Left Termination proof of /tmp/tmp8rVc12/insert-bfb.pl

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

0 Prolog

↳1 PrologToDTProblemTransformerProof (⇒, 389 ms)

↳2 TRIPLES

↳3 TriplesToPiDPProof (⇒, 399 ms)

↳4 PiDP

↳5 DependencyGraphProof (⇔, 0 ms)

↳6 AND

    ↳7 PiDP

        ↳8 UsableRulesProof (⇔, 0 ms)

        ↳9 PiDP

        ↳10 PiDPToQDPProof (⇔, 0 ms)

        ↳11 QDP

        ↳12 QDPSizeChangeProof (⇔, 0 ms)

        ↳13 YES

    ↳14 PiDP

        ↳15 UsableRulesProof (⇔, 0 ms)

        ↳16 PiDP

        ↳17 PiDPToQDPProof (⇔, 0 ms)

        ↳18 QDP

        ↳19 QDPSizeChangeProof (⇔, 1 ms)

        ↳20 YES

    ↳21 PiDP

        ↳22 PiDPToQDPProof (⇒, 0 ms)

        ↳23 QDP

        ↳24 QDPSizeChangeProof (⇔, 0 ms)

        ↳25 YES

(0) Obligation:

Clauses:

insert(X, void, tree(X, void, void)).
insert(X, tree(X, Left, Right), tree(X, Left, Right)).
insert(X, tree(Y, Left, Right), tree(Y, Left1, Right)) :- ','(less(X, Y), insert(X, Left, Left1)).
insert(X, tree(Y, Left, Right), tree(Y, Left, Right1)) :- ','(less(Y, X), insert(X, Right, Right1)).
less(0, s(X1)).
less(s(X), s(Y)) :- less(X, Y).

Query: insert(g,a,g)

(1) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph DT10.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="A: insert(T1, T2, T3)\n\nT1 is ground\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 0 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT1 is ground\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: true | insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 1 | insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 2 | insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 3\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT1 is ground\nT3 is ground\nX3 is free\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 1 | insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 2 | insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 3\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: true | insert(T9, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 2 | insert(T9, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 3\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 2 | insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 3\n\nT5 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T5, T2, tree(T5, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: insert(T9, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 2 | insert(T9, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 3\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: ','(less(T16, T16), insert(T16, T20, void)) | insert(T16, T2, tree(T16, void, void)), SCOPE: 1, CLAUSE: 3\n\nT16 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: insert(T9, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 3\n\nT9 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(T9, T2, tree(T9, void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: ','(less(T16, T16), insert(T16, T20, void)), SCOPE: 2, CLAUSE: 4 | ','(less(T16, T16), insert(T16, T20, void)), SCOPE: 2, CLAUSE: 5 | ?_2 | insert(T16, T2, tree(T16, void, void)), SCOPE: 1, CLAUSE: 3\n\nT16 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: ','(less(T16, T16), insert(T16, T20, void)), SCOPE: 2, CLAUSE: 5 | ?_2 | insert(T16, T2, tree(T16, void, void)), SCOPE: 1, CLAUSE: 3\n\nT16 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ','(less(T16, T16), insert(T16, T20, void)), SCOPE: 2, CLAUSE: 5\n\nT16 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: ?_2 | insert(T16, T2, tree(T16, void, void)), SCOPE: 1, CLAUSE: 3\n\nT16 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="B: ','(less(T25, T25), insert(s(T25), T20, void))\n\nT25 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="D: less(T25, T25)\n\nT25 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: insert(s(T25), T20, void)\n\nT25 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: less(T25, T25), SCOPE: 3, CLAUSE: 4 | less(T25, T25), SCOPE: 3, CLAUSE: 5\n\nT25 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: less(T25, T25), SCOPE: 3, CLAUSE: 5\n\nT25 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: less(T28, T28)\n\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: insert(T16, T2, tree(T16, void, void)), SCOPE: 1, CLAUSE: 3\n\nT16 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="C: ','(less(T39, T39), insert(T39, T43, void))\n\nT39 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: less(T39, T39)\n\nT39 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: insert(T39, T43, void)\n\nT39 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: ','(less(T50, T50), insert(T50, T54, void))\n\nT50 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(T50, T2, tree(T50, void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: ','(less(T50, T50), insert(T50, T54, void)), SCOPE: 4, CLAUSE: 4 | ','(less(T50, T50), insert(T50, T54, void)), SCOPE: 4, CLAUSE: 5\n\nT50 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(T50, T2, tree(T50, void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ','(less(T50, T50), insert(T50, T54, void)), SCOPE: 4, CLAUSE: 5\n\nT50 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(T50, T2, tree(T50, void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: ','(less(T57, T57), insert(s(T57), T54, void))\n\nT57 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(s(T57), T2, tree(s(T57), void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: ','(less(T62, T62), insert(T62, T66, void)) | insert(T62, T2, tree(T62, void, void)), SCOPE: 1, CLAUSE: 3\n\nT62 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T62, T2, tree(T62, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 3\n\nT5 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T5, T2, tree(T5, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: ','(less(T62, T62), insert(T62, T66, void)), SCOPE: 5, CLAUSE: 4 | ','(less(T62, T62), insert(T62, T66, void)), SCOPE: 5, CLAUSE: 5 | ?_5 | insert(T62, T2, tree(T62, void, void)), SCOPE: 1, CLAUSE: 3\n\nT62 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T62, T2, tree(T62, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: ','(less(T62, T62), insert(T62, T66, void)), SCOPE: 5, CLAUSE: 5 | ?_5 | insert(T62, T2, tree(T62, void, void)), SCOPE: 1, CLAUSE: 3\n\nT62 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T62, T2, tree(T62, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: ','(less(T62, T62), insert(T62, T66, void)), SCOPE: 5, CLAUSE: 5\n\nT62 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T62, T2, tree(T62, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: ?_5 | insert(T62, T2, tree(T62, void, void)), SCOPE: 1, CLAUSE: 3\n\nT62 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T62, T2, tree(T62, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: ','(less(T71, T71), insert(s(T71), T66, void))\n\nT71 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(s(T71), T2, tree(s(T71), void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: insert(T62, T2, tree(T62, void, void)), SCOPE: 1, CLAUSE: 3\n\nT62 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T62, T2, tree(T62, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: ','(less(T80, T80), insert(T80, T84, void))\n\nT80 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T80, T2, tree(T80, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(less(T89, T89), insert(T89, T93, void))\n\nT89 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T89, T2, tree(T89, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: ','(less(T89, T89), insert(T89, T93, void)), SCOPE: 6, CLAUSE: 4 | ','(less(T89, T89), insert(T89, T93, void)), SCOPE: 6, CLAUSE: 5\n\nT89 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T89, T2, tree(T89, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: ','(less(T89, T89), insert(T89, T93, void)), SCOPE: 6, CLAUSE: 5\n\nT89 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T89, T2, tree(T89, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: ','(less(T96, T96), insert(s(T96), T93, void))\n\nT96 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(s(T96), T2, tree(s(T96), void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: true | insert(T100, T2, tree(T100, T101, T102)), SCOPE: 1, CLAUSE: 2 | insert(T100, T2, tree(T100, T101, T102)), SCOPE: 1, CLAUSE: 3\n\nT100 is ground\nT101 is ground\nT102 is ground\nX3 is free\ninsert(T100, T2, tree(T100, T101, T102)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT1 is ground\nT3 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, T3) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: insert(T100, T2, tree(T100, T101, T102)), SCOPE: 1, CLAUSE: 2 | insert(T100, T2, tree(T100, T101, T102)), SCOPE: 1, CLAUSE: 3\n\nT100 is ground\nT101 is ground\nT102 is ground\nX3 is free\ninsert(T100, T2, tree(T100, T101, T102)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: ','(less(T108, T108), insert(T108, T113, T112)) | insert(T108, T2, tree(T108, T112, T111)), SCOPE: 1, CLAUSE: 3\n\nT108 is ground\nT112 is ground\nT111 is ground\nX3 is free\ninsert(T108, T2, tree(T108, T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: insert(T100, T2, tree(T100, T101, T102)), SCOPE: 1, CLAUSE: 3\n\nT100 is ground\nT101 is ground\nT102 is ground\nX3 is free\nX156 is free\nX157 is free\nX158 is free\nX159 is free\nX160 is free\ninsert(T100, T2, tree(T100, T101, T102)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T100, T2, tree(T100, T101, T102)) !=? insert(X156, tree(X157, X158, X159), tree(X157, X160, X159))", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: ','(less(T108, T108), insert(T108, T113, T112)), SCOPE: 7, CLAUSE: 4 | ','(less(T108, T108), insert(T108, T113, T112)), SCOPE: 7, CLAUSE: 5 | ?_7 | insert(T108, T2, tree(T108, T112, T111)), SCOPE: 1, CLAUSE: 3\n\nT108 is ground\nT112 is ground\nT111 is ground\nX3 is free\ninsert(T108, T2, tree(T108, T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: ','(less(T108, T108), insert(T108, T113, T112)), SCOPE: 7, CLAUSE: 5 | ?_7 | insert(T108, T2, tree(T108, T112, T111)), SCOPE: 1, CLAUSE: 3\n\nT108 is ground\nT112 is ground\nT111 is ground\nX3 is free\ninsert(T108, T2, tree(T108, T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: ','(less(T108, T108), insert(T108, T113, T112)), SCOPE: 7, CLAUSE: 5\n\nT108 is ground\nT112 is ground\nT111 is ground\nX3 is free\ninsert(T108, T2, tree(T108, T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ?_7 | insert(T108, T2, tree(T108, T112, T111)), SCOPE: 1, CLAUSE: 3\n\nT108 is ground\nT112 is ground\nT111 is ground\nX3 is free\ninsert(T108, T2, tree(T108, T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: ','(less(T118, T118), insert(s(T118), T113, T112))\n\nT112 is ground\nT111 is ground\nT118 is ground\nX3 is free\ninsert(s(T118), T2, tree(s(T118), T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: less(T118, T118)\n\nT112 is ground\nT111 is ground\nT118 is ground\nX3 is free\ninsert(s(T118), T2, tree(s(T118), T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: insert(s(T118), T113, T112)\n\nT112 is ground\nT111 is ground\nT118 is ground\nX3 is free\ninsert(s(T118), T2, tree(s(T118), T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: insert(T108, T2, tree(T108, T112, T111)), SCOPE: 1, CLAUSE: 3\n\nT108 is ground\nT112 is ground\nT111 is ground\nX3 is free\ninsert(T108, T2, tree(T108, T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: ','(less(T131, T131), insert(T131, T136, T135))\n\nT131 is ground\nT133 is ground\nT135 is ground\nX3 is free\ninsert(T131, T2, tree(T131, T133, T135)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: less(T131, T131)\n\nT131 is ground\nT133 is ground\nT135 is ground\nX3 is free\ninsert(T131, T2, tree(T131, T133, T135)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: insert(T131, T136, T135)\n\nT131 is ground\nT133 is ground\nT135 is ground\nX3 is free\ninsert(T131, T2, tree(T131, T133, T135)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: ','(less(T144, T144), insert(T144, T149, T148))\n\nT144 is ground\nT146 is ground\nT148 is ground\nX3 is free\nX156 is free\nX157 is free\nX158 is free\nX159 is free\nX160 is free\ninsert(T144, T2, tree(T144, T146, T148)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T144, T2, tree(T144, T146, T148)) !=? insert(X156, tree(X157, X158, X159), tree(X157, X160, X159))", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: ','(less(T144, T144), insert(T144, T149, T148)), SCOPE: 8, CLAUSE: 4 | ','(less(T144, T144), insert(T144, T149, T148)), SCOPE: 8, CLAUSE: 5\n\nT144 is ground\nT146 is ground\nT148 is ground\nX3 is free\nX156 is free\nX157 is free\nX158 is free\nX159 is free\nX160 is free\ninsert(T144, T2, tree(T144, T146, T148)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T144, T2, tree(T144, T146, T148)) !=? insert(X156, tree(X157, X158, X159), tree(X157, X160, X159))", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: ','(less(T144, T144), insert(T144, T149, T148)), SCOPE: 8, CLAUSE: 5\n\nT144 is ground\nT146 is ground\nT148 is ground\nX3 is free\nX156 is free\nX157 is free\nX158 is free\nX159 is free\nX160 is free\ninsert(T144, T2, tree(T144, T146, T148)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T144, T2, tree(T144, T146, T148)) !=? insert(X156, tree(X157, X158, X159), tree(X157, X160, X159))", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: ','(less(T152, T152), insert(s(T152), T149, T148))\n\nT146 is ground\nT148 is ground\nT152 is ground\nX3 is free\nX156 is free\nX157 is free\nX158 is free\nX159 is free\nX160 is free\ninsert(s(T152), T2, tree(s(T152), T146, T148)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T152), T2, tree(s(T152), T146, T148)) !=? insert(X156, tree(X157, X158, X159), tree(X157, X160, X159))", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: less(T152, T152)\n\nT146 is ground\nT148 is ground\nT152 is ground\nX3 is free\nX156 is free\nX157 is free\nX158 is free\nX159 is free\nX160 is free\ninsert(s(T152), T2, tree(s(T152), T146, T148)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T152), T2, tree(s(T152), T146, T148)) !=? insert(X156, tree(X157, X158, X159), tree(X157, X160, X159))", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: insert(s(T152), T149, T148)\n\nT146 is ground\nT148 is ground\nT152 is ground\nX3 is free\nX156 is free\nX157 is free\nX158 is free\nX159 is free\nX160 is free\ninsert(s(T152), T2, tree(s(T152), T146, T148)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T152), T2, tree(s(T152), T146, T148)) !=? insert(X156, tree(X157, X158, X159), tree(X157, X160, X159))", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: ','(less(T160, T161), insert(T160, T165, T164)) | insert(T160, T2, tree(T161, T164, T163)), SCOPE: 1, CLAUSE: 3\n\nT160 is ground\nT161 is ground\nT164 is ground\nT163 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT1 is ground\nT3 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, T3) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: ','(less(T160, T161), insert(T160, T165, T164)), SCOPE: 9, CLAUSE: 4 | ','(less(T160, T161), insert(T160, T165, T164)), SCOPE: 9, CLAUSE: 5 | ?_9 | insert(T160, T2, tree(T161, T164, T163)), SCOPE: 1, CLAUSE: 3\n\nT160 is ground\nT161 is ground\nT164 is ground\nT163 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: ','(less(T160, T161), insert(T160, T165, T164)), SCOPE: 9, CLAUSE: 4\n\nT160 is ground\nT161 is ground\nT164 is ground\nT163 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: ','(less(T160, T161), insert(T160, T165, T164)), SCOPE: 9, CLAUSE: 5 | ?_9 | insert(T160, T2, tree(T161, T164, T163)), SCOPE: 1, CLAUSE: 3\n\nT160 is ground\nT161 is ground\nT164 is ground\nT163 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: insert(0, T165, T164)\n\nT164 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: ','(less(T160, T161), insert(T160, T165, T164)), SCOPE: 9, CLAUSE: 5\n\nT160 is ground\nT161 is ground\nT164 is ground\nT163 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: ?_9 | insert(T160, T2, tree(T161, T164, T163)), SCOPE: 1, CLAUSE: 3\n\nT160 is ground\nT161 is ground\nT164 is ground\nT163 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: ','(less(T179, T180), insert(s(T179), T165, T164))\n\nT164 is ground\nT163 is ground\nT179 is ground\nT180 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T179), T2, tree(s(T180), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T179), T2, tree(s(T180), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="E: less(T179, T180)\n\nT164 is ground\nT163 is ground\nT179 is ground\nT180 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T179), T2, tree(s(T180), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T179), T2, tree(s(T180), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: insert(s(T179), T165, T164)\n\nT164 is ground\nT163 is ground\nT179 is ground\nT180 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T179), T2, tree(s(T180), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T179), T2, tree(s(T180), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: less(T179, T180), SCOPE: 10, CLAUSE: 4 | less(T179, T180), SCOPE: 10, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT179 is ground\nT180 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T179), T2, tree(s(T180), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T179), T2, tree(s(T180), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: less(T179, T180), SCOPE: 10, CLAUSE: 4\n\nT164 is ground\nT163 is ground\nT179 is ground\nT180 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T179), T2, tree(s(T180), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T179), T2, tree(s(T180), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: less(T179, T180), SCOPE: 10, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT179 is ground\nT180 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T179), T2, tree(s(T180), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T179), T2, tree(s(T180), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: less(T194, T195)\n\nT164 is ground\nT163 is ground\nT194 is ground\nT195 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(T194)), T2, tree(s(s(T195)), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(T194)), T2, tree(s(s(T195)), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: less(T194, T195), SCOPE: 11, CLAUSE: 4 | less(T194, T195), SCOPE: 11, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT194 is ground\nT195 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(T194)), T2, tree(s(s(T195)), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(T194)), T2, tree(s(s(T195)), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: less(T194, T195), SCOPE: 11, CLAUSE: 4\n\nT164 is ground\nT163 is ground\nT194 is ground\nT195 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(T194)), T2, tree(s(s(T195)), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(T194)), T2, tree(s(s(T195)), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: less(T194, T195), SCOPE: 11, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT194 is ground\nT195 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(T194)), T2, tree(s(s(T195)), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(T194)), T2, tree(s(s(T195)), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: less(T207, T208)\n\nT164 is ground\nT163 is ground\nT207 is ground\nT208 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(T207))), T2, tree(s(s(s(T208))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(T207))), T2, tree(s(s(s(T208))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: less(T207, T208), SCOPE: 12, CLAUSE: 4 | less(T207, T208), SCOPE: 12, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT207 is ground\nT208 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(T207))), T2, tree(s(s(s(T208))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(T207))), T2, tree(s(s(s(T208))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: less(T207, T208), SCOPE: 12, CLAUSE: 4\n\nT164 is ground\nT163 is ground\nT207 is ground\nT208 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(T207))), T2, tree(s(s(s(T208))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(T207))), T2, tree(s(s(s(T208))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: less(T207, T208), SCOPE: 12, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT207 is ground\nT208 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(T207))), T2, tree(s(s(s(T208))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(T207))), T2, tree(s(s(s(T208))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: less(T220, T221)\n\nT164 is ground\nT163 is ground\nT220 is ground\nT221 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(T220)))), T2, tree(s(s(s(s(T221)))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(T220)))), T2, tree(s(s(s(s(T221)))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: less(T220, T221), SCOPE: 13, CLAUSE: 4 | less(T220, T221), SCOPE: 13, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT220 is ground\nT221 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(T220)))), T2, tree(s(s(s(s(T221)))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(T220)))), T2, tree(s(s(s(s(T221)))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: less(T220, T221), SCOPE: 13, CLAUSE: 4\n\nT164 is ground\nT163 is ground\nT220 is ground\nT221 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(T220)))), T2, tree(s(s(s(s(T221)))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(T220)))), T2, tree(s(s(s(s(T221)))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: less(T220, T221), SCOPE: 13, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT220 is ground\nT221 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(T220)))), T2, tree(s(s(s(s(T221)))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(T220)))), T2, tree(s(s(s(s(T221)))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: less(T233, T234)\n\nT164 is ground\nT163 is ground\nT233 is ground\nT234 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(T233))))), T2, tree(s(s(s(s(s(T234))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(T233))))), T2, tree(s(s(s(s(s(T234))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: less(T233, T234), SCOPE: 14, CLAUSE: 4 | less(T233, T234), SCOPE: 14, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT233 is ground\nT234 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(T233))))), T2, tree(s(s(s(s(s(T234))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(T233))))), T2, tree(s(s(s(s(s(T234))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: less(T233, T234), SCOPE: 14, CLAUSE: 4\n\nT164 is ground\nT163 is ground\nT233 is ground\nT234 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(T233))))), T2, tree(s(s(s(s(s(T234))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(T233))))), T2, tree(s(s(s(s(s(T234))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: less(T233, T234), SCOPE: 14, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT233 is ground\nT234 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(T233))))), T2, tree(s(s(s(s(s(T234))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(T233))))), T2, tree(s(s(s(s(s(T234))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: less(T246, T247)\n\nT164 is ground\nT163 is ground\nT246 is ground\nT247 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(s(T246)))))), T2, tree(s(s(s(s(s(s(T247)))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(T246)))))), T2, tree(s(s(s(s(s(s(T247)))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: less(T246, T247), SCOPE: 15, CLAUSE: 4 | less(T246, T247), SCOPE: 15, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT246 is ground\nT247 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(s(T246)))))), T2, tree(s(s(s(s(s(s(T247)))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(T246)))))), T2, tree(s(s(s(s(s(s(T247)))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: less(T246, T247), SCOPE: 15, CLAUSE: 4\n\nT164 is ground\nT163 is ground\nT246 is ground\nT247 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(s(T246)))))), T2, tree(s(s(s(s(s(s(T247)))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(T246)))))), T2, tree(s(s(s(s(s(s(T247)))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: less(T246, T247), SCOPE: 15, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT246 is ground\nT247 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(s(T246)))))), T2, tree(s(s(s(s(s(s(T247)))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(T246)))))), T2, tree(s(s(s(s(s(s(T247)))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: less(T259, T260)\n\nT164 is ground\nT163 is ground\nT259 is ground\nT260 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(s(s(T259))))))), T2, tree(s(s(s(s(s(s(s(T260))))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(s(T259))))))), T2, tree(s(s(s(s(s(s(s(T260))))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: less(T259, T260), SCOPE: 16, CLAUSE: 4 | less(T259, T260), SCOPE: 16, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT259 is ground\nT260 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(s(s(T259))))))), T2, tree(s(s(s(s(s(s(s(T260))))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(s(T259))))))), T2, tree(s(s(s(s(s(s(s(T260))))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: less(T259, T260), SCOPE: 16, CLAUSE: 4\n\nT164 is ground\nT163 is ground\nT259 is ground\nT260 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(s(s(T259))))))), T2, tree(s(s(s(s(s(s(s(T260))))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(s(T259))))))), T2, tree(s(s(s(s(s(s(s(T260))))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: less(T259, T260), SCOPE: 16, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT259 is ground\nT260 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(s(s(T259))))))), T2, tree(s(s(s(s(s(s(s(T260))))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(s(T259))))))), T2, tree(s(s(s(s(s(s(s(T260))))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: less(T272, T273)\n\nT164 is ground\nT163 is ground\nT272 is ground\nT273 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(s(s(s(T272)))))))), T2, tree(s(s(s(s(s(s(s(s(T273)))))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(s(s(T272)))))))), T2, tree(s(s(s(s(s(s(s(s(T273)))))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="F: less(T272, T273)\n\nT272 is ground\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: less(T272, T273), SCOPE: 17, CLAUSE: 4 | less(T272, T273), SCOPE: 17, CLAUSE: 5\n\nT272 is ground\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: less(T272, T273), SCOPE: 17, CLAUSE: 4\n\nT272 is ground\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: less(T272, T273), SCOPE: 17, CLAUSE: 5\n\nT272 is ground\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: less(T289, T290)\n\nT289 is ground\nT290 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: insert(T160, T2, tree(T161, T164, T163)), SCOPE: 1, CLAUSE: 3\n\nT160 is ground\nT161 is ground\nT164 is ground\nT163 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: ','(less(T306, T305), insert(T305, T310, T309))\n\nT305 is ground\nT306 is ground\nT307 is ground\nT309 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T305, T2, tree(T306, T307, T309)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T305, T2, tree(T306, T307, T309)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: less(T306, T305)\n\nT305 is ground\nT306 is ground\nT307 is ground\nT309 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T305, T2, tree(T306, T307, T309)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T305, T2, tree(T306, T307, T309)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: insert(T305, T310, T309)\n\nT305 is ground\nT306 is ground\nT307 is ground\nT309 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T305, T2, tree(T306, T307, T309)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T305, T2, tree(T306, T307, T309)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: ','(less(T323, T322), insert(T322, T327, T326))\n\nT322 is ground\nT323 is ground\nT324 is ground\nT326 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T322, T2, tree(T323, T324, T326)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T322, T2, tree(T323, T324, T326)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: ','(less(T323, T322), insert(T322, T327, T326)), SCOPE: 18, CLAUSE: 4 | ','(less(T323, T322), insert(T322, T327, T326)), SCOPE: 18, CLAUSE: 5\n\nT322 is ground\nT323 is ground\nT324 is ground\nT326 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T322, T2, tree(T323, T324, T326)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T322, T2, tree(T323, T324, T326)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: ','(less(T323, T322), insert(T322, T327, T326)), SCOPE: 18, CLAUSE: 4\n\nT322 is ground\nT323 is ground\nT324 is ground\nT326 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T322, T2, tree(T323, T324, T326)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T322, T2, tree(T323, T324, T326)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: ','(less(T323, T322), insert(T322, T327, T326)), SCOPE: 18, CLAUSE: 5\n\nT322 is ground\nT323 is ground\nT324 is ground\nT326 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T322, T2, tree(T323, T324, T326)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T322, T2, tree(T323, T324, T326)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: insert(s(T332), T327, T326)\n\nT326 is ground\nT332 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: ','(less(T339, T340), insert(s(T340), T327, T326))\n\nT324 is ground\nT326 is ground\nT339 is ground\nT340 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T340), T2, tree(s(T339), T324, T326)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T340), T2, tree(s(T339), T324, T326)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: less(T339, T340)\n\nT324 is ground\nT326 is ground\nT339 is ground\nT340 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T340), T2, tree(s(T339), T324, T326)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T340), T2, tree(s(T339), T324, T326)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: insert(s(T340), T327, T326)\n\nT324 is ground\nT326 is ground\nT339 is ground\nT340 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T340), T2, tree(s(T339), T324, T326)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T340), T2, tree(s(T339), T324, T326)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 171 [arrowhead = none ];
171 -> 2;

172 [label="EVAL with clause\ninsert(X3, void, tree(X3, void, void)).\nand substitutionT1 -> T5,\nX3 -> T5,\nT2 -> void,\nT3 -> tree(T5, void, void)", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 172 [arrowhead = none ];
172 -> 3;

173 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2 -> 173 [arrowhead = none ];
173 -> 4;

174 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 174 [arrowhead = none ];
174 -> 5;

175 [label="EVAL with clause\ninsert(X148, tree(X148, X149, X150), tree(X148, X149, X150)).\nand substitutionT1 -> T100,\nX148 -> T100,\nX149 -> T101,\nX150 -> T102,\nT2 -> tree(T100, T101, T102),\nT3 -> tree(T100, T101, T102)", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 175 [arrowhead = none ];
175 -> 51;

176 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 176 [arrowhead = none ];
176 -> 52;

177 [label="EVAL with clause\ninsert(X7, tree(X7, X8, X9), tree(X7, X8, X9)).\nand substitutionT5 -> T9,\nX7 -> T9,\nX8 -> void,\nX9 -> void,\nT2 -> tree(T9, void, void),\nT10 -> void,\nT11 -> void", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 177 [arrowhead = none ];
177 -> 6;

178 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 178 [arrowhead = none ];
178 -> 7;

179 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 179 [arrowhead = none ];
179 -> 8;

180 [label="EVAL with clause\ninsert(X91, tree(X92, X93, X94), tree(X92, X95, X94)) :- ','(less(X91, X92), insert(X91, X93, X95)).\nand substitutionT5 -> T62,\nX91 -> T62,\nX92 -> T62,\nX93 -> T66,\nX94 -> void,\nT2 -> tree(T62, T66, void),\nT63 -> T62,\nX95 -> void,\nT65 -> void,\nT64 -> T66", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 180 [arrowhead = none ];
180 -> 34;

181 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 181 [arrowhead = none ];
181 -> 35;

182 [label="EVAL with clause\ninsert(X15, tree(X16, X17, X18), tree(X16, X19, X18)) :- ','(less(X15, X16), insert(X15, X17, X19)).\nand substitutionT9 -> T16,\nX15 -> T16,\nX16 -> T16,\nX17 -> T20,\nX18 -> void,\nT2 -> tree(T16, T20, void),\nT17 -> T16,\nX19 -> void,\nT19 -> void,\nT18 -> T20", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 182 [arrowhead = none ];
182 -> 9;

183 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 183 [arrowhead = none ];
183 -> 10;

184 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 184 [arrowhead = none ];
184 -> 11;

185 [label="EVAL with clause\ninsert(X72, tree(X73, X74, X75), tree(X73, X74, X76)) :- ','(less(X73, X72), insert(X72, X75, X76)).\nand substitutionT9 -> T50,\nX72 -> T50,\nX73 -> T50,\nX74 -> void,\nX75 -> T54,\nT2 -> tree(T50, void, T54),\nT51 -> T50,\nT52 -> void,\nX76 -> void,\nT53 -> T54", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 185 [arrowhead = none ];
185 -> 28;

186 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
10 -> 186 [arrowhead = none ];
186 -> 29;

187 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 187 [arrowhead = none ];
187 -> 12;

188 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
12 -> 188 [arrowhead = none ];
188 -> 13;

189 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
12 -> 189 [arrowhead = none ];
189 -> 14;

190 [label="EVAL with clause\nless(s(X29), s(X30)) :- less(X29, X30).\nand substitutionX29 -> T25,\nT16 -> s(T25),\nX30 -> T25", fontsize=14, style = filled, fillcolor = lightblue];
13 -> 190 [arrowhead = none ];
190 -> 15;

191 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
13 -> 191 [arrowhead = none ];
191 -> 16;

192 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
14 -> 192 [arrowhead = none ];
192 -> 23;

193 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
15 -> 193 [arrowhead = none ];
193 -> 17;

194 [label="SPLIT 2\nnew knowledge:\nT25 is ground", fontsize=14, style = filled, fillcolor = violet];
15 -> 194 [arrowhead = none ];
194 -> 18;

195 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
17 -> 195 [arrowhead = none ];
195 -> 19;

196 [label="INSTANCE with matching:\nT1 -> s(T25)\nT2 -> T20\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
18 -> 196 [arrowhead = none , style=dashed];
196 -> 1[style=dashed];

197 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
19 -> 197 [arrowhead = none ];
197 -> 20;

198 [label="EVAL with clause\nless(s(X40), s(X41)) :- less(X40, X41).\nand substitutionX40 -> T28,\nT25 -> s(T28),\nX41 -> T28", fontsize=14, style = filled, fillcolor = lightblue];
20 -> 198 [arrowhead = none ];
198 -> 21;

199 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
20 -> 199 [arrowhead = none ];
199 -> 22;

200 [label="INSTANCE with matching:\nT25 -> T28", fontsize=14, style = filled, fillcolor = lightgrey];
21 -> 200 [arrowhead = none , style=dashed];
200 -> 17[style=dashed];

201 [label="EVAL with clause\ninsert(X56, tree(X57, X58, X59), tree(X57, X58, X60)) :- ','(less(X57, X56), insert(X56, X59, X60)).\nand substitutionT16 -> T39,\nX56 -> T39,\nX57 -> T39,\nX58 -> void,\nX59 -> T43,\nT2 -> tree(T39, void, T43),\nT40 -> T39,\nT41 -> void,\nX60 -> void,\nT42 -> T43", fontsize=14, style = filled, fillcolor = lightblue];
23 -> 201 [arrowhead = none ];
201 -> 24;

202 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
23 -> 202 [arrowhead = none ];
202 -> 25;

203 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
24 -> 203 [arrowhead = none ];
203 -> 26;

204 [label="SPLIT 2\nnew knowledge:\nT39 is ground", fontsize=14, style = filled, fillcolor = violet];
24 -> 204 [arrowhead = none ];
204 -> 27;

205 [label="INSTANCE with matching:\nT25 -> T39", fontsize=14, style = filled, fillcolor = lightgrey];
26 -> 205 [arrowhead = none , style=dashed];
205 -> 17[style=dashed];

206 [label="INSTANCE with matching:\nT1 -> T39\nT2 -> T43\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
27 -> 206 [arrowhead = none , style=dashed];
206 -> 1[style=dashed];

207 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
28 -> 207 [arrowhead = none ];
207 -> 30;

208 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 208 [arrowhead = none ];
208 -> 31;

209 [label="EVAL with clause\nless(s(X82), s(X83)) :- less(X82, X83).\nand substitutionX82 -> T57,\nT50 -> s(T57),\nX83 -> T57", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 209 [arrowhead = none ];
209 -> 32;

210 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
31 -> 210 [arrowhead = none ];
210 -> 33;

211 [label="INSTANCE with matching:\nT25 -> T57\nT20 -> T54", fontsize=14, style = filled, fillcolor = lightgrey];
32 -> 211 [arrowhead = none , style=dashed];
211 -> 15[style=dashed];

212 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
34 -> 212 [arrowhead = none ];
212 -> 36;

213 [label="EVAL with clause\ninsert(X131, tree(X132, X133, X134), tree(X132, X133, X135)) :- ','(less(X132, X131), insert(X131, X134, X135)).\nand substitutionT5 -> T89,\nX131 -> T89,\nX132 -> T89,\nX133 -> void,\nX134 -> T93,\nT2 -> tree(T89, void, T93),\nT90 -> T89,\nT91 -> void,\nX135 -> void,\nT92 -> T93", fontsize=14, style = filled, fillcolor = lightblue];
35 -> 213 [arrowhead = none ];
213 -> 45;

214 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
35 -> 214 [arrowhead = none ];
214 -> 46;

215 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
36 -> 215 [arrowhead = none ];
215 -> 37;

216 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
37 -> 216 [arrowhead = none ];
216 -> 38;

217 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
37 -> 217 [arrowhead = none ];
217 -> 39;

218 [label="EVAL with clause\nless(s(X105), s(X106)) :- less(X105, X106).\nand substitutionX105 -> T71,\nT62 -> s(T71),\nX106 -> T71", fontsize=14, style = filled, fillcolor = lightblue];
38 -> 218 [arrowhead = none ];
218 -> 40;

219 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
38 -> 219 [arrowhead = none ];
219 -> 41;

220 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
39 -> 220 [arrowhead = none ];
220 -> 42;

221 [label="INSTANCE with matching:\nT25 -> T71\nT20 -> T66", fontsize=14, style = filled, fillcolor = lightgrey];
40 -> 221 [arrowhead = none , style=dashed];
221 -> 15[style=dashed];

222 [label="EVAL with clause\ninsert(X119, tree(X120, X121, X122), tree(X120, X121, X123)) :- ','(less(X120, X119), insert(X119, X122, X123)).\nand substitutionT62 -> T80,\nX119 -> T80,\nX120 -> T80,\nX121 -> void,\nX122 -> T84,\nT2 -> tree(T80, void, T84),\nT81 -> T80,\nT82 -> void,\nX123 -> void,\nT83 -> T84", fontsize=14, style = filled, fillcolor = lightblue];
42 -> 222 [arrowhead = none ];
222 -> 43;

223 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
42 -> 223 [arrowhead = none ];
223 -> 44;

224 [label="INSTANCE with matching:\nT39 -> T80\nT43 -> T84", fontsize=14, style = filled, fillcolor = lightgrey];
43 -> 224 [arrowhead = none , style=dashed];
224 -> 24[style=dashed];

225 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
45 -> 225 [arrowhead = none ];
225 -> 47;

226 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
47 -> 226 [arrowhead = none ];
226 -> 48;

227 [label="EVAL with clause\nless(s(X141), s(X142)) :- less(X141, X142).\nand substitutionX141 -> T96,\nT89 -> s(T96),\nX142 -> T96", fontsize=14, style = filled, fillcolor = lightblue];
48 -> 227 [arrowhead = none ];
227 -> 49;

228 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
48 -> 228 [arrowhead = none ];
228 -> 50;

229 [label="INSTANCE with matching:\nT25 -> T96\nT20 -> T93", fontsize=14, style = filled, fillcolor = lightgrey];
49 -> 229 [arrowhead = none , style=dashed];
229 -> 15[style=dashed];

230 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
51 -> 230 [arrowhead = none ];
230 -> 53;

231 [label="EVAL with clause\ninsert(X227, tree(X228, X229, X230), tree(X228, X231, X230)) :- ','(less(X227, X228), insert(X227, X229, X231)).\nand substitutionT1 -> T160,\nX227 -> T160,\nX228 -> T161,\nX229 -> T165,\nX230 -> T163,\nT2 -> tree(T161, T165, T163),\nX231 -> T164,\nT3 -> tree(T161, T164, T163),\nT162 -> T165", fontsize=14, style = filled, fillcolor = lightblue];
52 -> 231 [arrowhead = none ];
231 -> 77;

232 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
52 -> 232 [arrowhead = none ];
232 -> 78;

233 [label="EVAL with clause\ninsert(X156, tree(X157, X158, X159), tree(X157, X160, X159)) :- ','(less(X156, X157), insert(X156, X158, X160)).\nand substitutionT100 -> T108,\nX156 -> T108,\nX157 -> T108,\nX158 -> T113,\nX159 -> T111,\nT2 -> tree(T108, T113, T111),\nT109 -> T108,\nT101 -> T112,\nX160 -> T112,\nT102 -> T111,\nT110 -> T113", fontsize=14, style = filled, fillcolor = lightblue];
53 -> 233 [arrowhead = none ];
233 -> 54;

234 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
53 -> 234 [arrowhead = none ];
234 -> 55;

235 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
54 -> 235 [arrowhead = none ];
235 -> 56;

236 [label="EVAL with clause\ninsert(X204, tree(X205, X206, X207), tree(X205, X206, X208)) :- ','(less(X205, X204), insert(X204, X207, X208)).\nand substitutionT100 -> T144,\nX204 -> T144,\nX205 -> T144,\nX206 -> T146,\nX207 -> T149,\nT2 -> tree(T144, T146, T149),\nT145 -> T144,\nT101 -> T146,\nT102 -> T148,\nX208 -> T148,\nT147 -> T149", fontsize=14, style = filled, fillcolor = lightblue];
55 -> 236 [arrowhead = none ];
236 -> 69;

237 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
55 -> 237 [arrowhead = none ];
237 -> 70;

238 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
56 -> 238 [arrowhead = none ];
238 -> 57;

239 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
57 -> 239 [arrowhead = none ];
239 -> 58;

240 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
57 -> 240 [arrowhead = none ];
240 -> 59;

241 [label="EVAL with clause\nless(s(X170), s(X171)) :- less(X170, X171).\nand substitutionX170 -> T118,\nT108 -> s(T118),\nX171 -> T118", fontsize=14, style = filled, fillcolor = lightblue];
58 -> 241 [arrowhead = none ];
241 -> 60;

242 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
58 -> 242 [arrowhead = none ];
242 -> 61;

243 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
59 -> 243 [arrowhead = none ];
243 -> 64;

244 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
60 -> 244 [arrowhead = none ];
244 -> 62;

245 [label="SPLIT 2\nnew knowledge:\nT118 is ground", fontsize=14, style = filled, fillcolor = violet];
60 -> 245 [arrowhead = none ];
245 -> 63;

246 [label="INSTANCE with matching:\nT25 -> T118", fontsize=14, style = filled, fillcolor = lightgrey];
62 -> 246 [arrowhead = none , style=dashed];
246 -> 17[style=dashed];

247 [label="INSTANCE with matching:\nT1 -> s(T118)\nT2 -> T113\nT3 -> T112", fontsize=14, style = filled, fillcolor = lightgrey];
63 -> 247 [arrowhead = none , style=dashed];
247 -> 1[style=dashed];

248 [label="EVAL with clause\ninsert(X188, tree(X189, X190, X191), tree(X189, X190, X192)) :- ','(less(X189, X188), insert(X188, X191, X192)).\nand substitutionT108 -> T131,\nX188 -> T131,\nX189 -> T131,\nX190 -> T133,\nX191 -> T136,\nT2 -> tree(T131, T133, T136),\nT132 -> T131,\nT112 -> T133,\nT111 -> T135,\nX192 -> T135,\nT134 -> T136", fontsize=14, style = filled, fillcolor = lightblue];
64 -> 248 [arrowhead = none ];
248 -> 65;

249 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
64 -> 249 [arrowhead = none ];
249 -> 66;

250 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
65 -> 250 [arrowhead = none ];
250 -> 67;

251 [label="SPLIT 2\nnew knowledge:\nT131 is ground", fontsize=14, style = filled, fillcolor = violet];
65 -> 251 [arrowhead = none ];
251 -> 68;

252 [label="INSTANCE with matching:\nT25 -> T131", fontsize=14, style = filled, fillcolor = lightgrey];
67 -> 252 [arrowhead = none , style=dashed];
252 -> 17[style=dashed];

253 [label="INSTANCE with matching:\nT1 -> T131\nT2 -> T136\nT3 -> T135", fontsize=14, style = filled, fillcolor = lightgrey];
68 -> 253 [arrowhead = none , style=dashed];
253 -> 1[style=dashed];

254 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
69 -> 254 [arrowhead = none ];
254 -> 71;

255 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
71 -> 255 [arrowhead = none ];
255 -> 72;

256 [label="EVAL with clause\nless(s(X214), s(X215)) :- less(X214, X215).\nand substitutionX214 -> T152,\nT144 -> s(T152),\nX215 -> T152", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 256 [arrowhead = none ];
256 -> 73;

257 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
72 -> 257 [arrowhead = none ];
257 -> 74;

258 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
73 -> 258 [arrowhead = none ];
258 -> 75;

259 [label="SPLIT 2\nnew knowledge:\nT152 is ground", fontsize=14, style = filled, fillcolor = violet];
73 -> 259 [arrowhead = none ];
259 -> 76;

260 [label="INSTANCE with matching:\nT25 -> T152", fontsize=14, style = filled, fillcolor = lightgrey];
75 -> 260 [arrowhead = none , style=dashed];
260 -> 17[style=dashed];

261 [label="INSTANCE with matching:\nT1 -> s(T152)\nT2 -> T149\nT3 -> T148", fontsize=14, style = filled, fillcolor = lightgrey];
76 -> 261 [arrowhead = none , style=dashed];
261 -> 1[style=dashed];

262 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
77 -> 262 [arrowhead = none ];
262 -> 79;

263 [label="EVAL with clause\ninsert(X387, tree(X388, X389, X390), tree(X388, X389, X391)) :- ','(less(X388, X387), insert(X387, X390, X391)).\nand substitutionT1 -> T322,\nX387 -> T322,\nX388 -> T323,\nX389 -> T324,\nX390 -> T327,\nT2 -> tree(T323, T324, T327),\nX391 -> T326,\nT3 -> tree(T323, T324, T326),\nT325 -> T327", fontsize=14, style = filled, fillcolor = lightblue];
78 -> 263 [arrowhead = none ];
263 -> 160;

264 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
78 -> 264 [arrowhead = none ];
264 -> 161;

265 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
79 -> 265 [arrowhead = none ];
265 -> 80;

266 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
79 -> 266 [arrowhead = none ];
266 -> 81;

267 [label="EVAL with clause\nless(0, s(X236)).\nand substitutionT160 -> 0,\nX236 -> T170,\nT161 -> s(T170)", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 267 [arrowhead = none ];
267 -> 82;

268 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
80 -> 268 [arrowhead = none ];
268 -> 83;

269 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
81 -> 269 [arrowhead = none ];
269 -> 84;

270 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
81 -> 270 [arrowhead = none ];
270 -> 85;

271 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T165\nT3 -> T164", fontsize=14, style = filled, fillcolor = lightgrey];
82 -> 271 [arrowhead = none , style=dashed];
271 -> 1[style=dashed];

272 [label="EVAL with clause\nless(s(X247), s(X248)) :- less(X247, X248).\nand substitutionX247 -> T179,\nT160 -> s(T179),\nX248 -> T180,\nT161 -> s(T180)", fontsize=14, style = filled, fillcolor = lightblue];
84 -> 272 [arrowhead = none ];
272 -> 86;

273 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
84 -> 273 [arrowhead = none ];
273 -> 87;

274 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
85 -> 274 [arrowhead = none ];
274 -> 155;

275 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
86 -> 275 [arrowhead = none ];
275 -> 88;

276 [label="SPLIT 2\nnew knowledge:\nT179 is ground\nT180 is ground", fontsize=14, style = filled, fillcolor = violet];
86 -> 276 [arrowhead = none ];
276 -> 89;

277 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
88 -> 277 [arrowhead = none ];
277 -> 90;

278 [label="INSTANCE with matching:\nT1 -> s(T179)\nT2 -> T165\nT3 -> T164", fontsize=14, style = filled, fillcolor = lightgrey];
89 -> 278 [arrowhead = none , style=dashed];
278 -> 1[style=dashed];

279 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
90 -> 279 [arrowhead = none ];
279 -> 91;

280 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
90 -> 280 [arrowhead = none ];
280 -> 92;

281 [label="EVAL with clause\nless(0, s(X257)).\nand substitutionT179 -> 0,\nX257 -> T189,\nT180 -> s(T189)", fontsize=14, style = filled, fillcolor = lightblue];
91 -> 281 [arrowhead = none ];
281 -> 93;

282 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
91 -> 282 [arrowhead = none ];
282 -> 94;

283 [label="EVAL with clause\nless(s(X262), s(X263)) :- less(X262, X263).\nand substitutionX262 -> T194,\nT179 -> s(T194),\nX263 -> T195,\nT180 -> s(T195)", fontsize=14, style = filled, fillcolor = lightblue];
92 -> 283 [arrowhead = none ];
283 -> 96;

284 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
92 -> 284 [arrowhead = none ];
284 -> 97;

285 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
93 -> 285 [arrowhead = none ];
285 -> 95;

286 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
96 -> 286 [arrowhead = none ];
286 -> 98;

287 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
98 -> 287 [arrowhead = none ];
287 -> 99;

288 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
98 -> 288 [arrowhead = none ];
288 -> 100;

289 [label="EVAL with clause\nless(0, s(X270)).\nand substitutionT194 -> 0,\nX270 -> T202,\nT195 -> s(T202)", fontsize=14, style = filled, fillcolor = lightblue];
99 -> 289 [arrowhead = none ];
289 -> 101;

290 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
99 -> 290 [arrowhead = none ];
290 -> 102;

291 [label="EVAL with clause\nless(s(X275), s(X276)) :- less(X275, X276).\nand substitutionX275 -> T207,\nT194 -> s(T207),\nX276 -> T208,\nT195 -> s(T208)", fontsize=14, style = filled, fillcolor = lightblue];
100 -> 291 [arrowhead = none ];
291 -> 104;

292 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
100 -> 292 [arrowhead = none ];
292 -> 105;

293 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
101 -> 293 [arrowhead = none ];
293 -> 103;

294 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
104 -> 294 [arrowhead = none ];
294 -> 106;

295 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
106 -> 295 [arrowhead = none ];
295 -> 107;

296 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
106 -> 296 [arrowhead = none ];
296 -> 108;

297 [label="EVAL with clause\nless(0, s(X283)).\nand substitutionT207 -> 0,\nX283 -> T215,\nT208 -> s(T215)", fontsize=14, style = filled, fillcolor = lightblue];
107 -> 297 [arrowhead = none ];
297 -> 109;

298 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
107 -> 298 [arrowhead = none ];
298 -> 110;

299 [label="EVAL with clause\nless(s(X288), s(X289)) :- less(X288, X289).\nand substitutionX288 -> T220,\nT207 -> s(T220),\nX289 -> T221,\nT208 -> s(T221)", fontsize=14, style = filled, fillcolor = lightblue];
108 -> 299 [arrowhead = none ];
299 -> 112;

300 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
108 -> 300 [arrowhead = none ];
300 -> 113;

301 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
109 -> 301 [arrowhead = none ];
301 -> 111;

302 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
112 -> 302 [arrowhead = none ];
302 -> 114;

303 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
114 -> 303 [arrowhead = none ];
303 -> 115;

304 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
114 -> 304 [arrowhead = none ];
304 -> 116;

305 [label="EVAL with clause\nless(0, s(X296)).\nand substitutionT220 -> 0,\nX296 -> T228,\nT221 -> s(T228)", fontsize=14, style = filled, fillcolor = lightblue];
115 -> 305 [arrowhead = none ];
305 -> 117;

306 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
115 -> 306 [arrowhead = none ];
306 -> 118;

307 [label="EVAL with clause\nless(s(X301), s(X302)) :- less(X301, X302).\nand substitutionX301 -> T233,\nT220 -> s(T233),\nX302 -> T234,\nT221 -> s(T234)", fontsize=14, style = filled, fillcolor = lightblue];
116 -> 307 [arrowhead = none ];
307 -> 120;

308 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
116 -> 308 [arrowhead = none ];
308 -> 121;

309 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
117 -> 309 [arrowhead = none ];
309 -> 119;

310 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
120 -> 310 [arrowhead = none ];
310 -> 122;

311 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
122 -> 311 [arrowhead = none ];
311 -> 123;

312 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
122 -> 312 [arrowhead = none ];
312 -> 124;

313 [label="EVAL with clause\nless(0, s(X309)).\nand substitutionT233 -> 0,\nX309 -> T241,\nT234 -> s(T241)", fontsize=14, style = filled, fillcolor = lightblue];
123 -> 313 [arrowhead = none ];
313 -> 125;

314 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
123 -> 314 [arrowhead = none ];
314 -> 126;

315 [label="EVAL with clause\nless(s(X314), s(X315)) :- less(X314, X315).\nand substitutionX314 -> T246,\nT233 -> s(T246),\nX315 -> T247,\nT234 -> s(T247)", fontsize=14, style = filled, fillcolor = lightblue];
124 -> 315 [arrowhead = none ];
315 -> 128;

316 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
124 -> 316 [arrowhead = none ];
316 -> 129;

317 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
125 -> 317 [arrowhead = none ];
317 -> 127;

318 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
128 -> 318 [arrowhead = none ];
318 -> 130;

319 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
130 -> 319 [arrowhead = none ];
319 -> 131;

320 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
130 -> 320 [arrowhead = none ];
320 -> 132;

321 [label="EVAL with clause\nless(0, s(X322)).\nand substitutionT246 -> 0,\nX322 -> T254,\nT247 -> s(T254)", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 321 [arrowhead = none ];
321 -> 133;

322 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
131 -> 322 [arrowhead = none ];
322 -> 134;

323 [label="EVAL with clause\nless(s(X327), s(X328)) :- less(X327, X328).\nand substitutionX327 -> T259,\nT246 -> s(T259),\nX328 -> T260,\nT247 -> s(T260)", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 323 [arrowhead = none ];
323 -> 136;

324 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
132 -> 324 [arrowhead = none ];
324 -> 137;

325 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
133 -> 325 [arrowhead = none ];
325 -> 135;

326 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
136 -> 326 [arrowhead = none ];
326 -> 138;

327 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
138 -> 327 [arrowhead = none ];
327 -> 139;

328 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
138 -> 328 [arrowhead = none ];
328 -> 140;

329 [label="EVAL with clause\nless(0, s(X335)).\nand substitutionT259 -> 0,\nX335 -> T267,\nT260 -> s(T267)", fontsize=14, style = filled, fillcolor = lightblue];
139 -> 329 [arrowhead = none ];
329 -> 141;

330 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
139 -> 330 [arrowhead = none ];
330 -> 142;

331 [label="EVAL with clause\nless(s(X340), s(X341)) :- less(X340, X341).\nand substitutionX340 -> T272,\nT259 -> s(T272),\nX341 -> T273,\nT260 -> s(T273)", fontsize=14, style = filled, fillcolor = lightblue];
140 -> 331 [arrowhead = none ];
331 -> 144;

332 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
140 -> 332 [arrowhead = none ];
332 -> 145;

333 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
141 -> 333 [arrowhead = none ];
333 -> 143;

334 [label="GENERALIZATION\nT276 <-- s(s(s(s(s(s(s(T272)))))))\nT277 <-- s(s(s(s(s(s(s(T273)))))))\n\nNew Knowledge:\nT276 is ground\nT277 is ground", fontsize=14, style = filled, fillcolor = violet];
144 -> 334 [arrowhead = none ];
334 -> 146;

335 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
146 -> 335 [arrowhead = none ];
335 -> 147;

336 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
147 -> 336 [arrowhead = none ];
336 -> 148;

337 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
147 -> 337 [arrowhead = none ];
337 -> 149;

338 [label="EVAL with clause\nless(0, s(X350)).\nand substitutionT272 -> 0,\nX350 -> T284,\nT273 -> s(T284)", fontsize=14, style = filled, fillcolor = lightblue];
148 -> 338 [arrowhead = none ];
338 -> 150;

339 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
148 -> 339 [arrowhead = none ];
339 -> 151;

340 [label="EVAL with clause\nless(s(X355), s(X356)) :- less(X355, X356).\nand substitutionX355 -> T289,\nT272 -> s(T289),\nX356 -> T290,\nT273 -> s(T290)", fontsize=14, style = filled, fillcolor = lightblue];
149 -> 340 [arrowhead = none ];
340 -> 153;

341 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
149 -> 341 [arrowhead = none ];
341 -> 154;

342 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
150 -> 342 [arrowhead = none ];
342 -> 152;

343 [label="INSTANCE with matching:\nT272 -> T289\nT273 -> T290", fontsize=14, style = filled, fillcolor = lightgrey];
153 -> 343 [arrowhead = none , style=dashed];
343 -> 146[style=dashed];

344 [label="EVAL with clause\ninsert(X371, tree(X372, X373, X374), tree(X372, X373, X375)) :- ','(less(X372, X371), insert(X371, X374, X375)).\nand substitutionT160 -> T305,\nX371 -> T305,\nX372 -> T306,\nX373 -> T307,\nX374 -> T310,\nT2 -> tree(T306, T307, T310),\nT161 -> T306,\nT164 -> T307,\nT163 -> T309,\nX375 -> T309,\nT308 -> T310", fontsize=14, style = filled, fillcolor = lightblue];
155 -> 344 [arrowhead = none ];
344 -> 156;

345 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
155 -> 345 [arrowhead = none ];
345 -> 157;

346 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
156 -> 346 [arrowhead = none ];
346 -> 158;

347 [label="SPLIT 2\nnew knowledge:\nT306 is ground\nT305 is ground", fontsize=14, style = filled, fillcolor = violet];
156 -> 347 [arrowhead = none ];
347 -> 159;

348 [label="INSTANCE with matching:\nT272 -> T306\nT273 -> T305", fontsize=14, style = filled, fillcolor = lightgrey];
158 -> 348 [arrowhead = none , style=dashed];
348 -> 146[style=dashed];

349 [label="INSTANCE with matching:\nT1 -> T305\nT2 -> T310\nT3 -> T309", fontsize=14, style = filled, fillcolor = lightgrey];
159 -> 349 [arrowhead = none , style=dashed];
349 -> 1[style=dashed];

350 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
160 -> 350 [arrowhead = none ];
350 -> 162;

351 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
162 -> 351 [arrowhead = none ];
351 -> 163;

352 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
162 -> 352 [arrowhead = none ];
352 -> 164;

353 [label="EVAL with clause\nless(0, s(X396)).\nand substitutionT323 -> 0,\nX396 -> T332,\nT322 -> s(T332)", fontsize=14, style = filled, fillcolor = lightblue];
163 -> 353 [arrowhead = none ];
353 -> 165;

354 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
163 -> 354 [arrowhead = none ];
354 -> 166;

355 [label="EVAL with clause\nless(s(X403), s(X404)) :- less(X403, X404).\nand substitutionX403 -> T339,\nT323 -> s(T339),\nX404 -> T340,\nT322 -> s(T340)", fontsize=14, style = filled, fillcolor = lightblue];
164 -> 355 [arrowhead = none ];
355 -> 167;

356 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
164 -> 356 [arrowhead = none ];
356 -> 168;

357 [label="INSTANCE with matching:\nT1 -> s(T332)\nT2 -> T327\nT3 -> T326", fontsize=14, style = filled, fillcolor = lightgrey];
165 -> 357 [arrowhead = none , style=dashed];
357 -> 1[style=dashed];

358 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
167 -> 358 [arrowhead = none ];
358 -> 169;

359 [label="SPLIT 2\nnew knowledge:\nT339 is ground\nT340 is ground", fontsize=14, style = filled, fillcolor = violet];
167 -> 359 [arrowhead = none ];
359 -> 170;

360 [label="INSTANCE with matching:\nT272 -> T339\nT273 -> T340", fontsize=14, style = filled, fillcolor = lightgrey];
169 -> 360 [arrowhead = none , style=dashed];
360 -> 146[style=dashed];

361 [label="INSTANCE with matching:\nT1 -> s(T340)\nT2 -> T327\nT3 -> T326", fontsize=14, style = filled, fillcolor = lightgrey];
170 -> 361 [arrowhead = none , style=dashed];
361 -> 1[style=dashed];

}

(2) Obligation:

Triples:

lessD(s(X1)) :- lessD(X1).
pB(X1, X2) :- lessD(X1).
pB(X1, X2) :- ','(lesscD(X1), insertA(s(X1), X2, void)).
pC(X1, X2) :- lessD(X1).
pC(X1, X2) :- ','(lesscD(X1), insertA(X1, X2, void)).
lessF(s(X1), s(X2)) :- lessF(X1, X2).
insertA(s(X1), tree(s(X1), X2, void), tree(s(X1), void, void)) :- pB(X1, X2).
insertA(X1, tree(X1, void, X2), tree(X1, void, void)) :- pC(X1, X2).
insertA(s(X1), tree(s(X1), void, X2), tree(s(X1), void, void)) :- pB(X1, X2).
insertA(s(X1), tree(s(X1), X2, void), tree(s(X1), void, void)) :- pB(X1, X2).
insertA(X1, tree(X1, void, X2), tree(X1, void, void)) :- pC(X1, X2).
insertA(s(X1), tree(s(X1), void, X2), tree(s(X1), void, void)) :- pB(X1, X2).
insertA(s(X1), tree(s(X1), X2, X3), tree(s(X1), X4, X3)) :- lessD(X1).
insertA(s(X1), tree(s(X1), X2, X3), tree(s(X1), X4, X3)) :- ','(lesscD(X1), insertA(s(X1), X2, X4)).
insertA(X1, tree(X1, X2, X3), tree(X1, X2, X4)) :- lessD(X1).
insertA(X1, tree(X1, X2, X3), tree(X1, X2, X4)) :- ','(lesscD(X1), insertA(X1, X3, X4)).
insertA(s(X1), tree(s(X1), X2, X3), tree(s(X1), X2, X4)) :- lessD(X1).
insertA(s(X1), tree(s(X1), X2, X3), tree(s(X1), X2, X4)) :- ','(lesscD(X1), insertA(s(X1), X3, X4)).
insertA(0, tree(s(X1), X2, X3), tree(s(X1), X4, X3)) :- insertA(0, X2, X4).
insertA(s(s(s(s(s(s(s(s(X1)))))))), tree(s(s(s(s(s(s(s(s(X2)))))))), X3, X4), tree(s(s(s(s(s(s(s(s(X2)))))))), X5, X4)) :- lessF(X1, X2).
insertA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) :- ','(lesscE(X1, X2), insertA(s(X1), X3, X5)).
insertA(X1, tree(X2, X3, X4), tree(X2, X3, X5)) :- lessF(X2, X1).
insertA(X1, tree(X2, X3, X4), tree(X2, X3, X5)) :- ','(lesscF(X2, X1), insertA(X1, X4, X5)).
insertA(s(X1), tree(0, X2, X3), tree(0, X2, X4)) :- insertA(s(X1), X3, X4).
insertA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) :- lessF(X2, X1).
insertA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) :- ','(lesscF(X2, X1), insertA(s(X1), X4, X5)).

Clauses:

insertcA(X1, void, tree(X1, void, void)).
insertcA(X1, tree(X1, void, void), tree(X1, void, void)).
insertcA(s(X1), tree(s(X1), X2, void), tree(s(X1), void, void)) :- qcB(X1, X2).
insertcA(X1, tree(X1, void, X2), tree(X1, void, void)) :- qcC(X1, X2).
insertcA(s(X1), tree(s(X1), void, X2), tree(s(X1), void, void)) :- qcB(X1, X2).
insertcA(s(X1), tree(s(X1), X2, void), tree(s(X1), void, void)) :- qcB(X1, X2).
insertcA(X1, tree(X1, void, X2), tree(X1, void, void)) :- qcC(X1, X2).
insertcA(s(X1), tree(s(X1), void, X2), tree(s(X1), void, void)) :- qcB(X1, X2).
insertcA(X1, tree(X1, X2, X3), tree(X1, X2, X3)).
insertcA(s(X1), tree(s(X1), X2, X3), tree(s(X1), X4, X3)) :- ','(lesscD(X1), insertcA(s(X1), X2, X4)).
insertcA(X1, tree(X1, X2, X3), tree(X1, X2, X4)) :- ','(lesscD(X1), insertcA(X1, X3, X4)).
insertcA(s(X1), tree(s(X1), X2, X3), tree(s(X1), X2, X4)) :- ','(lesscD(X1), insertcA(s(X1), X3, X4)).
insertcA(0, tree(s(X1), X2, X3), tree(s(X1), X4, X3)) :- insertcA(0, X2, X4).
insertcA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) :- ','(lesscE(X1, X2), insertcA(s(X1), X3, X5)).
insertcA(X1, tree(X2, X3, X4), tree(X2, X3, X5)) :- ','(lesscF(X2, X1), insertcA(X1, X4, X5)).
insertcA(s(X1), tree(0, X2, X3), tree(0, X2, X4)) :- insertcA(s(X1), X3, X4).
insertcA(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) :- ','(lesscF(X2, X1), insertcA(s(X1), X4, X5)).
lesscD(s(X1)) :- lesscD(X1).
qcB(X1, X2) :- ','(lesscD(X1), insertcA(s(X1), X2, void)).
qcC(X1, X2) :- ','(lesscD(X1), insertcA(X1, X2, void)).
lesscF(0, s(X1)).
lesscF(s(X1), s(X2)) :- lesscF(X1, X2).
lesscE(0, s(X1)).
lesscE(s(0), s(s(X1))).
lesscE(s(s(0)), s(s(s(X1)))).
lesscE(s(s(s(0))), s(s(s(s(X1))))).
lesscE(s(s(s(s(0)))), s(s(s(s(s(X1)))))).
lesscE(s(s(s(s(s(0))))), s(s(s(s(s(s(X1))))))).
lesscE(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(X1)))))))).
lesscE(s(s(s(s(s(s(s(X1))))))), s(s(s(s(s(s(s(X2)))))))) :- lesscF(X1, X2).

Afs:

insertA(x1, x2, x3) = insertA(x1, x3)

(3) TriplesToPiDPProof (SOUND transformation)

We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes:
insertA_in: (b,f,b)
pB_in: (b,f)
lessD_in: (b)
lesscD_in: (b)
pC_in: (b,f)
lessF_in: (b,b)
lesscE_in: (b,b)
lesscF_in: (b,b)
Transforming TRIPLES into the following Term Rewriting System:
Pi DP problem:
The TRS P consists of the following rules:

INSERTA_IN_GAG(s(X1), tree(s(X1), X2, void), tree(s(X1), void, void)) → U9_GAG(X1, X2, pB_in_ga(X1, X2))
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, void), tree(s(X1), void, void)) → PB_IN_GA(X1, X2)
PB_IN_GA(X1, X2) → U2_GA(X1, X2, lessD_in_g(X1))
PB_IN_GA(X1, X2) → LESSD_IN_G(X1)
LESSD_IN_G(s(X1)) → U1_G(X1, lessD_in_g(X1))
LESSD_IN_G(s(X1)) → LESSD_IN_G(X1)
PB_IN_GA(X1, X2) → U3_GA(X1, X2, lesscD_in_g(X1))
U3_GA(X1, X2, lesscD_out_g(X1)) → U4_GA(X1, X2, insertA_in_gag(s(X1), X2, void))
U3_GA(X1, X2, lesscD_out_g(X1)) → INSERTA_IN_GAG(s(X1), X2, void)
INSERTA_IN_GAG(X1, tree(X1, void, X2), tree(X1, void, void)) → U10_GAG(X1, X2, pC_in_ga(X1, X2))
INSERTA_IN_GAG(X1, tree(X1, void, X2), tree(X1, void, void)) → PC_IN_GA(X1, X2)
PC_IN_GA(X1, X2) → U5_GA(X1, X2, lessD_in_g(X1))
PC_IN_GA(X1, X2) → LESSD_IN_G(X1)
PC_IN_GA(X1, X2) → U6_GA(X1, X2, lesscD_in_g(X1))
U6_GA(X1, X2, lesscD_out_g(X1)) → U7_GA(X1, X2, insertA_in_gag(X1, X2, void))
U6_GA(X1, X2, lesscD_out_g(X1)) → INSERTA_IN_GAG(X1, X2, void)
INSERTA_IN_GAG(s(X1), tree(s(X1), void, X2), tree(s(X1), void, void)) → U11_GAG(X1, X2, pB_in_ga(X1, X2))
INSERTA_IN_GAG(s(X1), tree(s(X1), void, X2), tree(s(X1), void, void)) → PB_IN_GA(X1, X2)
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → U12_GAG(X1, X2, X3, X4, lessD_in_g(X1))
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → LESSD_IN_G(X1)
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → U13_GAG(X1, X2, X3, X4, lesscD_in_g(X1))
U13_GAG(X1, X2, X3, X4, lesscD_out_g(X1)) → U14_GAG(X1, X2, X3, X4, insertA_in_gag(s(X1), X2, X4))
U13_GAG(X1, X2, X3, X4, lesscD_out_g(X1)) → INSERTA_IN_GAG(s(X1), X2, X4)
INSERTA_IN_GAG(X1, tree(X1, X2, X3), tree(X1, X2, X4)) → U15_GAG(X1, X2, X3, X4, lessD_in_g(X1))
INSERTA_IN_GAG(X1, tree(X1, X2, X3), tree(X1, X2, X4)) → LESSD_IN_G(X1)
INSERTA_IN_GAG(X1, tree(X1, X2, X3), tree(X1, X2, X4)) → U16_GAG(X1, X2, X3, X4, lesscD_in_g(X1))
U16_GAG(X1, X2, X3, X4, lesscD_out_g(X1)) → U17_GAG(X1, X2, X3, X4, insertA_in_gag(X1, X3, X4))
U16_GAG(X1, X2, X3, X4, lesscD_out_g(X1)) → INSERTA_IN_GAG(X1, X3, X4)
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X3), tree(s(X1), X2, X4)) → U18_GAG(X1, X2, X3, X4, lessD_in_g(X1))
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X3), tree(s(X1), X2, X4)) → LESSD_IN_G(X1)
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X3), tree(s(X1), X2, X4)) → U19_GAG(X1, X2, X3, X4, lesscD_in_g(X1))
U19_GAG(X1, X2, X3, X4, lesscD_out_g(X1)) → U20_GAG(X1, X2, X3, X4, insertA_in_gag(s(X1), X3, X4))
U19_GAG(X1, X2, X3, X4, lesscD_out_g(X1)) → INSERTA_IN_GAG(s(X1), X3, X4)
INSERTA_IN_GAG(0, tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → U21_GAG(X1, X2, X3, X4, insertA_in_gag(0, X2, X4))
INSERTA_IN_GAG(0, tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → INSERTA_IN_GAG(0, X2, X4)
INSERTA_IN_GAG(s(s(s(s(s(s(s(s(X1)))))))), tree(s(s(s(s(s(s(s(s(X2)))))))), X3, X4), tree(s(s(s(s(s(s(s(s(X2)))))))), X5, X4)) → U22_GAG(X1, X2, X3, X4, X5, lessF_in_gg(X1, X2))
INSERTA_IN_GAG(s(s(s(s(s(s(s(s(X1)))))))), tree(s(s(s(s(s(s(s(s(X2)))))))), X3, X4), tree(s(s(s(s(s(s(s(s(X2)))))))), X5, X4)) → LESSF_IN_GG(X1, X2)
LESSF_IN_GG(s(X1), s(X2)) → U8_GG(X1, X2, lessF_in_gg(X1, X2))
LESSF_IN_GG(s(X1), s(X2)) → LESSF_IN_GG(X1, X2)
INSERTA_IN_GAG(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) → U23_GAG(X1, X2, X3, X4, X5, lesscE_in_gg(X1, X2))
U23_GAG(X1, X2, X3, X4, X5, lesscE_out_gg(X1, X2)) → U24_GAG(X1, X2, X3, X4, X5, insertA_in_gag(s(X1), X3, X5))
U23_GAG(X1, X2, X3, X4, X5, lesscE_out_gg(X1, X2)) → INSERTA_IN_GAG(s(X1), X3, X5)
INSERTA_IN_GAG(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → U25_GAG(X1, X2, X3, X4, X5, lessF_in_gg(X2, X1))
INSERTA_IN_GAG(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → LESSF_IN_GG(X2, X1)
INSERTA_IN_GAG(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → U26_GAG(X1, X2, X3, X4, X5, lesscF_in_gg(X2, X1))
U26_GAG(X1, X2, X3, X4, X5, lesscF_out_gg(X2, X1)) → U27_GAG(X1, X2, X3, X4, X5, insertA_in_gag(X1, X4, X5))
U26_GAG(X1, X2, X3, X4, X5, lesscF_out_gg(X2, X1)) → INSERTA_IN_GAG(X1, X4, X5)
INSERTA_IN_GAG(s(X1), tree(0, X2, X3), tree(0, X2, X4)) → U28_GAG(X1, X2, X3, X4, insertA_in_gag(s(X1), X3, X4))
INSERTA_IN_GAG(s(X1), tree(0, X2, X3), tree(0, X2, X4)) → INSERTA_IN_GAG(s(X1), X3, X4)
INSERTA_IN_GAG(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) → U29_GAG(X1, X2, X3, X4, X5, lessF_in_gg(X2, X1))
INSERTA_IN_GAG(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) → LESSF_IN_GG(X2, X1)
INSERTA_IN_GAG(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) → U30_GAG(X1, X2, X3, X4, X5, lesscF_in_gg(X2, X1))
U30_GAG(X1, X2, X3, X4, X5, lesscF_out_gg(X2, X1)) → U31_GAG(X1, X2, X3, X4, X5, insertA_in_gag(s(X1), X4, X5))
U30_GAG(X1, X2, X3, X4, X5, lesscF_out_gg(X2, X1)) → INSERTA_IN_GAG(s(X1), X4, X5)

The TRS R consists of the following rules:

lesscD_in_g(s(X1)) → U50_g(X1, lesscD_in_g(X1))
U50_g(X1, lesscD_out_g(X1)) → lesscD_out_g(s(X1))
lesscE_in_gg(0, s(X1)) → lesscE_out_gg(0, s(X1))
lesscE_in_gg(s(0), s(s(X1))) → lesscE_out_gg(s(0), s(s(X1)))
lesscE_in_gg(s(s(0)), s(s(s(X1)))) → lesscE_out_gg(s(s(0)), s(s(s(X1))))
lesscE_in_gg(s(s(s(0))), s(s(s(s(X1))))) → lesscE_out_gg(s(s(s(0))), s(s(s(s(X1)))))
lesscE_in_gg(s(s(s(s(0)))), s(s(s(s(s(X1)))))) → lesscE_out_gg(s(s(s(s(0)))), s(s(s(s(s(X1))))))
lesscE_in_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(X1))))))) → lesscE_out_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(X1)))))))
lesscE_in_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(X1)))))))) → lesscE_out_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(X1))))))))
lesscE_in_gg(s(s(s(s(s(s(s(X1))))))), s(s(s(s(s(s(s(X2)))))))) → U56_gg(X1, X2, lesscF_in_gg(X1, X2))
lesscF_in_gg(0, s(X1)) → lesscF_out_gg(0, s(X1))
lesscF_in_gg(s(X1), s(X2)) → U55_gg(X1, X2, lesscF_in_gg(X1, X2))
U55_gg(X1, X2, lesscF_out_gg(X1, X2)) → lesscF_out_gg(s(X1), s(X2))
U56_gg(X1, X2, lesscF_out_gg(X1, X2)) → lesscE_out_gg(s(s(s(s(s(s(s(X1))))))), s(s(s(s(s(s(s(X2))))))))

The argument filtering Pi contains the following mapping:
insertA_in_gag(x1, x2, x3) = insertA_in_gag(x1, x3)
s(x1) = s(x1)
tree(x1, x2, x3) = tree(x1, x2, x3)
void = void
pB_in_ga(x1, x2) = pB_in_ga(x1)
lessD_in_g(x1) = lessD_in_g(x1)
lesscD_in_g(x1) = lesscD_in_g(x1)
U50_g(x1, x2) = U50_g(x1, x2)
lesscD_out_g(x1) = lesscD_out_g(x1)
pC_in_ga(x1, x2) = pC_in_ga(x1)
0 = 0
lessF_in_gg(x1, x2) = lessF_in_gg(x1, x2)
lesscE_in_gg(x1, x2) = lesscE_in_gg(x1, x2)
lesscE_out_gg(x1, x2) = lesscE_out_gg(x1, x2)
U56_gg(x1, x2, x3) = U56_gg(x1, x2, x3)
lesscF_in_gg(x1, x2) = lesscF_in_gg(x1, x2)
lesscF_out_gg(x1, x2) = lesscF_out_gg(x1, x2)
U55_gg(x1, x2, x3) = U55_gg(x1, x2, x3)
INSERTA_IN_GAG(x1, x2, x3) = INSERTA_IN_GAG(x1, x3)
U9_GAG(x1, x2, x3) = U9_GAG(x1, x3)
PB_IN_GA(x1, x2) = PB_IN_GA(x1)
U2_GA(x1, x2, x3) = U2_GA(x1, x3)
LESSD_IN_G(x1) = LESSD_IN_G(x1)
U1_G(x1, x2) = U1_G(x1, x2)
U3_GA(x1, x2, x3) = U3_GA(x1, x3)
U4_GA(x1, x2, x3) = U4_GA(x1, x3)
U10_GAG(x1, x2, x3) = U10_GAG(x1, x3)
PC_IN_GA(x1, x2) = PC_IN_GA(x1)
U5_GA(x1, x2, x3) = U5_GA(x1, x3)
U6_GA(x1, x2, x3) = U6_GA(x1, x3)
U7_GA(x1, x2, x3) = U7_GA(x1, x3)
U11_GAG(x1, x2, x3) = U11_GAG(x1, x3)
U12_GAG(x1, x2, x3, x4, x5) = U12_GAG(x1, x3, x4, x5)
U13_GAG(x1, x2, x3, x4, x5) = U13_GAG(x1, x3, x4, x5)
U14_GAG(x1, x2, x3, x4, x5) = U14_GAG(x1, x3, x4, x5)
U15_GAG(x1, x2, x3, x4, x5) = U15_GAG(x1, x2, x4, x5)
U16_GAG(x1, x2, x3, x4, x5) = U16_GAG(x1, x2, x4, x5)
U17_GAG(x1, x2, x3, x4, x5) = U17_GAG(x1, x2, x4, x5)
U18_GAG(x1, x2, x3, x4, x5) = U18_GAG(x1, x2, x4, x5)
U19_GAG(x1, x2, x3, x4, x5) = U19_GAG(x1, x2, x4, x5)
U20_GAG(x1, x2, x3, x4, x5) = U20_GAG(x1, x2, x4, x5)
U21_GAG(x1, x2, x3, x4, x5) = U21_GAG(x1, x3, x4, x5)
U22_GAG(x1, x2, x3, x4, x5, x6) = U22_GAG(x1, x2, x4, x5, x6)
LESSF_IN_GG(x1, x2) = LESSF_IN_GG(x1, x2)
U8_GG(x1, x2, x3) = U8_GG(x1, x2, x3)
U23_GAG(x1, x2, x3, x4, x5, x6) = U23_GAG(x1, x2, x4, x5, x6)
U24_GAG(x1, x2, x3, x4, x5, x6) = U24_GAG(x1, x2, x4, x5, x6)
U25_GAG(x1, x2, x3, x4, x5, x6) = U25_GAG(x1, x2, x3, x5, x6)
U26_GAG(x1, x2, x3, x4, x5, x6) = U26_GAG(x1, x2, x3, x5, x6)
U27_GAG(x1, x2, x3, x4, x5, x6) = U27_GAG(x1, x2, x3, x5, x6)
U28_GAG(x1, x2, x3, x4, x5) = U28_GAG(x1, x2, x4, x5)
U29_GAG(x1, x2, x3, x4, x5, x6) = U29_GAG(x1, x2, x3, x5, x6)
U30_GAG(x1, x2, x3, x4, x5, x6) = U30_GAG(x1, x2, x3, x5, x6)
U31_GAG(x1, x2, x3, x4, x5, x6) = U31_GAG(x1, x2, x3, x5, x6)

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

Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES

(4) Obligation:

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

INSERTA_IN_GAG(s(X1), tree(s(X1), X2, void), tree(s(X1), void, void)) → U9_GAG(X1, X2, pB_in_ga(X1, X2))
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, void), tree(s(X1), void, void)) → PB_IN_GA(X1, X2)
PB_IN_GA(X1, X2) → U2_GA(X1, X2, lessD_in_g(X1))
PB_IN_GA(X1, X2) → LESSD_IN_G(X1)
LESSD_IN_G(s(X1)) → U1_G(X1, lessD_in_g(X1))
LESSD_IN_G(s(X1)) → LESSD_IN_G(X1)
PB_IN_GA(X1, X2) → U3_GA(X1, X2, lesscD_in_g(X1))
U3_GA(X1, X2, lesscD_out_g(X1)) → U4_GA(X1, X2, insertA_in_gag(s(X1), X2, void))
U3_GA(X1, X2, lesscD_out_g(X1)) → INSERTA_IN_GAG(s(X1), X2, void)
INSERTA_IN_GAG(X1, tree(X1, void, X2), tree(X1, void, void)) → U10_GAG(X1, X2, pC_in_ga(X1, X2))
INSERTA_IN_GAG(X1, tree(X1, void, X2), tree(X1, void, void)) → PC_IN_GA(X1, X2)
PC_IN_GA(X1, X2) → U5_GA(X1, X2, lessD_in_g(X1))
PC_IN_GA(X1, X2) → LESSD_IN_G(X1)
PC_IN_GA(X1, X2) → U6_GA(X1, X2, lesscD_in_g(X1))
U6_GA(X1, X2, lesscD_out_g(X1)) → U7_GA(X1, X2, insertA_in_gag(X1, X2, void))
U6_GA(X1, X2, lesscD_out_g(X1)) → INSERTA_IN_GAG(X1, X2, void)
INSERTA_IN_GAG(s(X1), tree(s(X1), void, X2), tree(s(X1), void, void)) → U11_GAG(X1, X2, pB_in_ga(X1, X2))
INSERTA_IN_GAG(s(X1), tree(s(X1), void, X2), tree(s(X1), void, void)) → PB_IN_GA(X1, X2)
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → U12_GAG(X1, X2, X3, X4, lessD_in_g(X1))
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → LESSD_IN_G(X1)
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → U13_GAG(X1, X2, X3, X4, lesscD_in_g(X1))
U13_GAG(X1, X2, X3, X4, lesscD_out_g(X1)) → U14_GAG(X1, X2, X3, X4, insertA_in_gag(s(X1), X2, X4))
U13_GAG(X1, X2, X3, X4, lesscD_out_g(X1)) → INSERTA_IN_GAG(s(X1), X2, X4)
INSERTA_IN_GAG(X1, tree(X1, X2, X3), tree(X1, X2, X4)) → U15_GAG(X1, X2, X3, X4, lessD_in_g(X1))
INSERTA_IN_GAG(X1, tree(X1, X2, X3), tree(X1, X2, X4)) → LESSD_IN_G(X1)
INSERTA_IN_GAG(X1, tree(X1, X2, X3), tree(X1, X2, X4)) → U16_GAG(X1, X2, X3, X4, lesscD_in_g(X1))
U16_GAG(X1, X2, X3, X4, lesscD_out_g(X1)) → U17_GAG(X1, X2, X3, X4, insertA_in_gag(X1, X3, X4))
U16_GAG(X1, X2, X3, X4, lesscD_out_g(X1)) → INSERTA_IN_GAG(X1, X3, X4)
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X3), tree(s(X1), X2, X4)) → U18_GAG(X1, X2, X3, X4, lessD_in_g(X1))
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X3), tree(s(X1), X2, X4)) → LESSD_IN_G(X1)
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X3), tree(s(X1), X2, X4)) → U19_GAG(X1, X2, X3, X4, lesscD_in_g(X1))
U19_GAG(X1, X2, X3, X4, lesscD_out_g(X1)) → U20_GAG(X1, X2, X3, X4, insertA_in_gag(s(X1), X3, X4))
U19_GAG(X1, X2, X3, X4, lesscD_out_g(X1)) → INSERTA_IN_GAG(s(X1), X3, X4)
INSERTA_IN_GAG(0, tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → U21_GAG(X1, X2, X3, X4, insertA_in_gag(0, X2, X4))
INSERTA_IN_GAG(0, tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → INSERTA_IN_GAG(0, X2, X4)
INSERTA_IN_GAG(s(s(s(s(s(s(s(s(X1)))))))), tree(s(s(s(s(s(s(s(s(X2)))))))), X3, X4), tree(s(s(s(s(s(s(s(s(X2)))))))), X5, X4)) → U22_GAG(X1, X2, X3, X4, X5, lessF_in_gg(X1, X2))
INSERTA_IN_GAG(s(s(s(s(s(s(s(s(X1)))))))), tree(s(s(s(s(s(s(s(s(X2)))))))), X3, X4), tree(s(s(s(s(s(s(s(s(X2)))))))), X5, X4)) → LESSF_IN_GG(X1, X2)
LESSF_IN_GG(s(X1), s(X2)) → U8_GG(X1, X2, lessF_in_gg(X1, X2))
LESSF_IN_GG(s(X1), s(X2)) → LESSF_IN_GG(X1, X2)
INSERTA_IN_GAG(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) → U23_GAG(X1, X2, X3, X4, X5, lesscE_in_gg(X1, X2))
U23_GAG(X1, X2, X3, X4, X5, lesscE_out_gg(X1, X2)) → U24_GAG(X1, X2, X3, X4, X5, insertA_in_gag(s(X1), X3, X5))
U23_GAG(X1, X2, X3, X4, X5, lesscE_out_gg(X1, X2)) → INSERTA_IN_GAG(s(X1), X3, X5)
INSERTA_IN_GAG(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → U25_GAG(X1, X2, X3, X4, X5, lessF_in_gg(X2, X1))
INSERTA_IN_GAG(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → LESSF_IN_GG(X2, X1)
INSERTA_IN_GAG(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → U26_GAG(X1, X2, X3, X4, X5, lesscF_in_gg(X2, X1))
U26_GAG(X1, X2, X3, X4, X5, lesscF_out_gg(X2, X1)) → U27_GAG(X1, X2, X3, X4, X5, insertA_in_gag(X1, X4, X5))
U26_GAG(X1, X2, X3, X4, X5, lesscF_out_gg(X2, X1)) → INSERTA_IN_GAG(X1, X4, X5)
INSERTA_IN_GAG(s(X1), tree(0, X2, X3), tree(0, X2, X4)) → U28_GAG(X1, X2, X3, X4, insertA_in_gag(s(X1), X3, X4))
INSERTA_IN_GAG(s(X1), tree(0, X2, X3), tree(0, X2, X4)) → INSERTA_IN_GAG(s(X1), X3, X4)
INSERTA_IN_GAG(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) → U29_GAG(X1, X2, X3, X4, X5, lessF_in_gg(X2, X1))
INSERTA_IN_GAG(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) → LESSF_IN_GG(X2, X1)
INSERTA_IN_GAG(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) → U30_GAG(X1, X2, X3, X4, X5, lesscF_in_gg(X2, X1))
U30_GAG(X1, X2, X3, X4, X5, lesscF_out_gg(X2, X1)) → U31_GAG(X1, X2, X3, X4, X5, insertA_in_gag(s(X1), X4, X5))
U30_GAG(X1, X2, X3, X4, X5, lesscF_out_gg(X2, X1)) → INSERTA_IN_GAG(s(X1), X4, X5)

The TRS R consists of the following rules:

lesscD_in_g(s(X1)) → U50_g(X1, lesscD_in_g(X1))
U50_g(X1, lesscD_out_g(X1)) → lesscD_out_g(s(X1))
lesscE_in_gg(0, s(X1)) → lesscE_out_gg(0, s(X1))
lesscE_in_gg(s(0), s(s(X1))) → lesscE_out_gg(s(0), s(s(X1)))
lesscE_in_gg(s(s(0)), s(s(s(X1)))) → lesscE_out_gg(s(s(0)), s(s(s(X1))))
lesscE_in_gg(s(s(s(0))), s(s(s(s(X1))))) → lesscE_out_gg(s(s(s(0))), s(s(s(s(X1)))))
lesscE_in_gg(s(s(s(s(0)))), s(s(s(s(s(X1)))))) → lesscE_out_gg(s(s(s(s(0)))), s(s(s(s(s(X1))))))
lesscE_in_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(X1))))))) → lesscE_out_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(X1)))))))
lesscE_in_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(X1)))))))) → lesscE_out_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(X1))))))))
lesscE_in_gg(s(s(s(s(s(s(s(X1))))))), s(s(s(s(s(s(s(X2)))))))) → U56_gg(X1, X2, lesscF_in_gg(X1, X2))
lesscF_in_gg(0, s(X1)) → lesscF_out_gg(0, s(X1))
lesscF_in_gg(s(X1), s(X2)) → U55_gg(X1, X2, lesscF_in_gg(X1, X2))
U55_gg(X1, X2, lesscF_out_gg(X1, X2)) → lesscF_out_gg(s(X1), s(X2))
U56_gg(X1, X2, lesscF_out_gg(X1, X2)) → lesscE_out_gg(s(s(s(s(s(s(s(X1))))))), s(s(s(s(s(s(s(X2))))))))

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 3 SCCs with 38 less nodes.

(6) Complex Obligation (AND)

(7) Obligation:

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

LESSF_IN_GG(s(X1), s(X2)) → LESSF_IN_GG(X1, X2)

The TRS R consists of the following rules:

lesscD_in_g(s(X1)) → U50_g(X1, lesscD_in_g(X1))
U50_g(X1, lesscD_out_g(X1)) → lesscD_out_g(s(X1))
lesscE_in_gg(0, s(X1)) → lesscE_out_gg(0, s(X1))
lesscE_in_gg(s(0), s(s(X1))) → lesscE_out_gg(s(0), s(s(X1)))
lesscE_in_gg(s(s(0)), s(s(s(X1)))) → lesscE_out_gg(s(s(0)), s(s(s(X1))))
lesscE_in_gg(s(s(s(0))), s(s(s(s(X1))))) → lesscE_out_gg(s(s(s(0))), s(s(s(s(X1)))))
lesscE_in_gg(s(s(s(s(0)))), s(s(s(s(s(X1)))))) → lesscE_out_gg(s(s(s(s(0)))), s(s(s(s(s(X1))))))
lesscE_in_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(X1))))))) → lesscE_out_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(X1)))))))
lesscE_in_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(X1)))))))) → lesscE_out_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(X1))))))))
lesscE_in_gg(s(s(s(s(s(s(s(X1))))))), s(s(s(s(s(s(s(X2)))))))) → U56_gg(X1, X2, lesscF_in_gg(X1, X2))
lesscF_in_gg(0, s(X1)) → lesscF_out_gg(0, s(X1))
lesscF_in_gg(s(X1), s(X2)) → U55_gg(X1, X2, lesscF_in_gg(X1, X2))
U55_gg(X1, X2, lesscF_out_gg(X1, X2)) → lesscF_out_gg(s(X1), s(X2))
U56_gg(X1, X2, lesscF_out_gg(X1, X2)) → lesscE_out_gg(s(s(s(s(s(s(s(X1))))))), s(s(s(s(s(s(s(X2))))))))

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

(8) UsableRulesProof (EQUIVALENT transformation)

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

(9) Obligation:

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

LESSF_IN_GG(s(X1), s(X2)) → LESSF_IN_GG(X1, X2)

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

(10) PiDPToQDPProof (EQUIVALENT transformation)

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

(11) Obligation:

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

LESSF_IN_GG(s(X1), s(X2)) → LESSF_IN_GG(X1, X2)

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

(12) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

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

(13) YES

(14) Obligation:

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

LESSD_IN_G(s(X1)) → LESSD_IN_G(X1)

The TRS R consists of the following rules:

lesscD_in_g(s(X1)) → U50_g(X1, lesscD_in_g(X1))
U50_g(X1, lesscD_out_g(X1)) → lesscD_out_g(s(X1))
lesscE_in_gg(0, s(X1)) → lesscE_out_gg(0, s(X1))
lesscE_in_gg(s(0), s(s(X1))) → lesscE_out_gg(s(0), s(s(X1)))
lesscE_in_gg(s(s(0)), s(s(s(X1)))) → lesscE_out_gg(s(s(0)), s(s(s(X1))))
lesscE_in_gg(s(s(s(0))), s(s(s(s(X1))))) → lesscE_out_gg(s(s(s(0))), s(s(s(s(X1)))))
lesscE_in_gg(s(s(s(s(0)))), s(s(s(s(s(X1)))))) → lesscE_out_gg(s(s(s(s(0)))), s(s(s(s(s(X1))))))
lesscE_in_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(X1))))))) → lesscE_out_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(X1)))))))
lesscE_in_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(X1)))))))) → lesscE_out_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(X1))))))))
lesscE_in_gg(s(s(s(s(s(s(s(X1))))))), s(s(s(s(s(s(s(X2)))))))) → U56_gg(X1, X2, lesscF_in_gg(X1, X2))
lesscF_in_gg(0, s(X1)) → lesscF_out_gg(0, s(X1))
lesscF_in_gg(s(X1), s(X2)) → U55_gg(X1, X2, lesscF_in_gg(X1, X2))
U55_gg(X1, X2, lesscF_out_gg(X1, X2)) → lesscF_out_gg(s(X1), s(X2))
U56_gg(X1, X2, lesscF_out_gg(X1, X2)) → lesscE_out_gg(s(s(s(s(s(s(s(X1))))))), s(s(s(s(s(s(s(X2))))))))

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

(15) UsableRulesProof (EQUIVALENT transformation)

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

(16) Obligation:

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

LESSD_IN_G(s(X1)) → LESSD_IN_G(X1)

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

(17) PiDPToQDPProof (EQUIVALENT transformation)

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

(18) Obligation:

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

LESSD_IN_G(s(X1)) → LESSD_IN_G(X1)

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

(19) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

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

(20) YES

(21) Obligation:

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

INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → U13_GAG(X1, X2, X3, X4, lesscD_in_g(X1))
U13_GAG(X1, X2, X3, X4, lesscD_out_g(X1)) → INSERTA_IN_GAG(s(X1), X2, X4)
INSERTA_IN_GAG(X1, tree(X1, X2, X3), tree(X1, X2, X4)) → U16_GAG(X1, X2, X3, X4, lesscD_in_g(X1))
U16_GAG(X1, X2, X3, X4, lesscD_out_g(X1)) → INSERTA_IN_GAG(X1, X3, X4)
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X3), tree(s(X1), X2, X4)) → U19_GAG(X1, X2, X3, X4, lesscD_in_g(X1))
U19_GAG(X1, X2, X3, X4, lesscD_out_g(X1)) → INSERTA_IN_GAG(s(X1), X3, X4)
INSERTA_IN_GAG(s(X1), tree(s(X2), X3, X4), tree(s(X2), X5, X4)) → U23_GAG(X1, X2, X3, X4, X5, lesscE_in_gg(X1, X2))
U23_GAG(X1, X2, X3, X4, X5, lesscE_out_gg(X1, X2)) → INSERTA_IN_GAG(s(X1), X3, X5)
INSERTA_IN_GAG(X1, tree(X2, X3, X4), tree(X2, X3, X5)) → U26_GAG(X1, X2, X3, X4, X5, lesscF_in_gg(X2, X1))
U26_GAG(X1, X2, X3, X4, X5, lesscF_out_gg(X2, X1)) → INSERTA_IN_GAG(X1, X4, X5)
INSERTA_IN_GAG(0, tree(s(X1), X2, X3), tree(s(X1), X4, X3)) → INSERTA_IN_GAG(0, X2, X4)
INSERTA_IN_GAG(s(X1), tree(0, X2, X3), tree(0, X2, X4)) → INSERTA_IN_GAG(s(X1), X3, X4)
INSERTA_IN_GAG(s(X1), tree(s(X2), X3, X4), tree(s(X2), X3, X5)) → U30_GAG(X1, X2, X3, X4, X5, lesscF_in_gg(X2, X1))
U30_GAG(X1, X2, X3, X4, X5, lesscF_out_gg(X2, X1)) → INSERTA_IN_GAG(s(X1), X4, X5)

The TRS R consists of the following rules:

lesscD_in_g(s(X1)) → U50_g(X1, lesscD_in_g(X1))
U50_g(X1, lesscD_out_g(X1)) → lesscD_out_g(s(X1))
lesscE_in_gg(0, s(X1)) → lesscE_out_gg(0, s(X1))
lesscE_in_gg(s(0), s(s(X1))) → lesscE_out_gg(s(0), s(s(X1)))
lesscE_in_gg(s(s(0)), s(s(s(X1)))) → lesscE_out_gg(s(s(0)), s(s(s(X1))))
lesscE_in_gg(s(s(s(0))), s(s(s(s(X1))))) → lesscE_out_gg(s(s(s(0))), s(s(s(s(X1)))))
lesscE_in_gg(s(s(s(s(0)))), s(s(s(s(s(X1)))))) → lesscE_out_gg(s(s(s(s(0)))), s(s(s(s(s(X1))))))
lesscE_in_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(X1))))))) → lesscE_out_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(X1)))))))
lesscE_in_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(X1)))))))) → lesscE_out_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(X1))))))))
lesscE_in_gg(s(s(s(s(s(s(s(X1))))))), s(s(s(s(s(s(s(X2)))))))) → U56_gg(X1, X2, lesscF_in_gg(X1, X2))
lesscF_in_gg(0, s(X1)) → lesscF_out_gg(0, s(X1))
lesscF_in_gg(s(X1), s(X2)) → U55_gg(X1, X2, lesscF_in_gg(X1, X2))
U55_gg(X1, X2, lesscF_out_gg(X1, X2)) → lesscF_out_gg(s(X1), s(X2))
U56_gg(X1, X2, lesscF_out_gg(X1, X2)) → lesscE_out_gg(s(s(s(s(s(s(s(X1))))))), s(s(s(s(s(s(s(X2))))))))

The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
tree(x1, x2, x3) = tree(x1, x2, x3)
lesscD_in_g(x1) = lesscD_in_g(x1)
U50_g(x1, x2) = U50_g(x1, x2)
lesscD_out_g(x1) = lesscD_out_g(x1)
0 = 0
lesscE_in_gg(x1, x2) = lesscE_in_gg(x1, x2)
lesscE_out_gg(x1, x2) = lesscE_out_gg(x1, x2)
U56_gg(x1, x2, x3) = U56_gg(x1, x2, x3)
lesscF_in_gg(x1, x2) = lesscF_in_gg(x1, x2)
lesscF_out_gg(x1, x2) = lesscF_out_gg(x1, x2)
U55_gg(x1, x2, x3) = U55_gg(x1, x2, x3)
INSERTA_IN_GAG(x1, x2, x3) = INSERTA_IN_GAG(x1, x3)
U13_GAG(x1, x2, x3, x4, x5) = U13_GAG(x1, x3, x4, x5)
U16_GAG(x1, x2, x3, x4, x5) = U16_GAG(x1, x2, x4, x5)
U19_GAG(x1, x2, x3, x4, x5) = U19_GAG(x1, x2, x4, x5)
U23_GAG(x1, x2, x3, x4, x5, x6) = U23_GAG(x1, x2, x4, x5, x6)
U26_GAG(x1, x2, x3, x4, x5, x6) = U26_GAG(x1, x2, x3, x5, x6)
U30_GAG(x1, x2, x3, x4, x5, x6) = U30_GAG(x1, x2, x3, x5, x6)

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

(22) PiDPToQDPProof (SOUND transformation)

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

(23) Obligation:

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

INSERTA_IN_GAG(s(X1), tree(s(X1), X4, X3)) → U13_GAG(X1, X3, X4, lesscD_in_g(X1))
U13_GAG(X1, X3, X4, lesscD_out_g(X1)) → INSERTA_IN_GAG(s(X1), X4)
INSERTA_IN_GAG(X1, tree(X1, X2, X4)) → U16_GAG(X1, X2, X4, lesscD_in_g(X1))
U16_GAG(X1, X2, X4, lesscD_out_g(X1)) → INSERTA_IN_GAG(X1, X4)
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X4)) → U19_GAG(X1, X2, X4, lesscD_in_g(X1))
U19_GAG(X1, X2, X4, lesscD_out_g(X1)) → INSERTA_IN_GAG(s(X1), X4)
INSERTA_IN_GAG(s(X1), tree(s(X2), X5, X4)) → U23_GAG(X1, X2, X4, X5, lesscE_in_gg(X1, X2))
U23_GAG(X1, X2, X4, X5, lesscE_out_gg(X1, X2)) → INSERTA_IN_GAG(s(X1), X5)
INSERTA_IN_GAG(X1, tree(X2, X3, X5)) → U26_GAG(X1, X2, X3, X5, lesscF_in_gg(X2, X1))
U26_GAG(X1, X2, X3, X5, lesscF_out_gg(X2, X1)) → INSERTA_IN_GAG(X1, X5)
INSERTA_IN_GAG(0, tree(s(X1), X4, X3)) → INSERTA_IN_GAG(0, X4)
INSERTA_IN_GAG(s(X1), tree(0, X2, X4)) → INSERTA_IN_GAG(s(X1), X4)
INSERTA_IN_GAG(s(X1), tree(s(X2), X3, X5)) → U30_GAG(X1, X2, X3, X5, lesscF_in_gg(X2, X1))
U30_GAG(X1, X2, X3, X5, lesscF_out_gg(X2, X1)) → INSERTA_IN_GAG(s(X1), X5)

The TRS R consists of the following rules:

lesscD_in_g(s(X1)) → U50_g(X1, lesscD_in_g(X1))
U50_g(X1, lesscD_out_g(X1)) → lesscD_out_g(s(X1))
lesscE_in_gg(0, s(X1)) → lesscE_out_gg(0, s(X1))
lesscE_in_gg(s(0), s(s(X1))) → lesscE_out_gg(s(0), s(s(X1)))
lesscE_in_gg(s(s(0)), s(s(s(X1)))) → lesscE_out_gg(s(s(0)), s(s(s(X1))))
lesscE_in_gg(s(s(s(0))), s(s(s(s(X1))))) → lesscE_out_gg(s(s(s(0))), s(s(s(s(X1)))))
lesscE_in_gg(s(s(s(s(0)))), s(s(s(s(s(X1)))))) → lesscE_out_gg(s(s(s(s(0)))), s(s(s(s(s(X1))))))
lesscE_in_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(X1))))))) → lesscE_out_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(X1)))))))
lesscE_in_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(X1)))))))) → lesscE_out_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(X1))))))))
lesscE_in_gg(s(s(s(s(s(s(s(X1))))))), s(s(s(s(s(s(s(X2)))))))) → U56_gg(X1, X2, lesscF_in_gg(X1, X2))
lesscF_in_gg(0, s(X1)) → lesscF_out_gg(0, s(X1))
lesscF_in_gg(s(X1), s(X2)) → U55_gg(X1, X2, lesscF_in_gg(X1, X2))
U55_gg(X1, X2, lesscF_out_gg(X1, X2)) → lesscF_out_gg(s(X1), s(X2))
U56_gg(X1, X2, lesscF_out_gg(X1, X2)) → lesscE_out_gg(s(s(s(s(s(s(s(X1))))))), s(s(s(s(s(s(s(X2))))))))

The set Q consists of the following terms:

lesscD_in_g(x0)
U50_g(x0, x1)
lesscE_in_gg(x0, x1)
lesscF_in_gg(x0, x1)
U55_gg(x0, x1, x2)
U56_gg(x0, x1, x2)

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

(24) 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:

U13_GAG(X1, X3, X4, lesscD_out_g(X1)) → INSERTA_IN_GAG(s(X1), X4)
The graph contains the following edges 3 >= 2
INSERTA_IN_GAG(s(X1), tree(0, X2, X4)) → INSERTA_IN_GAG(s(X1), X4)
The graph contains the following edges 1 >= 1, 2 > 2
INSERTA_IN_GAG(s(X1), tree(s(X1), X4, X3)) → U13_GAG(X1, X3, X4, lesscD_in_g(X1))
The graph contains the following edges 1 > 1, 2 > 1, 2 > 2, 2 > 3
INSERTA_IN_GAG(0, tree(s(X1), X4, X3)) → INSERTA_IN_GAG(0, X4)
The graph contains the following edges 1 >= 1, 2 > 2
U16_GAG(X1, X2, X4, lesscD_out_g(X1)) → INSERTA_IN_GAG(X1, X4)
The graph contains the following edges 1 >= 1, 4 > 1, 3 >= 2
INSERTA_IN_GAG(X1, tree(X1, X2, X4)) → U16_GAG(X1, X2, X4, lesscD_in_g(X1))
The graph contains the following edges 1 >= 1, 2 > 1, 2 > 2, 2 > 3
U19_GAG(X1, X2, X4, lesscD_out_g(X1)) → INSERTA_IN_GAG(s(X1), X4)
The graph contains the following edges 3 >= 2
INSERTA_IN_GAG(s(X1), tree(s(X1), X2, X4)) → U19_GAG(X1, X2, X4, lesscD_in_g(X1))
The graph contains the following edges 1 > 1, 2 > 1, 2 > 2, 2 > 3
U23_GAG(X1, X2, X4, X5, lesscE_out_gg(X1, X2)) → INSERTA_IN_GAG(s(X1), X5)
The graph contains the following edges 4 >= 2
INSERTA_IN_GAG(s(X1), tree(s(X2), X5, X4)) → U23_GAG(X1, X2, X4, X5, lesscE_in_gg(X1, X2))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4
U26_GAG(X1, X2, X3, X5, lesscF_out_gg(X2, X1)) → INSERTA_IN_GAG(X1, X5)
The graph contains the following edges 1 >= 1, 5 > 1, 4 >= 2
U30_GAG(X1, X2, X3, X5, lesscF_out_gg(X2, X1)) → INSERTA_IN_GAG(s(X1), X5)
The graph contains the following edges 4 >= 2
INSERTA_IN_GAG(X1, tree(X2, X3, X5)) → U26_GAG(X1, X2, X3, X5, lesscF_in_gg(X2, X1))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4
INSERTA_IN_GAG(s(X1), tree(s(X2), X3, X5)) → U30_GAG(X1, X2, X3, X5, lesscF_in_gg(X2, X1))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4

(0) Obligation:

(1) PrologToDTProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) TriplesToPiDPProof (SOUND transformation)

(4) Obligation:

(5) DependencyGraphProof (EQUIVALENT transformation)

(6) Complex Obligation (AND)

(7) Obligation:

(8) UsableRulesProof (EQUIVALENT transformation)

(9) Obligation:

(10) PiDPToQDPProof (EQUIVALENT transformation)

(11) Obligation:

(12) QDPSizeChangeProof (EQUIVALENT transformation)

(13) YES

(14) Obligation:

(15) UsableRulesProof (EQUIVALENT transformation)

(16) Obligation:

(17) PiDPToQDPProof (EQUIVALENT transformation)

(18) Obligation:

(19) QDPSizeChangeProof (EQUIVALENT transformation)

(20) YES

(21) Obligation:

(22) PiDPToQDPProof (SOUND transformation)

(23) Obligation:

(24) QDPSizeChangeProof (EQUIVALENT transformation)

(25) YES