Left Termination proof of /tmp/tmpMlxNCm/insert-ffb.pl

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

0 Prolog

↳1 PrologToDTProblemTransformerProof (⇐)

↳2 TRIPLES

↳3 TriplesToPiDPProof (⇐)

↳4 PiDP

↳5 DependencyGraphProof (⇔)

↳6 AND

    ↳7 PiDP

        ↳8 UsableRulesProof (⇔)

        ↳9 PiDP

        ↳10 PiDPToQDPProof (⇐)

        ↳11 QDP

        ↳12 QDPSizeChangeProof (⇔)

        ↳13 YES

    ↳14 PiDP

        ↳15 UsableRulesProof (⇔)

        ↳16 PiDP

        ↳17 PiDPToQDPProof (⇐)

        ↳18 QDP

        ↳19 QDPSizeChangeProof (⇔)

        ↳20 YES

    ↳21 PiDP

        ↳22 UsableRulesProof (⇔)

        ↳23 PiDP

        ↳24 PiDPToQDPProof (⇔)

        ↳25 QDP

        ↳26 QDPSizeChangeProof (⇔)

        ↳27 YES

    ↳28 PiDP

        ↳29 UsableRulesProof (⇔)

        ↳30 PiDP

        ↳31 PiDPToQDPProof (⇔)

        ↳32 QDP

        ↳33 QDPSizeChangeProof (⇔)

        ↳34 YES

    ↳35 PiDP

        ↳36 UsableRulesProof (⇔)

        ↳37 PiDP

        ↳38 PiDPToQDPProof (⇐)

        ↳39 QDP

        ↳40 QDPSizeChangeProof (⇔)

        ↳41 YES

    ↳42 PiDP

        ↳43 UsableRulesProof (⇔)

        ↳44 PiDP

        ↳45 PiDPToQDPProof (⇐)

        ↳46 QDP

        ↳47 QDPSizeChangeProof (⇔)

        ↳48 YES

(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(a,a,g).

(1) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: insert(T1, T2, T3)\n\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\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: true | insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 1 | insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 2 | insert(T1, 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\nT3 is ground\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 1 | insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 3\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: true | insert(T1, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 3\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 3\n\nT5 is ground\ninsert(T1, 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(T1, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 3\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: ','(less(T20, T17), insert(T20, T21, void)) | insert(T1, T2, tree(T17, void, void)), SCOPE: 1, CLAUSE: 3\n\nT17 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: insert(T1, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 3\n\nT9 is ground\ninsert(T1, 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(T20, T17), insert(T20, T21, void)), SCOPE: 2, CLAUSE: 4 | ','(less(T20, T17), insert(T20, T21, void)), SCOPE: 2, CLAUSE: 5 | ?_2 | insert(T1, T2, tree(T17, void, void)), SCOPE: 1, CLAUSE: 3\n\nT17 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: ','(less(T20, T17), insert(T20, T21, void)), SCOPE: 2, CLAUSE: 4\n\nT17 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ','(less(T20, T17), insert(T20, T21, void)), SCOPE: 2, CLAUSE: 5 | ?_2 | insert(T1, T2, tree(T17, void, void)), SCOPE: 1, CLAUSE: 3\n\nT17 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: insert(0, T27, void)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ','(less(T20, T17), insert(T20, T21, void)), SCOPE: 2, CLAUSE: 5\n\nT17 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: ?_2 | insert(T1, T2, tree(T17, void, void)), SCOPE: 1, CLAUSE: 3\n\nT17 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: ','(less(T48, T47), insert(s(T48), T49, void))\n\nT47 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: less(T48, T47)\n\nT47 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: insert(s(T52), T53, void)\n\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: less(T48, T47), SCOPE: 3, CLAUSE: 4 | less(T48, T47), SCOPE: 3, CLAUSE: 5\n\nT47 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: less(T48, T47), SCOPE: 3, CLAUSE: 4\n\nT47 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: less(T48, T47), SCOPE: 3, CLAUSE: 5\n\nT47 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: less(T67, T66)\n\nT66 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: insert(T1, T2, tree(T17, void, void)), SCOPE: 1, CLAUSE: 3\n\nT17 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ','(less(T95, T98), insert(T98, T99, void))\n\nT95 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: less(T95, T98)\n\nT95 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: insert(T102, T103, void)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: less(T95, T98), SCOPE: 4, CLAUSE: 4 | less(T95, T98), SCOPE: 4, CLAUSE: 5\n\nT95 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: less(T95, T98), SCOPE: 4, CLAUSE: 4\n\nT95 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: less(T95, T98), SCOPE: 4, CLAUSE: 5\n\nT95 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: less(T115, T117)\n\nT115 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: ','(less(T141, T144), insert(T144, T145, void))\n\nT141 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(less(T141, T144), insert(T144, T145, void)), SCOPE: 5, CLAUSE: 4 | ','(less(T141, T144), insert(T144, T145, void)), SCOPE: 5, CLAUSE: 5\n\nT141 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: ','(less(T141, T144), insert(T144, T145, void)), SCOPE: 5, CLAUSE: 4\n\nT141 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: ','(less(T141, T144), insert(T144, T145, void)), SCOPE: 5, CLAUSE: 5\n\nT141 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: insert(s(T152), T151, void)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(less(T173, T175), insert(s(T175), T176, void))\n\nT173 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: less(T173, T175)\n\nT173 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: insert(s(T179), T180, void)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: ','(less(T207, T204), insert(T207, T208, void)) | insert(T1, T2, tree(T204, void, void)), SCOPE: 1, CLAUSE: 3\n\nT204 is ground\ninsert(T1, T2, tree(T204, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 3\n\nT5 is ground\ninsert(T1, T2, tree(T5, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))\ninsert(T1, T2, tree(T5, void, void)) !=? insert(X235, tree(X236, X237, X238), tree(X236, X239, X238))", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: ','(less(T207, T204), insert(T207, T208, void)), SCOPE: 6, CLAUSE: 4 | ','(less(T207, T204), insert(T207, T208, void)), SCOPE: 6, CLAUSE: 5 | ?_6 | insert(T1, T2, tree(T204, void, void)), SCOPE: 1, CLAUSE: 3\n\nT204 is ground\ninsert(T1, T2, tree(T204, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: ','(less(T207, T204), insert(T207, T208, void)), SCOPE: 6, CLAUSE: 4\n\nT204 is ground\ninsert(T1, T2, tree(T204, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: ','(less(T207, T204), insert(T207, T208, void)), SCOPE: 6, CLAUSE: 5 | ?_6 | insert(T1, T2, tree(T204, void, void)), SCOPE: 1, CLAUSE: 3\n\nT204 is ground\ninsert(T1, T2, tree(T204, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: insert(0, T214, void)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(less(T207, T204), insert(T207, T208, void)), SCOPE: 6, CLAUSE: 5\n\nT204 is ground\ninsert(T1, T2, tree(T204, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: ?_6 | insert(T1, T2, tree(T204, void, void)), SCOPE: 1, CLAUSE: 3\n\nT204 is ground\ninsert(T1, T2, tree(T204, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: ','(less(T235, T234), insert(s(T235), T236, void))\n\nT234 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: insert(T1, T2, tree(T204, void, void)), SCOPE: 1, CLAUSE: 3\n\nT204 is ground\ninsert(T1, T2, tree(T204, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: ','(less(T248, T251), insert(T251, T252, void))\n\nT248 is ground\ninsert(T1, T2, tree(T248, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: ','(less(T260, T263), insert(T263, T264, void))\n\nT260 is ground\ninsert(T1, T2, tree(T260, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: ','(less(T260, T263), insert(T263, T264, void)), SCOPE: 7, CLAUSE: 4 | ','(less(T260, T263), insert(T263, T264, void)), SCOPE: 7, CLAUSE: 5\n\nT260 is ground\ninsert(T1, T2, tree(T260, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: ','(less(T260, T263), insert(T263, T264, void)), SCOPE: 7, CLAUSE: 4\n\nT260 is ground\ninsert(T1, T2, tree(T260, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: ','(less(T260, T263), insert(T263, T264, void)), SCOPE: 7, CLAUSE: 5\n\nT260 is ground\ninsert(T1, T2, tree(T260, void, void)) !=? insert(X8, tree(X8, X9, X10), tree(X8, X9, X10))", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: insert(s(T271), T270, void)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: ','(less(T292, T294), insert(s(T294), T295, void))\n\nT292 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: true | insert(T1, T2, tree(T301, T302, T303)), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, tree(T301, T302, T303)), SCOPE: 1, CLAUSE: 3\n\nT301 is ground\nT302 is ground\nT303 is ground\ninsert(T1, T2, tree(T301, T302, T303)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT3 is ground\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, T3) !=? insert(X357, tree(X357, X358, X359), tree(X357, X358, X359))", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: insert(T1, T2, tree(T301, T302, T303)), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, tree(T301, T302, T303)), SCOPE: 1, CLAUSE: 3\n\nT301 is ground\nT302 is ground\nT303 is ground\ninsert(T1, T2, tree(T301, T302, T303)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: ','(less(T314, T310), insert(T314, T315, T313)) | insert(T1, T2, tree(T310, T313, T312)), SCOPE: 1, CLAUSE: 3\n\nT310 is ground\nT313 is ground\nT312 is ground\ninsert(T1, T2, tree(T310, T313, T312)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: insert(T1, T2, tree(T301, T302, T303)), SCOPE: 1, CLAUSE: 3\n\nT301 is ground\nT302 is ground\nT303 is ground\ninsert(T1, T2, tree(T301, T302, T303)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T301, T302, T303)) !=? insert(X368, tree(X369, X370, X371), tree(X369, X372, X371))", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: ','(less(T314, T310), insert(T314, T315, T313)), SCOPE: 8, CLAUSE: 4 | ','(less(T314, T310), insert(T314, T315, T313)), SCOPE: 8, CLAUSE: 5 | ?_8 | insert(T1, T2, tree(T310, T313, T312)), SCOPE: 1, CLAUSE: 3\n\nT310 is ground\nT313 is ground\nT312 is ground\ninsert(T1, T2, tree(T310, T313, T312)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: ','(less(T314, T310), insert(T314, T315, T313)), SCOPE: 8, CLAUSE: 4\n\nT310 is ground\nT313 is ground\ninsert(T1, T2, tree(T310, T313, T312)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: ','(less(T314, T310), insert(T314, T315, T313)), SCOPE: 8, CLAUSE: 5 | ?_8 | insert(T1, T2, tree(T310, T313, T312)), SCOPE: 1, CLAUSE: 3\n\nT310 is ground\nT313 is ground\nT312 is ground\ninsert(T1, T2, tree(T310, T313, T312)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: insert(0, T321, T313)\n\nT313 is ground\ninsert(T1, T2, tree(s(T320), T313, T312)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: ','(less(T314, T310), insert(T314, T315, T313)), SCOPE: 8, CLAUSE: 5\n\nT310 is ground\nT313 is ground\ninsert(T1, T2, tree(T310, T313, T312)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: ?_8 | insert(T1, T2, tree(T310, T313, T312)), SCOPE: 1, CLAUSE: 3\n\nT310 is ground\nT313 is ground\nT312 is ground\ninsert(T1, T2, tree(T310, T313, T312)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: ','(less(T332, T331), insert(s(T332), T333, T313))\n\nT313 is ground\nT331 is ground\ninsert(T1, T2, tree(s(T331), T313, T312)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: less(T332, T331)\n\nT331 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: insert(s(T336), T337, T313)\n\nT313 is ground\nT336 is ground\ninsert(T338, T339, tree(s(T331), T313, T340)) !=? insert(T341, void, tree(T341, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: insert(T1, T2, tree(T310, T313, T312)), SCOPE: 1, CLAUSE: 3\n\nT310 is ground\nT313 is ground\nT312 is ground\ninsert(T1, T2, tree(T310, T313, T312)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: ','(less(T357, T361), insert(T361, T362, T360))\n\nT357 is ground\nT360 is ground\ninsert(T1, T2, tree(T357, T358, T360)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: less(T357, T361)\n\nT357 is ground\ninsert(T1, T2, tree(T357, T358, T360)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: insert(T365, T366, T360)\n\nT360 is ground\ninsert(T367, T368, tree(T357, T369, T360)) !=? insert(T370, void, tree(T370, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: ','(less(T381, T385), insert(T385, T386, T384))\n\nT381 is ground\nT384 is ground\ninsert(T1, T2, tree(T381, T382, T384)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: ','(less(T381, T385), insert(T385, T386, T384)), SCOPE: 9, CLAUSE: 4 | ','(less(T381, T385), insert(T385, T386, T384)), SCOPE: 9, CLAUSE: 5\n\nT381 is ground\nT384 is ground\ninsert(T1, T2, tree(T381, T382, T384)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: ','(less(T381, T385), insert(T385, T386, T384)), SCOPE: 9, CLAUSE: 4\n\nT381 is ground\nT384 is ground\ninsert(T1, T2, tree(T381, T382, T384)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: ','(less(T381, T385), insert(T385, T386, T384)), SCOPE: 9, CLAUSE: 5\n\nT381 is ground\nT384 is ground\ninsert(T1, T2, tree(T381, T382, T384)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: insert(s(T393), T392, T384)\n\nT384 is ground\ninsert(T1, T2, tree(0, T382, T384)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: ','(less(T400, T402), insert(s(T402), T403, T384))\n\nT384 is ground\nT400 is ground\ninsert(T1, T2, tree(s(T400), T382, T384)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: less(T400, T402)\n\nT400 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: insert(s(T406), T407, T384)\n\nT384 is ground\ninsert(T408, T409, tree(s(T400), T410, T384)) !=? insert(T411, void, tree(T411, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: ','(less(T426, T422), insert(T426, T427, T425)) | insert(T1, T2, tree(T422, T425, T424)), SCOPE: 1, CLAUSE: 3\n\nT422 is ground\nT425 is ground\nT424 is ground\ninsert(T1, T2, tree(T422, T425, T424)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T422, T425, T424)) !=? insert(X357, tree(X357, X358, X359), tree(X357, X358, X359))", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT3 is ground\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, T3) !=? insert(X357, tree(X357, X358, X359), tree(X357, X358, X359))\ninsert(T1, T2, T3) !=? insert(X472, tree(X473, X474, X475), tree(X473, X476, X475))", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ','(less(T426, T422), insert(T426, T427, T425)), SCOPE: 10, CLAUSE: 4 | ','(less(T426, T422), insert(T426, T427, T425)), SCOPE: 10, CLAUSE: 5 | ?_10 | insert(T1, T2, tree(T422, T425, T424)), SCOPE: 1, CLAUSE: 3\n\nT422 is ground\nT425 is ground\nT424 is ground\ninsert(T1, T2, tree(T422, T425, T424)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T422, T425, T424)) !=? insert(X357, tree(X357, X358, X359), tree(X357, X358, X359))", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: ','(less(T426, T422), insert(T426, T427, T425)), SCOPE: 10, CLAUSE: 4\n\nT422 is ground\nT425 is ground\ninsert(T1, T2, tree(T422, T425, T424)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T422, T425, T424)) !=? insert(X357, tree(X357, X358, X359), tree(X357, X358, X359))", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: ','(less(T426, T422), insert(T426, T427, T425)), SCOPE: 10, CLAUSE: 5 | ?_10 | insert(T1, T2, tree(T422, T425, T424)), SCOPE: 1, CLAUSE: 3\n\nT422 is ground\nT425 is ground\nT424 is ground\ninsert(T1, T2, tree(T422, T425, T424)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T422, T425, T424)) !=? insert(X357, tree(X357, X358, X359), tree(X357, X358, X359))", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: insert(0, T433, T425)\n\nT425 is ground\ninsert(T1, T2, tree(s(T432), T425, T424)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: ','(less(T426, T422), insert(T426, T427, T425)), SCOPE: 10, CLAUSE: 5\n\nT422 is ground\nT425 is ground\ninsert(T1, T2, tree(T422, T425, T424)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T422, T425, T424)) !=? insert(X357, tree(X357, X358, X359), tree(X357, X358, X359))", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: ?_10 | insert(T1, T2, tree(T422, T425, T424)), SCOPE: 1, CLAUSE: 3\n\nT422 is ground\nT425 is ground\nT424 is ground\ninsert(T1, T2, tree(T422, T425, T424)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T422, T425, T424)) !=? insert(X357, tree(X357, X358, X359), tree(X357, X358, X359))", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: ','(less(T444, T443), insert(s(T444), T445, T425))\n\nT425 is ground\nT443 is ground\ninsert(T1, T2, tree(s(T443), T425, T424)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: less(T444, T443)\n\nT443 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: insert(s(T448), T449, T425)\n\nT425 is ground\nT448 is ground\ninsert(T450, T451, tree(s(T443), T425, T452)) !=? insert(T453, void, tree(T453, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: insert(T1, T2, tree(T422, T425, T424)), SCOPE: 1, CLAUSE: 3\n\nT422 is ground\nT425 is ground\nT424 is ground\ninsert(T1, T2, tree(T422, T425, T424)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T422, T425, T424)) !=? insert(X357, tree(X357, X358, X359), tree(X357, X358, X359))", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: ','(less(T469, T473), insert(T473, T474, T472))\n\nT469 is ground\nT472 is ground\ninsert(T1, T2, tree(T469, T470, T472)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T469, T470, T472)) !=? insert(X357, tree(X357, X358, X359), tree(X357, X358, X359))", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: less(T469, T473)\n\nT469 is ground\ninsert(T1, T2, tree(T469, T470, T472)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T469, T470, T472)) !=? insert(X357, tree(X357, X358, X359), tree(X357, X358, X359))", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: insert(T477, T478, T472)\n\nT472 is ground\ninsert(T479, T480, tree(T469, T481, T472)) !=? insert(T482, void, tree(T482, void, void))\ninsert(T479, T480, tree(T469, T481, T472)) !=? insert(T483, tree(T483, T484, T485), tree(T483, T484, T485))", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: ','(less(T496, T500), insert(T500, T501, T499))\n\nT496 is ground\nT499 is ground\ninsert(T1, T2, tree(T496, T497, T499)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T496, T497, T499)) !=? insert(X357, tree(X357, X358, X359), tree(X357, X358, X359))", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: ','(less(T496, T500), insert(T500, T501, T499)), SCOPE: 11, CLAUSE: 4 | ','(less(T496, T500), insert(T500, T501, T499)), SCOPE: 11, CLAUSE: 5\n\nT496 is ground\nT499 is ground\ninsert(T1, T2, tree(T496, T497, T499)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T496, T497, T499)) !=? insert(X357, tree(X357, X358, X359), tree(X357, X358, X359))", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: ','(less(T496, T500), insert(T500, T501, T499)), SCOPE: 11, CLAUSE: 4\n\nT496 is ground\nT499 is ground\ninsert(T1, T2, tree(T496, T497, T499)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T496, T497, T499)) !=? insert(X357, tree(X357, X358, X359), tree(X357, X358, X359))", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: ','(less(T496, T500), insert(T500, T501, T499)), SCOPE: 11, CLAUSE: 5\n\nT496 is ground\nT499 is ground\ninsert(T1, T2, tree(T496, T497, T499)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T496, T497, T499)) !=? insert(X357, tree(X357, X358, X359), tree(X357, X358, X359))", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: insert(s(T508), T507, T499)\n\nT499 is ground\ninsert(T1, T2, tree(0, T497, T499)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: ','(less(T515, T517), insert(s(T517), T518, T499))\n\nT499 is ground\nT515 is ground\ninsert(T1, T2, tree(s(T515), T497, T499)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: less(T515, T517)\n\nT515 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: insert(s(T521), T522, T499)\n\nT499 is ground\ninsert(T523, T524, tree(s(T515), T525, T499)) !=? insert(T526, void, tree(T526, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 138 [arrowhead = none ];
138 -> 2;

139 [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 -> 139 [arrowhead = none ];
139 -> 3;

140 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 140 [arrowhead = none ];
140 -> 4;

141 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 141 [arrowhead = none ];
141 -> 5;

142 [label="EVAL with clause\ninsert(X357, tree(X357, X358, X359), tree(X357, X358, X359)).\nand substitution\nT1 -> T301\nX357 -> T301\nX358 -> T302\nX359 -> T303\nT2 -> tree(T301, T302, T303)\nT3 -> tree(T301, T302, T303)", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 142 [arrowhead = none ];
142 -> 77;

143 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 143 [arrowhead = none ];
143 -> 78;

144 [label="EVAL with clause\ninsert(X8, tree(X8, X9, X10), tree(X8, X9, X10)).\nand substitution\nT1 -> T9\nX8 -> T9\nX9 -> void\nX10 -> void\nT2 -> tree(T9, void, void)\nT5 -> T9\nT10 -> void\nT11 -> void", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 144 [arrowhead = none ];
144 -> 6;

145 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 145 [arrowhead = none ];
145 -> 7;

146 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 146 [arrowhead = none ];
146 -> 8;

147 [label="EVAL with clause\ninsert(X235, tree(X236, X237, X238), tree(X236, X239, X238)) :- ','(less(X235, X236), insert(X235, X237, X239)).\nand substitution\nT1 -> T207\nX235 -> T207\nX236 -> T204\nX237 -> T208\nX238 -> void\nT2 -> tree(T204, T208, void)\nT5 -> T204\nX239 -> void\nT206 -> void\nT203 -> T207\nT205 -> T208", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 147 [arrowhead = none ];
147 -> 54;

148 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 148 [arrowhead = none ];
148 -> 55;

149 [label="EVAL with clause\ninsert(X19, tree(X20, X21, X22), tree(X20, X23, X22)) :- ','(less(X19, X20), insert(X19, X21, X23)).\nand substitution\nT1 -> T20\nX19 -> T20\nX20 -> T17\nX21 -> T21\nX22 -> void\nT2 -> tree(T17, T21, void)\nT9 -> T17\nX23 -> void\nT19 -> void\nT16 -> T20\nT18 -> T21", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 149 [arrowhead = none ];
149 -> 9;

150 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 150 [arrowhead = none ];
150 -> 10;

151 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 151 [arrowhead = none ];
151 -> 11;

152 [label="EVAL with clause\ninsert(X166, tree(X167, X168, X169), tree(X167, X168, X170)) :- ','(less(X167, X166), insert(X166, X169, X170)).\nand substitution\nT1 -> T144\nX166 -> T144\nX167 -> T141\nX168 -> void\nX169 -> T145\nT2 -> tree(T141, void, T145)\nT9 -> T141\nT142 -> void\nX170 -> void\nT140 -> T144\nT143 -> T145", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 152 [arrowhead = none ];
152 -> 43;

153 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 153 [arrowhead = none ];
153 -> 44;

154 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 154 [arrowhead = none ];
154 -> 12;

155 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 155 [arrowhead = none ];
155 -> 13;

156 [label="EVAL with clause\nless(0, s(X33)).\nand substitution\nT20 -> 0\nX33 -> T26\nT17 -> s(T26)\nT21 -> T27", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 156 [arrowhead = none ];
156 -> 14;

157 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 157 [arrowhead = none ];
157 -> 15;

158 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 158 [arrowhead = none ];
158 -> 16;

159 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 159 [arrowhead = none ];
159 -> 17;

160 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T27\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
14 -> 160 [arrowhead = none , style=dashed];
160 -> 1[style=dashed];

161 [label="EVAL with clause\nless(s(X61), s(X62)) :- less(X61, X62).\nand substitution\nX61 -> T48\nT20 -> s(T48)\nX62 -> T47\nT17 -> s(T47)\nT46 -> T48\nT21 -> T49", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 161 [arrowhead = none ];
161 -> 18;

162 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 162 [arrowhead = none ];
162 -> 19;

163 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 163 [arrowhead = none ];
163 -> 30;

164 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
18 -> 164 [arrowhead = none ];
164 -> 20;

165 [label="SPLIT 2\nnew knowledge:\nT52 is ground\nreplacements:\nT48 -> T52\nT49 -> T53", fontsize=14, style = filled, fillcolor = violet];
18 -> 165 [arrowhead = none ];
165 -> 21;

166 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
20 -> 166 [arrowhead = none ];
166 -> 22;

167 [label="INSTANCE with matching:\nT1 -> s(T52)\nT2 -> T53\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
21 -> 167 [arrowhead = none , style=dashed];
167 -> 1[style=dashed];

168 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
22 -> 168 [arrowhead = none ];
168 -> 23;

169 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
22 -> 169 [arrowhead = none ];
169 -> 24;

170 [label="EVAL with clause\nless(0, s(X73)).\nand substitution\nT48 -> 0\nX73 -> T60\nT47 -> s(T60)", fontsize=14, style = filled, fillcolor = lightblue];
23 -> 170 [arrowhead = none ];
170 -> 25;

171 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
23 -> 171 [arrowhead = none ];
171 -> 26;

172 [label="EVAL with clause\nless(s(X79), s(X80)) :- less(X79, X80).\nand substitution\nX79 -> T67\nT48 -> s(T67)\nX80 -> T66\nT47 -> s(T66)\nT65 -> T67", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 172 [arrowhead = none ];
172 -> 28;

173 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 173 [arrowhead = none ];
173 -> 29;

174 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
25 -> 174 [arrowhead = none ];
174 -> 27;

175 [label="INSTANCE with matching:\nT48 -> T67\nT47 -> T66", fontsize=14, style = filled, fillcolor = lightgrey];
28 -> 175 [arrowhead = none , style=dashed];
175 -> 20[style=dashed];

176 [label="EVAL with clause\ninsert(X113, tree(X114, X115, X116), tree(X114, X115, X117)) :- ','(less(X114, X113), insert(X113, X116, X117)).\nand substitution\nT1 -> T98\nX113 -> T98\nX114 -> T95\nX115 -> void\nX116 -> T99\nT2 -> tree(T95, void, T99)\nT17 -> T95\nT96 -> void\nX117 -> void\nT94 -> T98\nT97 -> T99", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 176 [arrowhead = none ];
176 -> 31;

177 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 177 [arrowhead = none ];
177 -> 32;

178 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
31 -> 178 [arrowhead = none ];
178 -> 33;

179 [label="SPLIT 2\nreplacements:\nT98 -> T102\nT99 -> T103", fontsize=14, style = filled, fillcolor = violet];
31 -> 179 [arrowhead = none ];
179 -> 34;

180 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
33 -> 180 [arrowhead = none ];
180 -> 35;

181 [label="INSTANCE with matching:\nT1 -> T102\nT2 -> T103\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
34 -> 181 [arrowhead = none , style=dashed];
181 -> 1[style=dashed];

182 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
35 -> 182 [arrowhead = none ];
182 -> 36;

183 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
35 -> 183 [arrowhead = none ];
183 -> 37;

184 [label="EVAL with clause\nless(0, s(X131)).\nand substitution\nT95 -> 0\nX131 -> T110\nT98 -> s(T110)", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 184 [arrowhead = none ];
184 -> 38;

185 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 185 [arrowhead = none ];
185 -> 39;

186 [label="EVAL with clause\nless(s(X137), s(X138)) :- less(X137, X138).\nand substitution\nX137 -> T115\nT95 -> s(T115)\nX138 -> T117\nT98 -> s(T117)\nT116 -> T117", fontsize=14, style = filled, fillcolor = lightblue];
37 -> 186 [arrowhead = none ];
186 -> 41;

187 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
37 -> 187 [arrowhead = none ];
187 -> 42;

188 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
38 -> 188 [arrowhead = none ];
188 -> 40;

189 [label="INSTANCE with matching:\nT95 -> T115\nT98 -> T117", fontsize=14, style = filled, fillcolor = lightgrey];
41 -> 189 [arrowhead = none , style=dashed];
189 -> 33[style=dashed];

190 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
43 -> 190 [arrowhead = none ];
190 -> 45;

191 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
45 -> 191 [arrowhead = none ];
191 -> 46;

192 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
45 -> 192 [arrowhead = none ];
192 -> 47;

193 [label="EVAL with clause\nless(0, s(X180)).\nand substitution\nT141 -> 0\nX180 -> T152\nT144 -> s(T152)\nT145 -> T151\nT150 -> T152", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 193 [arrowhead = none ];
193 -> 48;

194 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 194 [arrowhead = none ];
194 -> 49;

195 [label="EVAL with clause\nless(s(X204), s(X205)) :- less(X204, X205).\nand substitution\nX204 -> T173\nT141 -> s(T173)\nX205 -> T175\nT144 -> s(T175)\nT174 -> T175\nT145 -> T176", fontsize=14, style = filled, fillcolor = lightblue];
47 -> 195 [arrowhead = none ];
195 -> 50;

196 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
47 -> 196 [arrowhead = none ];
196 -> 51;

197 [label="INSTANCE with matching:\nT1 -> s(T152)\nT2 -> T151\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
48 -> 197 [arrowhead = none , style=dashed];
197 -> 1[style=dashed];

198 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
50 -> 198 [arrowhead = none ];
198 -> 52;

199 [label="SPLIT 2\nreplacements:\nT175 -> T179\nT176 -> T180", fontsize=14, style = filled, fillcolor = violet];
50 -> 199 [arrowhead = none ];
199 -> 53;

200 [label="INSTANCE with matching:\nT95 -> T173\nT98 -> T175", fontsize=14, style = filled, fillcolor = lightgrey];
52 -> 200 [arrowhead = none , style=dashed];
200 -> 33[style=dashed];

201 [label="INSTANCE with matching:\nT1 -> s(T179)\nT2 -> T180\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
53 -> 201 [arrowhead = none , style=dashed];
201 -> 1[style=dashed];

202 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
54 -> 202 [arrowhead = none ];
202 -> 56;

203 [label="EVAL with clause\ninsert(X310, tree(X311, X312, X313), tree(X311, X312, X314)) :- ','(less(X311, X310), insert(X310, X313, X314)).\nand substitution\nT1 -> T263\nX310 -> T263\nX311 -> T260\nX312 -> void\nX313 -> T264\nT2 -> tree(T260, void, T264)\nT5 -> T260\nT261 -> void\nX314 -> void\nT259 -> T263\nT262 -> T264", fontsize=14, style = filled, fillcolor = lightblue];
55 -> 203 [arrowhead = none ];
203 -> 68;

204 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
55 -> 204 [arrowhead = none ];
204 -> 69;

205 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
56 -> 205 [arrowhead = none ];
205 -> 57;

206 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
56 -> 206 [arrowhead = none ];
206 -> 58;

207 [label="EVAL with clause\nless(0, s(X249)).\nand substitution\nT207 -> 0\nX249 -> T213\nT204 -> s(T213)\nT208 -> T214", fontsize=14, style = filled, fillcolor = lightblue];
57 -> 207 [arrowhead = none ];
207 -> 59;

208 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
57 -> 208 [arrowhead = none ];
208 -> 60;

209 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
58 -> 209 [arrowhead = none ];
209 -> 61;

210 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
58 -> 210 [arrowhead = none ];
210 -> 62;

211 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T214\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
59 -> 211 [arrowhead = none , style=dashed];
211 -> 1[style=dashed];

212 [label="EVAL with clause\nless(s(X277), s(X278)) :- less(X277, X278).\nand substitution\nX277 -> T235\nT207 -> s(T235)\nX278 -> T234\nT204 -> s(T234)\nT233 -> T235\nT208 -> T236", fontsize=14, style = filled, fillcolor = lightblue];
61 -> 212 [arrowhead = none ];
212 -> 63;

213 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
61 -> 213 [arrowhead = none ];
213 -> 64;

214 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
62 -> 214 [arrowhead = none ];
214 -> 65;

215 [label="INSTANCE with matching:\nT48 -> T235\nT47 -> T234\nT49 -> T236", fontsize=14, style = filled, fillcolor = lightgrey];
63 -> 215 [arrowhead = none , style=dashed];
215 -> 18[style=dashed];

216 [label="EVAL with clause\ninsert(X293, tree(X294, X295, X296), tree(X294, X295, X297)) :- ','(less(X294, X293), insert(X293, X296, X297)).\nand substitution\nT1 -> T251\nX293 -> T251\nX294 -> T248\nX295 -> void\nX296 -> T252\nT2 -> tree(T248, void, T252)\nT204 -> T248\nT249 -> void\nX297 -> void\nT247 -> T251\nT250 -> T252", fontsize=14, style = filled, fillcolor = lightblue];
65 -> 216 [arrowhead = none ];
216 -> 66;

217 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
65 -> 217 [arrowhead = none ];
217 -> 67;

218 [label="INSTANCE with matching:\nT141 -> T248\nT144 -> T251\nT145 -> T252", fontsize=14, style = filled, fillcolor = lightgrey];
66 -> 218 [arrowhead = none , style=dashed];
218 -> 43[style=dashed];

219 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
68 -> 219 [arrowhead = none ];
219 -> 70;

220 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
70 -> 220 [arrowhead = none ];
220 -> 71;

221 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
70 -> 221 [arrowhead = none ];
221 -> 72;

222 [label="EVAL with clause\nless(0, s(X324)).\nand substitution\nT260 -> 0\nX324 -> T271\nT263 -> s(T271)\nT264 -> T270\nT269 -> T271", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 222 [arrowhead = none ];
222 -> 73;

223 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 223 [arrowhead = none ];
223 -> 74;

224 [label="EVAL with clause\nless(s(X348), s(X349)) :- less(X348, X349).\nand substitution\nX348 -> T292\nT260 -> s(T292)\nX349 -> T294\nT263 -> s(T294)\nT293 -> T294\nT264 -> T295", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 224 [arrowhead = none ];
224 -> 75;

225 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 225 [arrowhead = none ];
225 -> 76;

226 [label="INSTANCE with matching:\nT1 -> s(T271)\nT2 -> T270\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
73 -> 226 [arrowhead = none , style=dashed];
226 -> 1[style=dashed];

227 [label="INSTANCE with matching:\nT173 -> T292\nT175 -> T294\nT176 -> T295", fontsize=14, style = filled, fillcolor = lightgrey];
75 -> 227 [arrowhead = none , style=dashed];
227 -> 50[style=dashed];

228 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
77 -> 228 [arrowhead = none ];
228 -> 79;

229 [label="EVAL with clause\ninsert(X472, tree(X473, X474, X475), tree(X473, X476, X475)) :- ','(less(X472, X473), insert(X472, X474, X476)).\nand substitution\nT1 -> T426\nX472 -> T426\nX473 -> T422\nX474 -> T427\nX475 -> T424\nT2 -> tree(T422, T427, T424)\nX476 -> T425\nT3 -> tree(T422, T425, T424)\nT421 -> T426\nT423 -> T427", fontsize=14, style = filled, fillcolor = lightblue];
78 -> 229 [arrowhead = none ];
229 -> 109;

230 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
78 -> 230 [arrowhead = none ];
230 -> 110;

231 [label="EVAL with clause\ninsert(X368, tree(X369, X370, X371), tree(X369, X372, X371)) :- ','(less(X368, X369), insert(X368, X370, X372)).\nand substitution\nT1 -> T314\nX368 -> T314\nX369 -> T310\nX370 -> T315\nX371 -> T312\nT2 -> tree(T310, T315, T312)\nT301 -> T310\nT302 -> T313\nX372 -> T313\nT303 -> T312\nT309 -> T314\nT311 -> T315", fontsize=14, style = filled, fillcolor = lightblue];
79 -> 231 [arrowhead = none ];
231 -> 80;

232 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
79 -> 232 [arrowhead = none ];
232 -> 81;

233 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
80 -> 233 [arrowhead = none ];
233 -> 82;

234 [label="EVAL with clause\ninsert(X435, tree(X436, X437, X438), tree(X436, X437, X439)) :- ','(less(X436, X435), insert(X435, X438, X439)).\nand substitution\nT1 -> T385\nX435 -> T385\nX436 -> T381\nX437 -> T382\nX438 -> T386\nT2 -> tree(T381, T382, T386)\nT301 -> T381\nT302 -> T382\nT303 -> T384\nX439 -> T384\nT380 -> T385\nT383 -> T386", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 234 [arrowhead = none ];
234 -> 98;

235 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 235 [arrowhead = none ];
235 -> 99;

236 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
82 -> 236 [arrowhead = none ];
236 -> 83;

237 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
82 -> 237 [arrowhead = none ];
237 -> 84;

238 [label="EVAL with clause\nless(0, s(X382)).\nand substitution\nT314 -> 0\nX382 -> T320\nT310 -> s(T320)\nT315 -> T321", fontsize=14, style = filled, fillcolor = lightblue];
83 -> 238 [arrowhead = none ];
238 -> 85;

239 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
83 -> 239 [arrowhead = none ];
239 -> 86;

240 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
84 -> 240 [arrowhead = none ];
240 -> 87;

241 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
84 -> 241 [arrowhead = none ];
241 -> 88;

242 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T321\nT3 -> T313", fontsize=14, style = filled, fillcolor = lightgrey];
85 -> 242 [arrowhead = none , style=dashed];
242 -> 1[style=dashed];

243 [label="EVAL with clause\nless(s(X394), s(X395)) :- less(X394, X395).\nand substitution\nX394 -> T332\nT314 -> s(T332)\nX395 -> T331\nT310 -> s(T331)\nT330 -> T332\nT315 -> T333", fontsize=14, style = filled, fillcolor = lightblue];
87 -> 243 [arrowhead = none ];
243 -> 89;

244 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
87 -> 244 [arrowhead = none ];
244 -> 90;

245 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
88 -> 245 [arrowhead = none ];
245 -> 93;

246 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
89 -> 246 [arrowhead = none ];
246 -> 91;

247 [label="SPLIT 2\nnew knowledge:\nT336 is ground\nreplacements:\nT332 -> T336\nT333 -> T337\nT1 -> T338\nT2 -> T339\nT312 -> T340\nX3 -> T341", fontsize=14, style = filled, fillcolor = violet];
89 -> 247 [arrowhead = none ];
247 -> 92;

248 [label="INSTANCE with matching:\nT48 -> T332\nT47 -> T331", fontsize=14, style = filled, fillcolor = lightgrey];
91 -> 248 [arrowhead = none , style=dashed];
248 -> 20[style=dashed];

249 [label="INSTANCE with matching:\nT1 -> s(T336)\nT2 -> T337\nT3 -> T313", fontsize=14, style = filled, fillcolor = lightgrey];
92 -> 249 [arrowhead = none , style=dashed];
249 -> 1[style=dashed];

250 [label="EVAL with clause\ninsert(X414, tree(X415, X416, X417), tree(X415, X416, X418)) :- ','(less(X415, X414), insert(X414, X417, X418)).\nand substitution\nT1 -> T361\nX414 -> T361\nX415 -> T357\nX416 -> T358\nX417 -> T362\nT2 -> tree(T357, T358, T362)\nT310 -> T357\nT313 -> T358\nT312 -> T360\nX418 -> T360\nT356 -> T361\nT359 -> T362", fontsize=14, style = filled, fillcolor = lightblue];
93 -> 250 [arrowhead = none ];
250 -> 94;

251 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
93 -> 251 [arrowhead = none ];
251 -> 95;

252 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
94 -> 252 [arrowhead = none ];
252 -> 96;

253 [label="SPLIT 2\nreplacements:\nT361 -> T365\nT362 -> T366\nT1 -> T367\nT2 -> T368\nT358 -> T369\nX3 -> T370", fontsize=14, style = filled, fillcolor = violet];
94 -> 253 [arrowhead = none ];
253 -> 97;

254 [label="INSTANCE with matching:\nT173 -> T357\nT175 -> T361", fontsize=14, style = filled, fillcolor = lightgrey];
96 -> 254 [arrowhead = none , style=dashed];
254 -> 52[style=dashed];

255 [label="INSTANCE with matching:\nT1 -> T365\nT2 -> T366\nT3 -> T360", fontsize=14, style = filled, fillcolor = lightgrey];
97 -> 255 [arrowhead = none , style=dashed];
255 -> 1[style=dashed];

256 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
98 -> 256 [arrowhead = none ];
256 -> 100;

257 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
100 -> 257 [arrowhead = none ];
257 -> 101;

258 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
100 -> 258 [arrowhead = none ];
258 -> 102;

259 [label="EVAL with clause\nless(0, s(X449)).\nand substitution\nT381 -> 0\nX449 -> T393\nT385 -> s(T393)\nT386 -> T392\nT391 -> T393", fontsize=14, style = filled, fillcolor = lightblue];
101 -> 259 [arrowhead = none ];
259 -> 103;

260 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
101 -> 260 [arrowhead = none ];
260 -> 104;

261 [label="EVAL with clause\nless(s(X457), s(X458)) :- less(X457, X458).\nand substitution\nX457 -> T400\nT381 -> s(T400)\nX458 -> T402\nT385 -> s(T402)\nT401 -> T402\nT386 -> T403", fontsize=14, style = filled, fillcolor = lightblue];
102 -> 261 [arrowhead = none ];
261 -> 105;

262 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
102 -> 262 [arrowhead = none ];
262 -> 106;

263 [label="INSTANCE with matching:\nT1 -> s(T393)\nT2 -> T392\nT3 -> T384", fontsize=14, style = filled, fillcolor = lightgrey];
103 -> 263 [arrowhead = none , style=dashed];
263 -> 1[style=dashed];

264 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
105 -> 264 [arrowhead = none ];
264 -> 107;

265 [label="SPLIT 2\nreplacements:\nT402 -> T406\nT403 -> T407\nT1 -> T408\nT2 -> T409\nT382 -> T410\nX3 -> T411", fontsize=14, style = filled, fillcolor = violet];
105 -> 265 [arrowhead = none ];
265 -> 108;

266 [label="INSTANCE with matching:\nT173 -> T400\nT175 -> T402", fontsize=14, style = filled, fillcolor = lightgrey];
107 -> 266 [arrowhead = none , style=dashed];
266 -> 52[style=dashed];

267 [label="INSTANCE with matching:\nT1 -> s(T406)\nT2 -> T407\nT3 -> T384", fontsize=14, style = filled, fillcolor = lightgrey];
108 -> 267 [arrowhead = none , style=dashed];
267 -> 1[style=dashed];

268 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
109 -> 268 [arrowhead = none ];
268 -> 111;

269 [label="EVAL with clause\ninsert(X539, tree(X540, X541, X542), tree(X540, X541, X543)) :- ','(less(X540, X539), insert(X539, X542, X543)).\nand substitution\nT1 -> T500\nX539 -> T500\nX540 -> T496\nX541 -> T497\nX542 -> T501\nT2 -> tree(T496, T497, T501)\nX543 -> T499\nT3 -> tree(T496, T497, T499)\nT495 -> T500\nT498 -> T501", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 269 [arrowhead = none ];
269 -> 127;

270 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 270 [arrowhead = none ];
270 -> 128;

271 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
111 -> 271 [arrowhead = none ];
271 -> 112;

272 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
111 -> 272 [arrowhead = none ];
272 -> 113;

273 [label="EVAL with clause\nless(0, s(X486)).\nand substitution\nT426 -> 0\nX486 -> T432\nT422 -> s(T432)\nT427 -> T433", fontsize=14, style = filled, fillcolor = lightblue];
112 -> 273 [arrowhead = none ];
273 -> 114;

274 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
112 -> 274 [arrowhead = none ];
274 -> 115;

275 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
113 -> 275 [arrowhead = none ];
275 -> 116;

276 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
113 -> 276 [arrowhead = none ];
276 -> 117;

277 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T433\nT3 -> T425", fontsize=14, style = filled, fillcolor = lightgrey];
114 -> 277 [arrowhead = none , style=dashed];
277 -> 1[style=dashed];

278 [label="EVAL with clause\nless(s(X498), s(X499)) :- less(X498, X499).\nand substitution\nX498 -> T444\nT426 -> s(T444)\nX499 -> T443\nT422 -> s(T443)\nT442 -> T444\nT427 -> T445", fontsize=14, style = filled, fillcolor = lightblue];
116 -> 278 [arrowhead = none ];
278 -> 118;

279 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
116 -> 279 [arrowhead = none ];
279 -> 119;

280 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
117 -> 280 [arrowhead = none ];
280 -> 122;

281 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
118 -> 281 [arrowhead = none ];
281 -> 120;

282 [label="SPLIT 2\nnew knowledge:\nT448 is ground\nreplacements:\nT444 -> T448\nT445 -> T449\nT1 -> T450\nT2 -> T451\nT424 -> T452\nX3 -> T453", fontsize=14, style = filled, fillcolor = violet];
118 -> 282 [arrowhead = none ];
282 -> 121;

283 [label="INSTANCE with matching:\nT332 -> T444\nT331 -> T443", fontsize=14, style = filled, fillcolor = lightgrey];
120 -> 283 [arrowhead = none , style=dashed];
283 -> 91[style=dashed];

284 [label="INSTANCE with matching:\nT1 -> s(T448)\nT2 -> T449\nT3 -> T425", fontsize=14, style = filled, fillcolor = lightgrey];
121 -> 284 [arrowhead = none , style=dashed];
284 -> 1[style=dashed];

285 [label="EVAL with clause\ninsert(X518, tree(X519, X520, X521), tree(X519, X520, X522)) :- ','(less(X519, X518), insert(X518, X521, X522)).\nand substitution\nT1 -> T473\nX518 -> T473\nX519 -> T469\nX520 -> T470\nX521 -> T474\nT2 -> tree(T469, T470, T474)\nT422 -> T469\nT425 -> T470\nT424 -> T472\nX522 -> T472\nT468 -> T473\nT471 -> T474", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 285 [arrowhead = none ];
285 -> 123;

286 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 286 [arrowhead = none ];
286 -> 124;

287 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
123 -> 287 [arrowhead = none ];
287 -> 125;

288 [label="SPLIT 2\nreplacements:\nT473 -> T477\nT474 -> T478\nT1 -> T479\nT2 -> T480\nT470 -> T481\nX3 -> T482\nX357 -> T483\nX358 -> T484\nX359 -> T485", fontsize=14, style = filled, fillcolor = violet];
123 -> 288 [arrowhead = none ];
288 -> 126;

289 [label="INSTANCE with matching:\nT400 -> T469\nT402 -> T473", fontsize=14, style = filled, fillcolor = lightgrey];
125 -> 289 [arrowhead = none , style=dashed];
289 -> 107[style=dashed];

290 [label="INSTANCE with matching:\nT1 -> T477\nT2 -> T478\nT3 -> T472", fontsize=14, style = filled, fillcolor = lightgrey];
126 -> 290 [arrowhead = none , style=dashed];
290 -> 1[style=dashed];

291 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
127 -> 291 [arrowhead = none ];
291 -> 129;

292 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
129 -> 292 [arrowhead = none ];
292 -> 130;

293 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
129 -> 293 [arrowhead = none ];
293 -> 131;

294 [label="EVAL with clause\nless(0, s(X553)).\nand substitution\nT496 -> 0\nX553 -> T508\nT500 -> s(T508)\nT501 -> T507\nT506 -> T508", fontsize=14, style = filled, fillcolor = lightblue];
130 -> 294 [arrowhead = none ];
294 -> 132;

295 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
130 -> 295 [arrowhead = none ];
295 -> 133;

296 [label="EVAL with clause\nless(s(X561), s(X562)) :- less(X561, X562).\nand substitution\nX561 -> T515\nT496 -> s(T515)\nX562 -> T517\nT500 -> s(T517)\nT516 -> T517\nT501 -> T518", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 296 [arrowhead = none ];
296 -> 134;

297 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 297 [arrowhead = none ];
297 -> 135;

298 [label="INSTANCE with matching:\nT1 -> s(T508)\nT2 -> T507\nT3 -> T499", fontsize=14, style = filled, fillcolor = lightgrey];
132 -> 298 [arrowhead = none , style=dashed];
298 -> 1[style=dashed];

299 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
134 -> 299 [arrowhead = none ];
299 -> 136;

300 [label="SPLIT 2\nreplacements:\nT517 -> T521\nT518 -> T522\nT1 -> T523\nT2 -> T524\nT497 -> T525\nX3 -> T526", fontsize=14, style = filled, fillcolor = violet];
134 -> 300 [arrowhead = none ];
300 -> 137;

301 [label="INSTANCE with matching:\nT400 -> T515\nT402 -> T517", fontsize=14, style = filled, fillcolor = lightgrey];
136 -> 301 [arrowhead = none , style=dashed];
301 -> 107[style=dashed];

302 [label="INSTANCE with matching:\nT1 -> s(T521)\nT2 -> T522\nT3 -> T499", fontsize=14, style = filled, fillcolor = lightgrey];
137 -> 302 [arrowhead = none , style=dashed];
302 -> 1[style=dashed];

}

(2) Obligation:

Triples:

less20(s(T67), s(T66)) :- less20(T67, T66).
less33(s(T115), s(T117)) :- less33(T115, T117).
p18(T48, T47, T49) :- less20(T48, T47).
p18(T52, T47, T53) :- ','(lessc20(T52, T47), insert1(s(T52), T53, void)).
p43(0, s(T152), T151) :- insert1(s(T152), T151, void).
p43(s(T173), s(T175), T176) :- p50(T173, T175, T176).
p50(T173, T175, T176) :- less33(T173, T175).
p50(T173, T179, T180) :- ','(lessc33(T173, T179), insert1(s(T179), T180, void)).
insert1(0, tree(s(T26), T27, void), tree(s(T26), void, void)) :- insert1(0, T27, void).
insert1(s(T48), tree(s(T47), T49, void), tree(s(T47), void, void)) :- p18(T48, T47, T49).
insert1(T98, tree(T95, void, T99), tree(T95, void, void)) :- less33(T95, T98).
insert1(T102, tree(T95, void, T103), tree(T95, void, void)) :- ','(lessc33(T95, T102), insert1(T102, T103, void)).
insert1(T144, tree(T141, void, T145), tree(T141, void, void)) :- p43(T141, T144, T145).
insert1(0, tree(s(T213), T214, void), tree(s(T213), void, void)) :- insert1(0, T214, void).
insert1(s(T235), tree(s(T234), T236, void), tree(s(T234), void, void)) :- p18(T235, T234, T236).
insert1(T251, tree(T248, void, T252), tree(T248, void, void)) :- p43(T248, T251, T252).
insert1(s(T271), tree(0, void, T270), tree(0, void, void)) :- insert1(s(T271), T270, void).
insert1(s(T294), tree(s(T292), void, T295), tree(s(T292), void, void)) :- p50(T292, T294, T295).
insert1(0, tree(s(T320), T321, T312), tree(s(T320), T313, T312)) :- insert1(0, T321, T313).
insert1(s(T332), tree(s(T331), T333, T312), tree(s(T331), T313, T312)) :- less20(T332, T331).
insert1(s(T336), tree(s(T331), T337, T340), tree(s(T331), T313, T340)) :- ','(lessc20(T336, T331), insert1(s(T336), T337, T313)).
insert1(T361, tree(T357, T358, T362), tree(T357, T358, T360)) :- less33(T357, T361).
insert1(T365, tree(T357, T369, T366), tree(T357, T369, T360)) :- ','(lessc33(T357, T365), insert1(T365, T366, T360)).
insert1(s(T393), tree(0, T382, T392), tree(0, T382, T384)) :- insert1(s(T393), T392, T384).
insert1(s(T402), tree(s(T400), T382, T403), tree(s(T400), T382, T384)) :- less33(T400, T402).
insert1(s(T406), tree(s(T400), T410, T407), tree(s(T400), T410, T384)) :- ','(lessc33(T400, T406), insert1(s(T406), T407, T384)).
insert1(0, tree(s(T432), T433, T424), tree(s(T432), T425, T424)) :- insert1(0, T433, T425).
insert1(s(T444), tree(s(T443), T445, T424), tree(s(T443), T425, T424)) :- less20(T444, T443).
insert1(s(T448), tree(s(T443), T449, T452), tree(s(T443), T425, T452)) :- ','(lessc20(T448, T443), insert1(s(T448), T449, T425)).
insert1(T473, tree(T469, T470, T474), tree(T469, T470, T472)) :- less33(T469, T473).
insert1(T477, tree(T469, T481, T478), tree(T469, T481, T472)) :- ','(lessc33(T469, T477), insert1(T477, T478, T472)).
insert1(s(T508), tree(0, T497, T507), tree(0, T497, T499)) :- insert1(s(T508), T507, T499).
insert1(s(T517), tree(s(T515), T497, T518), tree(s(T515), T497, T499)) :- less33(T515, T517).
insert1(s(T521), tree(s(T515), T525, T522), tree(s(T515), T525, T499)) :- ','(lessc33(T515, T521), insert1(s(T521), T522, T499)).

Clauses:

insertc1(T5, void, tree(T5, void, void)).
insertc1(T9, tree(T9, void, void), tree(T9, void, void)).
insertc1(0, tree(s(T26), T27, void), tree(s(T26), void, void)) :- insertc1(0, T27, void).
insertc1(s(T48), tree(s(T47), T49, void), tree(s(T47), void, void)) :- qc18(T48, T47, T49).
insertc1(T102, tree(T95, void, T103), tree(T95, void, void)) :- ','(lessc33(T95, T102), insertc1(T102, T103, void)).
insertc1(T144, tree(T141, void, T145), tree(T141, void, void)) :- qc43(T141, T144, T145).
insertc1(0, tree(s(T213), T214, void), tree(s(T213), void, void)) :- insertc1(0, T214, void).
insertc1(s(T235), tree(s(T234), T236, void), tree(s(T234), void, void)) :- qc18(T235, T234, T236).
insertc1(T251, tree(T248, void, T252), tree(T248, void, void)) :- qc43(T248, T251, T252).
insertc1(s(T271), tree(0, void, T270), tree(0, void, void)) :- insertc1(s(T271), T270, void).
insertc1(s(T294), tree(s(T292), void, T295), tree(s(T292), void, void)) :- qc50(T292, T294, T295).
insertc1(T301, tree(T301, T302, T303), tree(T301, T302, T303)).
insertc1(0, tree(s(T320), T321, T312), tree(s(T320), T313, T312)) :- insertc1(0, T321, T313).
insertc1(s(T336), tree(s(T331), T337, T340), tree(s(T331), T313, T340)) :- ','(lessc20(T336, T331), insertc1(s(T336), T337, T313)).
insertc1(T365, tree(T357, T369, T366), tree(T357, T369, T360)) :- ','(lessc33(T357, T365), insertc1(T365, T366, T360)).
insertc1(s(T393), tree(0, T382, T392), tree(0, T382, T384)) :- insertc1(s(T393), T392, T384).
insertc1(s(T406), tree(s(T400), T410, T407), tree(s(T400), T410, T384)) :- ','(lessc33(T400, T406), insertc1(s(T406), T407, T384)).
insertc1(0, tree(s(T432), T433, T424), tree(s(T432), T425, T424)) :- insertc1(0, T433, T425).
insertc1(s(T448), tree(s(T443), T449, T452), tree(s(T443), T425, T452)) :- ','(lessc20(T448, T443), insertc1(s(T448), T449, T425)).
insertc1(T477, tree(T469, T481, T478), tree(T469, T481, T472)) :- ','(lessc33(T469, T477), insertc1(T477, T478, T472)).
insertc1(s(T508), tree(0, T497, T507), tree(0, T497, T499)) :- insertc1(s(T508), T507, T499).
insertc1(s(T521), tree(s(T515), T525, T522), tree(s(T515), T525, T499)) :- ','(lessc33(T515, T521), insertc1(s(T521), T522, T499)).
lessc20(0, s(T60)).
lessc20(s(T67), s(T66)) :- lessc20(T67, T66).
lessc33(0, s(T110)).
lessc33(s(T115), s(T117)) :- lessc33(T115, T117).
qc18(T52, T47, T53) :- ','(lessc20(T52, T47), insertc1(s(T52), T53, void)).
qc43(0, s(T152), T151) :- insertc1(s(T152), T151, void).
qc43(s(T173), s(T175), T176) :- qc50(T173, T175, T176).
qc50(T173, T179, T180) :- ','(lessc33(T173, T179), insertc1(s(T179), T180, void)).

Afs:

insert1(x1, x2, x3) = insert1(x3)

(3) TriplesToPiDPProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
insert1_in: (f,f,b) (b,f,b)
p18_in: (b,b,f) (f,b,f)
less20_in: (b,b) (f,b)
lessc20_in: (b,b) (f,b)
less33_in: (b,b) (b,f)
lessc33_in: (b,b) (b,f)
p43_in: (b,b,f) (b,f,f)
p50_in: (b,b,f) (b,f,f)
Transforming TRIPLES into the following Term Rewriting System:
Pi DP problem:
The TRS P consists of the following rules:

INSERT1_IN_AAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U11_AAG(T26, T27, insert1_in_gag(0, T27, void))
INSERT1_IN_AAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → INSERT1_IN_GAG(0, T27, void)
INSERT1_IN_GAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U11_GAG(T26, T27, insert1_in_gag(0, T27, void))
INSERT1_IN_GAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → INSERT1_IN_GAG(0, T27, void)
INSERT1_IN_GAG(s(T48), tree(s(T47), T49, void), tree(s(T47), void, void)) → U12_GAG(T48, T47, T49, p18_in_gga(T48, T47, T49))
INSERT1_IN_GAG(s(T48), tree(s(T47), T49, void), tree(s(T47), void, void)) → P18_IN_GGA(T48, T47, T49)
P18_IN_GGA(T48, T47, T49) → U3_GGA(T48, T47, T49, less20_in_gg(T48, T47))
P18_IN_GGA(T48, T47, T49) → LESS20_IN_GG(T48, T47)
LESS20_IN_GG(s(T67), s(T66)) → U1_GG(T67, T66, less20_in_gg(T67, T66))
LESS20_IN_GG(s(T67), s(T66)) → LESS20_IN_GG(T67, T66)
P18_IN_GGA(T52, T47, T53) → U4_GGA(T52, T47, T53, lessc20_in_gg(T52, T47))
U4_GGA(T52, T47, T53, lessc20_out_gg(T52, T47)) → U5_GGA(T52, T47, T53, insert1_in_gag(s(T52), T53, void))
U4_GGA(T52, T47, T53, lessc20_out_gg(T52, T47)) → INSERT1_IN_GAG(s(T52), T53, void)
INSERT1_IN_GAG(T98, tree(T95, void, T99), tree(T95, void, void)) → U13_GAG(T98, T95, T99, less33_in_gg(T95, T98))
INSERT1_IN_GAG(T98, tree(T95, void, T99), tree(T95, void, void)) → LESS33_IN_GG(T95, T98)
LESS33_IN_GG(s(T115), s(T117)) → U2_GG(T115, T117, less33_in_gg(T115, T117))
LESS33_IN_GG(s(T115), s(T117)) → LESS33_IN_GG(T115, T117)
INSERT1_IN_GAG(T102, tree(T95, void, T103), tree(T95, void, void)) → U14_GAG(T102, T95, T103, lessc33_in_gg(T95, T102))
U14_GAG(T102, T95, T103, lessc33_out_gg(T95, T102)) → U15_GAG(T102, T95, T103, insert1_in_gag(T102, T103, void))
U14_GAG(T102, T95, T103, lessc33_out_gg(T95, T102)) → INSERT1_IN_GAG(T102, T103, void)
INSERT1_IN_GAG(T144, tree(T141, void, T145), tree(T141, void, void)) → U16_GAG(T144, T141, T145, p43_in_gga(T141, T144, T145))
INSERT1_IN_GAG(T144, tree(T141, void, T145), tree(T141, void, void)) → P43_IN_GGA(T141, T144, T145)
P43_IN_GGA(0, s(T152), T151) → U6_GGA(T152, T151, insert1_in_gag(s(T152), T151, void))
P43_IN_GGA(0, s(T152), T151) → INSERT1_IN_GAG(s(T152), T151, void)
INSERT1_IN_GAG(0, tree(s(T213), T214, void), tree(s(T213), void, void)) → U17_GAG(T213, T214, insert1_in_gag(0, T214, void))
INSERT1_IN_GAG(s(T235), tree(s(T234), T236, void), tree(s(T234), void, void)) → U18_GAG(T235, T234, T236, p18_in_gga(T235, T234, T236))
INSERT1_IN_GAG(T251, tree(T248, void, T252), tree(T248, void, void)) → U19_GAG(T251, T248, T252, p43_in_gga(T248, T251, T252))
P43_IN_GGA(s(T173), s(T175), T176) → U7_GGA(T173, T175, T176, p50_in_gga(T173, T175, T176))
P43_IN_GGA(s(T173), s(T175), T176) → P50_IN_GGA(T173, T175, T176)
P50_IN_GGA(T173, T175, T176) → U8_GGA(T173, T175, T176, less33_in_gg(T173, T175))
P50_IN_GGA(T173, T175, T176) → LESS33_IN_GG(T173, T175)
P50_IN_GGA(T173, T179, T180) → U9_GGA(T173, T179, T180, lessc33_in_gg(T173, T179))
U9_GGA(T173, T179, T180, lessc33_out_gg(T173, T179)) → U10_GGA(T173, T179, T180, insert1_in_gag(s(T179), T180, void))
U9_GGA(T173, T179, T180, lessc33_out_gg(T173, T179)) → INSERT1_IN_GAG(s(T179), T180, void)
INSERT1_IN_GAG(s(T271), tree(0, void, T270), tree(0, void, void)) → U20_GAG(T271, T270, insert1_in_gag(s(T271), T270, void))
INSERT1_IN_GAG(s(T271), tree(0, void, T270), tree(0, void, void)) → INSERT1_IN_GAG(s(T271), T270, void)
INSERT1_IN_GAG(s(T294), tree(s(T292), void, T295), tree(s(T292), void, void)) → U21_GAG(T294, T292, T295, p50_in_gga(T292, T294, T295))
INSERT1_IN_GAG(s(T294), tree(s(T292), void, T295), tree(s(T292), void, void)) → P50_IN_GGA(T292, T294, T295)
INSERT1_IN_GAG(0, tree(s(T320), T321, T312), tree(s(T320), T313, T312)) → U22_GAG(T320, T321, T312, T313, insert1_in_gag(0, T321, T313))
INSERT1_IN_GAG(0, tree(s(T320), T321, T312), tree(s(T320), T313, T312)) → INSERT1_IN_GAG(0, T321, T313)
INSERT1_IN_GAG(s(T332), tree(s(T331), T333, T312), tree(s(T331), T313, T312)) → U23_GAG(T332, T331, T333, T312, T313, less20_in_gg(T332, T331))
INSERT1_IN_GAG(s(T332), tree(s(T331), T333, T312), tree(s(T331), T313, T312)) → LESS20_IN_GG(T332, T331)
INSERT1_IN_GAG(s(T336), tree(s(T331), T337, T340), tree(s(T331), T313, T340)) → U24_GAG(T336, T331, T337, T340, T313, lessc20_in_gg(T336, T331))
U24_GAG(T336, T331, T337, T340, T313, lessc20_out_gg(T336, T331)) → U25_GAG(T336, T331, T337, T340, T313, insert1_in_gag(s(T336), T337, T313))
U24_GAG(T336, T331, T337, T340, T313, lessc20_out_gg(T336, T331)) → INSERT1_IN_GAG(s(T336), T337, T313)
INSERT1_IN_GAG(T361, tree(T357, T358, T362), tree(T357, T358, T360)) → U26_GAG(T361, T357, T358, T362, T360, less33_in_gg(T357, T361))
INSERT1_IN_GAG(T361, tree(T357, T358, T362), tree(T357, T358, T360)) → LESS33_IN_GG(T357, T361)
INSERT1_IN_GAG(T365, tree(T357, T369, T366), tree(T357, T369, T360)) → U27_GAG(T365, T357, T369, T366, T360, lessc33_in_gg(T357, T365))
U27_GAG(T365, T357, T369, T366, T360, lessc33_out_gg(T357, T365)) → U28_GAG(T365, T357, T369, T366, T360, insert1_in_gag(T365, T366, T360))
U27_GAG(T365, T357, T369, T366, T360, lessc33_out_gg(T357, T365)) → INSERT1_IN_GAG(T365, T366, T360)
INSERT1_IN_GAG(s(T393), tree(0, T382, T392), tree(0, T382, T384)) → U29_GAG(T393, T382, T392, T384, insert1_in_gag(s(T393), T392, T384))
INSERT1_IN_GAG(s(T393), tree(0, T382, T392), tree(0, T382, T384)) → INSERT1_IN_GAG(s(T393), T392, T384)
INSERT1_IN_GAG(s(T402), tree(s(T400), T382, T403), tree(s(T400), T382, T384)) → U30_GAG(T402, T400, T382, T403, T384, less33_in_gg(T400, T402))
INSERT1_IN_GAG(s(T402), tree(s(T400), T382, T403), tree(s(T400), T382, T384)) → LESS33_IN_GG(T400, T402)
INSERT1_IN_GAG(s(T406), tree(s(T400), T410, T407), tree(s(T400), T410, T384)) → U31_GAG(T406, T400, T410, T407, T384, lessc33_in_gg(T400, T406))
U31_GAG(T406, T400, T410, T407, T384, lessc33_out_gg(T400, T406)) → U32_GAG(T406, T400, T410, T407, T384, insert1_in_gag(s(T406), T407, T384))
U31_GAG(T406, T400, T410, T407, T384, lessc33_out_gg(T400, T406)) → INSERT1_IN_GAG(s(T406), T407, T384)
INSERT1_IN_GAG(0, tree(s(T432), T433, T424), tree(s(T432), T425, T424)) → U33_GAG(T432, T433, T424, T425, insert1_in_gag(0, T433, T425))
INSERT1_IN_GAG(s(T444), tree(s(T443), T445, T424), tree(s(T443), T425, T424)) → U34_GAG(T444, T443, T445, T424, T425, less20_in_gg(T444, T443))
INSERT1_IN_GAG(s(T448), tree(s(T443), T449, T452), tree(s(T443), T425, T452)) → U35_GAG(T448, T443, T449, T452, T425, lessc20_in_gg(T448, T443))
U35_GAG(T448, T443, T449, T452, T425, lessc20_out_gg(T448, T443)) → U36_GAG(T448, T443, T449, T452, T425, insert1_in_gag(s(T448), T449, T425))
U35_GAG(T448, T443, T449, T452, T425, lessc20_out_gg(T448, T443)) → INSERT1_IN_GAG(s(T448), T449, T425)
INSERT1_IN_GAG(T473, tree(T469, T470, T474), tree(T469, T470, T472)) → U37_GAG(T473, T469, T470, T474, T472, less33_in_gg(T469, T473))
INSERT1_IN_GAG(T477, tree(T469, T481, T478), tree(T469, T481, T472)) → U38_GAG(T477, T469, T481, T478, T472, lessc33_in_gg(T469, T477))
U38_GAG(T477, T469, T481, T478, T472, lessc33_out_gg(T469, T477)) → U39_GAG(T477, T469, T481, T478, T472, insert1_in_gag(T477, T478, T472))
U38_GAG(T477, T469, T481, T478, T472, lessc33_out_gg(T469, T477)) → INSERT1_IN_GAG(T477, T478, T472)
INSERT1_IN_GAG(s(T508), tree(0, T497, T507), tree(0, T497, T499)) → U40_GAG(T508, T497, T507, T499, insert1_in_gag(s(T508), T507, T499))
INSERT1_IN_GAG(s(T517), tree(s(T515), T497, T518), tree(s(T515), T497, T499)) → U41_GAG(T517, T515, T497, T518, T499, less33_in_gg(T515, T517))
INSERT1_IN_GAG(s(T521), tree(s(T515), T525, T522), tree(s(T515), T525, T499)) → U42_GAG(T521, T515, T525, T522, T499, lessc33_in_gg(T515, T521))
U42_GAG(T521, T515, T525, T522, T499, lessc33_out_gg(T515, T521)) → U43_GAG(T521, T515, T525, T522, T499, insert1_in_gag(s(T521), T522, T499))
U42_GAG(T521, T515, T525, T522, T499, lessc33_out_gg(T515, T521)) → INSERT1_IN_GAG(s(T521), T522, T499)
INSERT1_IN_AAG(s(T48), tree(s(T47), T49, void), tree(s(T47), void, void)) → U12_AAG(T48, T47, T49, p18_in_aga(T48, T47, T49))
INSERT1_IN_AAG(s(T48), tree(s(T47), T49, void), tree(s(T47), void, void)) → P18_IN_AGA(T48, T47, T49)
P18_IN_AGA(T48, T47, T49) → U3_AGA(T48, T47, T49, less20_in_ag(T48, T47))
P18_IN_AGA(T48, T47, T49) → LESS20_IN_AG(T48, T47)
LESS20_IN_AG(s(T67), s(T66)) → U1_AG(T67, T66, less20_in_ag(T67, T66))
LESS20_IN_AG(s(T67), s(T66)) → LESS20_IN_AG(T67, T66)
P18_IN_AGA(T52, T47, T53) → U4_AGA(T52, T47, T53, lessc20_in_ag(T52, T47))
U4_AGA(T52, T47, T53, lessc20_out_ag(T52, T47)) → U5_AGA(T52, T47, T53, insert1_in_gag(s(T52), T53, void))
U4_AGA(T52, T47, T53, lessc20_out_ag(T52, T47)) → INSERT1_IN_GAG(s(T52), T53, void)
INSERT1_IN_AAG(T98, tree(T95, void, T99), tree(T95, void, void)) → U13_AAG(T98, T95, T99, less33_in_ga(T95, T98))
INSERT1_IN_AAG(T98, tree(T95, void, T99), tree(T95, void, void)) → LESS33_IN_GA(T95, T98)
LESS33_IN_GA(s(T115), s(T117)) → U2_GA(T115, T117, less33_in_ga(T115, T117))
LESS33_IN_GA(s(T115), s(T117)) → LESS33_IN_GA(T115, T117)
INSERT1_IN_AAG(T102, tree(T95, void, T103), tree(T95, void, void)) → U14_AAG(T102, T95, T103, lessc33_in_ga(T95, T102))
U14_AAG(T102, T95, T103, lessc33_out_ga(T95, T102)) → U15_AAG(T102, T95, T103, insert1_in_aag(T102, T103, void))
U14_AAG(T102, T95, T103, lessc33_out_ga(T95, T102)) → INSERT1_IN_AAG(T102, T103, void)
INSERT1_IN_AAG(T144, tree(T141, void, T145), tree(T141, void, void)) → U16_AAG(T144, T141, T145, p43_in_gaa(T141, T144, T145))
INSERT1_IN_AAG(T144, tree(T141, void, T145), tree(T141, void, void)) → P43_IN_GAA(T141, T144, T145)
P43_IN_GAA(0, s(T152), T151) → U6_GAA(T152, T151, insert1_in_aag(s(T152), T151, void))
P43_IN_GAA(0, s(T152), T151) → INSERT1_IN_AAG(s(T152), T151, void)
INSERT1_IN_AAG(0, tree(s(T213), T214, void), tree(s(T213), void, void)) → U17_AAG(T213, T214, insert1_in_gag(0, T214, void))
INSERT1_IN_AAG(s(T235), tree(s(T234), T236, void), tree(s(T234), void, void)) → U18_AAG(T235, T234, T236, p18_in_aga(T235, T234, T236))
INSERT1_IN_AAG(T251, tree(T248, void, T252), tree(T248, void, void)) → U19_AAG(T251, T248, T252, p43_in_gaa(T248, T251, T252))
P43_IN_GAA(s(T173), s(T175), T176) → U7_GAA(T173, T175, T176, p50_in_gaa(T173, T175, T176))
P43_IN_GAA(s(T173), s(T175), T176) → P50_IN_GAA(T173, T175, T176)
P50_IN_GAA(T173, T175, T176) → U8_GAA(T173, T175, T176, less33_in_ga(T173, T175))
P50_IN_GAA(T173, T175, T176) → LESS33_IN_GA(T173, T175)
P50_IN_GAA(T173, T179, T180) → U9_GAA(T173, T179, T180, lessc33_in_ga(T173, T179))
U9_GAA(T173, T179, T180, lessc33_out_ga(T173, T179)) → U10_GAA(T173, T179, T180, insert1_in_aag(s(T179), T180, void))
U9_GAA(T173, T179, T180, lessc33_out_ga(T173, T179)) → INSERT1_IN_AAG(s(T179), T180, void)
INSERT1_IN_AAG(s(T271), tree(0, void, T270), tree(0, void, void)) → U20_AAG(T271, T270, insert1_in_aag(s(T271), T270, void))
INSERT1_IN_AAG(s(T271), tree(0, void, T270), tree(0, void, void)) → INSERT1_IN_AAG(s(T271), T270, void)
INSERT1_IN_AAG(s(T294), tree(s(T292), void, T295), tree(s(T292), void, void)) → U21_AAG(T294, T292, T295, p50_in_gaa(T292, T294, T295))
INSERT1_IN_AAG(s(T294), tree(s(T292), void, T295), tree(s(T292), void, void)) → P50_IN_GAA(T292, T294, T295)
INSERT1_IN_AAG(0, tree(s(T320), T321, T312), tree(s(T320), T313, T312)) → U22_AAG(T320, T321, T312, T313, insert1_in_gag(0, T321, T313))
INSERT1_IN_AAG(0, tree(s(T320), T321, T312), tree(s(T320), T313, T312)) → INSERT1_IN_GAG(0, T321, T313)
INSERT1_IN_AAG(s(T332), tree(s(T331), T333, T312), tree(s(T331), T313, T312)) → U23_AAG(T332, T331, T333, T312, T313, less20_in_ag(T332, T331))
INSERT1_IN_AAG(s(T332), tree(s(T331), T333, T312), tree(s(T331), T313, T312)) → LESS20_IN_AG(T332, T331)
INSERT1_IN_AAG(s(T336), tree(s(T331), T337, T340), tree(s(T331), T313, T340)) → U24_AAG(T336, T331, T337, T340, T313, lessc20_in_ag(T336, T331))
U24_AAG(T336, T331, T337, T340, T313, lessc20_out_ag(T336, T331)) → U25_AAG(T336, T331, T337, T340, T313, insert1_in_gag(s(T336), T337, T313))
U24_AAG(T336, T331, T337, T340, T313, lessc20_out_ag(T336, T331)) → INSERT1_IN_GAG(s(T336), T337, T313)
INSERT1_IN_AAG(T361, tree(T357, T358, T362), tree(T357, T358, T360)) → U26_AAG(T361, T357, T358, T362, T360, less33_in_ga(T357, T361))
INSERT1_IN_AAG(T361, tree(T357, T358, T362), tree(T357, T358, T360)) → LESS33_IN_GA(T357, T361)
INSERT1_IN_AAG(T365, tree(T357, T369, T366), tree(T357, T369, T360)) → U27_AAG(T365, T357, T369, T366, T360, lessc33_in_ga(T357, T365))
U27_AAG(T365, T357, T369, T366, T360, lessc33_out_ga(T357, T365)) → U28_AAG(T365, T357, T369, T366, T360, insert1_in_aag(T365, T366, T360))
U27_AAG(T365, T357, T369, T366, T360, lessc33_out_ga(T357, T365)) → INSERT1_IN_AAG(T365, T366, T360)
INSERT1_IN_AAG(s(T393), tree(0, T382, T392), tree(0, T382, T384)) → U29_AAG(T393, T382, T392, T384, insert1_in_aag(s(T393), T392, T384))
INSERT1_IN_AAG(s(T393), tree(0, T382, T392), tree(0, T382, T384)) → INSERT1_IN_AAG(s(T393), T392, T384)
INSERT1_IN_AAG(s(T402), tree(s(T400), T382, T403), tree(s(T400), T382, T384)) → U30_AAG(T402, T400, T382, T403, T384, less33_in_ga(T400, T402))
INSERT1_IN_AAG(s(T402), tree(s(T400), T382, T403), tree(s(T400), T382, T384)) → LESS33_IN_GA(T400, T402)
INSERT1_IN_AAG(s(T406), tree(s(T400), T410, T407), tree(s(T400), T410, T384)) → U31_AAG(T406, T400, T410, T407, T384, lessc33_in_ga(T400, T406))
U31_AAG(T406, T400, T410, T407, T384, lessc33_out_ga(T400, T406)) → U32_AAG(T406, T400, T410, T407, T384, insert1_in_aag(s(T406), T407, T384))
U31_AAG(T406, T400, T410, T407, T384, lessc33_out_ga(T400, T406)) → INSERT1_IN_AAG(s(T406), T407, T384)
INSERT1_IN_AAG(0, tree(s(T432), T433, T424), tree(s(T432), T425, T424)) → U33_AAG(T432, T433, T424, T425, insert1_in_gag(0, T433, T425))
INSERT1_IN_AAG(s(T444), tree(s(T443), T445, T424), tree(s(T443), T425, T424)) → U34_AAG(T444, T443, T445, T424, T425, less20_in_ag(T444, T443))
INSERT1_IN_AAG(s(T448), tree(s(T443), T449, T452), tree(s(T443), T425, T452)) → U35_AAG(T448, T443, T449, T452, T425, lessc20_in_ag(T448, T443))
U35_AAG(T448, T443, T449, T452, T425, lessc20_out_ag(T448, T443)) → U36_AAG(T448, T443, T449, T452, T425, insert1_in_gag(s(T448), T449, T425))
U35_AAG(T448, T443, T449, T452, T425, lessc20_out_ag(T448, T443)) → INSERT1_IN_GAG(s(T448), T449, T425)
INSERT1_IN_AAG(T473, tree(T469, T470, T474), tree(T469, T470, T472)) → U37_AAG(T473, T469, T470, T474, T472, less33_in_ga(T469, T473))
INSERT1_IN_AAG(T477, tree(T469, T481, T478), tree(T469, T481, T472)) → U38_AAG(T477, T469, T481, T478, T472, lessc33_in_ga(T469, T477))
U38_AAG(T477, T469, T481, T478, T472, lessc33_out_ga(T469, T477)) → U39_AAG(T477, T469, T481, T478, T472, insert1_in_aag(T477, T478, T472))
U38_AAG(T477, T469, T481, T478, T472, lessc33_out_ga(T469, T477)) → INSERT1_IN_AAG(T477, T478, T472)
INSERT1_IN_AAG(s(T508), tree(0, T497, T507), tree(0, T497, T499)) → U40_AAG(T508, T497, T507, T499, insert1_in_aag(s(T508), T507, T499))
INSERT1_IN_AAG(s(T517), tree(s(T515), T497, T518), tree(s(T515), T497, T499)) → U41_AAG(T517, T515, T497, T518, T499, less33_in_ga(T515, T517))
INSERT1_IN_AAG(s(T521), tree(s(T515), T525, T522), tree(s(T515), T525, T499)) → U42_AAG(T521, T515, T525, T522, T499, lessc33_in_ga(T515, T521))
U42_AAG(T521, T515, T525, T522, T499, lessc33_out_ga(T515, T521)) → U43_AAG(T521, T515, T525, T522, T499, insert1_in_aag(s(T521), T522, T499))
U42_AAG(T521, T515, T525, T522, T499, lessc33_out_ga(T515, T521)) → INSERT1_IN_AAG(s(T521), T522, T499)

The TRS R consists of the following rules:

lessc20_in_gg(0, s(T60)) → lessc20_out_gg(0, s(T60))
lessc20_in_gg(s(T67), s(T66)) → U71_gg(T67, T66, lessc20_in_gg(T67, T66))
U71_gg(T67, T66, lessc20_out_gg(T67, T66)) → lessc20_out_gg(s(T67), s(T66))
lessc33_in_gg(0, s(T110)) → lessc33_out_gg(0, s(T110))
lessc33_in_gg(s(T115), s(T117)) → U72_gg(T115, T117, lessc33_in_gg(T115, T117))
U72_gg(T115, T117, lessc33_out_gg(T115, T117)) → lessc33_out_gg(s(T115), s(T117))
lessc20_in_ag(0, s(T60)) → lessc20_out_ag(0, s(T60))
lessc20_in_ag(s(T67), s(T66)) → U71_ag(T67, T66, lessc20_in_ag(T67, T66))
U71_ag(T67, T66, lessc20_out_ag(T67, T66)) → lessc20_out_ag(s(T67), s(T66))
lessc33_in_ga(0, s(T110)) → lessc33_out_ga(0, s(T110))
lessc33_in_ga(s(T115), s(T117)) → U72_ga(T115, T117, lessc33_in_ga(T115, T117))
U72_ga(T115, T117, lessc33_out_ga(T115, T117)) → lessc33_out_ga(s(T115), s(T117))

The argument filtering Pi contains the following mapping:
insert1_in_aag(x1, x2, x3) = insert1_in_aag(x3)
tree(x1, x2, x3) = tree(x1, x2, x3)
s(x1) = s(x1)
void = void
insert1_in_gag(x1, x2, x3) = insert1_in_gag(x1, x3)
0 = 0
p18_in_gga(x1, x2, x3) = p18_in_gga(x1, x2)
less20_in_gg(x1, x2) = less20_in_gg(x1, x2)
lessc20_in_gg(x1, x2) = lessc20_in_gg(x1, x2)
lessc20_out_gg(x1, x2) = lessc20_out_gg(x1, x2)
U71_gg(x1, x2, x3) = U71_gg(x1, x2, x3)
less33_in_gg(x1, x2) = less33_in_gg(x1, x2)
lessc33_in_gg(x1, x2) = lessc33_in_gg(x1, x2)
lessc33_out_gg(x1, x2) = lessc33_out_gg(x1, x2)
U72_gg(x1, x2, x3) = U72_gg(x1, x2, x3)
p43_in_gga(x1, x2, x3) = p43_in_gga(x1, x2)
p50_in_gga(x1, x2, x3) = p50_in_gga(x1, x2)
p18_in_aga(x1, x2, x3) = p18_in_aga(x2)
less20_in_ag(x1, x2) = less20_in_ag(x2)
lessc20_in_ag(x1, x2) = lessc20_in_ag(x2)
lessc20_out_ag(x1, x2) = lessc20_out_ag(x1, x2)
U71_ag(x1, x2, x3) = U71_ag(x2, x3)
less33_in_ga(x1, x2) = less33_in_ga(x1)
lessc33_in_ga(x1, x2) = lessc33_in_ga(x1)
lessc33_out_ga(x1, x2) = lessc33_out_ga(x1)
U72_ga(x1, x2, x3) = U72_ga(x1, x3)
p43_in_gaa(x1, x2, x3) = p43_in_gaa(x1)
p50_in_gaa(x1, x2, x3) = p50_in_gaa(x1)
INSERT1_IN_AAG(x1, x2, x3) = INSERT1_IN_AAG(x3)
U11_AAG(x1, x2, x3) = U11_AAG(x1, x3)
INSERT1_IN_GAG(x1, x2, x3) = INSERT1_IN_GAG(x1, x3)
U11_GAG(x1, x2, x3) = U11_GAG(x1, x3)
U12_GAG(x1, x2, x3, x4) = U12_GAG(x1, x2, x4)
P18_IN_GGA(x1, x2, x3) = P18_IN_GGA(x1, x2)
U3_GGA(x1, x2, x3, x4) = U3_GGA(x1, x2, x4)
LESS20_IN_GG(x1, x2) = LESS20_IN_GG(x1, x2)
U1_GG(x1, x2, x3) = U1_GG(x1, x2, x3)
U4_GGA(x1, x2, x3, x4) = U4_GGA(x1, x2, x4)
U5_GGA(x1, x2, x3, x4) = U5_GGA(x1, x2, x4)
U13_GAG(x1, x2, x3, x4) = U13_GAG(x1, x2, x4)
LESS33_IN_GG(x1, x2) = LESS33_IN_GG(x1, x2)
U2_GG(x1, x2, x3) = U2_GG(x1, x2, x3)
U14_GAG(x1, x2, x3, x4) = U14_GAG(x1, x2, x4)
U15_GAG(x1, x2, x3, x4) = U15_GAG(x1, x2, x4)
U16_GAG(x1, x2, x3, x4) = U16_GAG(x1, x2, x4)
P43_IN_GGA(x1, x2, x3) = P43_IN_GGA(x1, x2)
U6_GGA(x1, x2, x3) = U6_GGA(x1, x3)
U17_GAG(x1, x2, x3) = U17_GAG(x1, x3)
U18_GAG(x1, x2, x3, x4) = U18_GAG(x1, x2, x4)
U19_GAG(x1, x2, x3, x4) = U19_GAG(x1, x2, x4)
U7_GGA(x1, x2, x3, x4) = U7_GGA(x1, x2, x4)
P50_IN_GGA(x1, x2, x3) = P50_IN_GGA(x1, x2)
U8_GGA(x1, x2, x3, x4) = U8_GGA(x1, x2, x4)
U9_GGA(x1, x2, x3, x4) = U9_GGA(x1, x2, x4)
U10_GGA(x1, x2, x3, x4) = U10_GGA(x1, x2, x4)
U20_GAG(x1, x2, x3) = U20_GAG(x1, x3)
U21_GAG(x1, x2, x3, x4) = U21_GAG(x1, x2, x4)
U22_GAG(x1, x2, x3, x4, x5) = U22_GAG(x1, x3, x4, x5)
U23_GAG(x1, x2, x3, x4, x5, x6) = U23_GAG(x1, x2, x4, x5, x6)
U24_GAG(x1, x2, x3, x4, x5, x6) = U24_GAG(x1, x2, x4, x5, x6)
U25_GAG(x1, x2, x3, x4, x5, x6) = U25_GAG(x1, x2, x4, x5, x6)
U26_GAG(x1, x2, x3, x4, x5, x6) = U26_GAG(x1, x2, x3, x5, x6)
U27_GAG(x1, x2, x3, x4, x5, x6) = U27_GAG(x1, x2, x3, x5, x6)
U28_GAG(x1, x2, x3, x4, x5, x6) = U28_GAG(x1, x2, x3, x5, x6)
U29_GAG(x1, x2, x3, x4, x5) = U29_GAG(x1, x2, x4, x5)
U30_GAG(x1, x2, x3, x4, x5, x6) = U30_GAG(x1, x2, x3, x5, x6)
U31_GAG(x1, x2, x3, x4, x5, x6) = U31_GAG(x1, x2, x3, x5, x6)
U32_GAG(x1, x2, x3, x4, x5, x6) = U32_GAG(x1, x2, x3, x5, x6)
U33_GAG(x1, x2, x3, x4, x5) = U33_GAG(x1, x3, x4, x5)
U34_GAG(x1, x2, x3, x4, x5, x6) = U34_GAG(x1, x2, x4, x5, x6)
U35_GAG(x1, x2, x3, x4, x5, x6) = U35_GAG(x1, x2, x4, x5, x6)
U36_GAG(x1, x2, x3, x4, x5, x6) = U36_GAG(x1, x2, x4, x5, x6)
U37_GAG(x1, x2, x3, x4, x5, x6) = U37_GAG(x1, x2, x3, x5, x6)
U38_GAG(x1, x2, x3, x4, x5, x6) = U38_GAG(x1, x2, x3, x5, x6)
U39_GAG(x1, x2, x3, x4, x5, x6) = U39_GAG(x1, x2, x3, x5, x6)
U40_GAG(x1, x2, x3, x4, x5) = U40_GAG(x1, x2, x4, x5)
U41_GAG(x1, x2, x3, x4, x5, x6) = U41_GAG(x1, x2, x3, x5, x6)
U42_GAG(x1, x2, x3, x4, x5, x6) = U42_GAG(x1, x2, x3, x5, x6)
U43_GAG(x1, x2, x3, x4, x5, x6) = U43_GAG(x1, x2, x3, x5, x6)
U12_AAG(x1, x2, x3, x4) = U12_AAG(x2, x4)
P18_IN_AGA(x1, x2, x3) = P18_IN_AGA(x2)
U3_AGA(x1, x2, x3, x4) = U3_AGA(x2, x4)
LESS20_IN_AG(x1, x2) = LESS20_IN_AG(x2)
U1_AG(x1, x2, x3) = U1_AG(x2, x3)
U4_AGA(x1, x2, x3, x4) = U4_AGA(x2, x4)
U5_AGA(x1, x2, x3, x4) = U5_AGA(x1, x2, x4)
U13_AAG(x1, x2, x3, x4) = U13_AAG(x2, x4)
LESS33_IN_GA(x1, x2) = LESS33_IN_GA(x1)
U2_GA(x1, x2, x3) = U2_GA(x1, x3)
U14_AAG(x1, x2, x3, x4) = U14_AAG(x2, x4)
U15_AAG(x1, x2, x3, x4) = U15_AAG(x2, x4)
U16_AAG(x1, x2, x3, x4) = U16_AAG(x2, x4)
P43_IN_GAA(x1, x2, x3) = P43_IN_GAA(x1)
U6_GAA(x1, x2, x3) = U6_GAA(x3)
U17_AAG(x1, x2, x3) = U17_AAG(x1, x3)
U18_AAG(x1, x2, x3, x4) = U18_AAG(x2, x4)
U19_AAG(x1, x2, x3, x4) = U19_AAG(x2, x4)
U7_GAA(x1, x2, x3, x4) = U7_GAA(x1, x4)
P50_IN_GAA(x1, x2, x3) = P50_IN_GAA(x1)
U8_GAA(x1, x2, x3, x4) = U8_GAA(x1, x4)
U9_GAA(x1, x2, x3, x4) = U9_GAA(x1, x4)
U10_GAA(x1, x2, x3, x4) = U10_GAA(x1, x4)
U20_AAG(x1, x2, x3) = U20_AAG(x3)
U21_AAG(x1, x2, x3, x4) = U21_AAG(x2, x4)
U22_AAG(x1, x2, x3, x4, x5) = U22_AAG(x1, x3, x4, x5)
U23_AAG(x1, x2, x3, x4, x5, x6) = U23_AAG(x2, x4, x5, x6)
U24_AAG(x1, x2, x3, x4, x5, x6) = U24_AAG(x2, x4, x5, x6)
U25_AAG(x1, x2, x3, x4, x5, x6) = U25_AAG(x1, x2, x4, x5, x6)
U26_AAG(x1, x2, x3, x4, x5, x6) = U26_AAG(x2, x3, x5, x6)
U27_AAG(x1, x2, x3, x4, x5, x6) = U27_AAG(x2, x3, x5, x6)
U28_AAG(x1, x2, x3, x4, x5, x6) = U28_AAG(x2, x3, x5, x6)
U29_AAG(x1, x2, x3, x4, x5) = U29_AAG(x2, x4, x5)
U30_AAG(x1, x2, x3, x4, x5, x6) = U30_AAG(x2, x3, x5, x6)
U31_AAG(x1, x2, x3, x4, x5, x6) = U31_AAG(x2, x3, x5, x6)
U32_AAG(x1, x2, x3, x4, x5, x6) = U32_AAG(x2, x3, x5, x6)
U33_AAG(x1, x2, x3, x4, x5) = U33_AAG(x1, x3, x4, x5)
U34_AAG(x1, x2, x3, x4, x5, x6) = U34_AAG(x2, x4, x5, x6)
U35_AAG(x1, x2, x3, x4, x5, x6) = U35_AAG(x2, x4, x5, x6)
U36_AAG(x1, x2, x3, x4, x5, x6) = U36_AAG(x1, x2, x4, x5, x6)
U37_AAG(x1, x2, x3, x4, x5, x6) = U37_AAG(x2, x3, x5, x6)
U38_AAG(x1, x2, x3, x4, x5, x6) = U38_AAG(x2, x3, x5, x6)
U39_AAG(x1, x2, x3, x4, x5, x6) = U39_AAG(x2, x3, x5, x6)
U40_AAG(x1, x2, x3, x4, x5) = U40_AAG(x2, x4, x5)
U41_AAG(x1, x2, x3, x4, x5, x6) = U41_AAG(x2, x3, x5, x6)
U42_AAG(x1, x2, x3, x4, x5, x6) = U42_AAG(x2, x3, x5, x6)
U43_AAG(x1, x2, x3, x4, x5, x6) = U43_AAG(x2, x3, x5, x6)

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

Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES

(4) Obligation:

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

INSERT1_IN_AAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U11_AAG(T26, T27, insert1_in_gag(0, T27, void))
INSERT1_IN_AAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → INSERT1_IN_GAG(0, T27, void)
INSERT1_IN_GAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U11_GAG(T26, T27, insert1_in_gag(0, T27, void))
INSERT1_IN_GAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → INSERT1_IN_GAG(0, T27, void)
INSERT1_IN_GAG(s(T48), tree(s(T47), T49, void), tree(s(T47), void, void)) → U12_GAG(T48, T47, T49, p18_in_gga(T48, T47, T49))
INSERT1_IN_GAG(s(T48), tree(s(T47), T49, void), tree(s(T47), void, void)) → P18_IN_GGA(T48, T47, T49)
P18_IN_GGA(T48, T47, T49) → U3_GGA(T48, T47, T49, less20_in_gg(T48, T47))
P18_IN_GGA(T48, T47, T49) → LESS20_IN_GG(T48, T47)
LESS20_IN_GG(s(T67), s(T66)) → U1_GG(T67, T66, less20_in_gg(T67, T66))
LESS20_IN_GG(s(T67), s(T66)) → LESS20_IN_GG(T67, T66)
P18_IN_GGA(T52, T47, T53) → U4_GGA(T52, T47, T53, lessc20_in_gg(T52, T47))
U4_GGA(T52, T47, T53, lessc20_out_gg(T52, T47)) → U5_GGA(T52, T47, T53, insert1_in_gag(s(T52), T53, void))
U4_GGA(T52, T47, T53, lessc20_out_gg(T52, T47)) → INSERT1_IN_GAG(s(T52), T53, void)
INSERT1_IN_GAG(T98, tree(T95, void, T99), tree(T95, void, void)) → U13_GAG(T98, T95, T99, less33_in_gg(T95, T98))
INSERT1_IN_GAG(T98, tree(T95, void, T99), tree(T95, void, void)) → LESS33_IN_GG(T95, T98)
LESS33_IN_GG(s(T115), s(T117)) → U2_GG(T115, T117, less33_in_gg(T115, T117))
LESS33_IN_GG(s(T115), s(T117)) → LESS33_IN_GG(T115, T117)
INSERT1_IN_GAG(T102, tree(T95, void, T103), tree(T95, void, void)) → U14_GAG(T102, T95, T103, lessc33_in_gg(T95, T102))
U14_GAG(T102, T95, T103, lessc33_out_gg(T95, T102)) → U15_GAG(T102, T95, T103, insert1_in_gag(T102, T103, void))
U14_GAG(T102, T95, T103, lessc33_out_gg(T95, T102)) → INSERT1_IN_GAG(T102, T103, void)
INSERT1_IN_GAG(T144, tree(T141, void, T145), tree(T141, void, void)) → U16_GAG(T144, T141, T145, p43_in_gga(T141, T144, T145))
INSERT1_IN_GAG(T144, tree(T141, void, T145), tree(T141, void, void)) → P43_IN_GGA(T141, T144, T145)
P43_IN_GGA(0, s(T152), T151) → U6_GGA(T152, T151, insert1_in_gag(s(T152), T151, void))
P43_IN_GGA(0, s(T152), T151) → INSERT1_IN_GAG(s(T152), T151, void)
INSERT1_IN_GAG(0, tree(s(T213), T214, void), tree(s(T213), void, void)) → U17_GAG(T213, T214, insert1_in_gag(0, T214, void))
INSERT1_IN_GAG(s(T235), tree(s(T234), T236, void), tree(s(T234), void, void)) → U18_GAG(T235, T234, T236, p18_in_gga(T235, T234, T236))
INSERT1_IN_GAG(T251, tree(T248, void, T252), tree(T248, void, void)) → U19_GAG(T251, T248, T252, p43_in_gga(T248, T251, T252))
P43_IN_GGA(s(T173), s(T175), T176) → U7_GGA(T173, T175, T176, p50_in_gga(T173, T175, T176))
P43_IN_GGA(s(T173), s(T175), T176) → P50_IN_GGA(T173, T175, T176)
P50_IN_GGA(T173, T175, T176) → U8_GGA(T173, T175, T176, less33_in_gg(T173, T175))
P50_IN_GGA(T173, T175, T176) → LESS33_IN_GG(T173, T175)
P50_IN_GGA(T173, T179, T180) → U9_GGA(T173, T179, T180, lessc33_in_gg(T173, T179))
U9_GGA(T173, T179, T180, lessc33_out_gg(T173, T179)) → U10_GGA(T173, T179, T180, insert1_in_gag(s(T179), T180, void))
U9_GGA(T173, T179, T180, lessc33_out_gg(T173, T179)) → INSERT1_IN_GAG(s(T179), T180, void)
INSERT1_IN_GAG(s(T271), tree(0, void, T270), tree(0, void, void)) → U20_GAG(T271, T270, insert1_in_gag(s(T271), T270, void))
INSERT1_IN_GAG(s(T271), tree(0, void, T270), tree(0, void, void)) → INSERT1_IN_GAG(s(T271), T270, void)
INSERT1_IN_GAG(s(T294), tree(s(T292), void, T295), tree(s(T292), void, void)) → U21_GAG(T294, T292, T295, p50_in_gga(T292, T294, T295))
INSERT1_IN_GAG(s(T294), tree(s(T292), void, T295), tree(s(T292), void, void)) → P50_IN_GGA(T292, T294, T295)
INSERT1_IN_GAG(0, tree(s(T320), T321, T312), tree(s(T320), T313, T312)) → U22_GAG(T320, T321, T312, T313, insert1_in_gag(0, T321, T313))
INSERT1_IN_GAG(0, tree(s(T320), T321, T312), tree(s(T320), T313, T312)) → INSERT1_IN_GAG(0, T321, T313)
INSERT1_IN_GAG(s(T332), tree(s(T331), T333, T312), tree(s(T331), T313, T312)) → U23_GAG(T332, T331, T333, T312, T313, less20_in_gg(T332, T331))
INSERT1_IN_GAG(s(T332), tree(s(T331), T333, T312), tree(s(T331), T313, T312)) → LESS20_IN_GG(T332, T331)
INSERT1_IN_GAG(s(T336), tree(s(T331), T337, T340), tree(s(T331), T313, T340)) → U24_GAG(T336, T331, T337, T340, T313, lessc20_in_gg(T336, T331))
U24_GAG(T336, T331, T337, T340, T313, lessc20_out_gg(T336, T331)) → U25_GAG(T336, T331, T337, T340, T313, insert1_in_gag(s(T336), T337, T313))
U24_GAG(T336, T331, T337, T340, T313, lessc20_out_gg(T336, T331)) → INSERT1_IN_GAG(s(T336), T337, T313)
INSERT1_IN_GAG(T361, tree(T357, T358, T362), tree(T357, T358, T360)) → U26_GAG(T361, T357, T358, T362, T360, less33_in_gg(T357, T361))
INSERT1_IN_GAG(T361, tree(T357, T358, T362), tree(T357, T358, T360)) → LESS33_IN_GG(T357, T361)
INSERT1_IN_GAG(T365, tree(T357, T369, T366), tree(T357, T369, T360)) → U27_GAG(T365, T357, T369, T366, T360, lessc33_in_gg(T357, T365))
U27_GAG(T365, T357, T369, T366, T360, lessc33_out_gg(T357, T365)) → U28_GAG(T365, T357, T369, T366, T360, insert1_in_gag(T365, T366, T360))
U27_GAG(T365, T357, T369, T366, T360, lessc33_out_gg(T357, T365)) → INSERT1_IN_GAG(T365, T366, T360)
INSERT1_IN_GAG(s(T393), tree(0, T382, T392), tree(0, T382, T384)) → U29_GAG(T393, T382, T392, T384, insert1_in_gag(s(T393), T392, T384))
INSERT1_IN_GAG(s(T393), tree(0, T382, T392), tree(0, T382, T384)) → INSERT1_IN_GAG(s(T393), T392, T384)
INSERT1_IN_GAG(s(T402), tree(s(T400), T382, T403), tree(s(T400), T382, T384)) → U30_GAG(T402, T400, T382, T403, T384, less33_in_gg(T400, T402))
INSERT1_IN_GAG(s(T402), tree(s(T400), T382, T403), tree(s(T400), T382, T384)) → LESS33_IN_GG(T400, T402)
INSERT1_IN_GAG(s(T406), tree(s(T400), T410, T407), tree(s(T400), T410, T384)) → U31_GAG(T406, T400, T410, T407, T384, lessc33_in_gg(T400, T406))
U31_GAG(T406, T400, T410, T407, T384, lessc33_out_gg(T400, T406)) → U32_GAG(T406, T400, T410, T407, T384, insert1_in_gag(s(T406), T407, T384))
U31_GAG(T406, T400, T410, T407, T384, lessc33_out_gg(T400, T406)) → INSERT1_IN_GAG(s(T406), T407, T384)
INSERT1_IN_GAG(0, tree(s(T432), T433, T424), tree(s(T432), T425, T424)) → U33_GAG(T432, T433, T424, T425, insert1_in_gag(0, T433, T425))
INSERT1_IN_GAG(s(T444), tree(s(T443), T445, T424), tree(s(T443), T425, T424)) → U34_GAG(T444, T443, T445, T424, T425, less20_in_gg(T444, T443))
INSERT1_IN_GAG(s(T448), tree(s(T443), T449, T452), tree(s(T443), T425, T452)) → U35_GAG(T448, T443, T449, T452, T425, lessc20_in_gg(T448, T443))
U35_GAG(T448, T443, T449, T452, T425, lessc20_out_gg(T448, T443)) → U36_GAG(T448, T443, T449, T452, T425, insert1_in_gag(s(T448), T449, T425))
U35_GAG(T448, T443, T449, T452, T425, lessc20_out_gg(T448, T443)) → INSERT1_IN_GAG(s(T448), T449, T425)
INSERT1_IN_GAG(T473, tree(T469, T470, T474), tree(T469, T470, T472)) → U37_GAG(T473, T469, T470, T474, T472, less33_in_gg(T469, T473))
INSERT1_IN_GAG(T477, tree(T469, T481, T478), tree(T469, T481, T472)) → U38_GAG(T477, T469, T481, T478, T472, lessc33_in_gg(T469, T477))
U38_GAG(T477, T469, T481, T478, T472, lessc33_out_gg(T469, T477)) → U39_GAG(T477, T469, T481, T478, T472, insert1_in_gag(T477, T478, T472))
U38_GAG(T477, T469, T481, T478, T472, lessc33_out_gg(T469, T477)) → INSERT1_IN_GAG(T477, T478, T472)
INSERT1_IN_GAG(s(T508), tree(0, T497, T507), tree(0, T497, T499)) → U40_GAG(T508, T497, T507, T499, insert1_in_gag(s(T508), T507, T499))
INSERT1_IN_GAG(s(T517), tree(s(T515), T497, T518), tree(s(T515), T497, T499)) → U41_GAG(T517, T515, T497, T518, T499, less33_in_gg(T515, T517))
INSERT1_IN_GAG(s(T521), tree(s(T515), T525, T522), tree(s(T515), T525, T499)) → U42_GAG(T521, T515, T525, T522, T499, lessc33_in_gg(T515, T521))
U42_GAG(T521, T515, T525, T522, T499, lessc33_out_gg(T515, T521)) → U43_GAG(T521, T515, T525, T522, T499, insert1_in_gag(s(T521), T522, T499))
U42_GAG(T521, T515, T525, T522, T499, lessc33_out_gg(T515, T521)) → INSERT1_IN_GAG(s(T521), T522, T499)
INSERT1_IN_AAG(s(T48), tree(s(T47), T49, void), tree(s(T47), void, void)) → U12_AAG(T48, T47, T49, p18_in_aga(T48, T47, T49))
INSERT1_IN_AAG(s(T48), tree(s(T47), T49, void), tree(s(T47), void, void)) → P18_IN_AGA(T48, T47, T49)
P18_IN_AGA(T48, T47, T49) → U3_AGA(T48, T47, T49, less20_in_ag(T48, T47))
P18_IN_AGA(T48, T47, T49) → LESS20_IN_AG(T48, T47)
LESS20_IN_AG(s(T67), s(T66)) → U1_AG(T67, T66, less20_in_ag(T67, T66))
LESS20_IN_AG(s(T67), s(T66)) → LESS20_IN_AG(T67, T66)
P18_IN_AGA(T52, T47, T53) → U4_AGA(T52, T47, T53, lessc20_in_ag(T52, T47))
U4_AGA(T52, T47, T53, lessc20_out_ag(T52, T47)) → U5_AGA(T52, T47, T53, insert1_in_gag(s(T52), T53, void))
U4_AGA(T52, T47, T53, lessc20_out_ag(T52, T47)) → INSERT1_IN_GAG(s(T52), T53, void)
INSERT1_IN_AAG(T98, tree(T95, void, T99), tree(T95, void, void)) → U13_AAG(T98, T95, T99, less33_in_ga(T95, T98))
INSERT1_IN_AAG(T98, tree(T95, void, T99), tree(T95, void, void)) → LESS33_IN_GA(T95, T98)
LESS33_IN_GA(s(T115), s(T117)) → U2_GA(T115, T117, less33_in_ga(T115, T117))
LESS33_IN_GA(s(T115), s(T117)) → LESS33_IN_GA(T115, T117)
INSERT1_IN_AAG(T102, tree(T95, void, T103), tree(T95, void, void)) → U14_AAG(T102, T95, T103, lessc33_in_ga(T95, T102))
U14_AAG(T102, T95, T103, lessc33_out_ga(T95, T102)) → U15_AAG(T102, T95, T103, insert1_in_aag(T102, T103, void))
U14_AAG(T102, T95, T103, lessc33_out_ga(T95, T102)) → INSERT1_IN_AAG(T102, T103, void)
INSERT1_IN_AAG(T144, tree(T141, void, T145), tree(T141, void, void)) → U16_AAG(T144, T141, T145, p43_in_gaa(T141, T144, T145))
INSERT1_IN_AAG(T144, tree(T141, void, T145), tree(T141, void, void)) → P43_IN_GAA(T141, T144, T145)
P43_IN_GAA(0, s(T152), T151) → U6_GAA(T152, T151, insert1_in_aag(s(T152), T151, void))
P43_IN_GAA(0, s(T152), T151) → INSERT1_IN_AAG(s(T152), T151, void)
INSERT1_IN_AAG(0, tree(s(T213), T214, void), tree(s(T213), void, void)) → U17_AAG(T213, T214, insert1_in_gag(0, T214, void))
INSERT1_IN_AAG(s(T235), tree(s(T234), T236, void), tree(s(T234), void, void)) → U18_AAG(T235, T234, T236, p18_in_aga(T235, T234, T236))
INSERT1_IN_AAG(T251, tree(T248, void, T252), tree(T248, void, void)) → U19_AAG(T251, T248, T252, p43_in_gaa(T248, T251, T252))
P43_IN_GAA(s(T173), s(T175), T176) → U7_GAA(T173, T175, T176, p50_in_gaa(T173, T175, T176))
P43_IN_GAA(s(T173), s(T175), T176) → P50_IN_GAA(T173, T175, T176)
P50_IN_GAA(T173, T175, T176) → U8_GAA(T173, T175, T176, less33_in_ga(T173, T175))
P50_IN_GAA(T173, T175, T176) → LESS33_IN_GA(T173, T175)
P50_IN_GAA(T173, T179, T180) → U9_GAA(T173, T179, T180, lessc33_in_ga(T173, T179))
U9_GAA(T173, T179, T180, lessc33_out_ga(T173, T179)) → U10_GAA(T173, T179, T180, insert1_in_aag(s(T179), T180, void))
U9_GAA(T173, T179, T180, lessc33_out_ga(T173, T179)) → INSERT1_IN_AAG(s(T179), T180, void)
INSERT1_IN_AAG(s(T271), tree(0, void, T270), tree(0, void, void)) → U20_AAG(T271, T270, insert1_in_aag(s(T271), T270, void))
INSERT1_IN_AAG(s(T271), tree(0, void, T270), tree(0, void, void)) → INSERT1_IN_AAG(s(T271), T270, void)
INSERT1_IN_AAG(s(T294), tree(s(T292), void, T295), tree(s(T292), void, void)) → U21_AAG(T294, T292, T295, p50_in_gaa(T292, T294, T295))
INSERT1_IN_AAG(s(T294), tree(s(T292), void, T295), tree(s(T292), void, void)) → P50_IN_GAA(T292, T294, T295)
INSERT1_IN_AAG(0, tree(s(T320), T321, T312), tree(s(T320), T313, T312)) → U22_AAG(T320, T321, T312, T313, insert1_in_gag(0, T321, T313))
INSERT1_IN_AAG(0, tree(s(T320), T321, T312), tree(s(T320), T313, T312)) → INSERT1_IN_GAG(0, T321, T313)
INSERT1_IN_AAG(s(T332), tree(s(T331), T333, T312), tree(s(T331), T313, T312)) → U23_AAG(T332, T331, T333, T312, T313, less20_in_ag(T332, T331))
INSERT1_IN_AAG(s(T332), tree(s(T331), T333, T312), tree(s(T331), T313, T312)) → LESS20_IN_AG(T332, T331)
INSERT1_IN_AAG(s(T336), tree(s(T331), T337, T340), tree(s(T331), T313, T340)) → U24_AAG(T336, T331, T337, T340, T313, lessc20_in_ag(T336, T331))
U24_AAG(T336, T331, T337, T340, T313, lessc20_out_ag(T336, T331)) → U25_AAG(T336, T331, T337, T340, T313, insert1_in_gag(s(T336), T337, T313))
U24_AAG(T336, T331, T337, T340, T313, lessc20_out_ag(T336, T331)) → INSERT1_IN_GAG(s(T336), T337, T313)
INSERT1_IN_AAG(T361, tree(T357, T358, T362), tree(T357, T358, T360)) → U26_AAG(T361, T357, T358, T362, T360, less33_in_ga(T357, T361))
INSERT1_IN_AAG(T361, tree(T357, T358, T362), tree(T357, T358, T360)) → LESS33_IN_GA(T357, T361)
INSERT1_IN_AAG(T365, tree(T357, T369, T366), tree(T357, T369, T360)) → U27_AAG(T365, T357, T369, T366, T360, lessc33_in_ga(T357, T365))
U27_AAG(T365, T357, T369, T366, T360, lessc33_out_ga(T357, T365)) → U28_AAG(T365, T357, T369, T366, T360, insert1_in_aag(T365, T366, T360))
U27_AAG(T365, T357, T369, T366, T360, lessc33_out_ga(T357, T365)) → INSERT1_IN_AAG(T365, T366, T360)
INSERT1_IN_AAG(s(T393), tree(0, T382, T392), tree(0, T382, T384)) → U29_AAG(T393, T382, T392, T384, insert1_in_aag(s(T393), T392, T384))
INSERT1_IN_AAG(s(T393), tree(0, T382, T392), tree(0, T382, T384)) → INSERT1_IN_AAG(s(T393), T392, T384)
INSERT1_IN_AAG(s(T402), tree(s(T400), T382, T403), tree(s(T400), T382, T384)) → U30_AAG(T402, T400, T382, T403, T384, less33_in_ga(T400, T402))
INSERT1_IN_AAG(s(T402), tree(s(T400), T382, T403), tree(s(T400), T382, T384)) → LESS33_IN_GA(T400, T402)
INSERT1_IN_AAG(s(T406), tree(s(T400), T410, T407), tree(s(T400), T410, T384)) → U31_AAG(T406, T400, T410, T407, T384, lessc33_in_ga(T400, T406))
U31_AAG(T406, T400, T410, T407, T384, lessc33_out_ga(T400, T406)) → U32_AAG(T406, T400, T410, T407, T384, insert1_in_aag(s(T406), T407, T384))
U31_AAG(T406, T400, T410, T407, T384, lessc33_out_ga(T400, T406)) → INSERT1_IN_AAG(s(T406), T407, T384)
INSERT1_IN_AAG(0, tree(s(T432), T433, T424), tree(s(T432), T425, T424)) → U33_AAG(T432, T433, T424, T425, insert1_in_gag(0, T433, T425))
INSERT1_IN_AAG(s(T444), tree(s(T443), T445, T424), tree(s(T443), T425, T424)) → U34_AAG(T444, T443, T445, T424, T425, less20_in_ag(T444, T443))
INSERT1_IN_AAG(s(T448), tree(s(T443), T449, T452), tree(s(T443), T425, T452)) → U35_AAG(T448, T443, T449, T452, T425, lessc20_in_ag(T448, T443))
U35_AAG(T448, T443, T449, T452, T425, lessc20_out_ag(T448, T443)) → U36_AAG(T448, T443, T449, T452, T425, insert1_in_gag(s(T448), T449, T425))
U35_AAG(T448, T443, T449, T452, T425, lessc20_out_ag(T448, T443)) → INSERT1_IN_GAG(s(T448), T449, T425)
INSERT1_IN_AAG(T473, tree(T469, T470, T474), tree(T469, T470, T472)) → U37_AAG(T473, T469, T470, T474, T472, less33_in_ga(T469, T473))
INSERT1_IN_AAG(T477, tree(T469, T481, T478), tree(T469, T481, T472)) → U38_AAG(T477, T469, T481, T478, T472, lessc33_in_ga(T469, T477))
U38_AAG(T477, T469, T481, T478, T472, lessc33_out_ga(T469, T477)) → U39_AAG(T477, T469, T481, T478, T472, insert1_in_aag(T477, T478, T472))
U38_AAG(T477, T469, T481, T478, T472, lessc33_out_ga(T469, T477)) → INSERT1_IN_AAG(T477, T478, T472)
INSERT1_IN_AAG(s(T508), tree(0, T497, T507), tree(0, T497, T499)) → U40_AAG(T508, T497, T507, T499, insert1_in_aag(s(T508), T507, T499))
INSERT1_IN_AAG(s(T517), tree(s(T515), T497, T518), tree(s(T515), T497, T499)) → U41_AAG(T517, T515, T497, T518, T499, less33_in_ga(T515, T517))
INSERT1_IN_AAG(s(T521), tree(s(T515), T525, T522), tree(s(T515), T525, T499)) → U42_AAG(T521, T515, T525, T522, T499, lessc33_in_ga(T515, T521))
U42_AAG(T521, T515, T525, T522, T499, lessc33_out_ga(T515, T521)) → U43_AAG(T521, T515, T525, T522, T499, insert1_in_aag(s(T521), T522, T499))
U42_AAG(T521, T515, T525, T522, T499, lessc33_out_ga(T515, T521)) → INSERT1_IN_AAG(s(T521), T522, T499)

The TRS R consists of the following rules:

lessc20_in_gg(0, s(T60)) → lessc20_out_gg(0, s(T60))
lessc20_in_gg(s(T67), s(T66)) → U71_gg(T67, T66, lessc20_in_gg(T67, T66))
U71_gg(T67, T66, lessc20_out_gg(T67, T66)) → lessc20_out_gg(s(T67), s(T66))
lessc33_in_gg(0, s(T110)) → lessc33_out_gg(0, s(T110))
lessc33_in_gg(s(T115), s(T117)) → U72_gg(T115, T117, lessc33_in_gg(T115, T117))
U72_gg(T115, T117, lessc33_out_gg(T115, T117)) → lessc33_out_gg(s(T115), s(T117))
lessc20_in_ag(0, s(T60)) → lessc20_out_ag(0, s(T60))
lessc20_in_ag(s(T67), s(T66)) → U71_ag(T67, T66, lessc20_in_ag(T67, T66))
U71_ag(T67, T66, lessc20_out_ag(T67, T66)) → lessc20_out_ag(s(T67), s(T66))
lessc33_in_ga(0, s(T110)) → lessc33_out_ga(0, s(T110))
lessc33_in_ga(s(T115), s(T117)) → U72_ga(T115, T117, lessc33_in_ga(T115, T117))
U72_ga(T115, T117, lessc33_out_ga(T115, T117)) → lessc33_out_ga(s(T115), s(T117))

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 6 SCCs with 111 less nodes.

(6) Complex Obligation (AND)

(7) Obligation:

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

LESS33_IN_GA(s(T115), s(T117)) → LESS33_IN_GA(T115, T117)

The TRS R consists of the following rules:

lessc20_in_gg(0, s(T60)) → lessc20_out_gg(0, s(T60))
lessc20_in_gg(s(T67), s(T66)) → U71_gg(T67, T66, lessc20_in_gg(T67, T66))
U71_gg(T67, T66, lessc20_out_gg(T67, T66)) → lessc20_out_gg(s(T67), s(T66))
lessc33_in_gg(0, s(T110)) → lessc33_out_gg(0, s(T110))
lessc33_in_gg(s(T115), s(T117)) → U72_gg(T115, T117, lessc33_in_gg(T115, T117))
U72_gg(T115, T117, lessc33_out_gg(T115, T117)) → lessc33_out_gg(s(T115), s(T117))
lessc20_in_ag(0, s(T60)) → lessc20_out_ag(0, s(T60))
lessc20_in_ag(s(T67), s(T66)) → U71_ag(T67, T66, lessc20_in_ag(T67, T66))
U71_ag(T67, T66, lessc20_out_ag(T67, T66)) → lessc20_out_ag(s(T67), s(T66))
lessc33_in_ga(0, s(T110)) → lessc33_out_ga(0, s(T110))
lessc33_in_ga(s(T115), s(T117)) → U72_ga(T115, T117, lessc33_in_ga(T115, T117))
U72_ga(T115, T117, lessc33_out_ga(T115, T117)) → lessc33_out_ga(s(T115), s(T117))

The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
0 = 0
lessc20_in_gg(x1, x2) = lessc20_in_gg(x1, x2)
lessc20_out_gg(x1, x2) = lessc20_out_gg(x1, x2)
U71_gg(x1, x2, x3) = U71_gg(x1, x2, x3)
lessc33_in_gg(x1, x2) = lessc33_in_gg(x1, x2)
lessc33_out_gg(x1, x2) = lessc33_out_gg(x1, x2)
U72_gg(x1, x2, x3) = U72_gg(x1, x2, x3)
lessc20_in_ag(x1, x2) = lessc20_in_ag(x2)
lessc20_out_ag(x1, x2) = lessc20_out_ag(x1, x2)
U71_ag(x1, x2, x3) = U71_ag(x2, x3)
lessc33_in_ga(x1, x2) = lessc33_in_ga(x1)
lessc33_out_ga(x1, x2) = lessc33_out_ga(x1)
U72_ga(x1, x2, x3) = U72_ga(x1, x3)
LESS33_IN_GA(x1, x2) = LESS33_IN_GA(x1)

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

(8) UsableRulesProof (EQUIVALENT transformation)

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

(9) Obligation:

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

LESS33_IN_GA(s(T115), s(T117)) → LESS33_IN_GA(T115, T117)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
LESS33_IN_GA(x1, x2) = LESS33_IN_GA(x1)

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

(10) PiDPToQDPProof (SOUND transformation)

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

(11) Obligation:

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

LESS33_IN_GA(s(T115)) → LESS33_IN_GA(T115)

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

(12) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

LESS33_IN_GA(s(T115)) → LESS33_IN_GA(T115)
The graph contains the following edges 1 > 1

(13) YES

(14) Obligation:

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

LESS20_IN_AG(s(T67), s(T66)) → LESS20_IN_AG(T67, T66)

The TRS R consists of the following rules:

lessc20_in_gg(0, s(T60)) → lessc20_out_gg(0, s(T60))
lessc20_in_gg(s(T67), s(T66)) → U71_gg(T67, T66, lessc20_in_gg(T67, T66))
U71_gg(T67, T66, lessc20_out_gg(T67, T66)) → lessc20_out_gg(s(T67), s(T66))
lessc33_in_gg(0, s(T110)) → lessc33_out_gg(0, s(T110))
lessc33_in_gg(s(T115), s(T117)) → U72_gg(T115, T117, lessc33_in_gg(T115, T117))
U72_gg(T115, T117, lessc33_out_gg(T115, T117)) → lessc33_out_gg(s(T115), s(T117))
lessc20_in_ag(0, s(T60)) → lessc20_out_ag(0, s(T60))
lessc20_in_ag(s(T67), s(T66)) → U71_ag(T67, T66, lessc20_in_ag(T67, T66))
U71_ag(T67, T66, lessc20_out_ag(T67, T66)) → lessc20_out_ag(s(T67), s(T66))
lessc33_in_ga(0, s(T110)) → lessc33_out_ga(0, s(T110))
lessc33_in_ga(s(T115), s(T117)) → U72_ga(T115, T117, lessc33_in_ga(T115, T117))
U72_ga(T115, T117, lessc33_out_ga(T115, T117)) → lessc33_out_ga(s(T115), s(T117))

The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
0 = 0
lessc20_in_gg(x1, x2) = lessc20_in_gg(x1, x2)
lessc20_out_gg(x1, x2) = lessc20_out_gg(x1, x2)
U71_gg(x1, x2, x3) = U71_gg(x1, x2, x3)
lessc33_in_gg(x1, x2) = lessc33_in_gg(x1, x2)
lessc33_out_gg(x1, x2) = lessc33_out_gg(x1, x2)
U72_gg(x1, x2, x3) = U72_gg(x1, x2, x3)
lessc20_in_ag(x1, x2) = lessc20_in_ag(x2)
lessc20_out_ag(x1, x2) = lessc20_out_ag(x1, x2)
U71_ag(x1, x2, x3) = U71_ag(x2, x3)
lessc33_in_ga(x1, x2) = lessc33_in_ga(x1)
lessc33_out_ga(x1, x2) = lessc33_out_ga(x1)
U72_ga(x1, x2, x3) = U72_ga(x1, x3)
LESS20_IN_AG(x1, x2) = LESS20_IN_AG(x2)

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

(15) UsableRulesProof (EQUIVALENT transformation)

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

(16) Obligation:

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

LESS20_IN_AG(s(T67), s(T66)) → LESS20_IN_AG(T67, T66)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
LESS20_IN_AG(x1, x2) = LESS20_IN_AG(x2)

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

(17) PiDPToQDPProof (SOUND transformation)

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

(18) Obligation:

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

LESS20_IN_AG(s(T66)) → LESS20_IN_AG(T66)

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

(19) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

LESS20_IN_AG(s(T66)) → LESS20_IN_AG(T66)
The graph contains the following edges 1 > 1

(20) YES

(21) Obligation:

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

LESS33_IN_GG(s(T115), s(T117)) → LESS33_IN_GG(T115, T117)

The TRS R consists of the following rules:

lessc20_in_gg(0, s(T60)) → lessc20_out_gg(0, s(T60))
lessc20_in_gg(s(T67), s(T66)) → U71_gg(T67, T66, lessc20_in_gg(T67, T66))
U71_gg(T67, T66, lessc20_out_gg(T67, T66)) → lessc20_out_gg(s(T67), s(T66))
lessc33_in_gg(0, s(T110)) → lessc33_out_gg(0, s(T110))
lessc33_in_gg(s(T115), s(T117)) → U72_gg(T115, T117, lessc33_in_gg(T115, T117))
U72_gg(T115, T117, lessc33_out_gg(T115, T117)) → lessc33_out_gg(s(T115), s(T117))
lessc20_in_ag(0, s(T60)) → lessc20_out_ag(0, s(T60))
lessc20_in_ag(s(T67), s(T66)) → U71_ag(T67, T66, lessc20_in_ag(T67, T66))
U71_ag(T67, T66, lessc20_out_ag(T67, T66)) → lessc20_out_ag(s(T67), s(T66))
lessc33_in_ga(0, s(T110)) → lessc33_out_ga(0, s(T110))
lessc33_in_ga(s(T115), s(T117)) → U72_ga(T115, T117, lessc33_in_ga(T115, T117))
U72_ga(T115, T117, lessc33_out_ga(T115, T117)) → lessc33_out_ga(s(T115), s(T117))

The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
0 = 0
lessc20_in_gg(x1, x2) = lessc20_in_gg(x1, x2)
lessc20_out_gg(x1, x2) = lessc20_out_gg(x1, x2)
U71_gg(x1, x2, x3) = U71_gg(x1, x2, x3)
lessc33_in_gg(x1, x2) = lessc33_in_gg(x1, x2)
lessc33_out_gg(x1, x2) = lessc33_out_gg(x1, x2)
U72_gg(x1, x2, x3) = U72_gg(x1, x2, x3)
lessc20_in_ag(x1, x2) = lessc20_in_ag(x2)
lessc20_out_ag(x1, x2) = lessc20_out_ag(x1, x2)
U71_ag(x1, x2, x3) = U71_ag(x2, x3)
lessc33_in_ga(x1, x2) = lessc33_in_ga(x1)
lessc33_out_ga(x1, x2) = lessc33_out_ga(x1)
U72_ga(x1, x2, x3) = U72_ga(x1, x3)
LESS33_IN_GG(x1, x2) = LESS33_IN_GG(x1, x2)

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

(22) UsableRulesProof (EQUIVALENT transformation)

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

(23) Obligation:

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

LESS33_IN_GG(s(T115), s(T117)) → LESS33_IN_GG(T115, T117)

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

(24) PiDPToQDPProof (EQUIVALENT transformation)

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

(25) Obligation:

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

LESS33_IN_GG(s(T115), s(T117)) → LESS33_IN_GG(T115, T117)

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

(26) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

LESS33_IN_GG(s(T115), s(T117)) → LESS33_IN_GG(T115, T117)
The graph contains the following edges 1 > 1, 2 > 2

(27) YES

(28) Obligation:

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

LESS20_IN_GG(s(T67), s(T66)) → LESS20_IN_GG(T67, T66)

The TRS R consists of the following rules:

lessc20_in_gg(0, s(T60)) → lessc20_out_gg(0, s(T60))
lessc20_in_gg(s(T67), s(T66)) → U71_gg(T67, T66, lessc20_in_gg(T67, T66))
U71_gg(T67, T66, lessc20_out_gg(T67, T66)) → lessc20_out_gg(s(T67), s(T66))
lessc33_in_gg(0, s(T110)) → lessc33_out_gg(0, s(T110))
lessc33_in_gg(s(T115), s(T117)) → U72_gg(T115, T117, lessc33_in_gg(T115, T117))
U72_gg(T115, T117, lessc33_out_gg(T115, T117)) → lessc33_out_gg(s(T115), s(T117))
lessc20_in_ag(0, s(T60)) → lessc20_out_ag(0, s(T60))
lessc20_in_ag(s(T67), s(T66)) → U71_ag(T67, T66, lessc20_in_ag(T67, T66))
U71_ag(T67, T66, lessc20_out_ag(T67, T66)) → lessc20_out_ag(s(T67), s(T66))
lessc33_in_ga(0, s(T110)) → lessc33_out_ga(0, s(T110))
lessc33_in_ga(s(T115), s(T117)) → U72_ga(T115, T117, lessc33_in_ga(T115, T117))
U72_ga(T115, T117, lessc33_out_ga(T115, T117)) → lessc33_out_ga(s(T115), s(T117))

The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
0 = 0
lessc20_in_gg(x1, x2) = lessc20_in_gg(x1, x2)
lessc20_out_gg(x1, x2) = lessc20_out_gg(x1, x2)
U71_gg(x1, x2, x3) = U71_gg(x1, x2, x3)
lessc33_in_gg(x1, x2) = lessc33_in_gg(x1, x2)
lessc33_out_gg(x1, x2) = lessc33_out_gg(x1, x2)
U72_gg(x1, x2, x3) = U72_gg(x1, x2, x3)
lessc20_in_ag(x1, x2) = lessc20_in_ag(x2)
lessc20_out_ag(x1, x2) = lessc20_out_ag(x1, x2)
U71_ag(x1, x2, x3) = U71_ag(x2, x3)
lessc33_in_ga(x1, x2) = lessc33_in_ga(x1)
lessc33_out_ga(x1, x2) = lessc33_out_ga(x1)
U72_ga(x1, x2, x3) = U72_ga(x1, x3)
LESS20_IN_GG(x1, x2) = LESS20_IN_GG(x1, x2)

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

(29) UsableRulesProof (EQUIVALENT transformation)

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

(30) Obligation:

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

LESS20_IN_GG(s(T67), s(T66)) → LESS20_IN_GG(T67, T66)

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

(31) PiDPToQDPProof (EQUIVALENT transformation)

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

(32) Obligation:

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

LESS20_IN_GG(s(T67), s(T66)) → LESS20_IN_GG(T67, T66)

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

(33) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

LESS20_IN_GG(s(T67), s(T66)) → LESS20_IN_GG(T67, T66)
The graph contains the following edges 1 > 1, 2 > 2

(34) YES

(35) Obligation:

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

INSERT1_IN_GAG(T365, tree(T357, T369, T366), tree(T357, T369, T360)) → U27_GAG(T365, T357, T369, T366, T360, lessc33_in_gg(T357, T365))
U27_GAG(T365, T357, T369, T366, T360, lessc33_out_gg(T357, T365)) → INSERT1_IN_GAG(T365, T366, T360)
INSERT1_IN_GAG(0, tree(s(T320), T321, T312), tree(s(T320), T313, T312)) → INSERT1_IN_GAG(0, T321, T313)
INSERT1_IN_GAG(T477, tree(T469, T481, T478), tree(T469, T481, T472)) → U38_GAG(T477, T469, T481, T478, T472, lessc33_in_gg(T469, T477))
U38_GAG(T477, T469, T481, T478, T472, lessc33_out_gg(T469, T477)) → INSERT1_IN_GAG(T477, T478, T472)
INSERT1_IN_GAG(s(T336), tree(s(T331), T337, T340), tree(s(T331), T313, T340)) → U24_GAG(T336, T331, T337, T340, T313, lessc20_in_gg(T336, T331))
U24_GAG(T336, T331, T337, T340, T313, lessc20_out_gg(T336, T331)) → INSERT1_IN_GAG(s(T336), T337, T313)
INSERT1_IN_GAG(s(T393), tree(0, T382, T392), tree(0, T382, T384)) → INSERT1_IN_GAG(s(T393), T392, T384)
INSERT1_IN_GAG(s(T406), tree(s(T400), T410, T407), tree(s(T400), T410, T384)) → U31_GAG(T406, T400, T410, T407, T384, lessc33_in_gg(T400, T406))
U31_GAG(T406, T400, T410, T407, T384, lessc33_out_gg(T400, T406)) → INSERT1_IN_GAG(s(T406), T407, T384)
INSERT1_IN_GAG(s(T448), tree(s(T443), T449, T452), tree(s(T443), T425, T452)) → U35_GAG(T448, T443, T449, T452, T425, lessc20_in_gg(T448, T443))
U35_GAG(T448, T443, T449, T452, T425, lessc20_out_gg(T448, T443)) → INSERT1_IN_GAG(s(T448), T449, T425)
INSERT1_IN_GAG(s(T521), tree(s(T515), T525, T522), tree(s(T515), T525, T499)) → U42_GAG(T521, T515, T525, T522, T499, lessc33_in_gg(T515, T521))
U42_GAG(T521, T515, T525, T522, T499, lessc33_out_gg(T515, T521)) → INSERT1_IN_GAG(s(T521), T522, T499)

The TRS R consists of the following rules:

lessc20_in_gg(0, s(T60)) → lessc20_out_gg(0, s(T60))
lessc20_in_gg(s(T67), s(T66)) → U71_gg(T67, T66, lessc20_in_gg(T67, T66))
U71_gg(T67, T66, lessc20_out_gg(T67, T66)) → lessc20_out_gg(s(T67), s(T66))
lessc33_in_gg(0, s(T110)) → lessc33_out_gg(0, s(T110))
lessc33_in_gg(s(T115), s(T117)) → U72_gg(T115, T117, lessc33_in_gg(T115, T117))
U72_gg(T115, T117, lessc33_out_gg(T115, T117)) → lessc33_out_gg(s(T115), s(T117))
lessc20_in_ag(0, s(T60)) → lessc20_out_ag(0, s(T60))
lessc20_in_ag(s(T67), s(T66)) → U71_ag(T67, T66, lessc20_in_ag(T67, T66))
U71_ag(T67, T66, lessc20_out_ag(T67, T66)) → lessc20_out_ag(s(T67), s(T66))
lessc33_in_ga(0, s(T110)) → lessc33_out_ga(0, s(T110))
lessc33_in_ga(s(T115), s(T117)) → U72_ga(T115, T117, lessc33_in_ga(T115, T117))
U72_ga(T115, T117, lessc33_out_ga(T115, T117)) → lessc33_out_ga(s(T115), s(T117))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
s(x1) = s(x1)
0 = 0
lessc20_in_gg(x1, x2) = lessc20_in_gg(x1, x2)
lessc20_out_gg(x1, x2) = lessc20_out_gg(x1, x2)
U71_gg(x1, x2, x3) = U71_gg(x1, x2, x3)
lessc33_in_gg(x1, x2) = lessc33_in_gg(x1, x2)
lessc33_out_gg(x1, x2) = lessc33_out_gg(x1, x2)
U72_gg(x1, x2, x3) = U72_gg(x1, x2, x3)
lessc20_in_ag(x1, x2) = lessc20_in_ag(x2)
lessc20_out_ag(x1, x2) = lessc20_out_ag(x1, x2)
U71_ag(x1, x2, x3) = U71_ag(x2, x3)
lessc33_in_ga(x1, x2) = lessc33_in_ga(x1)
lessc33_out_ga(x1, x2) = lessc33_out_ga(x1)
U72_ga(x1, x2, x3) = U72_ga(x1, x3)
INSERT1_IN_GAG(x1, x2, x3) = INSERT1_IN_GAG(x1, x3)
U24_GAG(x1, x2, x3, x4, x5, x6) = U24_GAG(x1, x2, x4, x5, x6)
U27_GAG(x1, x2, x3, x4, x5, x6) = U27_GAG(x1, x2, x3, x5, x6)
U31_GAG(x1, x2, x3, x4, x5, x6) = U31_GAG(x1, x2, x3, x5, x6)
U35_GAG(x1, x2, x3, x4, x5, x6) = U35_GAG(x1, x2, x4, x5, x6)
U38_GAG(x1, x2, x3, x4, x5, x6) = U38_GAG(x1, x2, x3, x5, x6)
U42_GAG(x1, x2, x3, x4, x5, x6) = U42_GAG(x1, x2, x3, x5, x6)

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

(36) UsableRulesProof (EQUIVALENT transformation)

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

(37) Obligation:

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

INSERT1_IN_GAG(T365, tree(T357, T369, T366), tree(T357, T369, T360)) → U27_GAG(T365, T357, T369, T366, T360, lessc33_in_gg(T357, T365))
U27_GAG(T365, T357, T369, T366, T360, lessc33_out_gg(T357, T365)) → INSERT1_IN_GAG(T365, T366, T360)
INSERT1_IN_GAG(0, tree(s(T320), T321, T312), tree(s(T320), T313, T312)) → INSERT1_IN_GAG(0, T321, T313)
INSERT1_IN_GAG(T477, tree(T469, T481, T478), tree(T469, T481, T472)) → U38_GAG(T477, T469, T481, T478, T472, lessc33_in_gg(T469, T477))
U38_GAG(T477, T469, T481, T478, T472, lessc33_out_gg(T469, T477)) → INSERT1_IN_GAG(T477, T478, T472)
INSERT1_IN_GAG(s(T336), tree(s(T331), T337, T340), tree(s(T331), T313, T340)) → U24_GAG(T336, T331, T337, T340, T313, lessc20_in_gg(T336, T331))
U24_GAG(T336, T331, T337, T340, T313, lessc20_out_gg(T336, T331)) → INSERT1_IN_GAG(s(T336), T337, T313)
INSERT1_IN_GAG(s(T393), tree(0, T382, T392), tree(0, T382, T384)) → INSERT1_IN_GAG(s(T393), T392, T384)
INSERT1_IN_GAG(s(T406), tree(s(T400), T410, T407), tree(s(T400), T410, T384)) → U31_GAG(T406, T400, T410, T407, T384, lessc33_in_gg(T400, T406))
U31_GAG(T406, T400, T410, T407, T384, lessc33_out_gg(T400, T406)) → INSERT1_IN_GAG(s(T406), T407, T384)
INSERT1_IN_GAG(s(T448), tree(s(T443), T449, T452), tree(s(T443), T425, T452)) → U35_GAG(T448, T443, T449, T452, T425, lessc20_in_gg(T448, T443))
U35_GAG(T448, T443, T449, T452, T425, lessc20_out_gg(T448, T443)) → INSERT1_IN_GAG(s(T448), T449, T425)
INSERT1_IN_GAG(s(T521), tree(s(T515), T525, T522), tree(s(T515), T525, T499)) → U42_GAG(T521, T515, T525, T522, T499, lessc33_in_gg(T515, T521))
U42_GAG(T521, T515, T525, T522, T499, lessc33_out_gg(T515, T521)) → INSERT1_IN_GAG(s(T521), T522, T499)

The TRS R consists of the following rules:

lessc33_in_gg(0, s(T110)) → lessc33_out_gg(0, s(T110))
lessc33_in_gg(s(T115), s(T117)) → U72_gg(T115, T117, lessc33_in_gg(T115, T117))
lessc20_in_gg(0, s(T60)) → lessc20_out_gg(0, s(T60))
lessc20_in_gg(s(T67), s(T66)) → U71_gg(T67, T66, lessc20_in_gg(T67, T66))
U72_gg(T115, T117, lessc33_out_gg(T115, T117)) → lessc33_out_gg(s(T115), s(T117))
U71_gg(T67, T66, lessc20_out_gg(T67, T66)) → lessc20_out_gg(s(T67), s(T66))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
s(x1) = s(x1)
0 = 0
lessc20_in_gg(x1, x2) = lessc20_in_gg(x1, x2)
lessc20_out_gg(x1, x2) = lessc20_out_gg(x1, x2)
U71_gg(x1, x2, x3) = U71_gg(x1, x2, x3)
lessc33_in_gg(x1, x2) = lessc33_in_gg(x1, x2)
lessc33_out_gg(x1, x2) = lessc33_out_gg(x1, x2)
U72_gg(x1, x2, x3) = U72_gg(x1, x2, x3)
INSERT1_IN_GAG(x1, x2, x3) = INSERT1_IN_GAG(x1, x3)
U24_GAG(x1, x2, x3, x4, x5, x6) = U24_GAG(x1, x2, x4, x5, x6)
U27_GAG(x1, x2, x3, x4, x5, x6) = U27_GAG(x1, x2, x3, x5, x6)
U31_GAG(x1, x2, x3, x4, x5, x6) = U31_GAG(x1, x2, x3, x5, x6)
U35_GAG(x1, x2, x3, x4, x5, x6) = U35_GAG(x1, x2, x4, x5, x6)
U38_GAG(x1, x2, x3, x4, x5, x6) = U38_GAG(x1, x2, x3, x5, x6)
U42_GAG(x1, x2, x3, x4, x5, x6) = U42_GAG(x1, x2, x3, x5, x6)

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

(38) PiDPToQDPProof (SOUND transformation)

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

(39) Obligation:

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

INSERT1_IN_GAG(T365, tree(T357, T369, T360)) → U27_GAG(T365, T357, T369, T360, lessc33_in_gg(T357, T365))
U27_GAG(T365, T357, T369, T360, lessc33_out_gg(T357, T365)) → INSERT1_IN_GAG(T365, T360)
INSERT1_IN_GAG(0, tree(s(T320), T313, T312)) → INSERT1_IN_GAG(0, T313)
INSERT1_IN_GAG(T477, tree(T469, T481, T472)) → U38_GAG(T477, T469, T481, T472, lessc33_in_gg(T469, T477))
U38_GAG(T477, T469, T481, T472, lessc33_out_gg(T469, T477)) → INSERT1_IN_GAG(T477, T472)
INSERT1_IN_GAG(s(T336), tree(s(T331), T313, T340)) → U24_GAG(T336, T331, T340, T313, lessc20_in_gg(T336, T331))
U24_GAG(T336, T331, T340, T313, lessc20_out_gg(T336, T331)) → INSERT1_IN_GAG(s(T336), T313)
INSERT1_IN_GAG(s(T393), tree(0, T382, T384)) → INSERT1_IN_GAG(s(T393), T384)
INSERT1_IN_GAG(s(T406), tree(s(T400), T410, T384)) → U31_GAG(T406, T400, T410, T384, lessc33_in_gg(T400, T406))
U31_GAG(T406, T400, T410, T384, lessc33_out_gg(T400, T406)) → INSERT1_IN_GAG(s(T406), T384)
INSERT1_IN_GAG(s(T448), tree(s(T443), T425, T452)) → U35_GAG(T448, T443, T452, T425, lessc20_in_gg(T448, T443))
U35_GAG(T448, T443, T452, T425, lessc20_out_gg(T448, T443)) → INSERT1_IN_GAG(s(T448), T425)
INSERT1_IN_GAG(s(T521), tree(s(T515), T525, T499)) → U42_GAG(T521, T515, T525, T499, lessc33_in_gg(T515, T521))
U42_GAG(T521, T515, T525, T499, lessc33_out_gg(T515, T521)) → INSERT1_IN_GAG(s(T521), T499)

The TRS R consists of the following rules:

lessc33_in_gg(0, s(T110)) → lessc33_out_gg(0, s(T110))
lessc33_in_gg(s(T115), s(T117)) → U72_gg(T115, T117, lessc33_in_gg(T115, T117))
lessc20_in_gg(0, s(T60)) → lessc20_out_gg(0, s(T60))
lessc20_in_gg(s(T67), s(T66)) → U71_gg(T67, T66, lessc20_in_gg(T67, T66))
U72_gg(T115, T117, lessc33_out_gg(T115, T117)) → lessc33_out_gg(s(T115), s(T117))
U71_gg(T67, T66, lessc20_out_gg(T67, T66)) → lessc20_out_gg(s(T67), s(T66))

The set Q consists of the following terms:

lessc33_in_gg(x0, x1)
lessc20_in_gg(x0, x1)
U72_gg(x0, x1, x2)
U71_gg(x0, x1, x2)

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

(40) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

U27_GAG(T365, T357, T369, T360, lessc33_out_gg(T357, T365)) → INSERT1_IN_GAG(T365, T360)
The graph contains the following edges 1 >= 1, 5 > 1, 4 >= 2
INSERT1_IN_GAG(T365, tree(T357, T369, T360)) → U27_GAG(T365, T357, T369, T360, lessc33_in_gg(T357, T365))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4
INSERT1_IN_GAG(0, tree(s(T320), T313, T312)) → INSERT1_IN_GAG(0, T313)
The graph contains the following edges 1 >= 1, 2 > 2
INSERT1_IN_GAG(s(T393), tree(0, T382, T384)) → INSERT1_IN_GAG(s(T393), T384)
The graph contains the following edges 1 >= 1, 2 > 2
U38_GAG(T477, T469, T481, T472, lessc33_out_gg(T469, T477)) → INSERT1_IN_GAG(T477, T472)
The graph contains the following edges 1 >= 1, 5 > 1, 4 >= 2
INSERT1_IN_GAG(T477, tree(T469, T481, T472)) → U38_GAG(T477, T469, T481, T472, lessc33_in_gg(T469, T477))
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4
U24_GAG(T336, T331, T340, T313, lessc20_out_gg(T336, T331)) → INSERT1_IN_GAG(s(T336), T313)
The graph contains the following edges 4 >= 2
INSERT1_IN_GAG(s(T336), tree(s(T331), T313, T340)) → U24_GAG(T336, T331, T340, T313, lessc20_in_gg(T336, T331))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4
U31_GAG(T406, T400, T410, T384, lessc33_out_gg(T400, T406)) → INSERT1_IN_GAG(s(T406), T384)
The graph contains the following edges 4 >= 2
INSERT1_IN_GAG(s(T406), tree(s(T400), T410, T384)) → U31_GAG(T406, T400, T410, T384, lessc33_in_gg(T400, T406))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4
U35_GAG(T448, T443, T452, T425, lessc20_out_gg(T448, T443)) → INSERT1_IN_GAG(s(T448), T425)
The graph contains the following edges 4 >= 2
U42_GAG(T521, T515, T525, T499, lessc33_out_gg(T515, T521)) → INSERT1_IN_GAG(s(T521), T499)
The graph contains the following edges 4 >= 2
INSERT1_IN_GAG(s(T448), tree(s(T443), T425, T452)) → U35_GAG(T448, T443, T452, T425, lessc20_in_gg(T448, T443))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4
INSERT1_IN_GAG(s(T521), tree(s(T515), T525, T499)) → U42_GAG(T521, T515, T525, T499, lessc33_in_gg(T515, T521))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3, 2 > 4

(41) YES

(42) Obligation:

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

INSERT1_IN_AAG(T365, tree(T357, T369, T366), tree(T357, T369, T360)) → U27_AAG(T365, T357, T369, T366, T360, lessc33_in_ga(T357, T365))
U27_AAG(T365, T357, T369, T366, T360, lessc33_out_ga(T357, T365)) → INSERT1_IN_AAG(T365, T366, T360)
INSERT1_IN_AAG(s(T393), tree(0, T382, T392), tree(0, T382, T384)) → INSERT1_IN_AAG(s(T393), T392, T384)
INSERT1_IN_AAG(s(T406), tree(s(T400), T410, T407), tree(s(T400), T410, T384)) → U31_AAG(T406, T400, T410, T407, T384, lessc33_in_ga(T400, T406))
U31_AAG(T406, T400, T410, T407, T384, lessc33_out_ga(T400, T406)) → INSERT1_IN_AAG(s(T406), T407, T384)
INSERT1_IN_AAG(T477, tree(T469, T481, T478), tree(T469, T481, T472)) → U38_AAG(T477, T469, T481, T478, T472, lessc33_in_ga(T469, T477))
U38_AAG(T477, T469, T481, T478, T472, lessc33_out_ga(T469, T477)) → INSERT1_IN_AAG(T477, T478, T472)
INSERT1_IN_AAG(s(T521), tree(s(T515), T525, T522), tree(s(T515), T525, T499)) → U42_AAG(T521, T515, T525, T522, T499, lessc33_in_ga(T515, T521))
U42_AAG(T521, T515, T525, T522, T499, lessc33_out_ga(T515, T521)) → INSERT1_IN_AAG(s(T521), T522, T499)

The TRS R consists of the following rules:

lessc20_in_gg(0, s(T60)) → lessc20_out_gg(0, s(T60))
lessc20_in_gg(s(T67), s(T66)) → U71_gg(T67, T66, lessc20_in_gg(T67, T66))
U71_gg(T67, T66, lessc20_out_gg(T67, T66)) → lessc20_out_gg(s(T67), s(T66))
lessc33_in_gg(0, s(T110)) → lessc33_out_gg(0, s(T110))
lessc33_in_gg(s(T115), s(T117)) → U72_gg(T115, T117, lessc33_in_gg(T115, T117))
U72_gg(T115, T117, lessc33_out_gg(T115, T117)) → lessc33_out_gg(s(T115), s(T117))
lessc20_in_ag(0, s(T60)) → lessc20_out_ag(0, s(T60))
lessc20_in_ag(s(T67), s(T66)) → U71_ag(T67, T66, lessc20_in_ag(T67, T66))
U71_ag(T67, T66, lessc20_out_ag(T67, T66)) → lessc20_out_ag(s(T67), s(T66))
lessc33_in_ga(0, s(T110)) → lessc33_out_ga(0, s(T110))
lessc33_in_ga(s(T115), s(T117)) → U72_ga(T115, T117, lessc33_in_ga(T115, T117))
U72_ga(T115, T117, lessc33_out_ga(T115, T117)) → lessc33_out_ga(s(T115), s(T117))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
s(x1) = s(x1)
0 = 0
lessc20_in_gg(x1, x2) = lessc20_in_gg(x1, x2)
lessc20_out_gg(x1, x2) = lessc20_out_gg(x1, x2)
U71_gg(x1, x2, x3) = U71_gg(x1, x2, x3)
lessc33_in_gg(x1, x2) = lessc33_in_gg(x1, x2)
lessc33_out_gg(x1, x2) = lessc33_out_gg(x1, x2)
U72_gg(x1, x2, x3) = U72_gg(x1, x2, x3)
lessc20_in_ag(x1, x2) = lessc20_in_ag(x2)
lessc20_out_ag(x1, x2) = lessc20_out_ag(x1, x2)
U71_ag(x1, x2, x3) = U71_ag(x2, x3)
lessc33_in_ga(x1, x2) = lessc33_in_ga(x1)
lessc33_out_ga(x1, x2) = lessc33_out_ga(x1)
U72_ga(x1, x2, x3) = U72_ga(x1, x3)
INSERT1_IN_AAG(x1, x2, x3) = INSERT1_IN_AAG(x3)
U27_AAG(x1, x2, x3, x4, x5, x6) = U27_AAG(x2, x3, x5, x6)
U31_AAG(x1, x2, x3, x4, x5, x6) = U31_AAG(x2, x3, x5, x6)
U38_AAG(x1, x2, x3, x4, x5, x6) = U38_AAG(x2, x3, x5, x6)
U42_AAG(x1, x2, x3, x4, x5, x6) = U42_AAG(x2, x3, x5, x6)

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

(43) UsableRulesProof (EQUIVALENT transformation)

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

(44) Obligation:

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

INSERT1_IN_AAG(T365, tree(T357, T369, T366), tree(T357, T369, T360)) → U27_AAG(T365, T357, T369, T366, T360, lessc33_in_ga(T357, T365))
U27_AAG(T365, T357, T369, T366, T360, lessc33_out_ga(T357, T365)) → INSERT1_IN_AAG(T365, T366, T360)
INSERT1_IN_AAG(s(T393), tree(0, T382, T392), tree(0, T382, T384)) → INSERT1_IN_AAG(s(T393), T392, T384)
INSERT1_IN_AAG(s(T406), tree(s(T400), T410, T407), tree(s(T400), T410, T384)) → U31_AAG(T406, T400, T410, T407, T384, lessc33_in_ga(T400, T406))
U31_AAG(T406, T400, T410, T407, T384, lessc33_out_ga(T400, T406)) → INSERT1_IN_AAG(s(T406), T407, T384)
INSERT1_IN_AAG(T477, tree(T469, T481, T478), tree(T469, T481, T472)) → U38_AAG(T477, T469, T481, T478, T472, lessc33_in_ga(T469, T477))
U38_AAG(T477, T469, T481, T478, T472, lessc33_out_ga(T469, T477)) → INSERT1_IN_AAG(T477, T478, T472)
INSERT1_IN_AAG(s(T521), tree(s(T515), T525, T522), tree(s(T515), T525, T499)) → U42_AAG(T521, T515, T525, T522, T499, lessc33_in_ga(T515, T521))
U42_AAG(T521, T515, T525, T522, T499, lessc33_out_ga(T515, T521)) → INSERT1_IN_AAG(s(T521), T522, T499)

The TRS R consists of the following rules:

lessc33_in_ga(0, s(T110)) → lessc33_out_ga(0, s(T110))
lessc33_in_ga(s(T115), s(T117)) → U72_ga(T115, T117, lessc33_in_ga(T115, T117))
U72_ga(T115, T117, lessc33_out_ga(T115, T117)) → lessc33_out_ga(s(T115), s(T117))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
s(x1) = s(x1)
0 = 0
lessc33_in_ga(x1, x2) = lessc33_in_ga(x1)
lessc33_out_ga(x1, x2) = lessc33_out_ga(x1)
U72_ga(x1, x2, x3) = U72_ga(x1, x3)
INSERT1_IN_AAG(x1, x2, x3) = INSERT1_IN_AAG(x3)
U27_AAG(x1, x2, x3, x4, x5, x6) = U27_AAG(x2, x3, x5, x6)
U31_AAG(x1, x2, x3, x4, x5, x6) = U31_AAG(x2, x3, x5, x6)
U38_AAG(x1, x2, x3, x4, x5, x6) = U38_AAG(x2, x3, x5, x6)
U42_AAG(x1, x2, x3, x4, x5, x6) = U42_AAG(x2, x3, x5, x6)

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

(45) PiDPToQDPProof (SOUND transformation)

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

(46) Obligation:

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

INSERT1_IN_AAG(tree(T357, T369, T360)) → U27_AAG(T357, T369, T360, lessc33_in_ga(T357))
U27_AAG(T357, T369, T360, lessc33_out_ga(T357)) → INSERT1_IN_AAG(T360)
INSERT1_IN_AAG(tree(0, T382, T384)) → INSERT1_IN_AAG(T384)
INSERT1_IN_AAG(tree(s(T400), T410, T384)) → U31_AAG(T400, T410, T384, lessc33_in_ga(T400))
U31_AAG(T400, T410, T384, lessc33_out_ga(T400)) → INSERT1_IN_AAG(T384)
INSERT1_IN_AAG(tree(T469, T481, T472)) → U38_AAG(T469, T481, T472, lessc33_in_ga(T469))
U38_AAG(T469, T481, T472, lessc33_out_ga(T469)) → INSERT1_IN_AAG(T472)
INSERT1_IN_AAG(tree(s(T515), T525, T499)) → U42_AAG(T515, T525, T499, lessc33_in_ga(T515))
U42_AAG(T515, T525, T499, lessc33_out_ga(T515)) → INSERT1_IN_AAG(T499)

The TRS R consists of the following rules:

lessc33_in_ga(0) → lessc33_out_ga(0)
lessc33_in_ga(s(T115)) → U72_ga(T115, lessc33_in_ga(T115))
U72_ga(T115, lessc33_out_ga(T115)) → lessc33_out_ga(s(T115))

The set Q consists of the following terms:

lessc33_in_ga(x0)
U72_ga(x0, x1)

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

(47) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

U27_AAG(T357, T369, T360, lessc33_out_ga(T357)) → INSERT1_IN_AAG(T360)
The graph contains the following edges 3 >= 1
INSERT1_IN_AAG(tree(0, T382, T384)) → INSERT1_IN_AAG(T384)
The graph contains the following edges 1 > 1
INSERT1_IN_AAG(tree(T357, T369, T360)) → U27_AAG(T357, T369, T360, lessc33_in_ga(T357))
The graph contains the following edges 1 > 1, 1 > 2, 1 > 3
U31_AAG(T400, T410, T384, lessc33_out_ga(T400)) → INSERT1_IN_AAG(T384)
The graph contains the following edges 3 >= 1
INSERT1_IN_AAG(tree(s(T400), T410, T384)) → U31_AAG(T400, T410, T384, lessc33_in_ga(T400))
The graph contains the following edges 1 > 1, 1 > 2, 1 > 3
U38_AAG(T469, T481, T472, lessc33_out_ga(T469)) → INSERT1_IN_AAG(T472)
The graph contains the following edges 3 >= 1
U42_AAG(T515, T525, T499, lessc33_out_ga(T515)) → INSERT1_IN_AAG(T499)
The graph contains the following edges 3 >= 1
INSERT1_IN_AAG(tree(T469, T481, T472)) → U38_AAG(T469, T481, T472, lessc33_in_ga(T469))
The graph contains the following edges 1 > 1, 1 > 2, 1 > 3
INSERT1_IN_AAG(tree(s(T515), T525, T499)) → U42_AAG(T515, T525, T499, lessc33_in_ga(T515))
The graph contains the following edges 1 > 1, 1 > 2, 1 > 3

(0) Obligation:

(1) PrologToDTProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) TriplesToPiDPProof (SOUND transformation)

(4) Obligation:

(5) DependencyGraphProof (EQUIVALENT transformation)

(6) Complex Obligation (AND)

(7) Obligation:

(8) UsableRulesProof (EQUIVALENT transformation)

(9) Obligation:

(10) PiDPToQDPProof (SOUND transformation)

(11) Obligation:

(12) QDPSizeChangeProof (EQUIVALENT transformation)

(13) YES

(14) Obligation:

(15) UsableRulesProof (EQUIVALENT transformation)

(16) Obligation:

(17) PiDPToQDPProof (SOUND transformation)

(18) Obligation:

(19) QDPSizeChangeProof (EQUIVALENT transformation)

(20) YES

(21) Obligation:

(22) UsableRulesProof (EQUIVALENT transformation)

(23) Obligation:

(24) PiDPToQDPProof (EQUIVALENT transformation)

(25) Obligation:

(26) QDPSizeChangeProof (EQUIVALENT transformation)

(27) YES

(28) Obligation:

(29) UsableRulesProof (EQUIVALENT transformation)

(30) Obligation:

(31) PiDPToQDPProof (EQUIVALENT transformation)

(32) Obligation:

(33) QDPSizeChangeProof (EQUIVALENT transformation)

(34) YES

(35) Obligation:

(36) UsableRulesProof (EQUIVALENT transformation)

(37) Obligation:

(38) PiDPToQDPProof (SOUND transformation)

(39) Obligation:

(40) QDPSizeChangeProof (EQUIVALENT transformation)

(41) YES

(42) Obligation:

(43) UsableRulesProof (EQUIVALENT transformation)

(44) Obligation:

(45) PiDPToQDPProof (SOUND transformation)

(46) Obligation:

(47) QDPSizeChangeProof (EQUIVALENT transformation)

(48) YES