Left Termination proof of /tmp/tmpaMCM8g/insert-bfb.pl

Left Termination of the query pattern insert_in_3(g, a, g) w.r.t. the given Prolog program could successfully be proven:

0 Prolog

↳1 PrologToPrologProblemTransformerProof (⇐)

↳2 Prolog

↳3 PrologToPiTRSProof (⇐)

↳4 PiTRS

↳5 DependencyPairsProof (⇔)

↳6 PiDP

↳7 DependencyGraphProof (⇔)

↳8 AND

    ↳9 PiDP

        ↳10 UsableRulesProof (⇔)

        ↳11 PiDP

        ↳12 PiDPToQDPProof (⇔)

        ↳13 QDP

        ↳14 QDPSizeChangeProof (⇔)

        ↳15 YES

    ↳16 PiDP

        ↳17 UsableRulesProof (⇔)

        ↳18 PiDP

        ↳19 PiDPToQDPProof (⇔)

        ↳20 QDP

        ↳21 QDPSizeChangeProof (⇔)

        ↳22 YES

    ↳23 PiDP

        ↳24 UsableRulesProof (⇔)

        ↳25 PiDP

        ↳26 PiDPToQDPProof (⇐)

        ↳27 QDP

        ↳28 QDPSizeChangeProof (⇔)

        ↳29 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).

Queries:

insert(g,a,g).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: 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\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\ninsert(T5, T2, tree(T5, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", 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\ninsert(T9, T2, tree(T9, void, void)) !=? insert(X19, tree(X20, X21, X22), tree(X20, X23, X22))", 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="15: ','(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="17: 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(T30, T30)\n\nT30 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="24: ','(less(T56, T56), insert(T56, T60, void))\n\nT56 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: less(T56, T56)\n\nT56 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: insert(T56, T60, void)\n\nT56 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: ','(less(T83, T83), insert(T83, T87, void))\n\nT83 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: ','(less(T83, T83), insert(T83, T87, void)), SCOPE: 4, CLAUSE: 4 | ','(less(T83, T83), insert(T83, T87, void)), SCOPE: 4, CLAUSE: 5\n\nT83 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ','(less(T83, T83), insert(T83, T87, void)), SCOPE: 4, CLAUSE: 5\n\nT83 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: ','(less(T90, T90), insert(s(T90), T87, void))\n\nT90 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: ','(less(T96, T96), insert(T96, T100, void)) | insert(T96, T2, tree(T96, void, void)), SCOPE: 1, CLAUSE: 3\n\nT96 is ground\ninsert(T96, T2, tree(T96, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 3\n\nT5 is ground\ninsert(T5, T2, tree(T5, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))\ninsert(T5, T2, tree(T5, void, void)) !=? insert(X160, tree(X161, X162, X163), tree(X161, X164, X163))", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: ','(less(T96, T96), insert(T96, T100, void)), SCOPE: 5, CLAUSE: 4 | ','(less(T96, T96), insert(T96, T100, void)), SCOPE: 5, CLAUSE: 5 | ?_5 | insert(T96, T2, tree(T96, void, void)), SCOPE: 1, CLAUSE: 3\n\nT96 is ground\ninsert(T96, T2, tree(T96, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: ','(less(T96, T96), insert(T96, T100, void)), SCOPE: 5, CLAUSE: 5 | ?_5 | insert(T96, T2, tree(T96, void, void)), SCOPE: 1, CLAUSE: 3\n\nT96 is ground\ninsert(T96, T2, tree(T96, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: ','(less(T96, T96), insert(T96, T100, void)), SCOPE: 5, CLAUSE: 5\n\nT96 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: ?_5 | insert(T96, T2, tree(T96, void, void)), SCOPE: 1, CLAUSE: 3\n\nT96 is ground\ninsert(T96, T2, tree(T96, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: ','(less(T105, T105), insert(s(T105), T100, void))\n\nT105 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: insert(T96, T2, tree(T96, void, void)), SCOPE: 1, CLAUSE: 3\n\nT96 is ground\ninsert(T96, T2, tree(T96, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: ','(less(T115, T115), insert(T115, T119, void))\n\nT115 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(less(T125, T125), insert(T125, T129, void))\n\nT125 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: ','(less(T125, T125), insert(T125, T129, void)), SCOPE: 6, CLAUSE: 4 | ','(less(T125, T125), insert(T125, T129, void)), SCOPE: 6, CLAUSE: 5\n\nT125 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: ','(less(T125, T125), insert(T125, T129, void)), SCOPE: 6, CLAUSE: 5\n\nT125 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: ','(less(T132, T132), insert(s(T132), T129, void))\n\nT132 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: true | insert(T137, T2, tree(T137, T138, T139)), SCOPE: 1, CLAUSE: 2 | insert(T137, T2, tree(T137, T138, T139)), SCOPE: 1, CLAUSE: 3\n\nT137 is ground\nT138 is ground\nT139 is ground\ninsert(T137, T2, tree(T137, T138, T139)) !=? 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\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, T3) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: insert(T137, T2, tree(T137, T138, T139)), SCOPE: 1, CLAUSE: 2 | insert(T137, T2, tree(T137, T138, T139)), SCOPE: 1, CLAUSE: 3\n\nT137 is ground\nT138 is ground\nT139 is ground\ninsert(T137, T2, tree(T137, T138, T139)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: ','(less(T145, T145), insert(T145, T150, T149)) | insert(T145, T2, tree(T145, T149, T148)), SCOPE: 1, CLAUSE: 3\n\nT145 is ground\nT149 is ground\nT148 is ground\ninsert(T145, T2, tree(T145, T149, T148)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: insert(T137, T2, tree(T137, T138, T139)), SCOPE: 1, CLAUSE: 3\n\nT137 is ground\nT138 is ground\nT139 is ground\ninsert(T137, T2, tree(T137, T138, T139)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T137, T2, tree(T137, T138, T139)) !=? insert(X253, tree(X254, X255, X256), tree(X254, X257, X256))", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: ','(less(T145, T145), insert(T145, T150, T149)), SCOPE: 7, CLAUSE: 4 | ','(less(T145, T145), insert(T145, T150, T149)), SCOPE: 7, CLAUSE: 5 | ?_7 | insert(T145, T2, tree(T145, T149, T148)), SCOPE: 1, CLAUSE: 3\n\nT145 is ground\nT149 is ground\nT148 is ground\ninsert(T145, T2, tree(T145, T149, T148)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: ','(less(T145, T145), insert(T145, T150, T149)), SCOPE: 7, CLAUSE: 5 | ?_7 | insert(T145, T2, tree(T145, T149, T148)), SCOPE: 1, CLAUSE: 3\n\nT145 is ground\nT149 is ground\nT148 is ground\ninsert(T145, T2, tree(T145, T149, T148)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: ','(less(T145, T145), insert(T145, T150, T149)), SCOPE: 7, CLAUSE: 5\n\nT145 is ground\nT149 is ground\ninsert(T145, T2, tree(T145, T149, T148)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ?_7 | insert(T145, T2, tree(T145, T149, T148)), SCOPE: 1, CLAUSE: 3\n\nT145 is ground\nT149 is ground\nT148 is ground\ninsert(T145, T2, tree(T145, T149, T148)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: ','(less(T155, T155), insert(s(T155), T150, T149))\n\nT149 is ground\nT155 is ground\ninsert(s(T155), T2, tree(s(T155), T149, T148)) !=? 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(T155, T155)\n\nT155 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: insert(s(T155), T150, T149)\n\nT149 is ground\nT155 is ground\ninsert(s(T155), T2, tree(s(T155), T149, T148)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: insert(T145, T2, tree(T145, T149, T148)), SCOPE: 1, CLAUSE: 3\n\nT145 is ground\nT149 is ground\nT148 is ground\ninsert(T145, T2, tree(T145, T149, T148)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: ','(less(T170, T170), insert(T170, T175, T174))\n\nT170 is ground\nT174 is ground\ninsert(T170, T2, tree(T170, T172, T174)) !=? 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(T170, T170)\n\nT170 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: insert(T170, T175, T174)\n\nT170 is ground\nT174 is ground\ninsert(T170, T2, tree(T170, T172, T174)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: ','(less(T185, T185), insert(T185, T190, T189))\n\nT185 is ground\nT189 is ground\ninsert(T185, T2, tree(T185, T187, T189)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: ','(less(T185, T185), insert(T185, T190, T189)), SCOPE: 8, CLAUSE: 4 | ','(less(T185, T185), insert(T185, T190, T189)), SCOPE: 8, CLAUSE: 5\n\nT185 is ground\nT189 is ground\ninsert(T185, T2, tree(T185, T187, T189)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: ','(less(T185, T185), insert(T185, T190, T189)), SCOPE: 8, CLAUSE: 5\n\nT185 is ground\nT189 is ground\ninsert(T185, T2, tree(T185, T187, T189)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: ','(less(T193, T193), insert(s(T193), T190, T189))\n\nT189 is ground\nT193 is ground\ninsert(s(T193), T2, tree(s(T193), T187, T189)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: less(T193, T193)\n\nT193 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: insert(s(T193), T190, T189)\n\nT189 is ground\nT193 is ground\ninsert(s(T193), T2, tree(s(T193), T187, T189)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: ','(less(T203, T204), insert(T203, T208, T207)) | insert(T203, T2, tree(T204, T207, T206)), SCOPE: 1, CLAUSE: 3\n\nT203 is ground\nT204 is ground\nT207 is ground\nT206 is ground\ninsert(T203, T2, tree(T204, T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T203, T2, tree(T204, T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT1 is ground\nT3 is ground\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, T3) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))\ninsert(T1, T2, T3) !=? insert(X355, tree(X356, X357, X358), tree(X356, X359, X358))", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: ','(less(T203, T204), insert(T203, T208, T207)), SCOPE: 9, CLAUSE: 4 | ','(less(T203, T204), insert(T203, T208, T207)), SCOPE: 9, CLAUSE: 5 | ?_9 | insert(T203, T2, tree(T204, T207, T206)), SCOPE: 1, CLAUSE: 3\n\nT203 is ground\nT204 is ground\nT207 is ground\nT206 is ground\ninsert(T203, T2, tree(T204, T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T203, T2, tree(T204, T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: ','(less(T203, T204), insert(T203, T208, T207)), SCOPE: 9, CLAUSE: 4\n\nT203 is ground\nT204 is ground\nT207 is ground\ninsert(T203, T2, tree(T204, T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T203, T2, tree(T204, T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: ','(less(T203, T204), insert(T203, T208, T207)), SCOPE: 9, CLAUSE: 5 | ?_9 | insert(T203, T2, tree(T204, T207, T206)), SCOPE: 1, CLAUSE: 3\n\nT203 is ground\nT204 is ground\nT207 is ground\nT206 is ground\ninsert(T203, T2, tree(T204, T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T203, T2, tree(T204, T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: insert(0, T208, T207)\n\nT207 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: ','(less(T203, T204), insert(T203, T208, T207)), SCOPE: 9, CLAUSE: 5\n\nT203 is ground\nT204 is ground\nT207 is ground\ninsert(T203, T2, tree(T204, T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T203, T2, tree(T204, T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: ?_9 | insert(T203, T2, tree(T204, T207, T206)), SCOPE: 1, CLAUSE: 3\n\nT203 is ground\nT204 is ground\nT207 is ground\nT206 is ground\ninsert(T203, T2, tree(T204, T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T203, T2, tree(T204, T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: ','(less(T222, T223), insert(s(T222), T208, T207))\n\nT207 is ground\nT222 is ground\nT223 is ground\ninsert(s(T222), T2, tree(s(T223), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T222), T2, tree(s(T223), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: less(T222, T223)\n\nT222 is ground\nT223 is ground\ninsert(s(T222), T2, tree(s(T223), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T222), T2, tree(s(T223), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: insert(s(T222), T208, T207)\n\nT207 is ground\nT222 is ground\ninsert(s(T222), T2, tree(s(T223), T207, T206)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: less(T222, T223), SCOPE: 10, CLAUSE: 4 | less(T222, T223), SCOPE: 10, CLAUSE: 5\n\nT222 is ground\nT223 is ground\ninsert(s(T222), T2, tree(s(T223), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T222), T2, tree(s(T223), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: less(T222, T223), SCOPE: 10, CLAUSE: 4\n\nT222 is ground\nT223 is ground\ninsert(s(T222), T2, tree(s(T223), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T222), T2, tree(s(T223), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: less(T222, T223), SCOPE: 10, CLAUSE: 5\n\nT222 is ground\nT223 is ground\ninsert(s(T222), T2, tree(s(T223), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T222), T2, tree(s(T223), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", 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(T237, T238)\n\nT237 is ground\nT238 is ground\ninsert(s(s(T237)), T2, tree(s(s(T238)), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(T237)), T2, tree(s(s(T238)), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: less(T237, T238), SCOPE: 11, CLAUSE: 4 | less(T237, T238), SCOPE: 11, CLAUSE: 5\n\nT237 is ground\nT238 is ground\ninsert(s(s(T237)), T2, tree(s(s(T238)), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(T237)), T2, tree(s(s(T238)), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: less(T237, T238), SCOPE: 11, CLAUSE: 4\n\nT237 is ground\nT238 is ground\ninsert(s(s(T237)), T2, tree(s(s(T238)), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(T237)), T2, tree(s(s(T238)), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: less(T237, T238), SCOPE: 11, CLAUSE: 5\n\nT237 is ground\nT238 is ground\ninsert(s(s(T237)), T2, tree(s(s(T238)), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(T237)), T2, tree(s(s(T238)), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", 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(T250, T251)\n\nT250 is ground\nT251 is ground\ninsert(s(s(s(T250))), T2, tree(s(s(s(T251))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(T250))), T2, tree(s(s(s(T251))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: less(T250, T251), SCOPE: 12, CLAUSE: 4 | less(T250, T251), SCOPE: 12, CLAUSE: 5\n\nT250 is ground\nT251 is ground\ninsert(s(s(s(T250))), T2, tree(s(s(s(T251))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(T250))), T2, tree(s(s(s(T251))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: less(T250, T251), SCOPE: 12, CLAUSE: 4\n\nT250 is ground\nT251 is ground\ninsert(s(s(s(T250))), T2, tree(s(s(s(T251))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(T250))), T2, tree(s(s(s(T251))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: less(T250, T251), SCOPE: 12, CLAUSE: 5\n\nT250 is ground\nT251 is ground\ninsert(s(s(s(T250))), T2, tree(s(s(s(T251))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(T250))), T2, tree(s(s(s(T251))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", 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(T263, T264)\n\nT263 is ground\nT264 is ground\ninsert(s(s(s(s(T263)))), T2, tree(s(s(s(s(T264)))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(T263)))), T2, tree(s(s(s(s(T264)))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: less(T263, T264), SCOPE: 13, CLAUSE: 4 | less(T263, T264), SCOPE: 13, CLAUSE: 5\n\nT263 is ground\nT264 is ground\ninsert(s(s(s(s(T263)))), T2, tree(s(s(s(s(T264)))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(T263)))), T2, tree(s(s(s(s(T264)))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: less(T263, T264), SCOPE: 13, CLAUSE: 4\n\nT263 is ground\nT264 is ground\ninsert(s(s(s(s(T263)))), T2, tree(s(s(s(s(T264)))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(T263)))), T2, tree(s(s(s(s(T264)))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: less(T263, T264), SCOPE: 13, CLAUSE: 5\n\nT263 is ground\nT264 is ground\ninsert(s(s(s(s(T263)))), T2, tree(s(s(s(s(T264)))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(T263)))), T2, tree(s(s(s(s(T264)))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", 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(T276, T277)\n\nT276 is ground\nT277 is ground\ninsert(s(s(s(s(s(T276))))), T2, tree(s(s(s(s(s(T277))))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(T276))))), T2, tree(s(s(s(s(s(T277))))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: less(T276, T277), SCOPE: 14, CLAUSE: 4 | less(T276, T277), SCOPE: 14, CLAUSE: 5\n\nT276 is ground\nT277 is ground\ninsert(s(s(s(s(s(T276))))), T2, tree(s(s(s(s(s(T277))))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(T276))))), T2, tree(s(s(s(s(s(T277))))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: less(T276, T277), SCOPE: 14, CLAUSE: 4\n\nT276 is ground\nT277 is ground\ninsert(s(s(s(s(s(T276))))), T2, tree(s(s(s(s(s(T277))))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(T276))))), T2, tree(s(s(s(s(s(T277))))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: less(T276, T277), SCOPE: 14, CLAUSE: 5\n\nT276 is ground\nT277 is ground\ninsert(s(s(s(s(s(T276))))), T2, tree(s(s(s(s(s(T277))))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(T276))))), T2, tree(s(s(s(s(s(T277))))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", 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(T289, T290)\n\nT289 is ground\nT290 is ground\ninsert(s(s(s(s(s(s(T289)))))), T2, tree(s(s(s(s(s(s(T290)))))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(T289)))))), T2, tree(s(s(s(s(s(s(T290)))))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: less(T289, T290), SCOPE: 15, CLAUSE: 4 | less(T289, T290), SCOPE: 15, CLAUSE: 5\n\nT289 is ground\nT290 is ground\ninsert(s(s(s(s(s(s(T289)))))), T2, tree(s(s(s(s(s(s(T290)))))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(T289)))))), T2, tree(s(s(s(s(s(s(T290)))))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: less(T289, T290), SCOPE: 15, CLAUSE: 4\n\nT289 is ground\nT290 is ground\ninsert(s(s(s(s(s(s(T289)))))), T2, tree(s(s(s(s(s(s(T290)))))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(T289)))))), T2, tree(s(s(s(s(s(s(T290)))))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: less(T289, T290), SCOPE: 15, CLAUSE: 5\n\nT289 is ground\nT290 is ground\ninsert(s(s(s(s(s(s(T289)))))), T2, tree(s(s(s(s(s(s(T290)))))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(T289)))))), T2, tree(s(s(s(s(s(s(T290)))))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", 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(T302, T303)\n\nT302 is ground\nT303 is ground\ninsert(s(s(s(s(s(s(s(T302))))))), T2, tree(s(s(s(s(s(s(s(T303))))))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(s(T302))))))), T2, tree(s(s(s(s(s(s(s(T303))))))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: less(T302, T303), SCOPE: 16, CLAUSE: 4 | less(T302, T303), SCOPE: 16, CLAUSE: 5\n\nT302 is ground\nT303 is ground\ninsert(s(s(s(s(s(s(s(T302))))))), T2, tree(s(s(s(s(s(s(s(T303))))))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(s(T302))))))), T2, tree(s(s(s(s(s(s(s(T303))))))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: less(T302, T303), SCOPE: 16, CLAUSE: 4\n\nT302 is ground\nT303 is ground\ninsert(s(s(s(s(s(s(s(T302))))))), T2, tree(s(s(s(s(s(s(s(T303))))))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(s(T302))))))), T2, tree(s(s(s(s(s(s(s(T303))))))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: less(T302, T303), SCOPE: 16, CLAUSE: 5\n\nT302 is ground\nT303 is ground\ninsert(s(s(s(s(s(s(s(T302))))))), T2, tree(s(s(s(s(s(s(s(T303))))))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(s(T302))))))), T2, tree(s(s(s(s(s(s(s(T303))))))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", 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(T315, T316)\n\nT315 is ground\nT316 is ground\ninsert(s(s(s(s(s(s(s(s(T315)))))))), T2, tree(s(s(s(s(s(s(s(s(T316)))))))), T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(s(s(T315)))))))), T2, tree(s(s(s(s(s(s(s(s(T316)))))))), T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: less(T315, T316)\n\nT315 is ground\nT316 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: less(T315, T316), SCOPE: 17, CLAUSE: 4 | less(T315, T316), SCOPE: 17, CLAUSE: 5\n\nT315 is ground\nT316 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: less(T315, T316), SCOPE: 17, CLAUSE: 4\n\nT315 is ground\nT316 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: less(T315, T316), SCOPE: 17, CLAUSE: 5\n\nT315 is ground\nT316 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(T332, T333)\n\nT332 is ground\nT333 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: insert(T203, T2, tree(T204, T207, T206)), SCOPE: 1, CLAUSE: 3\n\nT203 is ground\nT204 is ground\nT207 is ground\nT206 is ground\ninsert(T203, T2, tree(T204, T207, T206)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T203, T2, tree(T204, T207, T206)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: ','(less(T349, T348), insert(T348, T353, T352))\n\nT348 is ground\nT349 is ground\nT352 is ground\ninsert(T348, T2, tree(T349, T350, T352)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T348, T2, tree(T349, T350, T352)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: less(T349, T348)\n\nT348 is ground\nT349 is ground\ninsert(T348, T2, tree(T349, T350, T352)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T348, T2, tree(T349, T350, T352)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: insert(T348, T353, T352)\n\nT348 is ground\nT352 is ground\ninsert(T348, T2, tree(T349, T350, T352)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: ','(less(T366, T365), insert(T365, T370, T369))\n\nT365 is ground\nT366 is ground\nT369 is ground\ninsert(T365, T2, tree(T366, T367, T369)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T365, T2, tree(T366, T367, T369)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: ','(less(T366, T365), insert(T365, T370, T369)), SCOPE: 18, CLAUSE: 4 | ','(less(T366, T365), insert(T365, T370, T369)), SCOPE: 18, CLAUSE: 5\n\nT365 is ground\nT366 is ground\nT369 is ground\ninsert(T365, T2, tree(T366, T367, T369)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T365, T2, tree(T366, T367, T369)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: ','(less(T366, T365), insert(T365, T370, T369)), SCOPE: 18, CLAUSE: 4\n\nT365 is ground\nT366 is ground\nT369 is ground\ninsert(T365, T2, tree(T366, T367, T369)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T365, T2, tree(T366, T367, T369)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: ','(less(T366, T365), insert(T365, T370, T369)), SCOPE: 18, CLAUSE: 5\n\nT365 is ground\nT366 is ground\nT369 is ground\ninsert(T365, T2, tree(T366, T367, T369)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T365, T2, tree(T366, T367, T369)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: insert(s(T375), T370, T369)\n\nT369 is ground\nT375 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: ','(less(T382, T383), insert(s(T383), T370, T369))\n\nT369 is ground\nT382 is ground\nT383 is ground\ninsert(s(T383), T2, tree(s(T382), T367, T369)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T383), T2, tree(s(T382), T367, T369)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: less(T382, T383)\n\nT382 is ground\nT383 is ground\ninsert(s(T383), T2, tree(s(T382), T367, T369)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T383), T2, tree(s(T382), T367, T369)) !=? insert(X242, tree(X242, X243, X244), tree(X242, X243, X244))", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: insert(s(T383), T370, T369)\n\nT369 is ground\nT383 is ground\ninsert(s(T383), T2, tree(s(T382), T367, T369)) !=? insert(X3, void, tree(X3, void, void))", 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 substitution\nT1 -> 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 = lightblue];
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(X242, tree(X242, X243, X244), tree(X242, X243, X244)).\nand substitution\nT1 -> T137\nX242 -> T137\nX243 -> T138\nX244 -> T139\nT2 -> tree(T137, T138, T139)\nT3 -> tree(T137, T138, T139)", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 175 [arrowhead = none ];
175 -> 51;

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

177 [label="EVAL with clause\ninsert(X8, tree(X8, X9, X10), tree(X8, X9, X10)).\nand substitution\nT5 -> T9\nX8 -> T9\nX9 -> void\nX10 -> 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 = lightblue];
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(X160, tree(X161, X162, X163), tree(X161, X164, X163)) :- ','(less(X160, X161), insert(X160, X162, X164)).\nand substitution\nT5 -> T96\nX160 -> T96\nX161 -> T96\nX162 -> T100\nX163 -> void\nT2 -> tree(T96, T100, void)\nT97 -> T96\nX164 -> void\nT99 -> void\nT98 -> T100", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 180 [arrowhead = none ];
180 -> 34;

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

182 [label="EVAL with clause\ninsert(X19, tree(X20, X21, X22), tree(X20, X23, X22)) :- ','(less(X19, X20), insert(X19, X21, X23)).\nand substitution\nT9 -> T16\nX19 -> T16\nX20 -> T16\nX21 -> T20\nX22 -> void\nT2 -> tree(T16, T20, void)\nT17 -> T16\nX23 -> 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 = lightblue];
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(X132, tree(X133, X134, X135), tree(X133, X134, X136)) :- ','(less(X133, X132), insert(X132, X135, X136)).\nand substitution\nT9 -> T83\nX132 -> T83\nX133 -> T83\nX134 -> void\nX135 -> T87\nT2 -> tree(T83, void, T87)\nT84 -> T83\nT85 -> void\nX136 -> void\nT86 -> T87", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 185 [arrowhead = none ];
185 -> 28;

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

187 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = white];
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(X38), s(X39)) :- less(X38, X39).\nand substitution\nX38 -> T25\nT16 -> s(T25)\nX39 -> T25", fontsize=14, style = filled, fillcolor = lightblue];
13 -> 190 [arrowhead = none ];
190 -> 15;

191 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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", 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 = white];
19 -> 197 [arrowhead = none ];
197 -> 20;

198 [label="EVAL with clause\nless(s(X55), s(X56)) :- less(X55, X56).\nand substitution\nX55 -> T30\nT25 -> s(T30)\nX56 -> T30", fontsize=14, style = filled, fillcolor = lightblue];
20 -> 198 [arrowhead = none ];
198 -> 21;

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

200 [label="INSTANCE with matching:\nT25 -> T30", fontsize=14, style = filled, fillcolor = lightgrey];
21 -> 200 [arrowhead = none , style=dashed];
200 -> 17[style=dashed];

201 [label="EVAL with clause\ninsert(X91, tree(X92, X93, X94), tree(X92, X93, X95)) :- ','(less(X92, X91), insert(X91, X94, X95)).\nand substitution\nT16 -> T56\nX91 -> T56\nX92 -> T56\nX93 -> void\nX94 -> T60\nT2 -> tree(T56, void, T60)\nT57 -> T56\nT58 -> void\nX95 -> void\nT59 -> T60", fontsize=14, style = filled, fillcolor = lightblue];
23 -> 201 [arrowhead = none ];
201 -> 24;

202 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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", fontsize=14, style = filled, fillcolor = violet];
24 -> 204 [arrowhead = none ];
204 -> 27;

205 [label="INSTANCE with matching:\nT25 -> T56", fontsize=14, style = filled, fillcolor = lightgrey];
26 -> 205 [arrowhead = none , style=dashed];
205 -> 17[style=dashed];

206 [label="INSTANCE with matching:\nT1 -> T56\nT2 -> T60\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 = white];
30 -> 208 [arrowhead = none ];
208 -> 31;

209 [label="EVAL with clause\nless(s(X147), s(X148)) :- less(X147, X148).\nand substitution\nX147 -> T90\nT83 -> s(T90)\nX148 -> T90", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 209 [arrowhead = none ];
209 -> 32;

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

211 [label="INSTANCE with matching:\nT25 -> T90\nT20 -> T87", 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(X216, tree(X217, X218, X219), tree(X217, X218, X220)) :- ','(less(X217, X216), insert(X216, X219, X220)).\nand substitution\nT5 -> T125\nX216 -> T125\nX217 -> T125\nX218 -> void\nX219 -> T129\nT2 -> tree(T125, void, T129)\nT126 -> T125\nT127 -> void\nX220 -> void\nT128 -> T129", fontsize=14, style = filled, fillcolor = lightblue];
35 -> 213 [arrowhead = none ];
213 -> 45;

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

215 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = white];
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(X179), s(X180)) :- less(X179, X180).\nand substitution\nX179 -> T105\nT96 -> s(T105)\nX180 -> T105", fontsize=14, style = filled, fillcolor = lightblue];
38 -> 218 [arrowhead = none ];
218 -> 40;

219 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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 -> T105\nT20 -> T100", fontsize=14, style = filled, fillcolor = lightgrey];
40 -> 221 [arrowhead = none , style=dashed];
221 -> 15[style=dashed];

222 [label="EVAL with clause\ninsert(X197, tree(X198, X199, X200), tree(X198, X199, X201)) :- ','(less(X198, X197), insert(X197, X200, X201)).\nand substitution\nT96 -> T115\nX197 -> T115\nX198 -> T115\nX199 -> void\nX200 -> T119\nT2 -> tree(T115, void, T119)\nT116 -> T115\nT117 -> void\nX201 -> void\nT118 -> T119", fontsize=14, style = filled, fillcolor = lightblue];
42 -> 222 [arrowhead = none ];
222 -> 43;

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

224 [label="INSTANCE with matching:\nT83 -> T115\nT87 -> T119", fontsize=14, style = filled, fillcolor = lightgrey];
43 -> 224 [arrowhead = none , style=dashed];
224 -> 28[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 = white];
47 -> 226 [arrowhead = none ];
226 -> 48;

227 [label="EVAL with clause\nless(s(X231), s(X232)) :- less(X231, X232).\nand substitution\nX231 -> T132\nT125 -> s(T132)\nX232 -> T132", fontsize=14, style = filled, fillcolor = lightblue];
48 -> 227 [arrowhead = none ];
227 -> 49;

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

229 [label="INSTANCE with matching:\nT105 -> T132\nT100 -> T129", fontsize=14, style = filled, fillcolor = lightgrey];
49 -> 229 [arrowhead = none , style=dashed];
229 -> 40[style=dashed];

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

231 [label="EVAL with clause\ninsert(X355, tree(X356, X357, X358), tree(X356, X359, X358)) :- ','(less(X355, X356), insert(X355, X357, X359)).\nand substitution\nT1 -> T203\nX355 -> T203\nX356 -> T204\nX357 -> T208\nX358 -> T206\nT2 -> tree(T204, T208, T206)\nX359 -> T207\nT3 -> tree(T204, T207, T206)\nT205 -> T208", fontsize=14, style = filled, fillcolor = lightblue];
52 -> 231 [arrowhead = none ];
231 -> 77;

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

233 [label="EVAL with clause\ninsert(X253, tree(X254, X255, X256), tree(X254, X257, X256)) :- ','(less(X253, X254), insert(X253, X255, X257)).\nand substitution\nT137 -> T145\nX253 -> T145\nX254 -> T145\nX255 -> T150\nX256 -> T148\nT2 -> tree(T145, T150, T148)\nT146 -> T145\nT138 -> T149\nX257 -> T149\nT139 -> T148\nT147 -> T150", fontsize=14, style = filled, fillcolor = lightblue];
53 -> 233 [arrowhead = none ];
233 -> 54;

234 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X321, tree(X322, X323, X324), tree(X322, X323, X325)) :- ','(less(X322, X321), insert(X321, X324, X325)).\nand substitution\nT137 -> T185\nX321 -> T185\nX322 -> T185\nX323 -> T187\nX324 -> T190\nT2 -> tree(T185, T187, T190)\nT186 -> T185\nT138 -> T187\nT139 -> T189\nX325 -> T189\nT188 -> T190", fontsize=14, style = filled, fillcolor = lightblue];
55 -> 236 [arrowhead = none ];
236 -> 69;

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

238 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = white];
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(X272), s(X273)) :- less(X272, X273).\nand substitution\nX272 -> T155\nT145 -> s(T155)\nX273 -> T155", fontsize=14, style = filled, fillcolor = lightblue];
58 -> 241 [arrowhead = none ];
241 -> 60;

242 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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", fontsize=14, style = filled, fillcolor = violet];
60 -> 245 [arrowhead = none ];
245 -> 63;

246 [label="INSTANCE with matching:\nT25 -> T155", fontsize=14, style = filled, fillcolor = lightgrey];
62 -> 246 [arrowhead = none , style=dashed];
246 -> 17[style=dashed];

247 [label="INSTANCE with matching:\nT1 -> s(T155)\nT2 -> T150\nT3 -> T149", fontsize=14, style = filled, fillcolor = lightgrey];
63 -> 247 [arrowhead = none , style=dashed];
247 -> 1[style=dashed];

248 [label="EVAL with clause\ninsert(X296, tree(X297, X298, X299), tree(X297, X298, X300)) :- ','(less(X297, X296), insert(X296, X299, X300)).\nand substitution\nT145 -> T170\nX296 -> T170\nX297 -> T170\nX298 -> T172\nX299 -> T175\nT2 -> tree(T170, T172, T175)\nT171 -> T170\nT149 -> T172\nT148 -> T174\nX300 -> T174\nT173 -> T175", fontsize=14, style = filled, fillcolor = lightblue];
64 -> 248 [arrowhead = none ];
248 -> 65;

249 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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", fontsize=14, style = filled, fillcolor = violet];
65 -> 251 [arrowhead = none ];
251 -> 68;

252 [label="INSTANCE with matching:\nT155 -> T170", fontsize=14, style = filled, fillcolor = lightgrey];
67 -> 252 [arrowhead = none , style=dashed];
252 -> 62[style=dashed];

253 [label="INSTANCE with matching:\nT1 -> T170\nT2 -> T175\nT3 -> T174", 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 = white];
71 -> 255 [arrowhead = none ];
255 -> 72;

256 [label="EVAL with clause\nless(s(X336), s(X337)) :- less(X336, X337).\nand substitution\nX336 -> T193\nT185 -> s(T193)\nX337 -> T193", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 256 [arrowhead = none ];
256 -> 73;

257 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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", fontsize=14, style = filled, fillcolor = violet];
73 -> 259 [arrowhead = none ];
259 -> 76;

260 [label="INSTANCE with matching:\nT155 -> T193", fontsize=14, style = filled, fillcolor = lightgrey];
75 -> 260 [arrowhead = none , style=dashed];
260 -> 62[style=dashed];

261 [label="INSTANCE with matching:\nT1 -> s(T193)\nT2 -> T190\nT3 -> T189", 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(X552, tree(X553, X554, X555), tree(X553, X554, X556)) :- ','(less(X553, X552), insert(X552, X555, X556)).\nand substitution\nT1 -> T365\nX552 -> T365\nX553 -> T366\nX554 -> T367\nX555 -> T370\nT2 -> tree(T366, T367, T370)\nX556 -> T369\nT3 -> tree(T366, T367, T369)\nT368 -> T370", fontsize=14, style = filled, fillcolor = lightblue];
78 -> 263 [arrowhead = none ];
263 -> 160;

264 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X369)).\nand substitution\nT203 -> 0\nX369 -> T213\nT204 -> s(T213)", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 267 [arrowhead = none ];
267 -> 82;

268 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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 -> T208\nT3 -> T207", fontsize=14, style = filled, fillcolor = lightgrey];
82 -> 271 [arrowhead = none , style=dashed];
271 -> 1[style=dashed];

272 [label="EVAL with clause\nless(s(X381), s(X382)) :- less(X381, X382).\nand substitution\nX381 -> T222\nT203 -> s(T222)\nX382 -> T223\nT204 -> s(T223)", fontsize=14, style = filled, fillcolor = lightblue];
84 -> 272 [arrowhead = none ];
272 -> 86;

273 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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", 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(T222)\nT2 -> T208\nT3 -> T207", 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(X393)).\nand substitution\nT222 -> 0\nX393 -> T232\nT223 -> s(T232)", fontsize=14, style = filled, fillcolor = lightblue];
91 -> 281 [arrowhead = none ];
281 -> 93;

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

283 [label="EVAL with clause\nless(s(X399), s(X400)) :- less(X399, X400).\nand substitution\nX399 -> T237\nT222 -> s(T237)\nX400 -> T238\nT223 -> s(T238)", fontsize=14, style = filled, fillcolor = lightblue];
92 -> 283 [arrowhead = none ];
283 -> 96;

284 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X409)).\nand substitution\nT237 -> 0\nX409 -> T245\nT238 -> s(T245)", fontsize=14, style = filled, fillcolor = lightblue];
99 -> 289 [arrowhead = none ];
289 -> 101;

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

291 [label="EVAL with clause\nless(s(X415), s(X416)) :- less(X415, X416).\nand substitution\nX415 -> T250\nT237 -> s(T250)\nX416 -> T251\nT238 -> s(T251)", fontsize=14, style = filled, fillcolor = lightblue];
100 -> 291 [arrowhead = none ];
291 -> 104;

292 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X425)).\nand substitution\nT250 -> 0\nX425 -> T258\nT251 -> s(T258)", fontsize=14, style = filled, fillcolor = lightblue];
107 -> 297 [arrowhead = none ];
297 -> 109;

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

299 [label="EVAL with clause\nless(s(X431), s(X432)) :- less(X431, X432).\nand substitution\nX431 -> T263\nT250 -> s(T263)\nX432 -> T264\nT251 -> s(T264)", fontsize=14, style = filled, fillcolor = lightblue];
108 -> 299 [arrowhead = none ];
299 -> 112;

300 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X441)).\nand substitution\nT263 -> 0\nX441 -> T271\nT264 -> s(T271)", fontsize=14, style = filled, fillcolor = lightblue];
115 -> 305 [arrowhead = none ];
305 -> 117;

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

307 [label="EVAL with clause\nless(s(X447), s(X448)) :- less(X447, X448).\nand substitution\nX447 -> T276\nT263 -> s(T276)\nX448 -> T277\nT264 -> s(T277)", fontsize=14, style = filled, fillcolor = lightblue];
116 -> 307 [arrowhead = none ];
307 -> 120;

308 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X457)).\nand substitution\nT276 -> 0\nX457 -> T284\nT277 -> s(T284)", fontsize=14, style = filled, fillcolor = lightblue];
123 -> 313 [arrowhead = none ];
313 -> 125;

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

315 [label="EVAL with clause\nless(s(X463), s(X464)) :- less(X463, X464).\nand substitution\nX463 -> T289\nT276 -> s(T289)\nX464 -> T290\nT277 -> s(T290)", fontsize=14, style = filled, fillcolor = lightblue];
124 -> 315 [arrowhead = none ];
315 -> 128;

316 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X473)).\nand substitution\nT289 -> 0\nX473 -> T297\nT290 -> s(T297)", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 321 [arrowhead = none ];
321 -> 133;

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

323 [label="EVAL with clause\nless(s(X479), s(X480)) :- less(X479, X480).\nand substitution\nX479 -> T302\nT289 -> s(T302)\nX480 -> T303\nT290 -> s(T303)", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 323 [arrowhead = none ];
323 -> 136;

324 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X489)).\nand substitution\nT302 -> 0\nX489 -> T310\nT303 -> s(T310)", fontsize=14, style = filled, fillcolor = lightblue];
139 -> 329 [arrowhead = none ];
329 -> 141;

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

331 [label="EVAL with clause\nless(s(X495), s(X496)) :- less(X495, X496).\nand substitution\nX495 -> T315\nT302 -> s(T315)\nX496 -> T316\nT303 -> s(T316)", fontsize=14, style = filled, fillcolor = lightblue];
140 -> 331 [arrowhead = none ];
331 -> 144;

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

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

334 [label="GENERALIZATION\nT319 <-- s(s(s(s(s(s(s(T315)))))))\nT320 <-- s(s(s(s(s(s(s(T316)))))))\n\nNew Knowledge:\nT319 is ground\nT320 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(X507)).\nand substitution\nT315 -> 0\nX507 -> T327\nT316 -> s(T327)", fontsize=14, style = filled, fillcolor = lightblue];
148 -> 338 [arrowhead = none ];
338 -> 150;

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

340 [label="EVAL with clause\nless(s(X513), s(X514)) :- less(X513, X514).\nand substitution\nX513 -> T332\nT315 -> s(T332)\nX514 -> T333\nT316 -> s(T333)", fontsize=14, style = filled, fillcolor = lightblue];
149 -> 340 [arrowhead = none ];
340 -> 153;

341 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT315 -> T332\nT316 -> T333", fontsize=14, style = filled, fillcolor = lightgrey];
153 -> 343 [arrowhead = none , style=dashed];
343 -> 146[style=dashed];

344 [label="EVAL with clause\ninsert(X531, tree(X532, X533, X534), tree(X532, X533, X535)) :- ','(less(X532, X531), insert(X531, X534, X535)).\nand substitution\nT203 -> T348\nX531 -> T348\nX532 -> T349\nX533 -> T350\nX534 -> T353\nT2 -> tree(T349, T350, T353)\nT204 -> T349\nT207 -> T350\nT206 -> T352\nX535 -> T352\nT351 -> T353", fontsize=14, style = filled, fillcolor = lightblue];
155 -> 344 [arrowhead = none ];
344 -> 156;

345 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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", fontsize=14, style = filled, fillcolor = violet];
156 -> 347 [arrowhead = none ];
347 -> 159;

348 [label="INSTANCE with matching:\nT315 -> T349\nT316 -> T348", fontsize=14, style = filled, fillcolor = lightgrey];
158 -> 348 [arrowhead = none , style=dashed];
348 -> 146[style=dashed];

349 [label="INSTANCE with matching:\nT1 -> T348\nT2 -> T353\nT3 -> T352", 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(X566)).\nand substitution\nT366 -> 0\nX566 -> T375\nT365 -> s(T375)", fontsize=14, style = filled, fillcolor = lightblue];
163 -> 353 [arrowhead = none ];
353 -> 165;

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

355 [label="EVAL with clause\nless(s(X574), s(X575)) :- less(X574, X575).\nand substitution\nX574 -> T382\nT366 -> s(T382)\nX575 -> T383\nT365 -> s(T383)", fontsize=14, style = filled, fillcolor = lightblue];
164 -> 355 [arrowhead = none ];
355 -> 167;

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

357 [label="INSTANCE with matching:\nT1 -> s(T375)\nT2 -> T370\nT3 -> T369", 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", fontsize=14, style = filled, fillcolor = violet];
167 -> 359 [arrowhead = none ];
359 -> 170;

360 [label="INSTANCE with matching:\nT315 -> T382\nT316 -> T383", fontsize=14, style = filled, fillcolor = lightgrey];
169 -> 360 [arrowhead = none , style=dashed];
360 -> 146[style=dashed];

361 [label="INSTANCE with matching:\nT1 -> s(T383)\nT2 -> T370\nT3 -> T369", fontsize=14, style = filled, fillcolor = lightgrey];
170 -> 361 [arrowhead = none , style=dashed];
361 -> 1[style=dashed];

}

(2) Obligation:

Clauses:

less17(s(T30)) :- less17(T30).
p15(T25, T20) :- less17(T25).
p15(T25, T20) :- ','(less17(T25), insert1(s(T25), T20, void)).
p28(s(T90), T87) :- p15(T90, T87).
less146(0, s(T327)).
less146(s(T332), s(T333)) :- less146(T332, T333).
less88(0, s(T232)).
less88(s(0), s(s(T245))).
less88(s(s(0)), s(s(s(T258)))).
less88(s(s(s(0))), s(s(s(s(T271))))).
less88(s(s(s(s(0)))), s(s(s(s(s(T284)))))).
less88(s(s(s(s(s(0))))), s(s(s(s(s(s(T297))))))).
less88(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310)))))))).
less88(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316)))))))) :- less146(T315, T316).
insert1(T5, void, tree(T5, void, void)).
insert1(T9, tree(T9, void, void), tree(T9, void, void)).
insert1(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void)) :- p15(T25, T20).
insert1(T56, tree(T56, void, T60), tree(T56, void, void)) :- less17(T56).
insert1(T56, tree(T56, void, T60), tree(T56, void, void)) :- ','(less17(T56), insert1(T56, T60, void)).
insert1(T83, tree(T83, void, T87), tree(T83, void, void)) :- p28(T83, T87).
insert1(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void)) :- p15(T105, T100).
insert1(T115, tree(T115, void, T119), tree(T115, void, void)) :- p28(T115, T119).
insert1(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void)) :- p15(T132, T129).
insert1(T137, tree(T137, T138, T139), tree(T137, T138, T139)).
insert1(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148)) :- less17(T155).
insert1(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148)) :- ','(less17(T155), insert1(s(T155), T150, T149)).
insert1(T170, tree(T170, T172, T175), tree(T170, T172, T174)) :- less17(T170).
insert1(T170, tree(T170, T172, T175), tree(T170, T172, T174)) :- ','(less17(T170), insert1(T170, T175, T174)).
insert1(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189)) :- less17(T193).
insert1(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189)) :- ','(less17(T193), insert1(s(T193), T190, T189)).
insert1(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206)) :- insert1(0, T208, T207).
insert1(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206)) :- less88(T222, T223).
insert1(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206)) :- ','(less88(T222, T223), insert1(s(T222), T208, T207)).
insert1(T348, tree(T349, T350, T353), tree(T349, T350, T352)) :- less146(T349, T348).
insert1(T348, tree(T349, T350, T353), tree(T349, T350, T352)) :- ','(less146(T349, T348), insert1(T348, T353, T352)).
insert1(s(T375), tree(0, T367, T370), tree(0, T367, T369)) :- insert1(s(T375), T370, T369).
insert1(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369)) :- less146(T382, T383).
insert1(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369)) :- ','(less146(T382, T383), insert1(s(T383), T370, T369)).

Queries:

insert1(g,a,g).

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
insert1_in: (b,f,b)
p15_in: (b,f)
less17_in: (b)
p28_in: (b,f)
less88_in: (b,b)
less146_in: (b,b)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

insert1_in_gag(T5, void, tree(T5, void, void)) → insert1_out_gag(T5, void, tree(T5, void, void))
insert1_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insert1_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insert1_in_gag(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void)) → U7_gag(T25, T20, p15_in_ga(T25, T20))
p15_in_ga(T25, T20) → U2_ga(T25, T20, less17_in_g(T25))
less17_in_g(s(T30)) → U1_g(T30, less17_in_g(T30))
U1_g(T30, less17_out_g(T30)) → less17_out_g(s(T30))
U2_ga(T25, T20, less17_out_g(T25)) → p15_out_ga(T25, T20)
U2_ga(T25, T20, less17_out_g(T25)) → U3_ga(T25, T20, insert1_in_gag(s(T25), T20, void))
insert1_in_gag(T56, tree(T56, void, T60), tree(T56, void, void)) → U8_gag(T56, T60, less17_in_g(T56))
U8_gag(T56, T60, less17_out_g(T56)) → insert1_out_gag(T56, tree(T56, void, T60), tree(T56, void, void))
U8_gag(T56, T60, less17_out_g(T56)) → U9_gag(T56, T60, insert1_in_gag(T56, T60, void))
insert1_in_gag(T83, tree(T83, void, T87), tree(T83, void, void)) → U10_gag(T83, T87, p28_in_ga(T83, T87))
p28_in_ga(s(T90), T87) → U4_ga(T90, T87, p15_in_ga(T90, T87))
U4_ga(T90, T87, p15_out_ga(T90, T87)) → p28_out_ga(s(T90), T87)
U10_gag(T83, T87, p28_out_ga(T83, T87)) → insert1_out_gag(T83, tree(T83, void, T87), tree(T83, void, void))
insert1_in_gag(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void)) → U11_gag(T105, T100, p15_in_ga(T105, T100))
U11_gag(T105, T100, p15_out_ga(T105, T100)) → insert1_out_gag(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void))
insert1_in_gag(T115, tree(T115, void, T119), tree(T115, void, void)) → U12_gag(T115, T119, p28_in_ga(T115, T119))
U12_gag(T115, T119, p28_out_ga(T115, T119)) → insert1_out_gag(T115, tree(T115, void, T119), tree(T115, void, void))
insert1_in_gag(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void)) → U13_gag(T132, T129, p15_in_ga(T132, T129))
U13_gag(T132, T129, p15_out_ga(T132, T129)) → insert1_out_gag(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void))
insert1_in_gag(T137, tree(T137, T138, T139), tree(T137, T138, T139)) → insert1_out_gag(T137, tree(T137, T138, T139), tree(T137, T138, T139))
insert1_in_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148)) → U14_gag(T155, T150, T148, T149, less17_in_g(T155))
U14_gag(T155, T150, T148, T149, less17_out_g(T155)) → insert1_out_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148))
U14_gag(T155, T150, T148, T149, less17_out_g(T155)) → U15_gag(T155, T150, T148, T149, insert1_in_gag(s(T155), T150, T149))
insert1_in_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174)) → U16_gag(T170, T172, T175, T174, less17_in_g(T170))
U16_gag(T170, T172, T175, T174, less17_out_g(T170)) → insert1_out_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174))
U16_gag(T170, T172, T175, T174, less17_out_g(T170)) → U17_gag(T170, T172, T175, T174, insert1_in_gag(T170, T175, T174))
insert1_in_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189)) → U18_gag(T193, T187, T190, T189, less17_in_g(T193))
U18_gag(T193, T187, T190, T189, less17_out_g(T193)) → insert1_out_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189))
U18_gag(T193, T187, T190, T189, less17_out_g(T193)) → U19_gag(T193, T187, T190, T189, insert1_in_gag(s(T193), T190, T189))
insert1_in_gag(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206)) → U20_gag(T213, T208, T206, T207, insert1_in_gag(0, T208, T207))
insert1_in_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206)) → U21_gag(T222, T223, T208, T206, T207, less88_in_gg(T222, T223))
less88_in_gg(0, s(T232)) → less88_out_gg(0, s(T232))
less88_in_gg(s(0), s(s(T245))) → less88_out_gg(s(0), s(s(T245)))
less88_in_gg(s(s(0)), s(s(s(T258)))) → less88_out_gg(s(s(0)), s(s(s(T258))))
less88_in_gg(s(s(s(0))), s(s(s(s(T271))))) → less88_out_gg(s(s(s(0))), s(s(s(s(T271)))))
less88_in_gg(s(s(s(s(0)))), s(s(s(s(s(T284)))))) → less88_out_gg(s(s(s(s(0)))), s(s(s(s(s(T284))))))
less88_in_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297))))))) → less88_out_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297)))))))
less88_in_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310)))))))) → less88_out_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310))))))))
less88_in_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316)))))))) → U6_gg(T315, T316, less146_in_gg(T315, T316))
less146_in_gg(0, s(T327)) → less146_out_gg(0, s(T327))
less146_in_gg(s(T332), s(T333)) → U5_gg(T332, T333, less146_in_gg(T332, T333))
U5_gg(T332, T333, less146_out_gg(T332, T333)) → less146_out_gg(s(T332), s(T333))
U6_gg(T315, T316, less146_out_gg(T315, T316)) → less88_out_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316))))))))
U21_gag(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → insert1_out_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206))
U21_gag(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → U22_gag(T222, T223, T208, T206, T207, insert1_in_gag(s(T222), T208, T207))
insert1_in_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352)) → U23_gag(T348, T349, T350, T353, T352, less146_in_gg(T349, T348))
U23_gag(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → insert1_out_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352))
U23_gag(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → U24_gag(T348, T349, T350, T353, T352, insert1_in_gag(T348, T353, T352))
insert1_in_gag(s(T375), tree(0, T367, T370), tree(0, T367, T369)) → U25_gag(T375, T367, T370, T369, insert1_in_gag(s(T375), T370, T369))
insert1_in_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369)) → U26_gag(T383, T382, T367, T370, T369, less146_in_gg(T382, T383))
U26_gag(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → insert1_out_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369))
U26_gag(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → U27_gag(T383, T382, T367, T370, T369, insert1_in_gag(s(T383), T370, T369))
U27_gag(T383, T382, T367, T370, T369, insert1_out_gag(s(T383), T370, T369)) → insert1_out_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369))
U25_gag(T375, T367, T370, T369, insert1_out_gag(s(T375), T370, T369)) → insert1_out_gag(s(T375), tree(0, T367, T370), tree(0, T367, T369))
U24_gag(T348, T349, T350, T353, T352, insert1_out_gag(T348, T353, T352)) → insert1_out_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352))
U22_gag(T222, T223, T208, T206, T207, insert1_out_gag(s(T222), T208, T207)) → insert1_out_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206))
U20_gag(T213, T208, T206, T207, insert1_out_gag(0, T208, T207)) → insert1_out_gag(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206))
U19_gag(T193, T187, T190, T189, insert1_out_gag(s(T193), T190, T189)) → insert1_out_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189))
U17_gag(T170, T172, T175, T174, insert1_out_gag(T170, T175, T174)) → insert1_out_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174))
U15_gag(T155, T150, T148, T149, insert1_out_gag(s(T155), T150, T149)) → insert1_out_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148))
U9_gag(T56, T60, insert1_out_gag(T56, T60, void)) → insert1_out_gag(T56, tree(T56, void, T60), tree(T56, void, void))
U3_ga(T25, T20, insert1_out_gag(s(T25), T20, void)) → p15_out_ga(T25, T20)
U7_gag(T25, T20, p15_out_ga(T25, T20)) → insert1_out_gag(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void))

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

insert1_in_gag(T5, void, tree(T5, void, void)) → insert1_out_gag(T5, void, tree(T5, void, void))
insert1_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insert1_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insert1_in_gag(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void)) → U7_gag(T25, T20, p15_in_ga(T25, T20))
p15_in_ga(T25, T20) → U2_ga(T25, T20, less17_in_g(T25))
less17_in_g(s(T30)) → U1_g(T30, less17_in_g(T30))
U1_g(T30, less17_out_g(T30)) → less17_out_g(s(T30))
U2_ga(T25, T20, less17_out_g(T25)) → p15_out_ga(T25, T20)
U2_ga(T25, T20, less17_out_g(T25)) → U3_ga(T25, T20, insert1_in_gag(s(T25), T20, void))
insert1_in_gag(T56, tree(T56, void, T60), tree(T56, void, void)) → U8_gag(T56, T60, less17_in_g(T56))
U8_gag(T56, T60, less17_out_g(T56)) → insert1_out_gag(T56, tree(T56, void, T60), tree(T56, void, void))
U8_gag(T56, T60, less17_out_g(T56)) → U9_gag(T56, T60, insert1_in_gag(T56, T60, void))
insert1_in_gag(T83, tree(T83, void, T87), tree(T83, void, void)) → U10_gag(T83, T87, p28_in_ga(T83, T87))
p28_in_ga(s(T90), T87) → U4_ga(T90, T87, p15_in_ga(T90, T87))
U4_ga(T90, T87, p15_out_ga(T90, T87)) → p28_out_ga(s(T90), T87)
U10_gag(T83, T87, p28_out_ga(T83, T87)) → insert1_out_gag(T83, tree(T83, void, T87), tree(T83, void, void))
insert1_in_gag(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void)) → U11_gag(T105, T100, p15_in_ga(T105, T100))
U11_gag(T105, T100, p15_out_ga(T105, T100)) → insert1_out_gag(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void))
insert1_in_gag(T115, tree(T115, void, T119), tree(T115, void, void)) → U12_gag(T115, T119, p28_in_ga(T115, T119))
U12_gag(T115, T119, p28_out_ga(T115, T119)) → insert1_out_gag(T115, tree(T115, void, T119), tree(T115, void, void))
insert1_in_gag(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void)) → U13_gag(T132, T129, p15_in_ga(T132, T129))
U13_gag(T132, T129, p15_out_ga(T132, T129)) → insert1_out_gag(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void))
insert1_in_gag(T137, tree(T137, T138, T139), tree(T137, T138, T139)) → insert1_out_gag(T137, tree(T137, T138, T139), tree(T137, T138, T139))
insert1_in_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148)) → U14_gag(T155, T150, T148, T149, less17_in_g(T155))
U14_gag(T155, T150, T148, T149, less17_out_g(T155)) → insert1_out_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148))
U14_gag(T155, T150, T148, T149, less17_out_g(T155)) → U15_gag(T155, T150, T148, T149, insert1_in_gag(s(T155), T150, T149))
insert1_in_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174)) → U16_gag(T170, T172, T175, T174, less17_in_g(T170))
U16_gag(T170, T172, T175, T174, less17_out_g(T170)) → insert1_out_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174))
U16_gag(T170, T172, T175, T174, less17_out_g(T170)) → U17_gag(T170, T172, T175, T174, insert1_in_gag(T170, T175, T174))
insert1_in_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189)) → U18_gag(T193, T187, T190, T189, less17_in_g(T193))
U18_gag(T193, T187, T190, T189, less17_out_g(T193)) → insert1_out_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189))
U18_gag(T193, T187, T190, T189, less17_out_g(T193)) → U19_gag(T193, T187, T190, T189, insert1_in_gag(s(T193), T190, T189))
insert1_in_gag(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206)) → U20_gag(T213, T208, T206, T207, insert1_in_gag(0, T208, T207))
insert1_in_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206)) → U21_gag(T222, T223, T208, T206, T207, less88_in_gg(T222, T223))
less88_in_gg(0, s(T232)) → less88_out_gg(0, s(T232))
less88_in_gg(s(0), s(s(T245))) → less88_out_gg(s(0), s(s(T245)))
less88_in_gg(s(s(0)), s(s(s(T258)))) → less88_out_gg(s(s(0)), s(s(s(T258))))
less88_in_gg(s(s(s(0))), s(s(s(s(T271))))) → less88_out_gg(s(s(s(0))), s(s(s(s(T271)))))
less88_in_gg(s(s(s(s(0)))), s(s(s(s(s(T284)))))) → less88_out_gg(s(s(s(s(0)))), s(s(s(s(s(T284))))))
less88_in_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297))))))) → less88_out_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297)))))))
less88_in_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310)))))))) → less88_out_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310))))))))
less88_in_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316)))))))) → U6_gg(T315, T316, less146_in_gg(T315, T316))
less146_in_gg(0, s(T327)) → less146_out_gg(0, s(T327))
less146_in_gg(s(T332), s(T333)) → U5_gg(T332, T333, less146_in_gg(T332, T333))
U5_gg(T332, T333, less146_out_gg(T332, T333)) → less146_out_gg(s(T332), s(T333))
U6_gg(T315, T316, less146_out_gg(T315, T316)) → less88_out_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316))))))))
U21_gag(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → insert1_out_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206))
U21_gag(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → U22_gag(T222, T223, T208, T206, T207, insert1_in_gag(s(T222), T208, T207))
insert1_in_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352)) → U23_gag(T348, T349, T350, T353, T352, less146_in_gg(T349, T348))
U23_gag(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → insert1_out_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352))
U23_gag(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → U24_gag(T348, T349, T350, T353, T352, insert1_in_gag(T348, T353, T352))
insert1_in_gag(s(T375), tree(0, T367, T370), tree(0, T367, T369)) → U25_gag(T375, T367, T370, T369, insert1_in_gag(s(T375), T370, T369))
insert1_in_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369)) → U26_gag(T383, T382, T367, T370, T369, less146_in_gg(T382, T383))
U26_gag(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → insert1_out_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369))
U26_gag(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → U27_gag(T383, T382, T367, T370, T369, insert1_in_gag(s(T383), T370, T369))
U27_gag(T383, T382, T367, T370, T369, insert1_out_gag(s(T383), T370, T369)) → insert1_out_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369))
U25_gag(T375, T367, T370, T369, insert1_out_gag(s(T375), T370, T369)) → insert1_out_gag(s(T375), tree(0, T367, T370), tree(0, T367, T369))
U24_gag(T348, T349, T350, T353, T352, insert1_out_gag(T348, T353, T352)) → insert1_out_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352))
U22_gag(T222, T223, T208, T206, T207, insert1_out_gag(s(T222), T208, T207)) → insert1_out_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206))
U20_gag(T213, T208, T206, T207, insert1_out_gag(0, T208, T207)) → insert1_out_gag(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206))
U19_gag(T193, T187, T190, T189, insert1_out_gag(s(T193), T190, T189)) → insert1_out_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189))
U17_gag(T170, T172, T175, T174, insert1_out_gag(T170, T175, T174)) → insert1_out_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174))
U15_gag(T155, T150, T148, T149, insert1_out_gag(s(T155), T150, T149)) → insert1_out_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148))
U9_gag(T56, T60, insert1_out_gag(T56, T60, void)) → insert1_out_gag(T56, tree(T56, void, T60), tree(T56, void, void))
U3_ga(T25, T20, insert1_out_gag(s(T25), T20, void)) → p15_out_ga(T25, T20)
U7_gag(T25, T20, p15_out_ga(T25, T20)) → insert1_out_gag(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void))

(5) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
Pi DP problem:
The TRS P consists of the following rules:

INSERT1_IN_GAG(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void)) → U7_GAG(T25, T20, p15_in_ga(T25, T20))
INSERT1_IN_GAG(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void)) → P15_IN_GA(T25, T20)
P15_IN_GA(T25, T20) → U2_GA(T25, T20, less17_in_g(T25))
P15_IN_GA(T25, T20) → LESS17_IN_G(T25)
LESS17_IN_G(s(T30)) → U1_G(T30, less17_in_g(T30))
LESS17_IN_G(s(T30)) → LESS17_IN_G(T30)
U2_GA(T25, T20, less17_out_g(T25)) → U3_GA(T25, T20, insert1_in_gag(s(T25), T20, void))
U2_GA(T25, T20, less17_out_g(T25)) → INSERT1_IN_GAG(s(T25), T20, void)
INSERT1_IN_GAG(T56, tree(T56, void, T60), tree(T56, void, void)) → U8_GAG(T56, T60, less17_in_g(T56))
INSERT1_IN_GAG(T56, tree(T56, void, T60), tree(T56, void, void)) → LESS17_IN_G(T56)
U8_GAG(T56, T60, less17_out_g(T56)) → U9_GAG(T56, T60, insert1_in_gag(T56, T60, void))
U8_GAG(T56, T60, less17_out_g(T56)) → INSERT1_IN_GAG(T56, T60, void)
INSERT1_IN_GAG(T83, tree(T83, void, T87), tree(T83, void, void)) → U10_GAG(T83, T87, p28_in_ga(T83, T87))
INSERT1_IN_GAG(T83, tree(T83, void, T87), tree(T83, void, void)) → P28_IN_GA(T83, T87)
P28_IN_GA(s(T90), T87) → U4_GA(T90, T87, p15_in_ga(T90, T87))
P28_IN_GA(s(T90), T87) → P15_IN_GA(T90, T87)
INSERT1_IN_GAG(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void)) → U11_GAG(T105, T100, p15_in_ga(T105, T100))
INSERT1_IN_GAG(T115, tree(T115, void, T119), tree(T115, void, void)) → U12_GAG(T115, T119, p28_in_ga(T115, T119))
INSERT1_IN_GAG(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void)) → U13_GAG(T132, T129, p15_in_ga(T132, T129))
INSERT1_IN_GAG(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void)) → P15_IN_GA(T132, T129)
INSERT1_IN_GAG(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148)) → U14_GAG(T155, T150, T148, T149, less17_in_g(T155))
INSERT1_IN_GAG(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148)) → LESS17_IN_G(T155)
U14_GAG(T155, T150, T148, T149, less17_out_g(T155)) → U15_GAG(T155, T150, T148, T149, insert1_in_gag(s(T155), T150, T149))
U14_GAG(T155, T150, T148, T149, less17_out_g(T155)) → INSERT1_IN_GAG(s(T155), T150, T149)
INSERT1_IN_GAG(T170, tree(T170, T172, T175), tree(T170, T172, T174)) → U16_GAG(T170, T172, T175, T174, less17_in_g(T170))
INSERT1_IN_GAG(T170, tree(T170, T172, T175), tree(T170, T172, T174)) → LESS17_IN_G(T170)
U16_GAG(T170, T172, T175, T174, less17_out_g(T170)) → U17_GAG(T170, T172, T175, T174, insert1_in_gag(T170, T175, T174))
U16_GAG(T170, T172, T175, T174, less17_out_g(T170)) → INSERT1_IN_GAG(T170, T175, T174)
INSERT1_IN_GAG(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189)) → U18_GAG(T193, T187, T190, T189, less17_in_g(T193))
INSERT1_IN_GAG(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189)) → LESS17_IN_G(T193)
U18_GAG(T193, T187, T190, T189, less17_out_g(T193)) → U19_GAG(T193, T187, T190, T189, insert1_in_gag(s(T193), T190, T189))
U18_GAG(T193, T187, T190, T189, less17_out_g(T193)) → INSERT1_IN_GAG(s(T193), T190, T189)
INSERT1_IN_GAG(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206)) → U20_GAG(T213, T208, T206, T207, insert1_in_gag(0, T208, T207))
INSERT1_IN_GAG(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206)) → INSERT1_IN_GAG(0, T208, T207)
INSERT1_IN_GAG(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206)) → U21_GAG(T222, T223, T208, T206, T207, less88_in_gg(T222, T223))
INSERT1_IN_GAG(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206)) → LESS88_IN_GG(T222, T223)
LESS88_IN_GG(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316)))))))) → U6_GG(T315, T316, less146_in_gg(T315, T316))
LESS88_IN_GG(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316)))))))) → LESS146_IN_GG(T315, T316)
LESS146_IN_GG(s(T332), s(T333)) → U5_GG(T332, T333, less146_in_gg(T332, T333))
LESS146_IN_GG(s(T332), s(T333)) → LESS146_IN_GG(T332, T333)
U21_GAG(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → U22_GAG(T222, T223, T208, T206, T207, insert1_in_gag(s(T222), T208, T207))
U21_GAG(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → INSERT1_IN_GAG(s(T222), T208, T207)
INSERT1_IN_GAG(T348, tree(T349, T350, T353), tree(T349, T350, T352)) → U23_GAG(T348, T349, T350, T353, T352, less146_in_gg(T349, T348))
INSERT1_IN_GAG(T348, tree(T349, T350, T353), tree(T349, T350, T352)) → LESS146_IN_GG(T349, T348)
U23_GAG(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → U24_GAG(T348, T349, T350, T353, T352, insert1_in_gag(T348, T353, T352))
U23_GAG(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → INSERT1_IN_GAG(T348, T353, T352)
INSERT1_IN_GAG(s(T375), tree(0, T367, T370), tree(0, T367, T369)) → U25_GAG(T375, T367, T370, T369, insert1_in_gag(s(T375), T370, T369))
INSERT1_IN_GAG(s(T375), tree(0, T367, T370), tree(0, T367, T369)) → INSERT1_IN_GAG(s(T375), T370, T369)
INSERT1_IN_GAG(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369)) → U26_GAG(T383, T382, T367, T370, T369, less146_in_gg(T382, T383))
INSERT1_IN_GAG(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369)) → LESS146_IN_GG(T382, T383)
U26_GAG(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → U27_GAG(T383, T382, T367, T370, T369, insert1_in_gag(s(T383), T370, T369))
U26_GAG(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → INSERT1_IN_GAG(s(T383), T370, T369)

The TRS R consists of the following rules:

insert1_in_gag(T5, void, tree(T5, void, void)) → insert1_out_gag(T5, void, tree(T5, void, void))
insert1_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insert1_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insert1_in_gag(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void)) → U7_gag(T25, T20, p15_in_ga(T25, T20))
p15_in_ga(T25, T20) → U2_ga(T25, T20, less17_in_g(T25))
less17_in_g(s(T30)) → U1_g(T30, less17_in_g(T30))
U1_g(T30, less17_out_g(T30)) → less17_out_g(s(T30))
U2_ga(T25, T20, less17_out_g(T25)) → p15_out_ga(T25, T20)
U2_ga(T25, T20, less17_out_g(T25)) → U3_ga(T25, T20, insert1_in_gag(s(T25), T20, void))
insert1_in_gag(T56, tree(T56, void, T60), tree(T56, void, void)) → U8_gag(T56, T60, less17_in_g(T56))
U8_gag(T56, T60, less17_out_g(T56)) → insert1_out_gag(T56, tree(T56, void, T60), tree(T56, void, void))
U8_gag(T56, T60, less17_out_g(T56)) → U9_gag(T56, T60, insert1_in_gag(T56, T60, void))
insert1_in_gag(T83, tree(T83, void, T87), tree(T83, void, void)) → U10_gag(T83, T87, p28_in_ga(T83, T87))
p28_in_ga(s(T90), T87) → U4_ga(T90, T87, p15_in_ga(T90, T87))
U4_ga(T90, T87, p15_out_ga(T90, T87)) → p28_out_ga(s(T90), T87)
U10_gag(T83, T87, p28_out_ga(T83, T87)) → insert1_out_gag(T83, tree(T83, void, T87), tree(T83, void, void))
insert1_in_gag(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void)) → U11_gag(T105, T100, p15_in_ga(T105, T100))
U11_gag(T105, T100, p15_out_ga(T105, T100)) → insert1_out_gag(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void))
insert1_in_gag(T115, tree(T115, void, T119), tree(T115, void, void)) → U12_gag(T115, T119, p28_in_ga(T115, T119))
U12_gag(T115, T119, p28_out_ga(T115, T119)) → insert1_out_gag(T115, tree(T115, void, T119), tree(T115, void, void))
insert1_in_gag(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void)) → U13_gag(T132, T129, p15_in_ga(T132, T129))
U13_gag(T132, T129, p15_out_ga(T132, T129)) → insert1_out_gag(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void))
insert1_in_gag(T137, tree(T137, T138, T139), tree(T137, T138, T139)) → insert1_out_gag(T137, tree(T137, T138, T139), tree(T137, T138, T139))
insert1_in_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148)) → U14_gag(T155, T150, T148, T149, less17_in_g(T155))
U14_gag(T155, T150, T148, T149, less17_out_g(T155)) → insert1_out_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148))
U14_gag(T155, T150, T148, T149, less17_out_g(T155)) → U15_gag(T155, T150, T148, T149, insert1_in_gag(s(T155), T150, T149))
insert1_in_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174)) → U16_gag(T170, T172, T175, T174, less17_in_g(T170))
U16_gag(T170, T172, T175, T174, less17_out_g(T170)) → insert1_out_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174))
U16_gag(T170, T172, T175, T174, less17_out_g(T170)) → U17_gag(T170, T172, T175, T174, insert1_in_gag(T170, T175, T174))
insert1_in_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189)) → U18_gag(T193, T187, T190, T189, less17_in_g(T193))
U18_gag(T193, T187, T190, T189, less17_out_g(T193)) → insert1_out_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189))
U18_gag(T193, T187, T190, T189, less17_out_g(T193)) → U19_gag(T193, T187, T190, T189, insert1_in_gag(s(T193), T190, T189))
insert1_in_gag(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206)) → U20_gag(T213, T208, T206, T207, insert1_in_gag(0, T208, T207))
insert1_in_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206)) → U21_gag(T222, T223, T208, T206, T207, less88_in_gg(T222, T223))
less88_in_gg(0, s(T232)) → less88_out_gg(0, s(T232))
less88_in_gg(s(0), s(s(T245))) → less88_out_gg(s(0), s(s(T245)))
less88_in_gg(s(s(0)), s(s(s(T258)))) → less88_out_gg(s(s(0)), s(s(s(T258))))
less88_in_gg(s(s(s(0))), s(s(s(s(T271))))) → less88_out_gg(s(s(s(0))), s(s(s(s(T271)))))
less88_in_gg(s(s(s(s(0)))), s(s(s(s(s(T284)))))) → less88_out_gg(s(s(s(s(0)))), s(s(s(s(s(T284))))))
less88_in_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297))))))) → less88_out_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297)))))))
less88_in_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310)))))))) → less88_out_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310))))))))
less88_in_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316)))))))) → U6_gg(T315, T316, less146_in_gg(T315, T316))
less146_in_gg(0, s(T327)) → less146_out_gg(0, s(T327))
less146_in_gg(s(T332), s(T333)) → U5_gg(T332, T333, less146_in_gg(T332, T333))
U5_gg(T332, T333, less146_out_gg(T332, T333)) → less146_out_gg(s(T332), s(T333))
U6_gg(T315, T316, less146_out_gg(T315, T316)) → less88_out_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316))))))))
U21_gag(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → insert1_out_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206))
U21_gag(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → U22_gag(T222, T223, T208, T206, T207, insert1_in_gag(s(T222), T208, T207))
insert1_in_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352)) → U23_gag(T348, T349, T350, T353, T352, less146_in_gg(T349, T348))
U23_gag(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → insert1_out_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352))
U23_gag(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → U24_gag(T348, T349, T350, T353, T352, insert1_in_gag(T348, T353, T352))
insert1_in_gag(s(T375), tree(0, T367, T370), tree(0, T367, T369)) → U25_gag(T375, T367, T370, T369, insert1_in_gag(s(T375), T370, T369))
insert1_in_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369)) → U26_gag(T383, T382, T367, T370, T369, less146_in_gg(T382, T383))
U26_gag(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → insert1_out_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369))
U26_gag(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → U27_gag(T383, T382, T367, T370, T369, insert1_in_gag(s(T383), T370, T369))
U27_gag(T383, T382, T367, T370, T369, insert1_out_gag(s(T383), T370, T369)) → insert1_out_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369))
U25_gag(T375, T367, T370, T369, insert1_out_gag(s(T375), T370, T369)) → insert1_out_gag(s(T375), tree(0, T367, T370), tree(0, T367, T369))
U24_gag(T348, T349, T350, T353, T352, insert1_out_gag(T348, T353, T352)) → insert1_out_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352))
U22_gag(T222, T223, T208, T206, T207, insert1_out_gag(s(T222), T208, T207)) → insert1_out_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206))
U20_gag(T213, T208, T206, T207, insert1_out_gag(0, T208, T207)) → insert1_out_gag(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206))
U19_gag(T193, T187, T190, T189, insert1_out_gag(s(T193), T190, T189)) → insert1_out_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189))
U17_gag(T170, T172, T175, T174, insert1_out_gag(T170, T175, T174)) → insert1_out_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174))
U15_gag(T155, T150, T148, T149, insert1_out_gag(s(T155), T150, T149)) → insert1_out_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148))
U9_gag(T56, T60, insert1_out_gag(T56, T60, void)) → insert1_out_gag(T56, tree(T56, void, T60), tree(T56, void, void))
U3_ga(T25, T20, insert1_out_gag(s(T25), T20, void)) → p15_out_ga(T25, T20)
U7_gag(T25, T20, p15_out_ga(T25, T20)) → insert1_out_gag(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void))

The argument filtering Pi contains the following mapping:
insert1_in_gag(x1, x2, x3) = insert1_in_gag(x1, x3)
tree(x1, x2, x3) = tree(x1, x2, x3)
void = void
insert1_out_gag(x1, x2, x3) = insert1_out_gag
s(x1) = s(x1)
U7_gag(x1, x2, x3) = U7_gag(x3)
p15_in_ga(x1, x2) = p15_in_ga(x1)
U2_ga(x1, x2, x3) = U2_ga(x1, x3)
less17_in_g(x1) = less17_in_g(x1)
U1_g(x1, x2) = U1_g(x2)
less17_out_g(x1) = less17_out_g
p15_out_ga(x1, x2) = p15_out_ga
U3_ga(x1, x2, x3) = U3_ga(x3)
U8_gag(x1, x2, x3) = U8_gag(x1, x3)
U9_gag(x1, x2, x3) = U9_gag(x3)
U10_gag(x1, x2, x3) = U10_gag(x3)
p28_in_ga(x1, x2) = p28_in_ga(x1)
U4_ga(x1, x2, x3) = U4_ga(x3)
p28_out_ga(x1, x2) = p28_out_ga
U11_gag(x1, x2, x3) = U11_gag(x3)
U12_gag(x1, x2, x3) = U12_gag(x3)
U13_gag(x1, x2, x3) = U13_gag(x3)
U14_gag(x1, x2, x3, x4, x5) = U14_gag(x1, x4, x5)
U15_gag(x1, x2, x3, x4, x5) = U15_gag(x5)
U16_gag(x1, x2, x3, x4, x5) = U16_gag(x1, x4, x5)
U17_gag(x1, x2, x3, x4, x5) = U17_gag(x5)
U18_gag(x1, x2, x3, x4, x5) = U18_gag(x1, x4, x5)
U19_gag(x1, x2, x3, x4, x5) = U19_gag(x5)
0 = 0
U20_gag(x1, x2, x3, x4, x5) = U20_gag(x5)
U21_gag(x1, x2, x3, x4, x5, x6) = U21_gag(x1, x5, x6)
less88_in_gg(x1, x2) = less88_in_gg(x1, x2)
less88_out_gg(x1, x2) = less88_out_gg
U6_gg(x1, x2, x3) = U6_gg(x3)
less146_in_gg(x1, x2) = less146_in_gg(x1, x2)
less146_out_gg(x1, x2) = less146_out_gg
U5_gg(x1, x2, x3) = U5_gg(x3)
U22_gag(x1, x2, x3, x4, x5, x6) = U22_gag(x6)
U23_gag(x1, x2, x3, x4, x5, x6) = U23_gag(x1, x5, x6)
U24_gag(x1, x2, x3, x4, x5, x6) = U24_gag(x6)
U25_gag(x1, x2, x3, x4, x5) = U25_gag(x5)
U26_gag(x1, x2, x3, x4, x5, x6) = U26_gag(x1, x5, x6)
U27_gag(x1, x2, x3, x4, x5, x6) = U27_gag(x6)
INSERT1_IN_GAG(x1, x2, x3) = INSERT1_IN_GAG(x1, x3)
U7_GAG(x1, x2, x3) = U7_GAG(x3)
P15_IN_GA(x1, x2) = P15_IN_GA(x1)
U2_GA(x1, x2, x3) = U2_GA(x1, x3)
LESS17_IN_G(x1) = LESS17_IN_G(x1)
U1_G(x1, x2) = U1_G(x2)
U3_GA(x1, x2, x3) = U3_GA(x3)
U8_GAG(x1, x2, x3) = U8_GAG(x1, x3)
U9_GAG(x1, x2, x3) = U9_GAG(x3)
U10_GAG(x1, x2, x3) = U10_GAG(x3)
P28_IN_GA(x1, x2) = P28_IN_GA(x1)
U4_GA(x1, x2, x3) = U4_GA(x3)
U11_GAG(x1, x2, x3) = U11_GAG(x3)
U12_GAG(x1, x2, x3) = U12_GAG(x3)
U13_GAG(x1, x2, x3) = U13_GAG(x3)
U14_GAG(x1, x2, x3, x4, x5) = U14_GAG(x1, x4, x5)
U15_GAG(x1, x2, x3, x4, x5) = U15_GAG(x5)
U16_GAG(x1, x2, x3, x4, x5) = U16_GAG(x1, x4, x5)
U17_GAG(x1, x2, x3, x4, x5) = U17_GAG(x5)
U18_GAG(x1, x2, x3, x4, x5) = U18_GAG(x1, x4, x5)
U19_GAG(x1, x2, x3, x4, x5) = U19_GAG(x5)
U20_GAG(x1, x2, x3, x4, x5) = U20_GAG(x5)
U21_GAG(x1, x2, x3, x4, x5, x6) = U21_GAG(x1, x5, x6)
LESS88_IN_GG(x1, x2) = LESS88_IN_GG(x1, x2)
U6_GG(x1, x2, x3) = U6_GG(x3)
LESS146_IN_GG(x1, x2) = LESS146_IN_GG(x1, x2)
U5_GG(x1, x2, x3) = U5_GG(x3)
U22_GAG(x1, x2, x3, x4, x5, x6) = U22_GAG(x6)
U23_GAG(x1, x2, x3, x4, x5, x6) = U23_GAG(x1, x5, x6)
U24_GAG(x1, x2, x3, x4, x5, x6) = U24_GAG(x6)
U25_GAG(x1, x2, x3, x4, x5) = U25_GAG(x5)
U26_GAG(x1, x2, x3, x4, x5, x6) = U26_GAG(x1, x5, x6)
U27_GAG(x1, x2, x3, x4, x5, x6) = U27_GAG(x6)

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

(6) Obligation:

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

INSERT1_IN_GAG(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void)) → U7_GAG(T25, T20, p15_in_ga(T25, T20))
INSERT1_IN_GAG(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void)) → P15_IN_GA(T25, T20)
P15_IN_GA(T25, T20) → U2_GA(T25, T20, less17_in_g(T25))
P15_IN_GA(T25, T20) → LESS17_IN_G(T25)
LESS17_IN_G(s(T30)) → U1_G(T30, less17_in_g(T30))
LESS17_IN_G(s(T30)) → LESS17_IN_G(T30)
U2_GA(T25, T20, less17_out_g(T25)) → U3_GA(T25, T20, insert1_in_gag(s(T25), T20, void))
U2_GA(T25, T20, less17_out_g(T25)) → INSERT1_IN_GAG(s(T25), T20, void)
INSERT1_IN_GAG(T56, tree(T56, void, T60), tree(T56, void, void)) → U8_GAG(T56, T60, less17_in_g(T56))
INSERT1_IN_GAG(T56, tree(T56, void, T60), tree(T56, void, void)) → LESS17_IN_G(T56)
U8_GAG(T56, T60, less17_out_g(T56)) → U9_GAG(T56, T60, insert1_in_gag(T56, T60, void))
U8_GAG(T56, T60, less17_out_g(T56)) → INSERT1_IN_GAG(T56, T60, void)
INSERT1_IN_GAG(T83, tree(T83, void, T87), tree(T83, void, void)) → U10_GAG(T83, T87, p28_in_ga(T83, T87))
INSERT1_IN_GAG(T83, tree(T83, void, T87), tree(T83, void, void)) → P28_IN_GA(T83, T87)
P28_IN_GA(s(T90), T87) → U4_GA(T90, T87, p15_in_ga(T90, T87))
P28_IN_GA(s(T90), T87) → P15_IN_GA(T90, T87)
INSERT1_IN_GAG(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void)) → U11_GAG(T105, T100, p15_in_ga(T105, T100))
INSERT1_IN_GAG(T115, tree(T115, void, T119), tree(T115, void, void)) → U12_GAG(T115, T119, p28_in_ga(T115, T119))
INSERT1_IN_GAG(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void)) → U13_GAG(T132, T129, p15_in_ga(T132, T129))
INSERT1_IN_GAG(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void)) → P15_IN_GA(T132, T129)
INSERT1_IN_GAG(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148)) → U14_GAG(T155, T150, T148, T149, less17_in_g(T155))
INSERT1_IN_GAG(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148)) → LESS17_IN_G(T155)
U14_GAG(T155, T150, T148, T149, less17_out_g(T155)) → U15_GAG(T155, T150, T148, T149, insert1_in_gag(s(T155), T150, T149))
U14_GAG(T155, T150, T148, T149, less17_out_g(T155)) → INSERT1_IN_GAG(s(T155), T150, T149)
INSERT1_IN_GAG(T170, tree(T170, T172, T175), tree(T170, T172, T174)) → U16_GAG(T170, T172, T175, T174, less17_in_g(T170))
INSERT1_IN_GAG(T170, tree(T170, T172, T175), tree(T170, T172, T174)) → LESS17_IN_G(T170)
U16_GAG(T170, T172, T175, T174, less17_out_g(T170)) → U17_GAG(T170, T172, T175, T174, insert1_in_gag(T170, T175, T174))
U16_GAG(T170, T172, T175, T174, less17_out_g(T170)) → INSERT1_IN_GAG(T170, T175, T174)
INSERT1_IN_GAG(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189)) → U18_GAG(T193, T187, T190, T189, less17_in_g(T193))
INSERT1_IN_GAG(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189)) → LESS17_IN_G(T193)
U18_GAG(T193, T187, T190, T189, less17_out_g(T193)) → U19_GAG(T193, T187, T190, T189, insert1_in_gag(s(T193), T190, T189))
U18_GAG(T193, T187, T190, T189, less17_out_g(T193)) → INSERT1_IN_GAG(s(T193), T190, T189)
INSERT1_IN_GAG(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206)) → U20_GAG(T213, T208, T206, T207, insert1_in_gag(0, T208, T207))
INSERT1_IN_GAG(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206)) → INSERT1_IN_GAG(0, T208, T207)
INSERT1_IN_GAG(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206)) → U21_GAG(T222, T223, T208, T206, T207, less88_in_gg(T222, T223))
INSERT1_IN_GAG(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206)) → LESS88_IN_GG(T222, T223)
LESS88_IN_GG(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316)))))))) → U6_GG(T315, T316, less146_in_gg(T315, T316))
LESS88_IN_GG(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316)))))))) → LESS146_IN_GG(T315, T316)
LESS146_IN_GG(s(T332), s(T333)) → U5_GG(T332, T333, less146_in_gg(T332, T333))
LESS146_IN_GG(s(T332), s(T333)) → LESS146_IN_GG(T332, T333)
U21_GAG(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → U22_GAG(T222, T223, T208, T206, T207, insert1_in_gag(s(T222), T208, T207))
U21_GAG(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → INSERT1_IN_GAG(s(T222), T208, T207)
INSERT1_IN_GAG(T348, tree(T349, T350, T353), tree(T349, T350, T352)) → U23_GAG(T348, T349, T350, T353, T352, less146_in_gg(T349, T348))
INSERT1_IN_GAG(T348, tree(T349, T350, T353), tree(T349, T350, T352)) → LESS146_IN_GG(T349, T348)
U23_GAG(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → U24_GAG(T348, T349, T350, T353, T352, insert1_in_gag(T348, T353, T352))
U23_GAG(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → INSERT1_IN_GAG(T348, T353, T352)
INSERT1_IN_GAG(s(T375), tree(0, T367, T370), tree(0, T367, T369)) → U25_GAG(T375, T367, T370, T369, insert1_in_gag(s(T375), T370, T369))
INSERT1_IN_GAG(s(T375), tree(0, T367, T370), tree(0, T367, T369)) → INSERT1_IN_GAG(s(T375), T370, T369)
INSERT1_IN_GAG(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369)) → U26_GAG(T383, T382, T367, T370, T369, less146_in_gg(T382, T383))
INSERT1_IN_GAG(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369)) → LESS146_IN_GG(T382, T383)
U26_GAG(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → U27_GAG(T383, T382, T367, T370, T369, insert1_in_gag(s(T383), T370, T369))
U26_GAG(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → INSERT1_IN_GAG(s(T383), T370, T369)

The TRS R consists of the following rules:

insert1_in_gag(T5, void, tree(T5, void, void)) → insert1_out_gag(T5, void, tree(T5, void, void))
insert1_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insert1_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insert1_in_gag(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void)) → U7_gag(T25, T20, p15_in_ga(T25, T20))
p15_in_ga(T25, T20) → U2_ga(T25, T20, less17_in_g(T25))
less17_in_g(s(T30)) → U1_g(T30, less17_in_g(T30))
U1_g(T30, less17_out_g(T30)) → less17_out_g(s(T30))
U2_ga(T25, T20, less17_out_g(T25)) → p15_out_ga(T25, T20)
U2_ga(T25, T20, less17_out_g(T25)) → U3_ga(T25, T20, insert1_in_gag(s(T25), T20, void))
insert1_in_gag(T56, tree(T56, void, T60), tree(T56, void, void)) → U8_gag(T56, T60, less17_in_g(T56))
U8_gag(T56, T60, less17_out_g(T56)) → insert1_out_gag(T56, tree(T56, void, T60), tree(T56, void, void))
U8_gag(T56, T60, less17_out_g(T56)) → U9_gag(T56, T60, insert1_in_gag(T56, T60, void))
insert1_in_gag(T83, tree(T83, void, T87), tree(T83, void, void)) → U10_gag(T83, T87, p28_in_ga(T83, T87))
p28_in_ga(s(T90), T87) → U4_ga(T90, T87, p15_in_ga(T90, T87))
U4_ga(T90, T87, p15_out_ga(T90, T87)) → p28_out_ga(s(T90), T87)
U10_gag(T83, T87, p28_out_ga(T83, T87)) → insert1_out_gag(T83, tree(T83, void, T87), tree(T83, void, void))
insert1_in_gag(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void)) → U11_gag(T105, T100, p15_in_ga(T105, T100))
U11_gag(T105, T100, p15_out_ga(T105, T100)) → insert1_out_gag(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void))
insert1_in_gag(T115, tree(T115, void, T119), tree(T115, void, void)) → U12_gag(T115, T119, p28_in_ga(T115, T119))
U12_gag(T115, T119, p28_out_ga(T115, T119)) → insert1_out_gag(T115, tree(T115, void, T119), tree(T115, void, void))
insert1_in_gag(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void)) → U13_gag(T132, T129, p15_in_ga(T132, T129))
U13_gag(T132, T129, p15_out_ga(T132, T129)) → insert1_out_gag(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void))
insert1_in_gag(T137, tree(T137, T138, T139), tree(T137, T138, T139)) → insert1_out_gag(T137, tree(T137, T138, T139), tree(T137, T138, T139))
insert1_in_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148)) → U14_gag(T155, T150, T148, T149, less17_in_g(T155))
U14_gag(T155, T150, T148, T149, less17_out_g(T155)) → insert1_out_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148))
U14_gag(T155, T150, T148, T149, less17_out_g(T155)) → U15_gag(T155, T150, T148, T149, insert1_in_gag(s(T155), T150, T149))
insert1_in_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174)) → U16_gag(T170, T172, T175, T174, less17_in_g(T170))
U16_gag(T170, T172, T175, T174, less17_out_g(T170)) → insert1_out_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174))
U16_gag(T170, T172, T175, T174, less17_out_g(T170)) → U17_gag(T170, T172, T175, T174, insert1_in_gag(T170, T175, T174))
insert1_in_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189)) → U18_gag(T193, T187, T190, T189, less17_in_g(T193))
U18_gag(T193, T187, T190, T189, less17_out_g(T193)) → insert1_out_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189))
U18_gag(T193, T187, T190, T189, less17_out_g(T193)) → U19_gag(T193, T187, T190, T189, insert1_in_gag(s(T193), T190, T189))
insert1_in_gag(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206)) → U20_gag(T213, T208, T206, T207, insert1_in_gag(0, T208, T207))
insert1_in_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206)) → U21_gag(T222, T223, T208, T206, T207, less88_in_gg(T222, T223))
less88_in_gg(0, s(T232)) → less88_out_gg(0, s(T232))
less88_in_gg(s(0), s(s(T245))) → less88_out_gg(s(0), s(s(T245)))
less88_in_gg(s(s(0)), s(s(s(T258)))) → less88_out_gg(s(s(0)), s(s(s(T258))))
less88_in_gg(s(s(s(0))), s(s(s(s(T271))))) → less88_out_gg(s(s(s(0))), s(s(s(s(T271)))))
less88_in_gg(s(s(s(s(0)))), s(s(s(s(s(T284)))))) → less88_out_gg(s(s(s(s(0)))), s(s(s(s(s(T284))))))
less88_in_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297))))))) → less88_out_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297)))))))
less88_in_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310)))))))) → less88_out_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310))))))))
less88_in_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316)))))))) → U6_gg(T315, T316, less146_in_gg(T315, T316))
less146_in_gg(0, s(T327)) → less146_out_gg(0, s(T327))
less146_in_gg(s(T332), s(T333)) → U5_gg(T332, T333, less146_in_gg(T332, T333))
U5_gg(T332, T333, less146_out_gg(T332, T333)) → less146_out_gg(s(T332), s(T333))
U6_gg(T315, T316, less146_out_gg(T315, T316)) → less88_out_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316))))))))
U21_gag(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → insert1_out_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206))
U21_gag(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → U22_gag(T222, T223, T208, T206, T207, insert1_in_gag(s(T222), T208, T207))
insert1_in_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352)) → U23_gag(T348, T349, T350, T353, T352, less146_in_gg(T349, T348))
U23_gag(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → insert1_out_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352))
U23_gag(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → U24_gag(T348, T349, T350, T353, T352, insert1_in_gag(T348, T353, T352))
insert1_in_gag(s(T375), tree(0, T367, T370), tree(0, T367, T369)) → U25_gag(T375, T367, T370, T369, insert1_in_gag(s(T375), T370, T369))
insert1_in_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369)) → U26_gag(T383, T382, T367, T370, T369, less146_in_gg(T382, T383))
U26_gag(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → insert1_out_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369))
U26_gag(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → U27_gag(T383, T382, T367, T370, T369, insert1_in_gag(s(T383), T370, T369))
U27_gag(T383, T382, T367, T370, T369, insert1_out_gag(s(T383), T370, T369)) → insert1_out_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369))
U25_gag(T375, T367, T370, T369, insert1_out_gag(s(T375), T370, T369)) → insert1_out_gag(s(T375), tree(0, T367, T370), tree(0, T367, T369))
U24_gag(T348, T349, T350, T353, T352, insert1_out_gag(T348, T353, T352)) → insert1_out_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352))
U22_gag(T222, T223, T208, T206, T207, insert1_out_gag(s(T222), T208, T207)) → insert1_out_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206))
U20_gag(T213, T208, T206, T207, insert1_out_gag(0, T208, T207)) → insert1_out_gag(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206))
U19_gag(T193, T187, T190, T189, insert1_out_gag(s(T193), T190, T189)) → insert1_out_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189))
U17_gag(T170, T172, T175, T174, insert1_out_gag(T170, T175, T174)) → insert1_out_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174))
U15_gag(T155, T150, T148, T149, insert1_out_gag(s(T155), T150, T149)) → insert1_out_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148))
U9_gag(T56, T60, insert1_out_gag(T56, T60, void)) → insert1_out_gag(T56, tree(T56, void, T60), tree(T56, void, void))
U3_ga(T25, T20, insert1_out_gag(s(T25), T20, void)) → p15_out_ga(T25, T20)
U7_gag(T25, T20, p15_out_ga(T25, T20)) → insert1_out_gag(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void))

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 3 SCCs with 36 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

LESS146_IN_GG(s(T332), s(T333)) → LESS146_IN_GG(T332, T333)

The TRS R consists of the following rules:

insert1_in_gag(T5, void, tree(T5, void, void)) → insert1_out_gag(T5, void, tree(T5, void, void))
insert1_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insert1_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insert1_in_gag(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void)) → U7_gag(T25, T20, p15_in_ga(T25, T20))
p15_in_ga(T25, T20) → U2_ga(T25, T20, less17_in_g(T25))
less17_in_g(s(T30)) → U1_g(T30, less17_in_g(T30))
U1_g(T30, less17_out_g(T30)) → less17_out_g(s(T30))
U2_ga(T25, T20, less17_out_g(T25)) → p15_out_ga(T25, T20)
U2_ga(T25, T20, less17_out_g(T25)) → U3_ga(T25, T20, insert1_in_gag(s(T25), T20, void))
insert1_in_gag(T56, tree(T56, void, T60), tree(T56, void, void)) → U8_gag(T56, T60, less17_in_g(T56))
U8_gag(T56, T60, less17_out_g(T56)) → insert1_out_gag(T56, tree(T56, void, T60), tree(T56, void, void))
U8_gag(T56, T60, less17_out_g(T56)) → U9_gag(T56, T60, insert1_in_gag(T56, T60, void))
insert1_in_gag(T83, tree(T83, void, T87), tree(T83, void, void)) → U10_gag(T83, T87, p28_in_ga(T83, T87))
p28_in_ga(s(T90), T87) → U4_ga(T90, T87, p15_in_ga(T90, T87))
U4_ga(T90, T87, p15_out_ga(T90, T87)) → p28_out_ga(s(T90), T87)
U10_gag(T83, T87, p28_out_ga(T83, T87)) → insert1_out_gag(T83, tree(T83, void, T87), tree(T83, void, void))
insert1_in_gag(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void)) → U11_gag(T105, T100, p15_in_ga(T105, T100))
U11_gag(T105, T100, p15_out_ga(T105, T100)) → insert1_out_gag(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void))
insert1_in_gag(T115, tree(T115, void, T119), tree(T115, void, void)) → U12_gag(T115, T119, p28_in_ga(T115, T119))
U12_gag(T115, T119, p28_out_ga(T115, T119)) → insert1_out_gag(T115, tree(T115, void, T119), tree(T115, void, void))
insert1_in_gag(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void)) → U13_gag(T132, T129, p15_in_ga(T132, T129))
U13_gag(T132, T129, p15_out_ga(T132, T129)) → insert1_out_gag(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void))
insert1_in_gag(T137, tree(T137, T138, T139), tree(T137, T138, T139)) → insert1_out_gag(T137, tree(T137, T138, T139), tree(T137, T138, T139))
insert1_in_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148)) → U14_gag(T155, T150, T148, T149, less17_in_g(T155))
U14_gag(T155, T150, T148, T149, less17_out_g(T155)) → insert1_out_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148))
U14_gag(T155, T150, T148, T149, less17_out_g(T155)) → U15_gag(T155, T150, T148, T149, insert1_in_gag(s(T155), T150, T149))
insert1_in_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174)) → U16_gag(T170, T172, T175, T174, less17_in_g(T170))
U16_gag(T170, T172, T175, T174, less17_out_g(T170)) → insert1_out_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174))
U16_gag(T170, T172, T175, T174, less17_out_g(T170)) → U17_gag(T170, T172, T175, T174, insert1_in_gag(T170, T175, T174))
insert1_in_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189)) → U18_gag(T193, T187, T190, T189, less17_in_g(T193))
U18_gag(T193, T187, T190, T189, less17_out_g(T193)) → insert1_out_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189))
U18_gag(T193, T187, T190, T189, less17_out_g(T193)) → U19_gag(T193, T187, T190, T189, insert1_in_gag(s(T193), T190, T189))
insert1_in_gag(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206)) → U20_gag(T213, T208, T206, T207, insert1_in_gag(0, T208, T207))
insert1_in_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206)) → U21_gag(T222, T223, T208, T206, T207, less88_in_gg(T222, T223))
less88_in_gg(0, s(T232)) → less88_out_gg(0, s(T232))
less88_in_gg(s(0), s(s(T245))) → less88_out_gg(s(0), s(s(T245)))
less88_in_gg(s(s(0)), s(s(s(T258)))) → less88_out_gg(s(s(0)), s(s(s(T258))))
less88_in_gg(s(s(s(0))), s(s(s(s(T271))))) → less88_out_gg(s(s(s(0))), s(s(s(s(T271)))))
less88_in_gg(s(s(s(s(0)))), s(s(s(s(s(T284)))))) → less88_out_gg(s(s(s(s(0)))), s(s(s(s(s(T284))))))
less88_in_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297))))))) → less88_out_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297)))))))
less88_in_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310)))))))) → less88_out_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310))))))))
less88_in_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316)))))))) → U6_gg(T315, T316, less146_in_gg(T315, T316))
less146_in_gg(0, s(T327)) → less146_out_gg(0, s(T327))
less146_in_gg(s(T332), s(T333)) → U5_gg(T332, T333, less146_in_gg(T332, T333))
U5_gg(T332, T333, less146_out_gg(T332, T333)) → less146_out_gg(s(T332), s(T333))
U6_gg(T315, T316, less146_out_gg(T315, T316)) → less88_out_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316))))))))
U21_gag(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → insert1_out_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206))
U21_gag(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → U22_gag(T222, T223, T208, T206, T207, insert1_in_gag(s(T222), T208, T207))
insert1_in_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352)) → U23_gag(T348, T349, T350, T353, T352, less146_in_gg(T349, T348))
U23_gag(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → insert1_out_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352))
U23_gag(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → U24_gag(T348, T349, T350, T353, T352, insert1_in_gag(T348, T353, T352))
insert1_in_gag(s(T375), tree(0, T367, T370), tree(0, T367, T369)) → U25_gag(T375, T367, T370, T369, insert1_in_gag(s(T375), T370, T369))
insert1_in_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369)) → U26_gag(T383, T382, T367, T370, T369, less146_in_gg(T382, T383))
U26_gag(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → insert1_out_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369))
U26_gag(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → U27_gag(T383, T382, T367, T370, T369, insert1_in_gag(s(T383), T370, T369))
U27_gag(T383, T382, T367, T370, T369, insert1_out_gag(s(T383), T370, T369)) → insert1_out_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369))
U25_gag(T375, T367, T370, T369, insert1_out_gag(s(T375), T370, T369)) → insert1_out_gag(s(T375), tree(0, T367, T370), tree(0, T367, T369))
U24_gag(T348, T349, T350, T353, T352, insert1_out_gag(T348, T353, T352)) → insert1_out_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352))
U22_gag(T222, T223, T208, T206, T207, insert1_out_gag(s(T222), T208, T207)) → insert1_out_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206))
U20_gag(T213, T208, T206, T207, insert1_out_gag(0, T208, T207)) → insert1_out_gag(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206))
U19_gag(T193, T187, T190, T189, insert1_out_gag(s(T193), T190, T189)) → insert1_out_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189))
U17_gag(T170, T172, T175, T174, insert1_out_gag(T170, T175, T174)) → insert1_out_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174))
U15_gag(T155, T150, T148, T149, insert1_out_gag(s(T155), T150, T149)) → insert1_out_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148))
U9_gag(T56, T60, insert1_out_gag(T56, T60, void)) → insert1_out_gag(T56, tree(T56, void, T60), tree(T56, void, void))
U3_ga(T25, T20, insert1_out_gag(s(T25), T20, void)) → p15_out_ga(T25, T20)
U7_gag(T25, T20, p15_out_ga(T25, T20)) → insert1_out_gag(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void))

(10) UsableRulesProof (EQUIVALENT transformation)

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

(11) Obligation:

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

LESS146_IN_GG(s(T332), s(T333)) → LESS146_IN_GG(T332, T333)

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

(12) PiDPToQDPProof (EQUIVALENT transformation)

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

(13) Obligation:

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

LESS146_IN_GG(s(T332), s(T333)) → LESS146_IN_GG(T332, T333)

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

(14) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

LESS146_IN_GG(s(T332), s(T333)) → LESS146_IN_GG(T332, T333)
The graph contains the following edges 1 > 1, 2 > 2

(15) YES

(16) Obligation:

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

LESS17_IN_G(s(T30)) → LESS17_IN_G(T30)

The TRS R consists of the following rules:

insert1_in_gag(T5, void, tree(T5, void, void)) → insert1_out_gag(T5, void, tree(T5, void, void))
insert1_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insert1_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insert1_in_gag(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void)) → U7_gag(T25, T20, p15_in_ga(T25, T20))
p15_in_ga(T25, T20) → U2_ga(T25, T20, less17_in_g(T25))
less17_in_g(s(T30)) → U1_g(T30, less17_in_g(T30))
U1_g(T30, less17_out_g(T30)) → less17_out_g(s(T30))
U2_ga(T25, T20, less17_out_g(T25)) → p15_out_ga(T25, T20)
U2_ga(T25, T20, less17_out_g(T25)) → U3_ga(T25, T20, insert1_in_gag(s(T25), T20, void))
insert1_in_gag(T56, tree(T56, void, T60), tree(T56, void, void)) → U8_gag(T56, T60, less17_in_g(T56))
U8_gag(T56, T60, less17_out_g(T56)) → insert1_out_gag(T56, tree(T56, void, T60), tree(T56, void, void))
U8_gag(T56, T60, less17_out_g(T56)) → U9_gag(T56, T60, insert1_in_gag(T56, T60, void))
insert1_in_gag(T83, tree(T83, void, T87), tree(T83, void, void)) → U10_gag(T83, T87, p28_in_ga(T83, T87))
p28_in_ga(s(T90), T87) → U4_ga(T90, T87, p15_in_ga(T90, T87))
U4_ga(T90, T87, p15_out_ga(T90, T87)) → p28_out_ga(s(T90), T87)
U10_gag(T83, T87, p28_out_ga(T83, T87)) → insert1_out_gag(T83, tree(T83, void, T87), tree(T83, void, void))
insert1_in_gag(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void)) → U11_gag(T105, T100, p15_in_ga(T105, T100))
U11_gag(T105, T100, p15_out_ga(T105, T100)) → insert1_out_gag(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void))
insert1_in_gag(T115, tree(T115, void, T119), tree(T115, void, void)) → U12_gag(T115, T119, p28_in_ga(T115, T119))
U12_gag(T115, T119, p28_out_ga(T115, T119)) → insert1_out_gag(T115, tree(T115, void, T119), tree(T115, void, void))
insert1_in_gag(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void)) → U13_gag(T132, T129, p15_in_ga(T132, T129))
U13_gag(T132, T129, p15_out_ga(T132, T129)) → insert1_out_gag(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void))
insert1_in_gag(T137, tree(T137, T138, T139), tree(T137, T138, T139)) → insert1_out_gag(T137, tree(T137, T138, T139), tree(T137, T138, T139))
insert1_in_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148)) → U14_gag(T155, T150, T148, T149, less17_in_g(T155))
U14_gag(T155, T150, T148, T149, less17_out_g(T155)) → insert1_out_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148))
U14_gag(T155, T150, T148, T149, less17_out_g(T155)) → U15_gag(T155, T150, T148, T149, insert1_in_gag(s(T155), T150, T149))
insert1_in_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174)) → U16_gag(T170, T172, T175, T174, less17_in_g(T170))
U16_gag(T170, T172, T175, T174, less17_out_g(T170)) → insert1_out_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174))
U16_gag(T170, T172, T175, T174, less17_out_g(T170)) → U17_gag(T170, T172, T175, T174, insert1_in_gag(T170, T175, T174))
insert1_in_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189)) → U18_gag(T193, T187, T190, T189, less17_in_g(T193))
U18_gag(T193, T187, T190, T189, less17_out_g(T193)) → insert1_out_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189))
U18_gag(T193, T187, T190, T189, less17_out_g(T193)) → U19_gag(T193, T187, T190, T189, insert1_in_gag(s(T193), T190, T189))
insert1_in_gag(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206)) → U20_gag(T213, T208, T206, T207, insert1_in_gag(0, T208, T207))
insert1_in_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206)) → U21_gag(T222, T223, T208, T206, T207, less88_in_gg(T222, T223))
less88_in_gg(0, s(T232)) → less88_out_gg(0, s(T232))
less88_in_gg(s(0), s(s(T245))) → less88_out_gg(s(0), s(s(T245)))
less88_in_gg(s(s(0)), s(s(s(T258)))) → less88_out_gg(s(s(0)), s(s(s(T258))))
less88_in_gg(s(s(s(0))), s(s(s(s(T271))))) → less88_out_gg(s(s(s(0))), s(s(s(s(T271)))))
less88_in_gg(s(s(s(s(0)))), s(s(s(s(s(T284)))))) → less88_out_gg(s(s(s(s(0)))), s(s(s(s(s(T284))))))
less88_in_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297))))))) → less88_out_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297)))))))
less88_in_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310)))))))) → less88_out_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310))))))))
less88_in_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316)))))))) → U6_gg(T315, T316, less146_in_gg(T315, T316))
less146_in_gg(0, s(T327)) → less146_out_gg(0, s(T327))
less146_in_gg(s(T332), s(T333)) → U5_gg(T332, T333, less146_in_gg(T332, T333))
U5_gg(T332, T333, less146_out_gg(T332, T333)) → less146_out_gg(s(T332), s(T333))
U6_gg(T315, T316, less146_out_gg(T315, T316)) → less88_out_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316))))))))
U21_gag(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → insert1_out_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206))
U21_gag(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → U22_gag(T222, T223, T208, T206, T207, insert1_in_gag(s(T222), T208, T207))
insert1_in_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352)) → U23_gag(T348, T349, T350, T353, T352, less146_in_gg(T349, T348))
U23_gag(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → insert1_out_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352))
U23_gag(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → U24_gag(T348, T349, T350, T353, T352, insert1_in_gag(T348, T353, T352))
insert1_in_gag(s(T375), tree(0, T367, T370), tree(0, T367, T369)) → U25_gag(T375, T367, T370, T369, insert1_in_gag(s(T375), T370, T369))
insert1_in_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369)) → U26_gag(T383, T382, T367, T370, T369, less146_in_gg(T382, T383))
U26_gag(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → insert1_out_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369))
U26_gag(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → U27_gag(T383, T382, T367, T370, T369, insert1_in_gag(s(T383), T370, T369))
U27_gag(T383, T382, T367, T370, T369, insert1_out_gag(s(T383), T370, T369)) → insert1_out_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369))
U25_gag(T375, T367, T370, T369, insert1_out_gag(s(T375), T370, T369)) → insert1_out_gag(s(T375), tree(0, T367, T370), tree(0, T367, T369))
U24_gag(T348, T349, T350, T353, T352, insert1_out_gag(T348, T353, T352)) → insert1_out_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352))
U22_gag(T222, T223, T208, T206, T207, insert1_out_gag(s(T222), T208, T207)) → insert1_out_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206))
U20_gag(T213, T208, T206, T207, insert1_out_gag(0, T208, T207)) → insert1_out_gag(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206))
U19_gag(T193, T187, T190, T189, insert1_out_gag(s(T193), T190, T189)) → insert1_out_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189))
U17_gag(T170, T172, T175, T174, insert1_out_gag(T170, T175, T174)) → insert1_out_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174))
U15_gag(T155, T150, T148, T149, insert1_out_gag(s(T155), T150, T149)) → insert1_out_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148))
U9_gag(T56, T60, insert1_out_gag(T56, T60, void)) → insert1_out_gag(T56, tree(T56, void, T60), tree(T56, void, void))
U3_ga(T25, T20, insert1_out_gag(s(T25), T20, void)) → p15_out_ga(T25, T20)
U7_gag(T25, T20, p15_out_ga(T25, T20)) → insert1_out_gag(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void))

(17) UsableRulesProof (EQUIVALENT transformation)

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

(18) Obligation:

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

LESS17_IN_G(s(T30)) → LESS17_IN_G(T30)

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

(19) PiDPToQDPProof (EQUIVALENT transformation)

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

(20) Obligation:

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

LESS17_IN_G(s(T30)) → LESS17_IN_G(T30)

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

(21) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

LESS17_IN_G(s(T30)) → LESS17_IN_G(T30)
The graph contains the following edges 1 > 1

(22) YES

(23) Obligation:

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

INSERT1_IN_GAG(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148)) → U14_GAG(T155, T150, T148, T149, less17_in_g(T155))
U14_GAG(T155, T150, T148, T149, less17_out_g(T155)) → INSERT1_IN_GAG(s(T155), T150, T149)
INSERT1_IN_GAG(T170, tree(T170, T172, T175), tree(T170, T172, T174)) → U16_GAG(T170, T172, T175, T174, less17_in_g(T170))
U16_GAG(T170, T172, T175, T174, less17_out_g(T170)) → INSERT1_IN_GAG(T170, T175, T174)
INSERT1_IN_GAG(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189)) → U18_GAG(T193, T187, T190, T189, less17_in_g(T193))
U18_GAG(T193, T187, T190, T189, less17_out_g(T193)) → INSERT1_IN_GAG(s(T193), T190, T189)
INSERT1_IN_GAG(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206)) → U21_GAG(T222, T223, T208, T206, T207, less88_in_gg(T222, T223))
U21_GAG(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → INSERT1_IN_GAG(s(T222), T208, T207)
INSERT1_IN_GAG(T348, tree(T349, T350, T353), tree(T349, T350, T352)) → U23_GAG(T348, T349, T350, T353, T352, less146_in_gg(T349, T348))
U23_GAG(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → INSERT1_IN_GAG(T348, T353, T352)
INSERT1_IN_GAG(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206)) → INSERT1_IN_GAG(0, T208, T207)
INSERT1_IN_GAG(s(T375), tree(0, T367, T370), tree(0, T367, T369)) → INSERT1_IN_GAG(s(T375), T370, T369)
INSERT1_IN_GAG(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369)) → U26_GAG(T383, T382, T367, T370, T369, less146_in_gg(T382, T383))
U26_GAG(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → INSERT1_IN_GAG(s(T383), T370, T369)

The TRS R consists of the following rules:

insert1_in_gag(T5, void, tree(T5, void, void)) → insert1_out_gag(T5, void, tree(T5, void, void))
insert1_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insert1_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insert1_in_gag(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void)) → U7_gag(T25, T20, p15_in_ga(T25, T20))
p15_in_ga(T25, T20) → U2_ga(T25, T20, less17_in_g(T25))
less17_in_g(s(T30)) → U1_g(T30, less17_in_g(T30))
U1_g(T30, less17_out_g(T30)) → less17_out_g(s(T30))
U2_ga(T25, T20, less17_out_g(T25)) → p15_out_ga(T25, T20)
U2_ga(T25, T20, less17_out_g(T25)) → U3_ga(T25, T20, insert1_in_gag(s(T25), T20, void))
insert1_in_gag(T56, tree(T56, void, T60), tree(T56, void, void)) → U8_gag(T56, T60, less17_in_g(T56))
U8_gag(T56, T60, less17_out_g(T56)) → insert1_out_gag(T56, tree(T56, void, T60), tree(T56, void, void))
U8_gag(T56, T60, less17_out_g(T56)) → U9_gag(T56, T60, insert1_in_gag(T56, T60, void))
insert1_in_gag(T83, tree(T83, void, T87), tree(T83, void, void)) → U10_gag(T83, T87, p28_in_ga(T83, T87))
p28_in_ga(s(T90), T87) → U4_ga(T90, T87, p15_in_ga(T90, T87))
U4_ga(T90, T87, p15_out_ga(T90, T87)) → p28_out_ga(s(T90), T87)
U10_gag(T83, T87, p28_out_ga(T83, T87)) → insert1_out_gag(T83, tree(T83, void, T87), tree(T83, void, void))
insert1_in_gag(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void)) → U11_gag(T105, T100, p15_in_ga(T105, T100))
U11_gag(T105, T100, p15_out_ga(T105, T100)) → insert1_out_gag(s(T105), tree(s(T105), T100, void), tree(s(T105), void, void))
insert1_in_gag(T115, tree(T115, void, T119), tree(T115, void, void)) → U12_gag(T115, T119, p28_in_ga(T115, T119))
U12_gag(T115, T119, p28_out_ga(T115, T119)) → insert1_out_gag(T115, tree(T115, void, T119), tree(T115, void, void))
insert1_in_gag(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void)) → U13_gag(T132, T129, p15_in_ga(T132, T129))
U13_gag(T132, T129, p15_out_ga(T132, T129)) → insert1_out_gag(s(T132), tree(s(T132), void, T129), tree(s(T132), void, void))
insert1_in_gag(T137, tree(T137, T138, T139), tree(T137, T138, T139)) → insert1_out_gag(T137, tree(T137, T138, T139), tree(T137, T138, T139))
insert1_in_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148)) → U14_gag(T155, T150, T148, T149, less17_in_g(T155))
U14_gag(T155, T150, T148, T149, less17_out_g(T155)) → insert1_out_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148))
U14_gag(T155, T150, T148, T149, less17_out_g(T155)) → U15_gag(T155, T150, T148, T149, insert1_in_gag(s(T155), T150, T149))
insert1_in_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174)) → U16_gag(T170, T172, T175, T174, less17_in_g(T170))
U16_gag(T170, T172, T175, T174, less17_out_g(T170)) → insert1_out_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174))
U16_gag(T170, T172, T175, T174, less17_out_g(T170)) → U17_gag(T170, T172, T175, T174, insert1_in_gag(T170, T175, T174))
insert1_in_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189)) → U18_gag(T193, T187, T190, T189, less17_in_g(T193))
U18_gag(T193, T187, T190, T189, less17_out_g(T193)) → insert1_out_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189))
U18_gag(T193, T187, T190, T189, less17_out_g(T193)) → U19_gag(T193, T187, T190, T189, insert1_in_gag(s(T193), T190, T189))
insert1_in_gag(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206)) → U20_gag(T213, T208, T206, T207, insert1_in_gag(0, T208, T207))
insert1_in_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206)) → U21_gag(T222, T223, T208, T206, T207, less88_in_gg(T222, T223))
less88_in_gg(0, s(T232)) → less88_out_gg(0, s(T232))
less88_in_gg(s(0), s(s(T245))) → less88_out_gg(s(0), s(s(T245)))
less88_in_gg(s(s(0)), s(s(s(T258)))) → less88_out_gg(s(s(0)), s(s(s(T258))))
less88_in_gg(s(s(s(0))), s(s(s(s(T271))))) → less88_out_gg(s(s(s(0))), s(s(s(s(T271)))))
less88_in_gg(s(s(s(s(0)))), s(s(s(s(s(T284)))))) → less88_out_gg(s(s(s(s(0)))), s(s(s(s(s(T284))))))
less88_in_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297))))))) → less88_out_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297)))))))
less88_in_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310)))))))) → less88_out_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310))))))))
less88_in_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316)))))))) → U6_gg(T315, T316, less146_in_gg(T315, T316))
less146_in_gg(0, s(T327)) → less146_out_gg(0, s(T327))
less146_in_gg(s(T332), s(T333)) → U5_gg(T332, T333, less146_in_gg(T332, T333))
U5_gg(T332, T333, less146_out_gg(T332, T333)) → less146_out_gg(s(T332), s(T333))
U6_gg(T315, T316, less146_out_gg(T315, T316)) → less88_out_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316))))))))
U21_gag(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → insert1_out_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206))
U21_gag(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → U22_gag(T222, T223, T208, T206, T207, insert1_in_gag(s(T222), T208, T207))
insert1_in_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352)) → U23_gag(T348, T349, T350, T353, T352, less146_in_gg(T349, T348))
U23_gag(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → insert1_out_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352))
U23_gag(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → U24_gag(T348, T349, T350, T353, T352, insert1_in_gag(T348, T353, T352))
insert1_in_gag(s(T375), tree(0, T367, T370), tree(0, T367, T369)) → U25_gag(T375, T367, T370, T369, insert1_in_gag(s(T375), T370, T369))
insert1_in_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369)) → U26_gag(T383, T382, T367, T370, T369, less146_in_gg(T382, T383))
U26_gag(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → insert1_out_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369))
U26_gag(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → U27_gag(T383, T382, T367, T370, T369, insert1_in_gag(s(T383), T370, T369))
U27_gag(T383, T382, T367, T370, T369, insert1_out_gag(s(T383), T370, T369)) → insert1_out_gag(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369))
U25_gag(T375, T367, T370, T369, insert1_out_gag(s(T375), T370, T369)) → insert1_out_gag(s(T375), tree(0, T367, T370), tree(0, T367, T369))
U24_gag(T348, T349, T350, T353, T352, insert1_out_gag(T348, T353, T352)) → insert1_out_gag(T348, tree(T349, T350, T353), tree(T349, T350, T352))
U22_gag(T222, T223, T208, T206, T207, insert1_out_gag(s(T222), T208, T207)) → insert1_out_gag(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206))
U20_gag(T213, T208, T206, T207, insert1_out_gag(0, T208, T207)) → insert1_out_gag(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206))
U19_gag(T193, T187, T190, T189, insert1_out_gag(s(T193), T190, T189)) → insert1_out_gag(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189))
U17_gag(T170, T172, T175, T174, insert1_out_gag(T170, T175, T174)) → insert1_out_gag(T170, tree(T170, T172, T175), tree(T170, T172, T174))
U15_gag(T155, T150, T148, T149, insert1_out_gag(s(T155), T150, T149)) → insert1_out_gag(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148))
U9_gag(T56, T60, insert1_out_gag(T56, T60, void)) → insert1_out_gag(T56, tree(T56, void, T60), tree(T56, void, void))
U3_ga(T25, T20, insert1_out_gag(s(T25), T20, void)) → p15_out_ga(T25, T20)
U7_gag(T25, T20, p15_out_ga(T25, T20)) → insert1_out_gag(s(T25), tree(s(T25), T20, void), tree(s(T25), void, void))

(24) UsableRulesProof (EQUIVALENT transformation)

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

(25) Obligation:

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

INSERT1_IN_GAG(s(T155), tree(s(T155), T150, T148), tree(s(T155), T149, T148)) → U14_GAG(T155, T150, T148, T149, less17_in_g(T155))
U14_GAG(T155, T150, T148, T149, less17_out_g(T155)) → INSERT1_IN_GAG(s(T155), T150, T149)
INSERT1_IN_GAG(T170, tree(T170, T172, T175), tree(T170, T172, T174)) → U16_GAG(T170, T172, T175, T174, less17_in_g(T170))
U16_GAG(T170, T172, T175, T174, less17_out_g(T170)) → INSERT1_IN_GAG(T170, T175, T174)
INSERT1_IN_GAG(s(T193), tree(s(T193), T187, T190), tree(s(T193), T187, T189)) → U18_GAG(T193, T187, T190, T189, less17_in_g(T193))
U18_GAG(T193, T187, T190, T189, less17_out_g(T193)) → INSERT1_IN_GAG(s(T193), T190, T189)
INSERT1_IN_GAG(s(T222), tree(s(T223), T208, T206), tree(s(T223), T207, T206)) → U21_GAG(T222, T223, T208, T206, T207, less88_in_gg(T222, T223))
U21_GAG(T222, T223, T208, T206, T207, less88_out_gg(T222, T223)) → INSERT1_IN_GAG(s(T222), T208, T207)
INSERT1_IN_GAG(T348, tree(T349, T350, T353), tree(T349, T350, T352)) → U23_GAG(T348, T349, T350, T353, T352, less146_in_gg(T349, T348))
U23_GAG(T348, T349, T350, T353, T352, less146_out_gg(T349, T348)) → INSERT1_IN_GAG(T348, T353, T352)
INSERT1_IN_GAG(0, tree(s(T213), T208, T206), tree(s(T213), T207, T206)) → INSERT1_IN_GAG(0, T208, T207)
INSERT1_IN_GAG(s(T375), tree(0, T367, T370), tree(0, T367, T369)) → INSERT1_IN_GAG(s(T375), T370, T369)
INSERT1_IN_GAG(s(T383), tree(s(T382), T367, T370), tree(s(T382), T367, T369)) → U26_GAG(T383, T382, T367, T370, T369, less146_in_gg(T382, T383))
U26_GAG(T383, T382, T367, T370, T369, less146_out_gg(T382, T383)) → INSERT1_IN_GAG(s(T383), T370, T369)

The TRS R consists of the following rules:

less17_in_g(s(T30)) → U1_g(T30, less17_in_g(T30))
less88_in_gg(0, s(T232)) → less88_out_gg(0, s(T232))
less88_in_gg(s(0), s(s(T245))) → less88_out_gg(s(0), s(s(T245)))
less88_in_gg(s(s(0)), s(s(s(T258)))) → less88_out_gg(s(s(0)), s(s(s(T258))))
less88_in_gg(s(s(s(0))), s(s(s(s(T271))))) → less88_out_gg(s(s(s(0))), s(s(s(s(T271)))))
less88_in_gg(s(s(s(s(0)))), s(s(s(s(s(T284)))))) → less88_out_gg(s(s(s(s(0)))), s(s(s(s(s(T284))))))
less88_in_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297))))))) → less88_out_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297)))))))
less88_in_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310)))))))) → less88_out_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310))))))))
less88_in_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316)))))))) → U6_gg(T315, T316, less146_in_gg(T315, T316))
less146_in_gg(0, s(T327)) → less146_out_gg(0, s(T327))
less146_in_gg(s(T332), s(T333)) → U5_gg(T332, T333, less146_in_gg(T332, T333))
U1_g(T30, less17_out_g(T30)) → less17_out_g(s(T30))
U6_gg(T315, T316, less146_out_gg(T315, T316)) → less88_out_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316))))))))
U5_gg(T332, T333, less146_out_gg(T332, T333)) → less146_out_gg(s(T332), s(T333))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
s(x1) = s(x1)
less17_in_g(x1) = less17_in_g(x1)
U1_g(x1, x2) = U1_g(x2)
less17_out_g(x1) = less17_out_g
0 = 0
less88_in_gg(x1, x2) = less88_in_gg(x1, x2)
less88_out_gg(x1, x2) = less88_out_gg
U6_gg(x1, x2, x3) = U6_gg(x3)
less146_in_gg(x1, x2) = less146_in_gg(x1, x2)
less146_out_gg(x1, x2) = less146_out_gg
U5_gg(x1, x2, x3) = U5_gg(x3)
INSERT1_IN_GAG(x1, x2, x3) = INSERT1_IN_GAG(x1, x3)
U14_GAG(x1, x2, x3, x4, x5) = U14_GAG(x1, x4, x5)
U16_GAG(x1, x2, x3, x4, x5) = U16_GAG(x1, x4, x5)
U18_GAG(x1, x2, x3, x4, x5) = U18_GAG(x1, x4, x5)
U21_GAG(x1, x2, x3, x4, x5, x6) = U21_GAG(x1, x5, x6)
U23_GAG(x1, x2, x3, x4, x5, x6) = U23_GAG(x1, x5, x6)
U26_GAG(x1, x2, x3, x4, x5, x6) = U26_GAG(x1, x5, x6)

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

(26) PiDPToQDPProof (SOUND transformation)

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

(27) Obligation:

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

INSERT1_IN_GAG(s(T155), tree(s(T155), T149, T148)) → U14_GAG(T155, T149, less17_in_g(T155))
U14_GAG(T155, T149, less17_out_g) → INSERT1_IN_GAG(s(T155), T149)
INSERT1_IN_GAG(T170, tree(T170, T172, T174)) → U16_GAG(T170, T174, less17_in_g(T170))
U16_GAG(T170, T174, less17_out_g) → INSERT1_IN_GAG(T170, T174)
INSERT1_IN_GAG(s(T193), tree(s(T193), T187, T189)) → U18_GAG(T193, T189, less17_in_g(T193))
U18_GAG(T193, T189, less17_out_g) → INSERT1_IN_GAG(s(T193), T189)
INSERT1_IN_GAG(s(T222), tree(s(T223), T207, T206)) → U21_GAG(T222, T207, less88_in_gg(T222, T223))
U21_GAG(T222, T207, less88_out_gg) → INSERT1_IN_GAG(s(T222), T207)
INSERT1_IN_GAG(T348, tree(T349, T350, T352)) → U23_GAG(T348, T352, less146_in_gg(T349, T348))
U23_GAG(T348, T352, less146_out_gg) → INSERT1_IN_GAG(T348, T352)
INSERT1_IN_GAG(0, tree(s(T213), T207, T206)) → INSERT1_IN_GAG(0, T207)
INSERT1_IN_GAG(s(T375), tree(0, T367, T369)) → INSERT1_IN_GAG(s(T375), T369)
INSERT1_IN_GAG(s(T383), tree(s(T382), T367, T369)) → U26_GAG(T383, T369, less146_in_gg(T382, T383))
U26_GAG(T383, T369, less146_out_gg) → INSERT1_IN_GAG(s(T383), T369)

The TRS R consists of the following rules:

less17_in_g(s(T30)) → U1_g(less17_in_g(T30))
less88_in_gg(0, s(T232)) → less88_out_gg
less88_in_gg(s(0), s(s(T245))) → less88_out_gg
less88_in_gg(s(s(0)), s(s(s(T258)))) → less88_out_gg
less88_in_gg(s(s(s(0))), s(s(s(s(T271))))) → less88_out_gg
less88_in_gg(s(s(s(s(0)))), s(s(s(s(s(T284)))))) → less88_out_gg
less88_in_gg(s(s(s(s(s(0))))), s(s(s(s(s(s(T297))))))) → less88_out_gg
less88_in_gg(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T310)))))))) → less88_out_gg
less88_in_gg(s(s(s(s(s(s(s(T315))))))), s(s(s(s(s(s(s(T316)))))))) → U6_gg(less146_in_gg(T315, T316))
less146_in_gg(0, s(T327)) → less146_out_gg
less146_in_gg(s(T332), s(T333)) → U5_gg(less146_in_gg(T332, T333))
U1_g(less17_out_g) → less17_out_g
U6_gg(less146_out_gg) → less88_out_gg
U5_gg(less146_out_gg) → less146_out_gg

The set Q consists of the following terms:

less17_in_g(x0)
less88_in_gg(x0, x1)
less146_in_gg(x0, x1)
U1_g(x0)
U6_gg(x0)
U5_gg(x0)

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

(28) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

U14_GAG(T155, T149, less17_out_g) → INSERT1_IN_GAG(s(T155), T149)
The graph contains the following edges 2 >= 2
INSERT1_IN_GAG(s(T375), tree(0, T367, T369)) → INSERT1_IN_GAG(s(T375), T369)
The graph contains the following edges 1 >= 1, 2 > 2
INSERT1_IN_GAG(s(T155), tree(s(T155), T149, T148)) → U14_GAG(T155, T149, less17_in_g(T155))
The graph contains the following edges 1 > 1, 2 > 1, 2 > 2
INSERT1_IN_GAG(0, tree(s(T213), T207, T206)) → INSERT1_IN_GAG(0, T207)
The graph contains the following edges 1 >= 1, 2 > 2
U16_GAG(T170, T174, less17_out_g) → INSERT1_IN_GAG(T170, T174)
The graph contains the following edges 1 >= 1, 2 >= 2
INSERT1_IN_GAG(T170, tree(T170, T172, T174)) → U16_GAG(T170, T174, less17_in_g(T170))
The graph contains the following edges 1 >= 1, 2 > 1, 2 > 2
U18_GAG(T193, T189, less17_out_g) → INSERT1_IN_GAG(s(T193), T189)
The graph contains the following edges 2 >= 2
INSERT1_IN_GAG(s(T193), tree(s(T193), T187, T189)) → U18_GAG(T193, T189, less17_in_g(T193))
The graph contains the following edges 1 > 1, 2 > 1, 2 > 2
U21_GAG(T222, T207, less88_out_gg) → INSERT1_IN_GAG(s(T222), T207)
The graph contains the following edges 2 >= 2
INSERT1_IN_GAG(s(T222), tree(s(T223), T207, T206)) → U21_GAG(T222, T207, less88_in_gg(T222, T223))
The graph contains the following edges 1 > 1, 2 > 2
U23_GAG(T348, T352, less146_out_gg) → INSERT1_IN_GAG(T348, T352)
The graph contains the following edges 1 >= 1, 2 >= 2
U26_GAG(T383, T369, less146_out_gg) → INSERT1_IN_GAG(s(T383), T369)
The graph contains the following edges 2 >= 2
INSERT1_IN_GAG(T348, tree(T349, T350, T352)) → U23_GAG(T348, T352, less146_in_gg(T349, T348))
The graph contains the following edges 1 >= 1, 2 > 2
INSERT1_IN_GAG(s(T383), tree(s(T382), T367, T369)) → U26_GAG(T383, T369, less146_in_gg(T382, T383))
The graph contains the following edges 1 > 1, 2 > 2

(0) Obligation:

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) PrologToPiTRSProof (SOUND transformation)

(4) Obligation:

(5) DependencyPairsProof (EQUIVALENT transformation)

(6) Obligation:

(7) DependencyGraphProof (EQUIVALENT transformation)

(8) Complex Obligation (AND)

(9) Obligation:

(10) UsableRulesProof (EQUIVALENT transformation)

(11) Obligation:

(12) PiDPToQDPProof (EQUIVALENT transformation)

(13) Obligation:

(14) QDPSizeChangeProof (EQUIVALENT transformation)

(15) YES

(16) Obligation:

(17) UsableRulesProof (EQUIVALENT transformation)

(18) Obligation:

(19) PiDPToQDPProof (EQUIVALENT transformation)

(20) Obligation:

(21) QDPSizeChangeProof (EQUIVALENT transformation)

(22) YES

(23) Obligation:

(24) UsableRulesProof (EQUIVALENT transformation)

(25) Obligation:

(26) PiDPToQDPProof (SOUND transformation)

(27) Obligation:

(28) QDPSizeChangeProof (EQUIVALENT transformation)

(29) YES