4), tree(X2, X5, X4)) → PI_IN_GGGA(X1, X2, X3, X5)
PI_IN_GGGA(X1, X2, X3, X4) → U13_GGGA(X1, X2, X3, X4, lesscM_in_gg(X1, X2))
U13_GGGA(X1, X2, X3, X4, lesscM_out_gg(X1, X2)) → DELETEK_IN_GGA(X1, X3, X4)
DELETEK_IN_GGA(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → PJ_IN_GGGA(X2, X1, X4, X5)
PJ_IN_GGGA(X1, X2, X3, X4) → U19_GGGA(X1, X2, X3, X4, lesscM_in_gg(X1, X2))
U19_GGGA(X1, X2, X3, X4, lesscM_out_gg(X1, X2)) → DELETEK_IN_GGA(X2, X3, X4)

The TRS R consists of the following rules:

lesscM_in_gg(0, s(X1)) → lesscM_out_gg(0, s(X1))
lesscM_in_gg(s(X1), s(X2)) → U110_gg(X1, X2, lesscM_in_gg(X1, X2))
U110_gg(X1, X2, lesscM_out_gg(X1, X2)) → lesscM_out_gg(s(X1), s(X2))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3)  =  tree(x1, x2, x3)
s(x1)  =  s(x1)
0  =  0
lesscM_in_gg(x1, x2)  =  lesscM_in_gg(x1, x2)
lesscM_out_gg(x1, x2)  =  lesscM_out_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
PI_IN_GGGA(x1, x2, x3, x4)  =  PI_IN_GGGA(x1, x2, x3)
U13_GGGA(x1, x2, x3, x4, x5)  =  U13_GGGA(x1, x2, x3, x5)
DELETEK_IN_GGA(x1, x2, x3)  =  DELETEK_IN_GGA(x1, x2)
PJ_IN_GGGA(x1, x2, x3, x4)  =  PJ_IN_GGGA(x1, x2, x3)
U19_GGGA(x1, x2, x3, x4, x5)  =  U19_GGGA(x1, x2, x3, x5)

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

(26) PiDPToQDPProof (SOUND transformation)

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

(27) Obligation:

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

DELETEK_IN_GGA(X1, tree(X2, X3, X4)) → PI_IN_GGGA(X1, X2, X3)
PI_IN_GGGA(X1, X2, X3) → U13_GGGA(X1, X2, X3, lesscM_in_gg(X1, X2))
U13_GGGA(X1, X2, X3, lesscM_out_gg(X1, X2)) → DELETEK_IN_GGA(X1, X3)
DELETEK_IN_GGA(X1, tree(X2, X3, X4)) → PJ_IN_GGGA(X2, X1, X4)
PJ_IN_GGGA(X1, X2, X3) → U19_GGGA(X1, X2, X3, lesscM_in_gg(X1, X2))
U19_GGGA(X1, X2, X3, lesscM_out_gg(X1, X2)) → DELETEK_IN_GGA(X2, X3)

The TRS R consists of the following rules:

lesscM_in_gg(0, s(X1)) → lesscM_out_gg(0, s(X1))
lesscM_in_gg(s(X1), s(X2)) → U110_gg(X1, X2, lesscM_in_gg(X1, X2))
U110_gg(X1, X2, lesscM_out_gg(X1, X2)) → lesscM_out_gg(s(X1), s(X2))

The set Q consists of the following terms:

lesscM_in_gg(x0, x1)
U110_gg(x0, x1, x2)

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

(28) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• PI_IN_GGGA(X1, X2, X3) → U13_GGGA(X1, X2, X3, lesscM_in_gg(X1, X2))
  The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3

• U13_GGGA(X1, X2, X3, lesscM_out_gg(X1, X2)) → DELETEK_IN_GGA(X1, X3)
  The graph contains the following edges 1 >= 1, 4 > 1, 3 >= 2

• U19_GGGA(X1, X2, X3, lesscM_out_gg(X1, X2)) → DELETEK_IN_GGA(X2, X3)
  The graph contains the following edges 2 >= 1, 4 > 1, 3 >= 2

• DELETEK_IN_GGA(X1, tree(X2, X3, X4)) → PI_IN_GGGA(X1, X2, X3)
  The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3

• DELETEK_IN_GGA(X1, tree(X2, X3, X4)) → PJ_IN_GGGA(X2, X1, X4)
  The graph contains the following edges 2 > 1, 1 >= 2, 2 > 3

• PJ_IN_GGGA(X1, X2, X3) → U19_GGGA(X1, X2, X3, lesscM_in_gg(X1, X2))
  The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3

(29) YES

(30) Obligation:

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

LESSF_IN_GA(s(X1), s(X2)) → LESSF_IN_GA(X1, X2)

The TRS R consists of the following rules:

lesscF_in_ga(0, s(X1)) → lesscF_out_ga(0, s(X1))
lesscF_in_ga(s(X1), s(X2)) → U104_ga(X1, X2, lesscF_in_ga(X1, X2))
U104_ga(X1, X2, lesscF_out_ga(X1, X2)) → lesscF_out_ga(s(X1), s(X2))
lesscA_in_gg(0, s(X1)) → lesscA_out_gg(0, s(X1))
lesscA_in_gg(s(X1), s(X2)) → U69_gg(X1, X2, lesscA_in_gg(X1, X2))
U69_gg(X1, X2, lesscA_out_gg(X1, X2)) → lesscA_out_gg(s(X1), s(X2))
lesscA_in_ag(0, s(X1)) → lesscA_out_ag(0, s(X1))
lesscA_in_ag(s(X1), s(X2)) → U69_ag(X1, X2, lesscA_in_ag(X1, X2))
U69_ag(X1, X2, lesscA_out_ag(X1, X2)) → lesscA_out_ag(s(X1), s(X2))
lesscM_in_gg(0, s(X1)) → lesscM_out_gg(0, s(X1))
lesscM_in_gg(s(X1), s(X2)) → U110_gg(X1, X2, lesscM_in_gg(X1, X2))
U110_gg(X1, X2, lesscM_out_gg(X1, X2)) → lesscM_out_gg(s(X1), s(X2))

The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
lesscF_in_ga(x1, x2)  =  lesscF_in_ga(x1)
0  =  0
lesscF_out_ga(x1, x2)  =  lesscF_out_ga(x1)
U104_ga(x1, x2, x3)  =  U104_ga(x1, x3)
lesscA_in_gg(x1, x2)  =  lesscA_in_gg(x1, x2)
lesscA_out_gg(x1, x2)  =  lesscA_out_gg(x1, x2)
U69_gg(x1, x2, x3)  =  U69_gg(x1, x2, x3)
lesscA_in_ag(x1, x2)  =  lesscA_in_ag(x2)
lesscA_out_ag(x1, x2)  =  lesscA_out_ag(x1, x2)
U69_ag(x1, x2, x3)  =  U69_ag(x2, x3)
lesscM_in_gg(x1, x2)  =  lesscM_in_gg(x1, x2)
lesscM_out_gg(x1, x2)  =  lesscM_out_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
LESSF_IN_GA(x1, x2)  =  LESSF_IN_GA(x1)

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

(31) UsableRulesProof (EQUIVALENT transformation)

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

(32) Obligation:

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

LESSF_IN_GA(s(X1), s(X2)) → LESSF_IN_GA(X1, X2)

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

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

(33) PiDPToQDPProof (SOUND transformation)

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

(34) Obligation:

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

LESSF_IN_GA(s(X1)) → LESSF_IN_GA(X1)

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

(35) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• LESSF_IN_GA(s(X1)) → LESSF_IN_GA(X1)
  The graph contains the following edges 1 > 1

(36) YES

(37) Obligation:

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

LESSA_IN_AG(s(X1), s(X2)) → LESSA_IN_AG(X1, X2)

The TRS R consists of the following rules:

lesscF_in_ga(0, s(X1)) → lesscF_out_ga(0, s(X1))
lesscF_in_ga(s(X1), s(X2)) → U104_ga(X1, X2, lesscF_in_ga(X1, X2))
U104_ga(X1, X2, lesscF_out_ga(X1, X2)) → lesscF_out_ga(s(X1), s(X2))
lesscA_in_gg(0, s(X1)) → lesscA_out_gg(0, s(X1))
lesscA_in_gg(s(X1), s(X2)) → U69_gg(X1, X2, lesscA_in_gg(X1, X2))
U69_gg(X1, X2, lesscA_out_gg(X1, X2)) → lesscA_out_gg(s(X1), s(X2))
lesscA_in_ag(0, s(X1)) → lesscA_out_ag(0, s(X1))
lesscA_in_ag(s(X1), s(X2)) → U69_ag(X1, X2, lesscA_in_ag(X1, X2))
U69_ag(X1, X2, lesscA_out_ag(X1, X2)) → lesscA_out_ag(s(X1), s(X2))
lesscM_in_gg(0, s(X1)) → lesscM_out_gg(0, s(X1))
lesscM_in_gg(s(X1), s(X2)) → U110_gg(X1, X2, lesscM_in_gg(X1, X2))
U110_gg(X1, X2, lesscM_out_gg(X1, X2)) → lesscM_out_gg(s(X1), s(X2))

The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
lesscF_in_ga(x1, x2)  =  lesscF_in_ga(x1)
0  =  0
lesscF_out_ga(x1, x2)  =  lesscF_out_ga(x1)
U104_ga(x1, x2, x3)  =  U104_ga(x1, x3)
lesscA_in_gg(x1, x2)  =  lesscA_in_gg(x1, x2)
lesscA_out_gg(x1, x2)  =  lesscA_out_gg(x1, x2)
U69_gg(x1, x2, x3)  =  U69_gg(x1, x2, x3)
lesscA_in_ag(x1, x2)  =  lesscA_in_ag(x2)
lesscA_out_ag(x1, x2)  =  lesscA_out_ag(x1, x2)
U69_ag(x1, x2, x3)  =  U69_ag(x2, x3)
lesscM_in_gg(x1, x2)  =  lesscM_in_gg(x1, x2)
lesscM_out_gg(x1, x2)  =  lesscM_out_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
LESSA_IN_AG(x1, x2)  =  LESSA_IN_AG(x2)

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

(38) UsableRulesProof (EQUIVALENT transformation)

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

(39) Obligation:

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

LESSA_IN_AG(s(X1), s(X2)) → LESSA_IN_AG(X1, X2)

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

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

(40) PiDPToQDPProof (SOUND transformation)

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

(41) Obligation:

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

LESSA_IN_AG(s(X2)) → LESSA_IN_AG(X2)

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

(42) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• LESSA_IN_AG(s(X2)) → LESSA_IN_AG(X2)
  The graph contains the following edges 1 > 1

(43) YES

(44) Obligation:

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

DELETEB_IN_AGA(X1, tree(X2, void, X3), tree(X2, void, X4)) → PH_IN_GAGA(X2, X1, X3, X4)
PH_IN_GAGA(X1, X2, X3, X4) → U9_GAGA(X1, X2, X3, X4, lesscF_in_ga(X1, X2))
U9_GAGA(X1, X2, X3, X4, lesscF_out_ga(X1, X2)) → DELETEB_IN_AGA(X2, X3, X4)
DELETEB_IN_AGA(s(X1), tree(0, void, X2), tree(0, void, X3)) → DELETEB_IN_AGA(s(X1), X2, X3)
DELETEB_IN_AGA(s(X1), tree(s(X2), void, X3), tree(s(X2), void, X4)) → U37_AGA(X1, X2, X3, X4, lesscF_in_ga(X2, X1))
U37_AGA(X1, X2, X3, X4, lesscF_out_ga(X2, X1)) → DELETEB_IN_AGA(s(X1), X3, X4)
DELETEB_IN_AGA(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → PL_IN_GAGA(X2, X1, X4, X5)
PL_IN_GAGA(X1, X2, X3, X4) → U22_GAGA(X1, X2, X3, X4, lesscF_in_ga(X1, X2))
U22_GAGA(X1, X2, X3, X4, lesscF_out_ga(X1, X2)) → DELETEB_IN_AGA(X2, X3, X4)
DELETEB_IN_AGA(s(X1), tree(0, X2, X3), tree(0, X2, X4)) → DELETEB_IN_AGA(s(X1), X3, X4)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) → U66_AGA(X1, X2, X3, X4, X5, lesscF_in_ga(X2, X1))
U66_AGA(X1, X2, X3, X4, X5, lesscF_out_ga(X2, X1)) → DELETEB_IN_AGA(s(X1), X4, X5)

The TRS R consists of the following rules:

lesscF_in_ga(0, s(X1)) → lesscF_out_ga(0, s(X1))
lesscF_in_ga(s(X1), s(X2)) → U104_ga(X1, X2, lesscF_in_ga(X1, X2))
U104_ga(X1, X2, lesscF_out_ga(X1, X2)) → lesscF_out_ga(s(X1), s(X2))
lesscA_in_gg(0, s(X1)) → lesscA_out_gg(0, s(X1))
lesscA_in_gg(s(X1), s(X2)) → U69_gg(X1, X2, lesscA_in_gg(X1, X2))
U69_gg(X1, X2, lesscA_out_gg(X1, X2)) → lesscA_out_gg(s(X1), s(X2))
lesscA_in_ag(0, s(X1)) → lesscA_out_ag(0, s(X1))
lesscA_in_ag(s(X1), s(X2)) → U69_ag(X1, X2, lesscA_in_ag(X1, X2))
U69_ag(X1, X2, lesscA_out_ag(X1, X2)) → lesscA_out_ag(s(X1), s(X2))
lesscM_in_gg(0, s(X1)) → lesscM_out_gg(0, s(X1))
lesscM_in_gg(s(X1), s(X2)) → U110_gg(X1, X2, lesscM_in_gg(X1, X2))
U110_gg(X1, X2, lesscM_out_gg(X1, X2)) → lesscM_out_gg(s(X1), s(X2))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3)  =  tree(x1, x2, x3)
void  =  void
s(x1)  =  s(x1)
lesscF_in_ga(x1, x2)  =  lesscF_in_ga(x1)
0  =  0
lesscF_out_ga(x1, x2)  =  lesscF_out_ga(x1)
U104_ga(x1, x2, x3)  =  U104_ga(x1, x3)
lesscA_in_gg(x1, x2)  =  lesscA_in_gg(x1, x2)
lesscA_out_gg(x1, x2)  =  lesscA_out_gg(x1, x2)
U69_gg(x1, x2, x3)  =  U69_gg(x1, x2, x3)
lesscA_in_ag(x1, x2)  =  lesscA_in_ag(x2)
lesscA_out_ag(x1, x2)  =  lesscA_out_ag(x1, x2)
U69_ag(x1, x2, x3)  =  U69_ag(x2, x3)
lesscM_in_gg(x1, x2)  =  lesscM_in_gg(x1, x2)
lesscM_out_gg(x1, x2)  =  lesscM_out_gg(x1, x2)
U110_gg(x1, x2, x3)  =  U110_gg(x1, x2, x3)
DELETEB_IN_AGA(x1, x2, x3)  =  DELETEB_IN_AGA(x2)
PH_IN_GAGA(x1, x2, x3, x4)  =  PH_IN_GAGA(x1, x3)
U9_GAGA(x1, x2, x3, x4, x5)  =  U9_GAGA(x1, x3, x5)
U37_AGA(x1, x2, x3, x4, x5)  =  U37_AGA(x2, x3, x5)
PL_IN_GAGA(x1, x2, x3, x4)  =  PL_IN_GAGA(x1, x3)
U22_GAGA(x1, x2, x3, x4, x5)  =  U22_GAGA(x1, x3, x5)
U66_AGA(x1, x2, x3, x4, x5, x6)  =  U66_AGA(x2, x3, x4, x6)

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

(45) UsableRulesProof (EQUIVALENT transformation)

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

(46) Obligation:

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

DELETEB_IN_AGA(X1, tree(X2, void, X3), tree(X2, void, X4)) → PH_IN_GAGA(X2, X1, X3, X4)
PH_IN_GAGA(X1, X2, X3, X4) → U9_GAGA(X1, X2, X3, X4, lesscF_in_ga(X1, X2))
U9_GAGA(X1, X2, X3, X4, lesscF_out_ga(X1, X2)) → DELETEB_IN_AGA(X2, X3, X4)
DELETEB_IN_AGA(s(X1), tree(0, void, X2), tree(0, void, X3)) → DELETEB_IN_AGA(s(X1), X2, X3)
DELETEB_IN_AGA(s(X1), tree(s(X2), void, X3), tree(s(X2), void, X4)) → U37_AGA(X1, X2, X3, X4, lesscF_in_ga(X2, X1))
U37_AGA(X1, X2, X3, X4, lesscF_out_ga(X2, X1)) → DELETEB_IN_AGA(s(X1), X3, X4)
DELETEB_IN_AGA(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → PL_IN_GAGA(X2, X1, X4, X5)
PL_IN_GAGA(X1, X2, X3, X4) → U22_GAGA(X1, X2, X3, X4, lesscF_in_ga(X1, X2))
U22_GAGA(X1, X2, X3, X4, lesscF_out_ga(X1, X2)) → DELETEB_IN_AGA(X2, X3, X4)
DELETEB_IN_AGA(s(X1), tree(0, X2, X3), tree(0, X2, X4)) → DELETEB_IN_AGA(s(X1), X3, X4)
DELETEB_IN_AGA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) → U66_AGA(X1, X2, X3, X4, X5, lesscF_in_ga(X2, X1))
U66_AGA(X1, X2, X3, X4, X5, lesscF_out_ga(X2, X1)) → DELETEB_IN_AGA(s(X1), X4, X5)

The TRS R consists of the following rules:

lesscF_in_ga(0, s(X1)) → lesscF_out_ga(0, s(X1))
lesscF_in_ga(s(X1), s(X2)) → U104_ga(X1, X2, lesscF_in_ga(X1, X2))
U104_ga(X1, X2, lesscF_out_ga(X1, X2)) → lesscF_out_ga(s(X1), s(X2))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3)  =  tree(x1, x2, x3)
void  =  void
s(x1)  =  s(x1)
lesscF_in_ga(x1, x2)  =  lesscF_in_ga(x1)
0  =  0
lesscF_out_ga(x1, x2)  =  lesscF_out_ga(x1)
U104_ga(x1, x2, x3)  =  U104_ga(x1, x3)
DELETEB_IN_AGA(x1, x2, x3)  =  DELETEB_IN_AGA(x2)
PH_IN_GAGA(x1, x2, x3, x4)  =  PH_IN_GAGA(x1, x3)
U9_GAGA(x1, x2, x3, x4, x5)  =  U9_GAGA(x1, x3, x5)
U37_AGA(x1, x2, x3, x4, x5)  =  U37_AGA(x2, x3, x5)
PL_IN_GAGA(x1, x2, x3, x4)  =  PL_IN_GAGA(x1, x3)
U22_GAGA(x1, x2, x3, x4, x5)  =  U22_GAGA(x1, x3, x5)
U66_AGA(x1, x2, x3, x4, x5, x6)  =  U66_AGA(x2, x3, x4, x6)

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

(47) PiDPToQDPProof (SOUND transformation)

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

(48) Obligation:

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

DELETEB_IN_AGA(tree(X2, void, X3)) → PH_IN_GAGA(X2, X3)
PH_IN_GAGA(X1, X3) → U9_GAGA(X1, X3, lesscF_in_ga(X1))
U9_GAGA(X1, X3, lesscF_out_ga(X1)) → DELETEB_IN_AGA(X3)
DELETEB_IN_AGA(tree(0, void, X2)) → DELETEB_IN_AGA(X2)
DELETEB_IN_AGA(tree(s(X2), void, X3)) → U37_AGA(X2, X3, lesscF_in_ga(X2))
U37_AGA(X2, X3, lesscF_out_ga(X2)) → DELETEB_IN_AGA(X3)
DELETEB_IN_AGA(tree(X2, X3, X4)) → PL_IN_GAGA(X2, X4)
PL_IN_GAGA(X1, X3) → U22_GAGA(X1, X3, lesscF_in_ga(X1))
U22_GAGA(X1, X3, lesscF_out_ga(X1)) → DELETEB_IN_AGA(X3)
DELETEB_IN_AGA(tree(0, X2, X3)) → DELETEB_IN_AGA(X3)
DELETEB_IN_AGA(tree(s(X2), X3, X4)) → U66_AGA(X2, X3, X4, lesscF_in_ga(X2))
U66_AGA(X2, X3, X4, lesscF_out_ga(X2)) → DELETEB_IN_AGA(X4)

The TRS R consists of the following rules:

lesscF_in_ga(0) → lesscF_out_ga(0)
lesscF_in_ga(s(X1)) → U104_ga(X1, lesscF_in_ga(X1))
U104_ga(X1, lesscF_out_ga(X1)) → lesscF_out_ga(s(X1))

The set Q consists of the following terms:

lesscF_in_ga(x0)
U104_ga(x0, x1)

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

(49) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• PH_IN_GAGA(X1, X3) → U9_GAGA(X1, X3, lesscF_in_ga(X1))
  The graph contains the following edges 1 >= 1, 2 >= 2

• U9_GAGA(X1, X3, lesscF_out_ga(X1)) → DELETEB_IN_AGA(X3)
  The graph contains the following edges 2 >= 1

• DELETEB_IN_AGA(tree(X2, void, X3)) → PH_IN_GAGA(X2, X3)
  The graph contains the following edges 1 > 1, 1 > 2

• PL_IN_GAGA(X1, X3) → U22_GAGA(X1, X3, lesscF_in_ga(X1))
  The graph contains the following edges 1 >= 1, 2 >= 2

• U37_AGA(X2, X3, lesscF_out_ga(X2)) → DELETEB_IN_AGA(X3)
  The graph contains the following edges 2 >= 1

• DELETEB_IN_AGA(tree(s(X2), void, X3)) → U37_AGA(X2, X3, lesscF_in_ga(X2))
  The graph contains the following edges 1 > 1, 1 > 2

• U22_GAGA(X1, X3, lesscF_out_ga(X1)) → DELETEB_IN_AGA(X3)
  The graph contains the following edges 2 >= 1

• U66_AGA(X2, X3, X4, lesscF_out_ga(X2)) → DELETEB_IN_AGA(X4)
  The graph contains the following edges 3 >= 1

• DELETEB_IN_AGA(tree(X2, X3, X4)) → PL_IN_GAGA(X2, X4)
  The graph contains the following edges 1 > 1, 1 > 2

• DELETEB_IN_AGA(tree(s(X2), X3, X4)) → U66_AGA(X2, X3, X4, lesscF_in_ga(X2))
  The graph contains the following edges 1 > 1, 1 > 2, 1 > 3

• DELETEB_IN_AGA(tree(0, void, X2)) → DELETEB_IN_AGA(X2)
  The graph contains the following edges 1 > 1

• DELETEB_IN_AGA(tree(0, X2, X3)) → DELETEB_IN_AGA(X3)
  The graph contains the following edges 1 > 1

(50) YES