Runtime Complexity proof of /tmp/tmpNLOyvf/insert-bfb.pl

Runtime Complexity of the query pattern
insert(g,a,g)
w.r.t. the given Prolog program could be shown to be BOUNDS(O(1), O(n^2)).

0 Prolog

↳1 LPReorderTransformerProof (⇔, 0 ms)

↳2 Prolog

↳3 PrologToCdtProblemTransformerProof (UPPER BOUND (ID), 466 ms)

↳4 CdtProblem

    ↳5 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳6 CdtProblem

    ↳7 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳8 CdtProblem

    ↳9 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))), 1251 ms)

    ↳10 CdtProblem

    ↳11 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))), 1325 ms)

    ↳12 CdtProblem

    ↳13 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))), 1172 ms)

    ↳14 CdtProblem

    ↳15 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳16 CdtProblem

    ↳17 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳18 CdtProblem

↳19 PrologToCdtProblemTransformerProof (UPPER BOUND (ID), 661 ms)

↳20 CdtProblem

    ↳21 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 72 ms)

    ↳22 CdtProblem

    ↳23 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 94 ms)

    ↳24 CdtProblem

    ↳25 CdtKnowledgeProof (⇔, 0 ms)

    ↳26 CdtProblem

    ↳27 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))), 1861 ms)

    ↳28 CdtProblem

    ↳29 CdtKnowledgeProof (⇔, 0 ms)

    ↳30 CdtProblem

    ↳31 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))), 1531 ms)

    ↳32 CdtProblem

    ↳33 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))), 611 ms)

    ↳34 CdtProblem

    ↳35 CdtKnowledgeProof (⇔, 0 ms)

    ↳36 CdtProblem

    ↳37 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))), 402 ms)

    ↳38 CdtProblem

    ↳39 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))), 1336 ms)

    ↳40 CdtProblem

    ↳41 SIsEmptyProof (⇔, 0 ms)

    ↳42 BOUNDS(O(1), O(1))

(0) Obligation:

Clauses:

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

Query: insert(g,a,g)

(1) LPReorderTransformerProof (EQUIVALENT transformation)

Reordered facts before rules in definite LP [PROLOG].

(2) Obligation:

Clauses:

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

Query: insert(g,a,g)

(3) PrologToCdtProblemTransformerProof (UPPER BOUND (ID) transformation)

Built complexity over-approximating cdt problems from derivation graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
2 [label="2: insert(T1, T2, T3)\n\nT1 is ground\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
3 [label="3: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 0 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: true | insert(T6, T2, tree(T6, void, void)), SCOPE: 1, CLAUSE: 1 | insert(T6, T2, tree(T6, void, void)), SCOPE: 1, CLAUSE: 3 | insert(T6, T2, tree(T6, void, void)), SCOPE: 1, CLAUSE: 4\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT3 is ground\nX4 is free\ninsert(T1, T2, T3) !=? insert(X4, void, tree(X4, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: insert(T6, T2, tree(T6, void, void)), SCOPE: 1, CLAUSE: 1 | insert(T6, T2, tree(T6, void, void)), SCOPE: 1, CLAUSE: 3 | insert(T6, T2, tree(T6, void, void)), SCOPE: 1, CLAUSE: 4\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: true | insert(T13, T2, tree(T13, void, void)), SCOPE: 1, CLAUSE: 3 | insert(T13, T2, tree(T13, void, void)), SCOPE: 1, CLAUSE: 4\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: insert(T6, T2, tree(T6, void, void)), SCOPE: 1, CLAUSE: 3 | insert(T6, T2, tree(T6, void, void)), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\nX11 is free\nX12 is free\nX13 is free\ninsert(T6, T2, tree(T6, void, void)) !=? insert(X11, tree(X11, X12, X13), tree(X11, X12, X13))", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: insert(T13, T2, tree(T13, void, void)), SCOPE: 1, CLAUSE: 3 | insert(T13, T2, tree(T13, void, void)), SCOPE: 1, CLAUSE: 4\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: insert(T13, T2, tree(T13, void, void)), SCOPE: 1, CLAUSE: 3\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: insert(T13, T2, tree(T13, void, void)), SCOPE: 1, CLAUSE: 4\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: ','(less(T32, T32), insert(T32, T36, void))\n\nT32 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: less(T32, T32)\n\nT32 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: insert(T32, T36, void)\n\nT32 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: less(T32, T32), SCOPE: 2, CLAUSE: 2 | less(T32, T32), SCOPE: 2, CLAUSE: 5\n\nT32 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: less(T32, T32), SCOPE: 2, CLAUSE: 5\n\nT32 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: less(T39, T39)\n\nT39 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: ','(less(T50, T50), insert(T50, T54, void))\n\nT50 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: insert(T6, T2, tree(T6, void, void)), SCOPE: 1, CLAUSE: 3\n\nT6 is ground\nX11 is free\nX12 is free\nX13 is free\ninsert(T6, T2, tree(T6, void, void)) !=? insert(X11, tree(X11, X12, X13), tree(X11, X12, X13))", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: insert(T6, T2, tree(T6, void, void)), SCOPE: 1, CLAUSE: 4\n\nT6 is ground\nX11 is free\nX12 is free\nX13 is free\ninsert(T6, T2, tree(T6, void, void)) !=? insert(X11, tree(X11, X12, X13), tree(X11, X12, X13))", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: ','(less(T71, T71), insert(T71, T75, void))\n\nT71 is ground\nX11 is free\nX12 is free\nX13 is free\ninsert(T71, T2, tree(T71, void, void)) !=? insert(X11, tree(X11, X12, X13), tree(X11, X12, X13))", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ','(less(T84, T84), insert(T84, T88, void))\n\nT84 is ground\nX11 is free\nX12 is free\nX13 is free\ninsert(T84, T2, tree(T84, void, void)) !=? insert(X11, tree(X11, X12, X13), tree(X11, X12, X13))", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: true | insert(T95, T2, tree(T95, T96, T97)), SCOPE: 1, CLAUSE: 3 | insert(T95, T2, tree(T95, T96, T97)), SCOPE: 1, CLAUSE: 4\n\nT95 is ground\nT96 is ground\nT97 is ground\nX4 is free\ninsert(T95, T2, tree(T95, T96, T97)) !=? insert(X4, void, tree(X4, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT3 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(T1, T2, T3) !=? insert(X4, void, tree(X4, void, void))\ninsert(T1, T2, T3) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: insert(T95, T2, tree(T95, T96, T97)), SCOPE: 1, CLAUSE: 3 | insert(T95, T2, tree(T95, T96, T97)), SCOPE: 1, CLAUSE: 4\n\nT95 is ground\nT96 is ground\nT97 is ground\nX4 is free\ninsert(T95, T2, tree(T95, T96, T97)) !=? insert(X4, void, tree(X4, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: insert(T95, T2, tree(T95, T96, T97)), SCOPE: 1, CLAUSE: 3\n\nT95 is ground\nT96 is ground\nT97 is ground\nX4 is free\ninsert(T95, T2, tree(T95, T96, T97)) !=? insert(X4, void, tree(X4, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: insert(T95, T2, tree(T95, T96, T97)), SCOPE: 1, CLAUSE: 4\n\nT95 is ground\nT96 is ground\nT97 is ground\nX4 is free\ninsert(T95, T2, tree(T95, T96, T97)) !=? insert(X4, void, tree(X4, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: ','(less(T118, T118), insert(T118, T123, T122))\n\nT118 is ground\nT122 is ground\nT121 is ground\nX4 is free\ninsert(T118, T2, tree(T118, T122, T121)) !=? insert(X4, void, tree(X4, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: less(T118, T118)\n\nT118 is ground\nT122 is ground\nT121 is ground\nX4 is free\ninsert(T118, T2, tree(T118, T122, T121)) !=? insert(X4, void, tree(X4, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: insert(T118, T123, T122)\n\nT118 is ground\nT122 is ground\nT121 is ground\nX4 is free\ninsert(T118, T2, tree(T118, T122, T121)) !=? insert(X4, void, tree(X4, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: ','(less(T136, T136), insert(T136, T141, T140))\n\nT136 is ground\nT138 is ground\nT140 is ground\nX4 is free\ninsert(T136, T2, tree(T136, T138, T140)) !=? insert(X4, void, tree(X4, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: less(T136, T136)\n\nT136 is ground\nT138 is ground\nT140 is ground\nX4 is free\ninsert(T136, T2, tree(T136, T138, T140)) !=? insert(X4, void, tree(X4, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: insert(T136, T141, T140)\n\nT136 is ground\nT138 is ground\nT140 is ground\nX4 is free\ninsert(T136, T2, tree(T136, T138, T140)) !=? insert(X4, void, tree(X4, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT1 is ground\nT3 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(T1, T2, T3) !=? insert(X4, void, tree(X4, void, void))\ninsert(T1, T2, T3) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT3 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(T1, T2, T3) !=? insert(X4, void, tree(X4, void, void))\ninsert(T1, T2, T3) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: ','(less(T164, T165), insert(T164, T169, T168))\n\nT164 is ground\nT165 is ground\nT168 is ground\nT167 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(T164, T2, tree(T165, T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(T164, T2, tree(T165, T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: less(T164, T165)\n\nT164 is ground\nT165 is ground\nT168 is ground\nT167 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(T164, T2, tree(T165, T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(T164, T2, tree(T165, T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: insert(T164, T169, T168)\n\nT164 is ground\nT165 is ground\nT168 is ground\nT167 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(T164, T2, tree(T165, T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(T164, T2, tree(T165, T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: less(T164, T165), SCOPE: 3, CLAUSE: 2 | less(T164, T165), SCOPE: 3, CLAUSE: 5\n\nT164 is ground\nT165 is ground\nT168 is ground\nT167 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(T164, T2, tree(T165, T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(T164, T2, tree(T165, T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: true | less(0, s(T176)), SCOPE: 3, CLAUSE: 5\n\nT176 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: less(T164, T165), SCOPE: 3, CLAUSE: 5\n\nT164 is ground\nT165 is ground\nT168 is ground\nT167 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\nX207 is free\ninsert(T164, T2, tree(T165, T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(T164, T2, tree(T165, T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))\nless(T164, T165) !=? less(0, s(X207))", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: less(0, s(T176)), SCOPE: 3, CLAUSE: 5\n\nT176 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: less(T181, T182)\n\nT168 is ground\nT167 is ground\nT181 is ground\nT182 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(s(T181), T2, tree(s(T182), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(T181), T2, tree(s(T182), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: less(T181, T182), SCOPE: 4, CLAUSE: 2 | less(T181, T182), SCOPE: 4, CLAUSE: 5\n\nT168 is ground\nT167 is ground\nT181 is ground\nT182 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(s(T181), T2, tree(s(T182), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(T181), T2, tree(s(T182), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: true | less(0, s(T187)), SCOPE: 4, CLAUSE: 5\n\nT187 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: less(T181, T182), SCOPE: 4, CLAUSE: 5\n\nT168 is ground\nT167 is ground\nT181 is ground\nT182 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\nX220 is free\ninsert(s(T181), T2, tree(s(T182), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(T181), T2, tree(s(T182), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))\nless(T181, T182) !=? less(0, s(X220))", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: less(0, s(T187)), SCOPE: 4, CLAUSE: 5\n\nT187 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: less(T192, T193)\n\nT168 is ground\nT167 is ground\nT192 is ground\nT193 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(s(s(T192)), T2, tree(s(s(T193)), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(T192)), T2, tree(s(s(T193)), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: less(T192, T193), SCOPE: 5, CLAUSE: 2 | less(T192, T193), SCOPE: 5, CLAUSE: 5\n\nT168 is ground\nT167 is ground\nT192 is ground\nT193 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(s(s(T192)), T2, tree(s(s(T193)), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(T192)), T2, tree(s(s(T193)), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: true | less(0, s(T198)), SCOPE: 5, CLAUSE: 5\n\nT198 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: less(T192, T193), SCOPE: 5, CLAUSE: 5\n\nT168 is ground\nT167 is ground\nT192 is ground\nT193 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\nX233 is free\ninsert(s(s(T192)), T2, tree(s(s(T193)), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(T192)), T2, tree(s(s(T193)), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))\nless(T192, T193) !=? less(0, s(X233))", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: less(0, s(T198)), SCOPE: 5, CLAUSE: 5\n\nT198 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: less(T203, T204)\n\nT168 is ground\nT167 is ground\nT203 is ground\nT204 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(s(s(s(T203))), T2, tree(s(s(s(T204))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(T203))), T2, tree(s(s(s(T204))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: less(T203, T204), SCOPE: 6, CLAUSE: 2 | less(T203, T204), SCOPE: 6, CLAUSE: 5\n\nT168 is ground\nT167 is ground\nT203 is ground\nT204 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(s(s(s(T203))), T2, tree(s(s(s(T204))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(T203))), T2, tree(s(s(s(T204))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: true | less(0, s(T209)), SCOPE: 6, CLAUSE: 5\n\nT209 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: less(T203, T204), SCOPE: 6, CLAUSE: 5\n\nT168 is ground\nT167 is ground\nT203 is ground\nT204 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\nX246 is free\ninsert(s(s(s(T203))), T2, tree(s(s(s(T204))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(T203))), T2, tree(s(s(s(T204))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))\nless(T203, T204) !=? less(0, s(X246))", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: less(0, s(T209)), SCOPE: 6, CLAUSE: 5\n\nT209 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: less(T214, T215)\n\nT168 is ground\nT167 is ground\nT214 is ground\nT215 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(s(s(s(s(T214)))), T2, tree(s(s(s(s(T215)))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(s(T214)))), T2, tree(s(s(s(s(T215)))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: less(T214, T215), SCOPE: 7, CLAUSE: 2 | less(T214, T215), SCOPE: 7, CLAUSE: 5\n\nT168 is ground\nT167 is ground\nT214 is ground\nT215 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(s(s(s(s(T214)))), T2, tree(s(s(s(s(T215)))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(s(T214)))), T2, tree(s(s(s(s(T215)))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: true | less(0, s(T220)), SCOPE: 7, CLAUSE: 5\n\nT220 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: less(T214, T215), SCOPE: 7, CLAUSE: 5\n\nT168 is ground\nT167 is ground\nT214 is ground\nT215 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\nX259 is free\ninsert(s(s(s(s(T214)))), T2, tree(s(s(s(s(T215)))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(s(T214)))), T2, tree(s(s(s(s(T215)))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))\nless(T214, T215) !=? less(0, s(X259))", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: less(0, s(T220)), SCOPE: 7, CLAUSE: 5\n\nT220 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: less(T225, T226)\n\nT168 is ground\nT167 is ground\nT225 is ground\nT226 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(s(s(s(s(s(T225))))), T2, tree(s(s(s(s(s(T226))))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(s(s(T225))))), T2, tree(s(s(s(s(s(T226))))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: less(T225, T226), SCOPE: 8, CLAUSE: 2 | less(T225, T226), SCOPE: 8, CLAUSE: 5\n\nT168 is ground\nT167 is ground\nT225 is ground\nT226 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(s(s(s(s(s(T225))))), T2, tree(s(s(s(s(s(T226))))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(s(s(T225))))), T2, tree(s(s(s(s(s(T226))))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: true | less(0, s(T231)), SCOPE: 8, CLAUSE: 5\n\nT231 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: less(T225, T226), SCOPE: 8, CLAUSE: 5\n\nT168 is ground\nT167 is ground\nT225 is ground\nT226 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\nX272 is free\ninsert(s(s(s(s(s(T225))))), T2, tree(s(s(s(s(s(T226))))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(s(s(T225))))), T2, tree(s(s(s(s(s(T226))))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))\nless(T225, T226) !=? less(0, s(X272))", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: less(0, s(T231)), SCOPE: 8, CLAUSE: 5\n\nT231 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: less(T236, T237)\n\nT168 is ground\nT167 is ground\nT236 is ground\nT237 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(s(s(s(s(s(s(T236)))))), T2, tree(s(s(s(s(s(s(T237)))))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(s(s(s(T236)))))), T2, tree(s(s(s(s(s(s(T237)))))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: less(T236, T237), SCOPE: 9, CLAUSE: 2 | less(T236, T237), SCOPE: 9, CLAUSE: 5\n\nT168 is ground\nT167 is ground\nT236 is ground\nT237 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(s(s(s(s(s(s(T236)))))), T2, tree(s(s(s(s(s(s(T237)))))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(s(s(s(T236)))))), T2, tree(s(s(s(s(s(s(T237)))))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: true | less(0, s(T242)), SCOPE: 9, CLAUSE: 5\n\nT242 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: less(T236, T237), SCOPE: 9, CLAUSE: 5\n\nT168 is ground\nT167 is ground\nT236 is ground\nT237 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\nX285 is free\ninsert(s(s(s(s(s(s(T236)))))), T2, tree(s(s(s(s(s(s(T237)))))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(s(s(s(T236)))))), T2, tree(s(s(s(s(s(s(T237)))))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))\nless(T236, T237) !=? less(0, s(X285))", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: less(0, s(T242)), SCOPE: 9, CLAUSE: 5\n\nT242 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: less(T247, T248)\n\nT168 is ground\nT167 is ground\nT247 is ground\nT248 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(s(s(s(s(s(s(s(T247))))))), T2, tree(s(s(s(s(s(s(s(T248))))))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(s(s(s(s(T247))))))), T2, tree(s(s(s(s(s(s(s(T248))))))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: less(T247, T248), SCOPE: 10, CLAUSE: 2 | less(T247, T248), SCOPE: 10, CLAUSE: 5\n\nT168 is ground\nT167 is ground\nT247 is ground\nT248 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(s(s(s(s(s(s(s(T247))))))), T2, tree(s(s(s(s(s(s(s(T248))))))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(s(s(s(s(T247))))))), T2, tree(s(s(s(s(s(s(s(T248))))))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: true | less(0, s(T253)), SCOPE: 10, CLAUSE: 5\n\nT253 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: less(T247, T248), SCOPE: 10, CLAUSE: 5\n\nT168 is ground\nT167 is ground\nT247 is ground\nT248 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\nX298 is free\ninsert(s(s(s(s(s(s(s(T247))))))), T2, tree(s(s(s(s(s(s(s(T248))))))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(s(s(s(s(T247))))))), T2, tree(s(s(s(s(s(s(s(T248))))))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))\nless(T247, T248) !=? less(0, s(X298))", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: less(0, s(T253)), SCOPE: 10, CLAUSE: 5\n\nT253 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: less(T258, T259)\n\nT168 is ground\nT167 is ground\nT258 is ground\nT259 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(s(s(s(s(s(s(s(s(T258)))))))), T2, tree(s(s(s(s(s(s(s(s(T259)))))))), T168, T167)) !=? insert(X4, void, tree(X4, void, void))\ninsert(s(s(s(s(s(s(s(s(T258)))))))), T2, tree(s(s(s(s(s(s(s(s(T259)))))))), T168, T167)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
228 [label="228: less(T258, T259)\n\nT258 is ground\nT259 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
231 [label="231: less(T258, T259), SCOPE: 11, CLAUSE: 2 | less(T258, T259), SCOPE: 11, CLAUSE: 5\n\nT258 is ground\nT259 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
233 [label="233: true | less(0, s(T268)), SCOPE: 11, CLAUSE: 5\n\nT268 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
235 [label="235: less(T258, T259), SCOPE: 11, CLAUSE: 5\n\nT258 is ground\nT259 is ground\nX313 is free\nless(T258, T259) !=? less(0, s(X313))", fontsize=16, style=filled, fillcolor=lightyellow];
236 [label="236: less(0, s(T268)), SCOPE: 11, CLAUSE: 5\n\nT268 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
238 [label="238: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
239 [label="239: less(T273, T274)\n\nT273 is ground\nT274 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
240 [label="240: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
245 [label="245: ','(less(T290, T289), insert(T289, T294, T293))\n\nT289 is ground\nT290 is ground\nT291 is ground\nT293 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(T289, T2, tree(T290, T291, T293)) !=? insert(X4, void, tree(X4, void, void))\ninsert(T289, T2, tree(T290, T291, T293)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
248 [label="248: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
250 [label="250: less(T290, T289)\n\nT289 is ground\nT290 is ground\nT291 is ground\nT293 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(T289, T2, tree(T290, T291, T293)) !=? insert(X4, void, tree(X4, void, void))\ninsert(T289, T2, tree(T290, T291, T293)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
252 [label="252: insert(T289, T294, T293)\n\nT289 is ground\nT290 is ground\nT291 is ground\nT293 is ground\nX4 is free\nX121 is free\nX122 is free\nX123 is free\ninsert(T289, T2, tree(T290, T291, T293)) !=? insert(X4, void, tree(X4, void, void))\ninsert(T289, T2, tree(T290, T291, T293)) !=? insert(X121, tree(X121, X122, X123), tree(X121, X122, X123))", fontsize=16, style=filled, fillcolor=lightyellow];
253 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2 -> 253 [arrowhead = none ];
253 -> 3;

254 [label="EVAL with clause\ninsert(X4, void, tree(X4, void, void)).\nand substitutionT1 -> T6,\nX4 -> T6,\nT2 -> void,\nT3 -> tree(T6, void, void)", fontsize=14, style = filled, fillcolor = lightblue];
3 -> 254 [arrowhead = none ];
254 -> 6;

255 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 255 [arrowhead = none ];
255 -> 8;

256 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 256 [arrowhead = none ];
256 -> 10;

257 [label="EVAL with clause\ninsert(X121, tree(X121, X122, X123), tree(X121, X122, X123)).\nand substitutionT1 -> T95,\nX121 -> T95,\nX122 -> T96,\nX123 -> T97,\nT2 -> tree(T95, T96, T97),\nT3 -> tree(T95, T96, T97)", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 257 [arrowhead = none ];
257 -> 66;

258 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 258 [arrowhead = none ];
258 -> 68;

259 [label="EVAL with clause\ninsert(X11, tree(X11, X12, X13), tree(X11, X12, X13)).\nand substitutionT6 -> T13,\nX11 -> T13,\nX12 -> void,\nX13 -> void,\nT2 -> tree(T13, void, void),\nT14 -> void,\nT15 -> void", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 259 [arrowhead = none ];
259 -> 15;

260 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
10 -> 260 [arrowhead = none ];
260 -> 19;

261 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
15 -> 261 [arrowhead = none ];
261 -> 20;

262 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
19 -> 262 [arrowhead = none ];
262 -> 48;

263 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
19 -> 263 [arrowhead = none ];
263 -> 49;

264 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
20 -> 264 [arrowhead = none ];
264 -> 23;

265 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
20 -> 265 [arrowhead = none ];
265 -> 24;

266 [label="EVAL with clause\ninsert(X34, tree(X35, X36, X37), tree(X35, X38, X37)) :- ','(less(X34, X35), insert(X34, X36, X38)).\nand substitutionT13 -> T32,\nX34 -> T32,\nX35 -> T32,\nX36 -> T36,\nX37 -> void,\nT2 -> tree(T32, T36, void),\nT33 -> T32,\nX38 -> void,\nT35 -> void,\nT34 -> T36", fontsize=14, style = filled, fillcolor = lightblue];
23 -> 266 [arrowhead = none ];
266 -> 27;

267 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
23 -> 267 [arrowhead = none ];
267 -> 28;

268 [label="EVAL with clause\ninsert(X64, tree(X65, X66, X67), tree(X65, X66, X68)) :- ','(less(X65, X64), insert(X64, X67, X68)).\nand substitutionT13 -> T50,\nX64 -> T50,\nX65 -> T50,\nX66 -> void,\nX67 -> T54,\nT2 -> tree(T50, void, T54),\nT51 -> T50,\nT52 -> void,\nX68 -> void,\nT53 -> T54", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 268 [arrowhead = none ];
268 -> 43;

269 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
24 -> 269 [arrowhead = none ];
269 -> 45;

270 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
27 -> 270 [arrowhead = none ];
270 -> 29;

271 [label="SPLIT 2\nnew knowledge:\nT32 is ground", fontsize=14, style = filled, fillcolor = violet];
27 -> 271 [arrowhead = none ];
271 -> 31;

272 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
29 -> 272 [arrowhead = none ];
272 -> 34;

273 [label="INSTANCE with matching:\nT1 -> T32\nT2 -> T36\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
31 -> 273 [arrowhead = none , style=dashed];
273 -> 2[style=dashed];

274 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
34 -> 274 [arrowhead = none ];
274 -> 36;

275 [label="EVAL with clause\nless(s(X48), s(X49)) :- less(X48, X49).\nand substitutionX48 -> T39,\nT32 -> s(T39),\nX49 -> T39", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 275 [arrowhead = none ];
275 -> 39;

276 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
36 -> 276 [arrowhead = none ];
276 -> 40;

277 [label="INSTANCE with matching:\nT32 -> T39", fontsize=14, style = filled, fillcolor = lightgrey];
39 -> 277 [arrowhead = none , style=dashed];
277 -> 29[style=dashed];

278 [label="INSTANCE with matching:\nT32 -> T50\nT36 -> T54", fontsize=14, style = filled, fillcolor = lightgrey];
43 -> 278 [arrowhead = none , style=dashed];
278 -> 27[style=dashed];

279 [label="EVAL with clause\ninsert(X91, tree(X92, X93, X94), tree(X92, X95, X94)) :- ','(less(X91, X92), insert(X91, X93, X95)).\nand substitutionT6 -> T71,\nX91 -> T71,\nX92 -> T71,\nX93 -> T75,\nX94 -> void,\nT2 -> tree(T71, T75, void),\nT72 -> T71,\nX95 -> void,\nT74 -> void,\nT73 -> T75", fontsize=14, style = filled, fillcolor = lightblue];
48 -> 279 [arrowhead = none ];
279 -> 54;

280 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
48 -> 280 [arrowhead = none ];
280 -> 56;

281 [label="EVAL with clause\ninsert(X108, tree(X109, X110, X111), tree(X109, X110, X112)) :- ','(less(X109, X108), insert(X108, X111, X112)).\nand substitutionT6 -> T84,\nX108 -> T84,\nX109 -> T84,\nX110 -> void,\nX111 -> T88,\nT2 -> tree(T84, void, T88),\nT85 -> T84,\nT86 -> void,\nX112 -> void,\nT87 -> T88", fontsize=14, style = filled, fillcolor = lightblue];
49 -> 281 [arrowhead = none ];
281 -> 59;

282 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
49 -> 282 [arrowhead = none ];
282 -> 61;

283 [label="INSTANCE with matching:\nT32 -> T71\nT36 -> T75", fontsize=14, style = filled, fillcolor = lightgrey];
54 -> 283 [arrowhead = none , style=dashed];
283 -> 27[style=dashed];

284 [label="INSTANCE with matching:\nT32 -> T84\nT36 -> T88", fontsize=14, style = filled, fillcolor = lightgrey];
59 -> 284 [arrowhead = none , style=dashed];
284 -> 27[style=dashed];

285 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
66 -> 285 [arrowhead = none ];
285 -> 70;

286 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
68 -> 286 [arrowhead = none ];
286 -> 99;

287 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
68 -> 287 [arrowhead = none ];
287 -> 100;

288 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
70 -> 288 [arrowhead = none ];
288 -> 72;

289 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
70 -> 289 [arrowhead = none ];
289 -> 73;

290 [label="EVAL with clause\ninsert(X144, tree(X145, X146, X147), tree(X145, X148, X147)) :- ','(less(X144, X145), insert(X144, X146, X148)).\nand substitutionT95 -> T118,\nX144 -> T118,\nX145 -> T118,\nX146 -> T123,\nX147 -> T121,\nT2 -> tree(T118, T123, T121),\nT119 -> T118,\nT96 -> T122,\nX148 -> T122,\nT97 -> T121,\nT120 -> T123", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 290 [arrowhead = none ];
290 -> 76;

291 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
72 -> 291 [arrowhead = none ];
291 -> 77;

292 [label="EVAL with clause\ninsert(X165, tree(X166, X167, X168), tree(X166, X167, X169)) :- ','(less(X166, X165), insert(X165, X168, X169)).\nand substitutionT95 -> T136,\nX165 -> T136,\nX166 -> T136,\nX167 -> T138,\nX168 -> T141,\nT2 -> tree(T136, T138, T141),\nT137 -> T136,\nT96 -> T138,\nT97 -> T140,\nX169 -> T140,\nT139 -> T141", fontsize=14, style = filled, fillcolor = lightblue];
73 -> 292 [arrowhead = none ];
292 -> 86;

293 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
73 -> 293 [arrowhead = none ];
293 -> 87;

294 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
76 -> 294 [arrowhead = none ];
294 -> 78;

295 [label="SPLIT 2\nnew knowledge:\nT118 is ground", fontsize=14, style = filled, fillcolor = violet];
76 -> 295 [arrowhead = none ];
295 -> 80;

296 [label="INSTANCE with matching:\nT32 -> T118", fontsize=14, style = filled, fillcolor = lightgrey];
78 -> 296 [arrowhead = none , style=dashed];
296 -> 29[style=dashed];

297 [label="INSTANCE with matching:\nT1 -> T118\nT2 -> T123\nT3 -> T122", fontsize=14, style = filled, fillcolor = lightgrey];
80 -> 297 [arrowhead = none , style=dashed];
297 -> 2[style=dashed];

298 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
86 -> 298 [arrowhead = none ];
298 -> 91;

299 [label="SPLIT 2\nnew knowledge:\nT136 is ground", fontsize=14, style = filled, fillcolor = violet];
86 -> 299 [arrowhead = none ];
299 -> 92;

300 [label="INSTANCE with matching:\nT32 -> T136", fontsize=14, style = filled, fillcolor = lightgrey];
91 -> 300 [arrowhead = none , style=dashed];
300 -> 29[style=dashed];

301 [label="INSTANCE with matching:\nT1 -> T136\nT2 -> T141\nT3 -> T140", fontsize=14, style = filled, fillcolor = lightgrey];
92 -> 301 [arrowhead = none , style=dashed];
301 -> 2[style=dashed];

302 [label="EVAL with clause\ninsert(X196, tree(X197, X198, X199), tree(X197, X200, X199)) :- ','(less(X196, X197), insert(X196, X198, X200)).\nand substitutionT1 -> T164,\nX196 -> T164,\nX197 -> T165,\nX198 -> T169,\nX199 -> T167,\nT2 -> tree(T165, T169, T167),\nX200 -> T168,\nT3 -> tree(T165, T168, T167),\nT166 -> T169", fontsize=14, style = filled, fillcolor = lightblue];
99 -> 302 [arrowhead = none ];
302 -> 105;

303 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
99 -> 303 [arrowhead = none ];
303 -> 106;

304 [label="EVAL with clause\ninsert(X336, tree(X337, X338, X339), tree(X337, X338, X340)) :- ','(less(X337, X336), insert(X336, X339, X340)).\nand substitutionT1 -> T289,\nX336 -> T289,\nX337 -> T290,\nX338 -> T291,\nX339 -> T294,\nT2 -> tree(T290, T291, T294),\nX340 -> T293,\nT3 -> tree(T290, T291, T293),\nT292 -> T294", fontsize=14, style = filled, fillcolor = lightblue];
100 -> 304 [arrowhead = none ];
304 -> 245;

305 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
100 -> 305 [arrowhead = none ];
305 -> 248;

306 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
105 -> 306 [arrowhead = none ];
306 -> 108;

307 [label="SPLIT 2\nnew knowledge:\nT164 is ground\nT165 is ground", fontsize=14, style = filled, fillcolor = violet];
105 -> 307 [arrowhead = none ];
307 -> 109;

308 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
108 -> 308 [arrowhead = none ];
308 -> 112;

309 [label="INSTANCE with matching:\nT1 -> T164\nT2 -> T169\nT3 -> T168", fontsize=14, style = filled, fillcolor = lightgrey];
109 -> 309 [arrowhead = none , style=dashed];
309 -> 2[style=dashed];

310 [label="EVAL with clause\nless(0, s(X207)).\nand substitutionT164 -> 0,\nX207 -> T176,\nT165 -> s(T176)", fontsize=14, style = filled, fillcolor = lightblue];
112 -> 310 [arrowhead = none ];
310 -> 113;

311 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
112 -> 311 [arrowhead = none ];
311 -> 116;

312 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
113 -> 312 [arrowhead = none ];
312 -> 117;

313 [label="EVAL with clause\nless(s(X214), s(X215)) :- less(X214, X215).\nand substitutionX214 -> T181,\nT164 -> s(T181),\nX215 -> T182,\nT165 -> s(T182)", fontsize=14, style = filled, fillcolor = lightblue];
116 -> 313 [arrowhead = none ];
313 -> 119;

314 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
116 -> 314 [arrowhead = none ];
314 -> 120;

315 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
117 -> 315 [arrowhead = none ];
315 -> 118;

316 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
119 -> 316 [arrowhead = none ];
316 -> 124;

317 [label="EVAL with clause\nless(0, s(X220)).\nand substitutionT181 -> 0,\nX220 -> T187,\nT182 -> s(T187)", fontsize=14, style = filled, fillcolor = lightblue];
124 -> 317 [arrowhead = none ];
317 -> 126;

318 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
124 -> 318 [arrowhead = none ];
318 -> 128;

319 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
126 -> 319 [arrowhead = none ];
319 -> 129;

320 [label="EVAL with clause\nless(s(X227), s(X228)) :- less(X227, X228).\nand substitutionX227 -> T192,\nT181 -> s(T192),\nX228 -> T193,\nT182 -> s(T193)", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 320 [arrowhead = none ];
320 -> 132;

321 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
128 -> 321 [arrowhead = none ];
321 -> 134;

322 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 322 [arrowhead = none ];
322 -> 130;

323 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
132 -> 323 [arrowhead = none ];
323 -> 136;

324 [label="EVAL with clause\nless(0, s(X233)).\nand substitutionT192 -> 0,\nX233 -> T198,\nT193 -> s(T198)", fontsize=14, style = filled, fillcolor = lightblue];
136 -> 324 [arrowhead = none ];
324 -> 137;

325 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
136 -> 325 [arrowhead = none ];
325 -> 138;

326 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
137 -> 326 [arrowhead = none ];
326 -> 139;

327 [label="EVAL with clause\nless(s(X240), s(X241)) :- less(X240, X241).\nand substitutionX240 -> T203,\nT192 -> s(T203),\nX241 -> T204,\nT193 -> s(T204)", fontsize=14, style = filled, fillcolor = lightblue];
138 -> 327 [arrowhead = none ];
327 -> 145;

328 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
138 -> 328 [arrowhead = none ];
328 -> 146;

329 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
139 -> 329 [arrowhead = none ];
329 -> 141;

330 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
145 -> 330 [arrowhead = none ];
330 -> 152;

331 [label="EVAL with clause\nless(0, s(X246)).\nand substitutionT203 -> 0,\nX246 -> T209,\nT204 -> s(T209)", fontsize=14, style = filled, fillcolor = lightblue];
152 -> 331 [arrowhead = none ];
331 -> 153;

332 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
152 -> 332 [arrowhead = none ];
332 -> 155;

333 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
153 -> 333 [arrowhead = none ];
333 -> 156;

334 [label="EVAL with clause\nless(s(X253), s(X254)) :- less(X253, X254).\nand substitutionX253 -> T214,\nT203 -> s(T214),\nX254 -> T215,\nT204 -> s(T215)", fontsize=14, style = filled, fillcolor = lightblue];
155 -> 334 [arrowhead = none ];
334 -> 161;

335 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
155 -> 335 [arrowhead = none ];
335 -> 162;

336 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
156 -> 336 [arrowhead = none ];
336 -> 158;

337 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
161 -> 337 [arrowhead = none ];
337 -> 166;

338 [label="EVAL with clause\nless(0, s(X259)).\nand substitutionT214 -> 0,\nX259 -> T220,\nT215 -> s(T220)", fontsize=14, style = filled, fillcolor = lightblue];
166 -> 338 [arrowhead = none ];
338 -> 169;

339 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
166 -> 339 [arrowhead = none ];
339 -> 170;

340 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
169 -> 340 [arrowhead = none ];
340 -> 171;

341 [label="EVAL with clause\nless(s(X266), s(X267)) :- less(X266, X267).\nand substitutionX266 -> T225,\nT214 -> s(T225),\nX267 -> T226,\nT215 -> s(T226)", fontsize=14, style = filled, fillcolor = lightblue];
170 -> 341 [arrowhead = none ];
341 -> 175;

342 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
170 -> 342 [arrowhead = none ];
342 -> 176;

343 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
171 -> 343 [arrowhead = none ];
343 -> 172;

344 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
175 -> 344 [arrowhead = none ];
344 -> 179;

345 [label="EVAL with clause\nless(0, s(X272)).\nand substitutionT225 -> 0,\nX272 -> T231,\nT226 -> s(T231)", fontsize=14, style = filled, fillcolor = lightblue];
179 -> 345 [arrowhead = none ];
345 -> 181;

346 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
179 -> 346 [arrowhead = none ];
346 -> 185;

347 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
181 -> 347 [arrowhead = none ];
347 -> 186;

348 [label="EVAL with clause\nless(s(X279), s(X280)) :- less(X279, X280).\nand substitutionX279 -> T236,\nT225 -> s(T236),\nX280 -> T237,\nT226 -> s(T237)", fontsize=14, style = filled, fillcolor = lightblue];
185 -> 348 [arrowhead = none ];
348 -> 191;

349 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
185 -> 349 [arrowhead = none ];
349 -> 192;

350 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
186 -> 350 [arrowhead = none ];
350 -> 188;

351 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
191 -> 351 [arrowhead = none ];
351 -> 197;

352 [label="EVAL with clause\nless(0, s(X285)).\nand substitutionT236 -> 0,\nX285 -> T242,\nT237 -> s(T242)", fontsize=14, style = filled, fillcolor = lightblue];
197 -> 352 [arrowhead = none ];
352 -> 199;

353 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
197 -> 353 [arrowhead = none ];
353 -> 201;

354 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
199 -> 354 [arrowhead = none ];
354 -> 202;

355 [label="EVAL with clause\nless(s(X292), s(X293)) :- less(X292, X293).\nand substitutionX292 -> T247,\nT236 -> s(T247),\nX293 -> T248,\nT237 -> s(T248)", fontsize=14, style = filled, fillcolor = lightblue];
201 -> 355 [arrowhead = none ];
355 -> 205;

356 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
201 -> 356 [arrowhead = none ];
356 -> 207;

357 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
202 -> 357 [arrowhead = none ];
357 -> 204;

358 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
205 -> 358 [arrowhead = none ];
358 -> 212;

359 [label="EVAL with clause\nless(0, s(X298)).\nand substitutionT247 -> 0,\nX298 -> T253,\nT248 -> s(T253)", fontsize=14, style = filled, fillcolor = lightblue];
212 -> 359 [arrowhead = none ];
359 -> 215;

360 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
212 -> 360 [arrowhead = none ];
360 -> 216;

361 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
215 -> 361 [arrowhead = none ];
361 -> 217;

362 [label="EVAL with clause\nless(s(X305), s(X306)) :- less(X305, X306).\nand substitutionX305 -> T258,\nT247 -> s(T258),\nX306 -> T259,\nT248 -> s(T259)", fontsize=14, style = filled, fillcolor = lightblue];
216 -> 362 [arrowhead = none ];
362 -> 221;

363 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
216 -> 363 [arrowhead = none ];
363 -> 222;

364 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
217 -> 364 [arrowhead = none ];
364 -> 218;

365 [label="GENERALIZATION\nT262 <-- s(s(s(s(s(s(s(T258)))))))\nT263 <-- s(s(s(s(s(s(s(T259)))))))\n\nNew Knowledge:\nT262 is ground\nT263 is ground", fontsize=14, style = filled, fillcolor = violet];
221 -> 365 [arrowhead = none ];
365 -> 228;

366 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
228 -> 366 [arrowhead = none ];
366 -> 231;

367 [label="EVAL with clause\nless(0, s(X313)).\nand substitutionT258 -> 0,\nX313 -> T268,\nT259 -> s(T268)", fontsize=14, style = filled, fillcolor = lightblue];
231 -> 367 [arrowhead = none ];
367 -> 233;

368 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
231 -> 368 [arrowhead = none ];
368 -> 235;

369 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
233 -> 369 [arrowhead = none ];
369 -> 236;

370 [label="EVAL with clause\nless(s(X320), s(X321)) :- less(X320, X321).\nand substitutionX320 -> T273,\nT258 -> s(T273),\nX321 -> T274,\nT259 -> s(T274)", fontsize=14, style = filled, fillcolor = lightblue];
235 -> 370 [arrowhead = none ];
370 -> 239;

371 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
235 -> 371 [arrowhead = none ];
371 -> 240;

372 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
236 -> 372 [arrowhead = none ];
372 -> 238;

373 [label="INSTANCE with matching:\nT258 -> T273\nT259 -> T274", fontsize=14, style = filled, fillcolor = lightgrey];
239 -> 373 [arrowhead = none , style=dashed];
373 -> 228[style=dashed];

374 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
245 -> 374 [arrowhead = none ];
374 -> 250;

375 [label="SPLIT 2\nnew knowledge:\nT290 is ground\nT289 is ground", fontsize=14, style = filled, fillcolor = violet];
245 -> 375 [arrowhead = none ];
375 -> 252;

376 [label="INSTANCE with matching:\nT258 -> T290\nT259 -> T289", fontsize=14, style = filled, fillcolor = lightgrey];
250 -> 376 [arrowhead = none , style=dashed];
376 -> 228[style=dashed];

377 [label="INSTANCE with matching:\nT1 -> T289\nT2 -> T294\nT3 -> T293", fontsize=14, style = filled, fillcolor = lightgrey];
252 -> 377 [arrowhead = none , style=dashed];
377 -> 2[style=dashed];

}

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, void)) → f2_out1(void)
f2_in(z0, tree(z0, void, void)) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U1(f20_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f19_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U3(f70_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(z0, z1) → U4(f68_in(z0, z1), z0, z1)
U1(f20_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U1(f20_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U3(f70_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U3(f70_out2(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U4(f68_out1(z0), z1, z2) → f2_out1(z0)
U4(f68_out2(z0), z1, z2) → f2_out1(z0)
f228_in(0, s(z0)) → f228_out1
f228_in(s(z0), s(z1)) → U5(f228_in(z0, z1), s(z0), s(z1))
U5(f228_out1, s(z0), s(z1)) → f228_out1
f29_in(s(z0)) → U6(f29_in(z0), s(z0))
U6(f29_out1, s(z0)) → f29_out1
f108_in(0, s(z0)) → f108_out1
f108_in(s(0), s(s(z0))) → f108_out1
f108_in(s(s(0)), s(s(s(z0)))) → f108_out1
f108_in(s(s(s(0))), s(s(s(s(z0))))) → f108_out1
f108_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f108_out1
f108_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f108_out1
f108_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U7(f228_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U7(f228_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f108_out1
f99_in(z0, tree(z1, z2, z3)) → U8(f105_in(z0, z1, z2), z0, tree(z1, z2, z3))
U8(f105_out1(z0), z1, tree(z2, z3, z4)) → f99_out1(tree(z2, z0, z4))
f100_in(z0, tree(z1, z2, z3)) → U9(f245_in(z1, z0, z3), z0, tree(z1, z2, z3))
U9(f245_out1(z0), z1, tree(z2, z3, z4)) → f100_out1(tree(z2, z3, z0))
f48_in(z0) → U10(f27_in(z0), z0)
U10(f27_out1(z0), z1) → f48_out1(tree(z1, z0, void))
f49_in(z0) → U11(f27_in(z0), z0)
U11(f27_out1(z0), z1) → f49_out1(tree(z1, void, z0))
f72_in(z0, z1, z2) → U12(f76_in(z0, z1), z0, z1, z2)
U12(f76_out1(z0), z1, z2, z3) → f72_out1(tree(z1, z0, z3))
f73_in(z0, z1, z2) → U13(f86_in(z0, z2), z0, z1, z2)
U13(f86_out1(z0), z1, z2, z3) → f73_out1(tree(z1, z2, z0))
f23_in(z0) → U14(f27_in(z0), z0)
U14(f27_out1(z0), z1) → f23_out1(tree(z1, z0, void))
f24_in(z0) → U15(f27_in(z0), z0)
U15(f27_out1(z0), z1) → f24_out1(tree(z1, void, z0))
f27_in(z0) → U16(f29_in(z0), z0)
U16(f29_out1, z0) → U17(f2_in(z0, void), z0)
U17(f2_out1(z0), z1) → f27_out1(z0)
f76_in(z0, z1) → U18(f29_in(z0), z0, z1)
U18(f29_out1, z0, z1) → U19(f2_in(z0, z1), z0, z1)
U19(f2_out1(z0), z1, z2) → f76_out1(z0)
f86_in(z0, z1) → U20(f29_in(z0), z0, z1)
U20(f29_out1, z0, z1) → U21(f2_in(z0, z1), z0, z1)
U21(f2_out1(z0), z1, z2) → f86_out1(z0)
f105_in(z0, z1, z2) → U22(f108_in(z0, z1), z0, z1, z2)
U22(f108_out1, z0, z1, z2) → U23(f2_in(z0, z2), z0, z1, z2)
U23(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f245_in(z0, z1, z2) → U24(f228_in(z0, z1), z0, z1, z2)
U24(f228_out1, z0, z1, z2) → U25(f2_in(z1, z2), z0, z1, z2)
U25(f2_out1(z0), z1, z2, z3) → f245_out1(z0)
f19_in(z0) → U26(f48_in(z0), f49_in(z0), z0)
U26(f48_out1(z0), z1, z2) → f19_out1(z0)
U26(z0, f49_out1(z1), z2) → f19_out2(z1)
f20_in(z0) → U27(f23_in(z0), f24_in(z0), z0)
U27(f23_out1(z0), z1, z2) → f20_out1(z0)
U27(z0, f24_out1(z1), z2) → f20_out2(z1)
f68_in(z0, z1) → U28(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U28(f99_out1(z0), z1, z2, z3) → f68_out1(z0)
U28(z0, f100_out1(z1), z2, z3) → f68_out2(z1)
f70_in(z0, z1, z2) → U29(f72_in(z0, z1, z2), f73_in(z0, z1, z2), z0, z1, z2)
U29(f72_out1(z0), z1, z2, z3, z4) → f70_out1(z0)
U29(z0, f73_out1(z1), z2, z3, z4) → f70_out2(z1)

Tuples:

F2_IN(z0, tree(z0, void, void)) → c2(U1'(f20_in(z0), z0, tree(z0, void, void)), F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(U2'(f19_in(z0), z0, tree(z0, void, void)), F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(U3'(f70_in(z0, z1, z2), z0, tree(z0, z1, z2)), F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(U4'(f68_in(z0, z1), z0, z1), F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(U5'(f228_in(z0, z1), s(z0), s(z1)), F228_IN(z0, z1))
F29_IN(s(z0)) → c18(U6'(f29_in(z0), s(z0)), F29_IN(z0))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c28(U7'(f228_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))), F228_IN(z0, z1))
F99_IN(z0, tree(z1, z2, z3)) → c30(U8'(f105_in(z0, z1, z2), z0, tree(z1, z2, z3)), F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(U9'(f245_in(z1, z0, z3), z0, tree(z1, z2, z3)), F245_IN(z1, z0, z3))
F48_IN(z0) → c34(U10'(f27_in(z0), z0), F27_IN(z0))
F49_IN(z0) → c36(U11'(f27_in(z0), z0), F27_IN(z0))
F72_IN(z0, z1, z2) → c38(U12'(f76_in(z0, z1), z0, z1, z2), F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(U13'(f86_in(z0, z2), z0, z1, z2), F86_IN(z0, z2))
F23_IN(z0) → c42(U14'(f27_in(z0), z0), F27_IN(z0))
F24_IN(z0) → c44(U15'(f27_in(z0), z0), F27_IN(z0))
F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0))
U16'(f29_out1, z0) → c47(U17'(f2_in(z0, void), z0), F2_IN(z0, void))
F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
U18'(f29_out1, z0, z1) → c50(U19'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
U20'(f29_out1, z0, z1) → c53(U21'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
U22'(f108_out1, z0, z1, z2) → c56(U23'(f2_in(z0, z2), z0, z1, z2), F2_IN(z0, z2))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
U24'(f228_out1, z0, z1, z2) → c59(U25'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F19_IN(z0) → c61(U26'(f48_in(z0), f49_in(z0), z0), F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(U27'(f23_in(z0), f24_in(z0), z0), F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(U28'(f99_in(z0, z1), f100_in(z0, z1), z0, z1), F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(U29'(f72_in(z0, z1, z2), f73_in(z0, z1, z2), z0, z1, z2), F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))

S tuples:

F2_IN(z0, tree(z0, void, void)) → c2(U1'(f20_in(z0), z0, tree(z0, void, void)), F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(U2'(f19_in(z0), z0, tree(z0, void, void)), F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(U3'(f70_in(z0, z1, z2), z0, tree(z0, z1, z2)), F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(U4'(f68_in(z0, z1), z0, z1), F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(U5'(f228_in(z0, z1), s(z0), s(z1)), F228_IN(z0, z1))
F29_IN(s(z0)) → c18(U6'(f29_in(z0), s(z0)), F29_IN(z0))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c28(U7'(f228_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))), F228_IN(z0, z1))
F99_IN(z0, tree(z1, z2, z3)) → c30(U8'(f105_in(z0, z1, z2), z0, tree(z1, z2, z3)), F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(U9'(f245_in(z1, z0, z3), z0, tree(z1, z2, z3)), F245_IN(z1, z0, z3))
F48_IN(z0) → c34(U10'(f27_in(z0), z0), F27_IN(z0))
F49_IN(z0) → c36(U11'(f27_in(z0), z0), F27_IN(z0))
F72_IN(z0, z1, z2) → c38(U12'(f76_in(z0, z1), z0, z1, z2), F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(U13'(f86_in(z0, z2), z0, z1, z2), F86_IN(z0, z2))
F23_IN(z0) → c42(U14'(f27_in(z0), z0), F27_IN(z0))
F24_IN(z0) → c44(U15'(f27_in(z0), z0), F27_IN(z0))
F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0))
U16'(f29_out1, z0) → c47(U17'(f2_in(z0, void), z0), F2_IN(z0, void))
F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
U18'(f29_out1, z0, z1) → c50(U19'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
U20'(f29_out1, z0, z1) → c53(U21'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
U22'(f108_out1, z0, z1, z2) → c56(U23'(f2_in(z0, z2), z0, z1, z2), F2_IN(z0, z2))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
U24'(f228_out1, z0, z1, z2) → c59(U25'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F19_IN(z0) → c61(U26'(f48_in(z0), f49_in(z0), z0), F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(U27'(f23_in(z0), f24_in(z0), z0), F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(U28'(f99_in(z0, z1), f100_in(z0, z1), z0, z1), F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(U29'(f72_in(z0, z1, z2), f73_in(z0, z1, z2), z0, z1, z2), F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))

K tuples:none
Defined Rule Symbols:

f2_in, U1, U2, U3, U4, f228_in, U5, f29_in, U6, f108_in, U7, f99_in, U8, f100_in, U9, f48_in, U10, f49_in, U11, f72_in, U12, f73_in, U13, f23_in, U14, f24_in, U15, f27_in, U16, U17, f76_in, U18, U19, f86_in, U20, U21, f105_in, U22, U23, f245_in, U24, U25, f19_in, U26, f20_in, U27, f68_in, U28, f70_in, U29

Defined Pair Symbols:

F2_IN, F228_IN, F29_IN, F108_IN, F99_IN, F100_IN, F48_IN, F49_IN, F72_IN, F73_IN, F23_IN, F24_IN, F27_IN, U16', F76_IN, U18', F86_IN, U20', F105_IN, U22', F245_IN, U24', F19_IN, F20_IN, F68_IN, F70_IN

Compound Symbols:

c2, c3, c5, c6, c16, c18, c28, c30, c32, c34, c36, c38, c40, c42, c44, c46, c47, c49, c50, c52, c53, c55, c56, c58, c59, c61, c64, c67, c70

(5) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, void)) → f2_out1(void)
f2_in(z0, tree(z0, void, void)) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U1(f20_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f19_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U3(f70_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(z0, z1) → U4(f68_in(z0, z1), z0, z1)
U1(f20_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U1(f20_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U3(f70_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U3(f70_out2(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U4(f68_out1(z0), z1, z2) → f2_out1(z0)
U4(f68_out2(z0), z1, z2) → f2_out1(z0)
f228_in(0, s(z0)) → f228_out1
f228_in(s(z0), s(z1)) → U5(f228_in(z0, z1), s(z0), s(z1))
U5(f228_out1, s(z0), s(z1)) → f228_out1
f29_in(s(z0)) → U6(f29_in(z0), s(z0))
U6(f29_out1, s(z0)) → f29_out1
f108_in(0, s(z0)) → f108_out1
f108_in(s(0), s(s(z0))) → f108_out1
f108_in(s(s(0)), s(s(s(z0)))) → f108_out1
f108_in(s(s(s(0))), s(s(s(s(z0))))) → f108_out1
f108_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f108_out1
f108_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f108_out1
f108_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U7(f228_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U7(f228_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f108_out1
f99_in(z0, tree(z1, z2, z3)) → U8(f105_in(z0, z1, z2), z0, tree(z1, z2, z3))
U8(f105_out1(z0), z1, tree(z2, z3, z4)) → f99_out1(tree(z2, z0, z4))
f100_in(z0, tree(z1, z2, z3)) → U9(f245_in(z1, z0, z3), z0, tree(z1, z2, z3))
U9(f245_out1(z0), z1, tree(z2, z3, z4)) → f100_out1(tree(z2, z3, z0))
f48_in(z0) → U10(f27_in(z0), z0)
U10(f27_out1(z0), z1) → f48_out1(tree(z1, z0, void))
f49_in(z0) → U11(f27_in(z0), z0)
U11(f27_out1(z0), z1) → f49_out1(tree(z1, void, z0))
f72_in(z0, z1, z2) → U12(f76_in(z0, z1), z0, z1, z2)
U12(f76_out1(z0), z1, z2, z3) → f72_out1(tree(z1, z0, z3))
f73_in(z0, z1, z2) → U13(f86_in(z0, z2), z0, z1, z2)
U13(f86_out1(z0), z1, z2, z3) → f73_out1(tree(z1, z2, z0))
f23_in(z0) → U14(f27_in(z0), z0)
U14(f27_out1(z0), z1) → f23_out1(tree(z1, z0, void))
f24_in(z0) → U15(f27_in(z0), z0)
U15(f27_out1(z0), z1) → f24_out1(tree(z1, void, z0))
f27_in(z0) → U16(f29_in(z0), z0)
U16(f29_out1, z0) → U17(f2_in(z0, void), z0)
U17(f2_out1(z0), z1) → f27_out1(z0)
f76_in(z0, z1) → U18(f29_in(z0), z0, z1)
U18(f29_out1, z0, z1) → U19(f2_in(z0, z1), z0, z1)
U19(f2_out1(z0), z1, z2) → f76_out1(z0)
f86_in(z0, z1) → U20(f29_in(z0), z0, z1)
U20(f29_out1, z0, z1) → U21(f2_in(z0, z1), z0, z1)
U21(f2_out1(z0), z1, z2) → f86_out1(z0)
f105_in(z0, z1, z2) → U22(f108_in(z0, z1), z0, z1, z2)
U22(f108_out1, z0, z1, z2) → U23(f2_in(z0, z2), z0, z1, z2)
U23(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f245_in(z0, z1, z2) → U24(f228_in(z0, z1), z0, z1, z2)
U24(f228_out1, z0, z1, z2) → U25(f2_in(z1, z2), z0, z1, z2)
U25(f2_out1(z0), z1, z2, z3) → f245_out1(z0)
f19_in(z0) → U26(f48_in(z0), f49_in(z0), z0)
U26(f48_out1(z0), z1, z2) → f19_out1(z0)
U26(z0, f49_out1(z1), z2) → f19_out2(z1)
f20_in(z0) → U27(f23_in(z0), f24_in(z0), z0)
U27(f23_out1(z0), z1, z2) → f20_out1(z0)
U27(z0, f24_out1(z1), z2) → f20_out2(z1)
f68_in(z0, z1) → U28(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U28(f99_out1(z0), z1, z2, z3) → f68_out1(z0)
U28(z0, f100_out1(z1), z2, z3) → f68_out2(z1)
f70_in(z0, z1, z2) → U29(f72_in(z0, z1, z2), f73_in(z0, z1, z2), z0, z1, z2)
U29(f72_out1(z0), z1, z2, z3, z4) → f70_out1(z0)
U29(z0, f73_out1(z1), z2, z3, z4) → f70_out2(z1)

Tuples:

F2_IN(z0, tree(z0, void, void)) → c2(U1'(f20_in(z0), z0, tree(z0, void, void)), F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(U2'(f19_in(z0), z0, tree(z0, void, void)), F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(U3'(f70_in(z0, z1, z2), z0, tree(z0, z1, z2)), F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(U4'(f68_in(z0, z1), z0, z1), F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(U5'(f228_in(z0, z1), s(z0), s(z1)), F228_IN(z0, z1))
F29_IN(s(z0)) → c18(U6'(f29_in(z0), s(z0)), F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(U8'(f105_in(z0, z1, z2), z0, tree(z1, z2, z3)), F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(U9'(f245_in(z1, z0, z3), z0, tree(z1, z2, z3)), F245_IN(z1, z0, z3))
F48_IN(z0) → c34(U10'(f27_in(z0), z0), F27_IN(z0))
F49_IN(z0) → c36(U11'(f27_in(z0), z0), F27_IN(z0))
F72_IN(z0, z1, z2) → c38(U12'(f76_in(z0, z1), z0, z1, z2), F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(U13'(f86_in(z0, z2), z0, z1, z2), F86_IN(z0, z2))
F23_IN(z0) → c42(U14'(f27_in(z0), z0), F27_IN(z0))
F24_IN(z0) → c44(U15'(f27_in(z0), z0), F27_IN(z0))
F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0))
U16'(f29_out1, z0) → c47(U17'(f2_in(z0, void), z0), F2_IN(z0, void))
F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
U18'(f29_out1, z0, z1) → c50(U19'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
U20'(f29_out1, z0, z1) → c53(U21'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
U22'(f108_out1, z0, z1, z2) → c56(U23'(f2_in(z0, z2), z0, z1, z2), F2_IN(z0, z2))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
U24'(f228_out1, z0, z1, z2) → c59(U25'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F19_IN(z0) → c61(U26'(f48_in(z0), f49_in(z0), z0), F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(U27'(f23_in(z0), f24_in(z0), z0), F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(U28'(f99_in(z0, z1), f100_in(z0, z1), z0, z1), F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(U29'(f72_in(z0, z1, z2), f73_in(z0, z1, z2), z0, z1, z2), F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(U7'(f228_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))

S tuples:

F2_IN(z0, tree(z0, void, void)) → c2(U1'(f20_in(z0), z0, tree(z0, void, void)), F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(U2'(f19_in(z0), z0, tree(z0, void, void)), F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(U3'(f70_in(z0, z1, z2), z0, tree(z0, z1, z2)), F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(U4'(f68_in(z0, z1), z0, z1), F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(U5'(f228_in(z0, z1), s(z0), s(z1)), F228_IN(z0, z1))
F29_IN(s(z0)) → c18(U6'(f29_in(z0), s(z0)), F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(U8'(f105_in(z0, z1, z2), z0, tree(z1, z2, z3)), F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(U9'(f245_in(z1, z0, z3), z0, tree(z1, z2, z3)), F245_IN(z1, z0, z3))
F48_IN(z0) → c34(U10'(f27_in(z0), z0), F27_IN(z0))
F49_IN(z0) → c36(U11'(f27_in(z0), z0), F27_IN(z0))
F72_IN(z0, z1, z2) → c38(U12'(f76_in(z0, z1), z0, z1, z2), F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(U13'(f86_in(z0, z2), z0, z1, z2), F86_IN(z0, z2))
F23_IN(z0) → c42(U14'(f27_in(z0), z0), F27_IN(z0))
F24_IN(z0) → c44(U15'(f27_in(z0), z0), F27_IN(z0))
F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0))
U16'(f29_out1, z0) → c47(U17'(f2_in(z0, void), z0), F2_IN(z0, void))
F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
U18'(f29_out1, z0, z1) → c50(U19'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
U20'(f29_out1, z0, z1) → c53(U21'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
U22'(f108_out1, z0, z1, z2) → c56(U23'(f2_in(z0, z2), z0, z1, z2), F2_IN(z0, z2))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
U24'(f228_out1, z0, z1, z2) → c59(U25'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F19_IN(z0) → c61(U26'(f48_in(z0), f49_in(z0), z0), F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(U27'(f23_in(z0), f24_in(z0), z0), F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(U28'(f99_in(z0, z1), f100_in(z0, z1), z0, z1), F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(U29'(f72_in(z0, z1, z2), f73_in(z0, z1, z2), z0, z1, z2), F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(U7'(f228_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))

K tuples:none
Defined Rule Symbols:

f2_in, U1, U2, U3, U4, f228_in, U5, f29_in, U6, f108_in, U7, f99_in, U8, f100_in, U9, f48_in, U10, f49_in, U11, f72_in, U12, f73_in, U13, f23_in, U14, f24_in, U15, f27_in, U16, U17, f76_in, U18, U19, f86_in, U20, U21, f105_in, U22, U23, f245_in, U24, U25, f19_in, U26, f20_in, U27, f68_in, U28, f70_in, U29

Defined Pair Symbols:

F2_IN, F228_IN, F29_IN, F99_IN, F100_IN, F48_IN, F49_IN, F72_IN, F73_IN, F23_IN, F24_IN, F27_IN, U16', F76_IN, U18', F86_IN, U20', F105_IN, U22', F245_IN, U24', F19_IN, F20_IN, F68_IN, F70_IN, F108_IN

Compound Symbols:

c2, c3, c5, c6, c16, c18, c30, c32, c34, c36, c38, c40, c42, c44, c46, c47, c49, c50, c52, c53, c55, c56, c58, c59, c61, c64, c67, c70, c

(7) CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID) transformation)

Removed 24 trailing tuple parts

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, void)) → f2_out1(void)
f2_in(z0, tree(z0, void, void)) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U1(f20_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f19_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U3(f70_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(z0, z1) → U4(f68_in(z0, z1), z0, z1)
U1(f20_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U1(f20_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U3(f70_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U3(f70_out2(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U4(f68_out1(z0), z1, z2) → f2_out1(z0)
U4(f68_out2(z0), z1, z2) → f2_out1(z0)
f228_in(0, s(z0)) → f228_out1
f228_in(s(z0), s(z1)) → U5(f228_in(z0, z1), s(z0), s(z1))
U5(f228_out1, s(z0), s(z1)) → f228_out1
f29_in(s(z0)) → U6(f29_in(z0), s(z0))
U6(f29_out1, s(z0)) → f29_out1
f108_in(0, s(z0)) → f108_out1
f108_in(s(0), s(s(z0))) → f108_out1
f108_in(s(s(0)), s(s(s(z0)))) → f108_out1
f108_in(s(s(s(0))), s(s(s(s(z0))))) → f108_out1
f108_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f108_out1
f108_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f108_out1
f108_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U7(f228_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U7(f228_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f108_out1
f99_in(z0, tree(z1, z2, z3)) → U8(f105_in(z0, z1, z2), z0, tree(z1, z2, z3))
U8(f105_out1(z0), z1, tree(z2, z3, z4)) → f99_out1(tree(z2, z0, z4))
f100_in(z0, tree(z1, z2, z3)) → U9(f245_in(z1, z0, z3), z0, tree(z1, z2, z3))
U9(f245_out1(z0), z1, tree(z2, z3, z4)) → f100_out1(tree(z2, z3, z0))
f48_in(z0) → U10(f27_in(z0), z0)
U10(f27_out1(z0), z1) → f48_out1(tree(z1, z0, void))
f49_in(z0) → U11(f27_in(z0), z0)
U11(f27_out1(z0), z1) → f49_out1(tree(z1, void, z0))
f72_in(z0, z1, z2) → U12(f76_in(z0, z1), z0, z1, z2)
U12(f76_out1(z0), z1, z2, z3) → f72_out1(tree(z1, z0, z3))
f73_in(z0, z1, z2) → U13(f86_in(z0, z2), z0, z1, z2)
U13(f86_out1(z0), z1, z2, z3) → f73_out1(tree(z1, z2, z0))
f23_in(z0) → U14(f27_in(z0), z0)
U14(f27_out1(z0), z1) → f23_out1(tree(z1, z0, void))
f24_in(z0) → U15(f27_in(z0), z0)
U15(f27_out1(z0), z1) → f24_out1(tree(z1, void, z0))
f27_in(z0) → U16(f29_in(z0), z0)
U16(f29_out1, z0) → U17(f2_in(z0, void), z0)
U17(f2_out1(z0), z1) → f27_out1(z0)
f76_in(z0, z1) → U18(f29_in(z0), z0, z1)
U18(f29_out1, z0, z1) → U19(f2_in(z0, z1), z0, z1)
U19(f2_out1(z0), z1, z2) → f76_out1(z0)
f86_in(z0, z1) → U20(f29_in(z0), z0, z1)
U20(f29_out1, z0, z1) → U21(f2_in(z0, z1), z0, z1)
U21(f2_out1(z0), z1, z2) → f86_out1(z0)
f105_in(z0, z1, z2) → U22(f108_in(z0, z1), z0, z1, z2)
U22(f108_out1, z0, z1, z2) → U23(f2_in(z0, z2), z0, z1, z2)
U23(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f245_in(z0, z1, z2) → U24(f228_in(z0, z1), z0, z1, z2)
U24(f228_out1, z0, z1, z2) → U25(f2_in(z1, z2), z0, z1, z2)
U25(f2_out1(z0), z1, z2, z3) → f245_out1(z0)
f19_in(z0) → U26(f48_in(z0), f49_in(z0), z0)
U26(f48_out1(z0), z1, z2) → f19_out1(z0)
U26(z0, f49_out1(z1), z2) → f19_out2(z1)
f20_in(z0) → U27(f23_in(z0), f24_in(z0), z0)
U27(f23_out1(z0), z1, z2) → f20_out1(z0)
U27(z0, f24_out1(z1), z2) → f20_out2(z1)
f68_in(z0, z1) → U28(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U28(f99_out1(z0), z1, z2, z3) → f68_out1(z0)
U28(z0, f100_out1(z1), z2, z3) → f68_out2(z1)
f70_in(z0, z1, z2) → U29(f72_in(z0, z1, z2), f73_in(z0, z1, z2), z0, z1, z2)
U29(f72_out1(z0), z1, z2, z3, z4) → f70_out1(z0)
U29(z0, f73_out1(z1), z2, z3, z4) → f70_out2(z1)

Tuples:

F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0))
F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c2(F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(F228_IN(z0, z1))
F29_IN(s(z0)) → c18(F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(F245_IN(z1, z0, z3))
F48_IN(z0) → c34(F27_IN(z0))
F49_IN(z0) → c36(F27_IN(z0))
F72_IN(z0, z1, z2) → c38(F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(F86_IN(z0, z2))
F23_IN(z0) → c42(F27_IN(z0))
F24_IN(z0) → c44(F27_IN(z0))
U16'(f29_out1, z0) → c47(F2_IN(z0, void))
U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))
U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))
U22'(f108_out1, z0, z1, z2) → c56(F2_IN(z0, z2))
U24'(f228_out1, z0, z1, z2) → c59(F2_IN(z1, z2))
F19_IN(z0) → c61(F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c

S tuples:

F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0))
F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c2(F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(F228_IN(z0, z1))
F29_IN(s(z0)) → c18(F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(F245_IN(z1, z0, z3))
F48_IN(z0) → c34(F27_IN(z0))
F49_IN(z0) → c36(F27_IN(z0))
F72_IN(z0, z1, z2) → c38(F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(F86_IN(z0, z2))
F23_IN(z0) → c42(F27_IN(z0))
F24_IN(z0) → c44(F27_IN(z0))
U16'(f29_out1, z0) → c47(F2_IN(z0, void))
U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))
U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))
U22'(f108_out1, z0, z1, z2) → c56(F2_IN(z0, z2))
U24'(f228_out1, z0, z1, z2) → c59(F2_IN(z1, z2))
F19_IN(z0) → c61(F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c

K tuples:none
Defined Rule Symbols:

f2_in, U1, U2, U3, U4, f228_in, U5, f29_in, U6, f108_in, U7, f99_in, U8, f100_in, U9, f48_in, U10, f49_in, U11, f72_in, U12, f73_in, U13, f23_in, U14, f24_in, U15, f27_in, U16, U17, f76_in, U18, U19, f86_in, U20, U21, f105_in, U22, U23, f245_in, U24, U25, f19_in, U26, f20_in, U27, f68_in, U28, f70_in, U29

Defined Pair Symbols:

F27_IN, F76_IN, F86_IN, F105_IN, F245_IN, F108_IN, F2_IN, F228_IN, F29_IN, F99_IN, F100_IN, F48_IN, F49_IN, F72_IN, F73_IN, F23_IN, F24_IN, U16', U18', U20', U22', U24', F19_IN, F20_IN, F68_IN, F70_IN

Compound Symbols:

c46, c49, c52, c55, c58, c, c2, c3, c5, c6, c16, c18, c30, c32, c34, c36, c38, c40, c42, c44, c47, c50, c53, c56, c59, c61, c64, c67, c70, c

(9) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))

We considered the (Usable) Rules:

f228_in(0, s(z0)) → f228_out1
f228_in(s(z0), s(z1)) → U5(f228_in(z0, z1), s(z0), s(z1))
U5(f228_out1, s(z0), s(z1)) → f228_out1
f108_in(0, s(z0)) → f108_out1
f108_in(s(0), s(s(z0))) → f108_out1
f108_in(s(s(0)), s(s(s(z0)))) → f108_out1
f108_in(s(s(s(0))), s(s(s(s(z0))))) → f108_out1
f108_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f108_out1
f108_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f108_out1
f108_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U7(f228_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U7(f228_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f108_out1
f29_in(s(z0)) → U6(f29_in(z0), s(z0))
U6(f29_out1, s(z0)) → f29_out1

And the Tuples:

F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0))
F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c2(F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(F228_IN(z0, z1))
F29_IN(s(z0)) → c18(F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(F245_IN(z1, z0, z3))
F48_IN(z0) → c34(F27_IN(z0))
F49_IN(z0) → c36(F27_IN(z0))
F72_IN(z0, z1, z2) → c38(F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(F86_IN(z0, z2))
F23_IN(z0) → c42(F27_IN(z0))
F24_IN(z0) → c44(F27_IN(z0))
U16'(f29_out1, z0) → c47(F2_IN(z0, void))
U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))
U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))
U22'(f108_out1, z0, z1, z2) → c56(F2_IN(z0, z2))
U24'(f228_out1, z0, z1, z2) → c59(F2_IN(z1, z2))
F19_IN(z0) → c61(F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(0) = 0
POL(F100_IN(x₁, x₂)) = 0
POL(F105_IN(x₁, x₂, x₃)) = 0
POL(F108_IN(x₁, x₂)) = 0
POL(F19_IN(x₁)) = 0
POL(F20_IN(x₁)) = 0
POL(F228_IN(x₁, x₂)) = 0
POL(F23_IN(x₁)) = 0
POL(F245_IN(x₁, x₂, x₃)) = 0
POL(F24_IN(x₁)) = 0
POL(F27_IN(x₁)) = 0
POL(F29_IN(x₁)) = 0
POL(F2_IN(x₁, x₂)) = 0
POL(F48_IN(x₁)) = 0
POL(F49_IN(x₁)) = 0
POL(F68_IN(x₁, x₂)) = 0
POL(F70_IN(x₁, x₂, x₃)) = 0
POL(F72_IN(x₁, x₂, x₃)) = 0
POL(F73_IN(x₁, x₂, x₃)) = 0
POL(F76_IN(x₁, x₂)) = 0
POL(F86_IN(x₁, x₂)) = 0
POL(F99_IN(x₁, x₂)) = 0
POL(U16'(x₁, x₂)) = 0
POL(U18'(x₁, x₂, x₃)) = 0
POL(U20'(x₁, x₂, x₃)) = x₁
POL(U22'(x₁, x₂, x₃, x₄)) = 0
POL(U24'(x₁, x₂, x₃, x₄)) = 0
POL(U5(x₁, x₂, x₃)) = 0
POL(U6(x₁, x₂)) = x₁
POL(U7(x₁, x₂, x₃)) = 0
POL(c) = 0
POL(c(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c2(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c46(x₁, x₂)) = x₁ + x₂
POL(c47(x₁)) = x₁
POL(c49(x₁, x₂)) = x₁ + x₂
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c52(x₁, x₂)) = x₁ + x₂
POL(c53(x₁)) = x₁
POL(c55(x₁, x₂)) = x₁ + x₂
POL(c56(x₁)) = x₁
POL(c58(x₁, x₂)) = x₁ + x₂
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c61(x₁, x₂)) = x₁ + x₂
POL(c64(x₁, x₂)) = x₁ + x₂
POL(c67(x₁, x₂)) = x₁ + x₂
POL(c70(x₁, x₂)) = x₁ + x₂
POL(f108_in(x₁, x₂)) = 0
POL(f108_out1) = 0
POL(f228_in(x₁, x₂)) = 0
POL(f228_out1) = 0
POL(f29_in(x₁)) = 0
POL(f29_out1) = [1]
POL(s(x₁)) = 0
POL(tree(x₁, x₂, x₃)) = 0
POL(void) = 0

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, void)) → f2_out1(void)
f2_in(z0, tree(z0, void, void)) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U1(f20_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f19_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U3(f70_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(z0, z1) → U4(f68_in(z0, z1), z0, z1)
U1(f20_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U1(f20_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U3(f70_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U3(f70_out2(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U4(f68_out1(z0), z1, z2) → f2_out1(z0)
U4(f68_out2(z0), z1, z2) → f2_out1(z0)
f228_in(0, s(z0)) → f228_out1
f228_in(s(z0), s(z1)) → U5(f228_in(z0, z1), s(z0), s(z1))
U5(f228_out1, s(z0), s(z1)) → f228_out1
f29_in(s(z0)) → U6(f29_in(z0), s(z0))
U6(f29_out1, s(z0)) → f29_out1
f108_in(0, s(z0)) → f108_out1
f108_in(s(0), s(s(z0))) → f108_out1
f108_in(s(s(0)), s(s(s(z0)))) → f108_out1
f108_in(s(s(s(0))), s(s(s(s(z0))))) → f108_out1
f108_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f108_out1
f108_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f108_out1
f108_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U7(f228_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U7(f228_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f108_out1
f99_in(z0, tree(z1, z2, z3)) → U8(f105_in(z0, z1, z2), z0, tree(z1, z2, z3))
U8(f105_out1(z0), z1, tree(z2, z3, z4)) → f99_out1(tree(z2, z0, z4))
f100_in(z0, tree(z1, z2, z3)) → U9(f245_in(z1, z0, z3), z0, tree(z1, z2, z3))
U9(f245_out1(z0), z1, tree(z2, z3, z4)) → f100_out1(tree(z2, z3, z0))
f48_in(z0) → U10(f27_in(z0), z0)
U10(f27_out1(z0), z1) → f48_out1(tree(z1, z0, void))
f49_in(z0) → U11(f27_in(z0), z0)
U11(f27_out1(z0), z1) → f49_out1(tree(z1, void, z0))
f72_in(z0, z1, z2) → U12(f76_in(z0, z1), z0, z1, z2)
U12(f76_out1(z0), z1, z2, z3) → f72_out1(tree(z1, z0, z3))
f73_in(z0, z1, z2) → U13(f86_in(z0, z2), z0, z1, z2)
U13(f86_out1(z0), z1, z2, z3) → f73_out1(tree(z1, z2, z0))
f23_in(z0) → U14(f27_in(z0), z0)
U14(f27_out1(z0), z1) → f23_out1(tree(z1, z0, void))
f24_in(z0) → U15(f27_in(z0), z0)
U15(f27_out1(z0), z1) → f24_out1(tree(z1, void, z0))
f27_in(z0) → U16(f29_in(z0), z0)
U16(f29_out1, z0) → U17(f2_in(z0, void), z0)
U17(f2_out1(z0), z1) → f27_out1(z0)
f76_in(z0, z1) → U18(f29_in(z0), z0, z1)
U18(f29_out1, z0, z1) → U19(f2_in(z0, z1), z0, z1)
U19(f2_out1(z0), z1, z2) → f76_out1(z0)
f86_in(z0, z1) → U20(f29_in(z0), z0, z1)
U20(f29_out1, z0, z1) → U21(f2_in(z0, z1), z0, z1)
U21(f2_out1(z0), z1, z2) → f86_out1(z0)
f105_in(z0, z1, z2) → U22(f108_in(z0, z1), z0, z1, z2)
U22(f108_out1, z0, z1, z2) → U23(f2_in(z0, z2), z0, z1, z2)
U23(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f245_in(z0, z1, z2) → U24(f228_in(z0, z1), z0, z1, z2)
U24(f228_out1, z0, z1, z2) → U25(f2_in(z1, z2), z0, z1, z2)
U25(f2_out1(z0), z1, z2, z3) → f245_out1(z0)
f19_in(z0) → U26(f48_in(z0), f49_in(z0), z0)
U26(f48_out1(z0), z1, z2) → f19_out1(z0)
U26(z0, f49_out1(z1), z2) → f19_out2(z1)
f20_in(z0) → U27(f23_in(z0), f24_in(z0), z0)
U27(f23_out1(z0), z1, z2) → f20_out1(z0)
U27(z0, f24_out1(z1), z2) → f20_out2(z1)
f68_in(z0, z1) → U28(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U28(f99_out1(z0), z1, z2, z3) → f68_out1(z0)
U28(z0, f100_out1(z1), z2, z3) → f68_out2(z1)
f70_in(z0, z1, z2) → U29(f72_in(z0, z1, z2), f73_in(z0, z1, z2), z0, z1, z2)
U29(f72_out1(z0), z1, z2, z3, z4) → f70_out1(z0)
U29(z0, f73_out1(z1), z2, z3, z4) → f70_out2(z1)

Tuples:

F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0))
F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c2(F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(F228_IN(z0, z1))
F29_IN(s(z0)) → c18(F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(F245_IN(z1, z0, z3))
F48_IN(z0) → c34(F27_IN(z0))
F49_IN(z0) → c36(F27_IN(z0))
F72_IN(z0, z1, z2) → c38(F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(F86_IN(z0, z2))
F23_IN(z0) → c42(F27_IN(z0))
F24_IN(z0) → c44(F27_IN(z0))
U16'(f29_out1, z0) → c47(F2_IN(z0, void))
U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))
U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))
U22'(f108_out1, z0, z1, z2) → c56(F2_IN(z0, z2))
U24'(f228_out1, z0, z1, z2) → c59(F2_IN(z1, z2))
F19_IN(z0) → c61(F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c

S tuples:

F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0))
F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c2(F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(F228_IN(z0, z1))
F29_IN(s(z0)) → c18(F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(F245_IN(z1, z0, z3))
F48_IN(z0) → c34(F27_IN(z0))
F49_IN(z0) → c36(F27_IN(z0))
F72_IN(z0, z1, z2) → c38(F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(F86_IN(z0, z2))
F23_IN(z0) → c42(F27_IN(z0))
F24_IN(z0) → c44(F27_IN(z0))
U16'(f29_out1, z0) → c47(F2_IN(z0, void))
U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))
U22'(f108_out1, z0, z1, z2) → c56(F2_IN(z0, z2))
U24'(f228_out1, z0, z1, z2) → c59(F2_IN(z1, z2))
F19_IN(z0) → c61(F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c

K tuples:

U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, f228_in, U5, f29_in, U6, f108_in, U7, f99_in, U8, f100_in, U9, f48_in, U10, f49_in, U11, f72_in, U12, f73_in, U13, f23_in, U14, f24_in, U15, f27_in, U16, U17, f76_in, U18, U19, f86_in, U20, U21, f105_in, U22, U23, f245_in, U24, U25, f19_in, U26, f20_in, U27, f68_in, U28, f70_in, U29

Defined Pair Symbols:

F27_IN, F76_IN, F86_IN, F105_IN, F245_IN, F108_IN, F2_IN, F228_IN, F29_IN, F99_IN, F100_IN, F48_IN, F49_IN, F72_IN, F73_IN, F23_IN, F24_IN, U16', U18', U20', U22', U24', F19_IN, F20_IN, F68_IN, F70_IN

Compound Symbols:

c46, c49, c52, c55, c58, c, c2, c3, c5, c6, c16, c18, c30, c32, c34, c36, c38, c40, c42, c44, c47, c50, c53, c56, c59, c61, c64, c67, c70, c

(11) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))

We considered the (Usable) Rules:

f228_in(0, s(z0)) → f228_out1
f228_in(s(z0), s(z1)) → U5(f228_in(z0, z1), s(z0), s(z1))
U5(f228_out1, s(z0), s(z1)) → f228_out1
f108_in(0, s(z0)) → f108_out1
f108_in(s(0), s(s(z0))) → f108_out1
f108_in(s(s(0)), s(s(s(z0)))) → f108_out1
f108_in(s(s(s(0))), s(s(s(s(z0))))) → f108_out1
f108_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f108_out1
f108_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f108_out1
f108_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U7(f228_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U7(f228_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f108_out1
f29_in(s(z0)) → U6(f29_in(z0), s(z0))
U6(f29_out1, s(z0)) → f29_out1

And the Tuples:

F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0))
F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c2(F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(F228_IN(z0, z1))
F29_IN(s(z0)) → c18(F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(F245_IN(z1, z0, z3))
F48_IN(z0) → c34(F27_IN(z0))
F49_IN(z0) → c36(F27_IN(z0))
F72_IN(z0, z1, z2) → c38(F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(F86_IN(z0, z2))
F23_IN(z0) → c42(F27_IN(z0))
F24_IN(z0) → c44(F27_IN(z0))
U16'(f29_out1, z0) → c47(F2_IN(z0, void))
U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))
U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))
U22'(f108_out1, z0, z1, z2) → c56(F2_IN(z0, z2))
U24'(f228_out1, z0, z1, z2) → c59(F2_IN(z1, z2))
F19_IN(z0) → c61(F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(0) = 0
POL(F100_IN(x₁, x₂)) = 0
POL(F105_IN(x₁, x₂, x₃)) = 0
POL(F108_IN(x₁, x₂)) = 0
POL(F19_IN(x₁)) = 0
POL(F20_IN(x₁)) = 0
POL(F228_IN(x₁, x₂)) = 0
POL(F23_IN(x₁)) = 0
POL(F245_IN(x₁, x₂, x₃)) = 0
POL(F24_IN(x₁)) = 0
POL(F27_IN(x₁)) = 0
POL(F29_IN(x₁)) = 0
POL(F2_IN(x₁, x₂)) = 0
POL(F48_IN(x₁)) = 0
POL(F49_IN(x₁)) = 0
POL(F68_IN(x₁, x₂)) = 0
POL(F70_IN(x₁, x₂, x₃)) = 0
POL(F72_IN(x₁, x₂, x₃)) = 0
POL(F73_IN(x₁, x₂, x₃)) = 0
POL(F76_IN(x₁, x₂)) = 0
POL(F86_IN(x₁, x₂)) = 0
POL(F99_IN(x₁, x₂)) = 0
POL(U16'(x₁, x₂)) = 0
POL(U18'(x₁, x₂, x₃)) = [2]x₁
POL(U20'(x₁, x₂, x₃)) = [2]x₁
POL(U22'(x₁, x₂, x₃, x₄)) = 0
POL(U24'(x₁, x₂, x₃, x₄)) = 0
POL(U5(x₁, x₂, x₃)) = 0
POL(U6(x₁, x₂)) = [2]x₁
POL(U7(x₁, x₂, x₃)) = 0
POL(c) = 0
POL(c(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c2(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c46(x₁, x₂)) = x₁ + x₂
POL(c47(x₁)) = x₁
POL(c49(x₁, x₂)) = x₁ + x₂
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c52(x₁, x₂)) = x₁ + x₂
POL(c53(x₁)) = x₁
POL(c55(x₁, x₂)) = x₁ + x₂
POL(c56(x₁)) = x₁
POL(c58(x₁, x₂)) = x₁ + x₂
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c61(x₁, x₂)) = x₁ + x₂
POL(c64(x₁, x₂)) = x₁ + x₂
POL(c67(x₁, x₂)) = x₁ + x₂
POL(c70(x₁, x₂)) = x₁ + x₂
POL(f108_in(x₁, x₂)) = 0
POL(f108_out1) = 0
POL(f228_in(x₁, x₂)) = 0
POL(f228_out1) = 0
POL(f29_in(x₁)) = 0
POL(f29_out1) = [2]
POL(s(x₁)) = 0
POL(tree(x₁, x₂, x₃)) = 0
POL(void) = 0

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, void)) → f2_out1(void)
f2_in(z0, tree(z0, void, void)) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U1(f20_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f19_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U3(f70_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(z0, z1) → U4(f68_in(z0, z1), z0, z1)
U1(f20_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U1(f20_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U3(f70_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U3(f70_out2(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U4(f68_out1(z0), z1, z2) → f2_out1(z0)
U4(f68_out2(z0), z1, z2) → f2_out1(z0)
f228_in(0, s(z0)) → f228_out1
f228_in(s(z0), s(z1)) → U5(f228_in(z0, z1), s(z0), s(z1))
U5(f228_out1, s(z0), s(z1)) → f228_out1
f29_in(s(z0)) → U6(f29_in(z0), s(z0))
U6(f29_out1, s(z0)) → f29_out1
f108_in(0, s(z0)) → f108_out1
f108_in(s(0), s(s(z0))) → f108_out1
f108_in(s(s(0)), s(s(s(z0)))) → f108_out1
f108_in(s(s(s(0))), s(s(s(s(z0))))) → f108_out1
f108_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f108_out1
f108_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f108_out1
f108_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U7(f228_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U7(f228_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f108_out1
f99_in(z0, tree(z1, z2, z3)) → U8(f105_in(z0, z1, z2), z0, tree(z1, z2, z3))
U8(f105_out1(z0), z1, tree(z2, z3, z4)) → f99_out1(tree(z2, z0, z4))
f100_in(z0, tree(z1, z2, z3)) → U9(f245_in(z1, z0, z3), z0, tree(z1, z2, z3))
U9(f245_out1(z0), z1, tree(z2, z3, z4)) → f100_out1(tree(z2, z3, z0))
f48_in(z0) → U10(f27_in(z0), z0)
U10(f27_out1(z0), z1) → f48_out1(tree(z1, z0, void))
f49_in(z0) → U11(f27_in(z0), z0)
U11(f27_out1(z0), z1) → f49_out1(tree(z1, void, z0))
f72_in(z0, z1, z2) → U12(f76_in(z0, z1), z0, z1, z2)
U12(f76_out1(z0), z1, z2, z3) → f72_out1(tree(z1, z0, z3))
f73_in(z0, z1, z2) → U13(f86_in(z0, z2), z0, z1, z2)
U13(f86_out1(z0), z1, z2, z3) → f73_out1(tree(z1, z2, z0))
f23_in(z0) → U14(f27_in(z0), z0)
U14(f27_out1(z0), z1) → f23_out1(tree(z1, z0, void))
f24_in(z0) → U15(f27_in(z0), z0)
U15(f27_out1(z0), z1) → f24_out1(tree(z1, void, z0))
f27_in(z0) → U16(f29_in(z0), z0)
U16(f29_out1, z0) → U17(f2_in(z0, void), z0)
U17(f2_out1(z0), z1) → f27_out1(z0)
f76_in(z0, z1) → U18(f29_in(z0), z0, z1)
U18(f29_out1, z0, z1) → U19(f2_in(z0, z1), z0, z1)
U19(f2_out1(z0), z1, z2) → f76_out1(z0)
f86_in(z0, z1) → U20(f29_in(z0), z0, z1)
U20(f29_out1, z0, z1) → U21(f2_in(z0, z1), z0, z1)
U21(f2_out1(z0), z1, z2) → f86_out1(z0)
f105_in(z0, z1, z2) → U22(f108_in(z0, z1), z0, z1, z2)
U22(f108_out1, z0, z1, z2) → U23(f2_in(z0, z2), z0, z1, z2)
U23(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f245_in(z0, z1, z2) → U24(f228_in(z0, z1), z0, z1, z2)
U24(f228_out1, z0, z1, z2) → U25(f2_in(z1, z2), z0, z1, z2)
U25(f2_out1(z0), z1, z2, z3) → f245_out1(z0)
f19_in(z0) → U26(f48_in(z0), f49_in(z0), z0)
U26(f48_out1(z0), z1, z2) → f19_out1(z0)
U26(z0, f49_out1(z1), z2) → f19_out2(z1)
f20_in(z0) → U27(f23_in(z0), f24_in(z0), z0)
U27(f23_out1(z0), z1, z2) → f20_out1(z0)
U27(z0, f24_out1(z1), z2) → f20_out2(z1)
f68_in(z0, z1) → U28(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U28(f99_out1(z0), z1, z2, z3) → f68_out1(z0)
U28(z0, f100_out1(z1), z2, z3) → f68_out2(z1)
f70_in(z0, z1, z2) → U29(f72_in(z0, z1, z2), f73_in(z0, z1, z2), z0, z1, z2)
U29(f72_out1(z0), z1, z2, z3, z4) → f70_out1(z0)
U29(z0, f73_out1(z1), z2, z3, z4) → f70_out2(z1)

Tuples:

F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0))
F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c2(F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(F228_IN(z0, z1))
F29_IN(s(z0)) → c18(F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(F245_IN(z1, z0, z3))
F48_IN(z0) → c34(F27_IN(z0))
F49_IN(z0) → c36(F27_IN(z0))
F72_IN(z0, z1, z2) → c38(F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(F86_IN(z0, z2))
F23_IN(z0) → c42(F27_IN(z0))
F24_IN(z0) → c44(F27_IN(z0))
U16'(f29_out1, z0) → c47(F2_IN(z0, void))
U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))
U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))
U22'(f108_out1, z0, z1, z2) → c56(F2_IN(z0, z2))
U24'(f228_out1, z0, z1, z2) → c59(F2_IN(z1, z2))
F19_IN(z0) → c61(F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c

S tuples:

F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0))
F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c2(F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(F228_IN(z0, z1))
F29_IN(s(z0)) → c18(F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(F245_IN(z1, z0, z3))
F48_IN(z0) → c34(F27_IN(z0))
F49_IN(z0) → c36(F27_IN(z0))
F72_IN(z0, z1, z2) → c38(F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(F86_IN(z0, z2))
F23_IN(z0) → c42(F27_IN(z0))
F24_IN(z0) → c44(F27_IN(z0))
U16'(f29_out1, z0) → c47(F2_IN(z0, void))
U22'(f108_out1, z0, z1, z2) → c56(F2_IN(z0, z2))
U24'(f228_out1, z0, z1, z2) → c59(F2_IN(z1, z2))
F19_IN(z0) → c61(F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c

K tuples:

U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))
U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, f228_in, U5, f29_in, U6, f108_in, U7, f99_in, U8, f100_in, U9, f48_in, U10, f49_in, U11, f72_in, U12, f73_in, U13, f23_in, U14, f24_in, U15, f27_in, U16, U17, f76_in, U18, U19, f86_in, U20, U21, f105_in, U22, U23, f245_in, U24, U25, f19_in, U26, f20_in, U27, f68_in, U28, f70_in, U29

Defined Pair Symbols:

F27_IN, F76_IN, F86_IN, F105_IN, F245_IN, F108_IN, F2_IN, F228_IN, F29_IN, F99_IN, F100_IN, F48_IN, F49_IN, F72_IN, F73_IN, F23_IN, F24_IN, U16', U18', U20', U22', U24', F19_IN, F20_IN, F68_IN, F70_IN

Compound Symbols:

c46, c49, c52, c55, c58, c, c2, c3, c5, c6, c16, c18, c30, c32, c34, c36, c38, c40, c42, c44, c47, c50, c53, c56, c59, c61, c64, c67, c70, c

(13) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U16'(f29_out1, z0) → c47(F2_IN(z0, void))

We considered the (Usable) Rules:

f228_in(0, s(z0)) → f228_out1
f228_in(s(z0), s(z1)) → U5(f228_in(z0, z1), s(z0), s(z1))
U5(f228_out1, s(z0), s(z1)) → f228_out1
f108_in(0, s(z0)) → f108_out1
f108_in(s(0), s(s(z0))) → f108_out1
f108_in(s(s(0)), s(s(s(z0)))) → f108_out1
f108_in(s(s(s(0))), s(s(s(s(z0))))) → f108_out1
f108_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f108_out1
f108_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f108_out1
f108_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U7(f228_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U7(f228_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f108_out1
f29_in(s(z0)) → U6(f29_in(z0), s(z0))
U6(f29_out1, s(z0)) → f29_out1

And the Tuples:

F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0))
F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c2(F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(F228_IN(z0, z1))
F29_IN(s(z0)) → c18(F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(F245_IN(z1, z0, z3))
F48_IN(z0) → c34(F27_IN(z0))
F49_IN(z0) → c36(F27_IN(z0))
F72_IN(z0, z1, z2) → c38(F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(F86_IN(z0, z2))
F23_IN(z0) → c42(F27_IN(z0))
F24_IN(z0) → c44(F27_IN(z0))
U16'(f29_out1, z0) → c47(F2_IN(z0, void))
U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))
U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))
U22'(f108_out1, z0, z1, z2) → c56(F2_IN(z0, z2))
U24'(f228_out1, z0, z1, z2) → c59(F2_IN(z1, z2))
F19_IN(z0) → c61(F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(0) = 0
POL(F100_IN(x₁, x₂)) = 0
POL(F105_IN(x₁, x₂, x₃)) = 0
POL(F108_IN(x₁, x₂)) = 0
POL(F19_IN(x₁)) = 0
POL(F20_IN(x₁)) = 0
POL(F228_IN(x₁, x₂)) = 0
POL(F23_IN(x₁)) = 0
POL(F245_IN(x₁, x₂, x₃)) = 0
POL(F24_IN(x₁)) = 0
POL(F27_IN(x₁)) = 0
POL(F29_IN(x₁)) = 0
POL(F2_IN(x₁, x₂)) = 0
POL(F48_IN(x₁)) = 0
POL(F49_IN(x₁)) = 0
POL(F68_IN(x₁, x₂)) = 0
POL(F70_IN(x₁, x₂, x₃)) = 0
POL(F72_IN(x₁, x₂, x₃)) = 0
POL(F73_IN(x₁, x₂, x₃)) = 0
POL(F76_IN(x₁, x₂)) = 0
POL(F86_IN(x₁, x₂)) = 0
POL(F99_IN(x₁, x₂)) = 0
POL(U16'(x₁, x₂)) = [2]x₁
POL(U18'(x₁, x₂, x₃)) = 0
POL(U20'(x₁, x₂, x₃)) = [2]x₁
POL(U22'(x₁, x₂, x₃, x₄)) = 0
POL(U24'(x₁, x₂, x₃, x₄)) = 0
POL(U5(x₁, x₂, x₃)) = 0
POL(U6(x₁, x₂)) = x₁
POL(U7(x₁, x₂, x₃)) = 0
POL(c) = 0
POL(c(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c2(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c46(x₁, x₂)) = x₁ + x₂
POL(c47(x₁)) = x₁
POL(c49(x₁, x₂)) = x₁ + x₂
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c52(x₁, x₂)) = x₁ + x₂
POL(c53(x₁)) = x₁
POL(c55(x₁, x₂)) = x₁ + x₂
POL(c56(x₁)) = x₁
POL(c58(x₁, x₂)) = x₁ + x₂
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c61(x₁, x₂)) = x₁ + x₂
POL(c64(x₁, x₂)) = x₁ + x₂
POL(c67(x₁, x₂)) = x₁ + x₂
POL(c70(x₁, x₂)) = x₁ + x₂
POL(f108_in(x₁, x₂)) = 0
POL(f108_out1) = 0
POL(f228_in(x₁, x₂)) = 0
POL(f228_out1) = 0
POL(f29_in(x₁)) = 0
POL(f29_out1) = [2]
POL(s(x₁)) = 0
POL(tree(x₁, x₂, x₃)) = 0
POL(void) = 0

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, void)) → f2_out1(void)
f2_in(z0, tree(z0, void, void)) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U1(f20_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f19_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U3(f70_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(z0, z1) → U4(f68_in(z0, z1), z0, z1)
U1(f20_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U1(f20_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U3(f70_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U3(f70_out2(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U4(f68_out1(z0), z1, z2) → f2_out1(z0)
U4(f68_out2(z0), z1, z2) → f2_out1(z0)
f228_in(0, s(z0)) → f228_out1
f228_in(s(z0), s(z1)) → U5(f228_in(z0, z1), s(z0), s(z1))
U5(f228_out1, s(z0), s(z1)) → f228_out1
f29_in(s(z0)) → U6(f29_in(z0), s(z0))
U6(f29_out1, s(z0)) → f29_out1
f108_in(0, s(z0)) → f108_out1
f108_in(s(0), s(s(z0))) → f108_out1
f108_in(s(s(0)), s(s(s(z0)))) → f108_out1
f108_in(s(s(s(0))), s(s(s(s(z0))))) → f108_out1
f108_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f108_out1
f108_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f108_out1
f108_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U7(f228_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U7(f228_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f108_out1
f99_in(z0, tree(z1, z2, z3)) → U8(f105_in(z0, z1, z2), z0, tree(z1, z2, z3))
U8(f105_out1(z0), z1, tree(z2, z3, z4)) → f99_out1(tree(z2, z0, z4))
f100_in(z0, tree(z1, z2, z3)) → U9(f245_in(z1, z0, z3), z0, tree(z1, z2, z3))
U9(f245_out1(z0), z1, tree(z2, z3, z4)) → f100_out1(tree(z2, z3, z0))
f48_in(z0) → U10(f27_in(z0), z0)
U10(f27_out1(z0), z1) → f48_out1(tree(z1, z0, void))
f49_in(z0) → U11(f27_in(z0), z0)
U11(f27_out1(z0), z1) → f49_out1(tree(z1, void, z0))
f72_in(z0, z1, z2) → U12(f76_in(z0, z1), z0, z1, z2)
U12(f76_out1(z0), z1, z2, z3) → f72_out1(tree(z1, z0, z3))
f73_in(z0, z1, z2) → U13(f86_in(z0, z2), z0, z1, z2)
U13(f86_out1(z0), z1, z2, z3) → f73_out1(tree(z1, z2, z0))
f23_in(z0) → U14(f27_in(z0), z0)
U14(f27_out1(z0), z1) → f23_out1(tree(z1, z0, void))
f24_in(z0) → U15(f27_in(z0), z0)
U15(f27_out1(z0), z1) → f24_out1(tree(z1, void, z0))
f27_in(z0) → U16(f29_in(z0), z0)
U16(f29_out1, z0) → U17(f2_in(z0, void), z0)
U17(f2_out1(z0), z1) → f27_out1(z0)
f76_in(z0, z1) → U18(f29_in(z0), z0, z1)
U18(f29_out1, z0, z1) → U19(f2_in(z0, z1), z0, z1)
U19(f2_out1(z0), z1, z2) → f76_out1(z0)
f86_in(z0, z1) → U20(f29_in(z0), z0, z1)
U20(f29_out1, z0, z1) → U21(f2_in(z0, z1), z0, z1)
U21(f2_out1(z0), z1, z2) → f86_out1(z0)
f105_in(z0, z1, z2) → U22(f108_in(z0, z1), z0, z1, z2)
U22(f108_out1, z0, z1, z2) → U23(f2_in(z0, z2), z0, z1, z2)
U23(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f245_in(z0, z1, z2) → U24(f228_in(z0, z1), z0, z1, z2)
U24(f228_out1, z0, z1, z2) → U25(f2_in(z1, z2), z0, z1, z2)
U25(f2_out1(z0), z1, z2, z3) → f245_out1(z0)
f19_in(z0) → U26(f48_in(z0), f49_in(z0), z0)
U26(f48_out1(z0), z1, z2) → f19_out1(z0)
U26(z0, f49_out1(z1), z2) → f19_out2(z1)
f20_in(z0) → U27(f23_in(z0), f24_in(z0), z0)
U27(f23_out1(z0), z1, z2) → f20_out1(z0)
U27(z0, f24_out1(z1), z2) → f20_out2(z1)
f68_in(z0, z1) → U28(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U28(f99_out1(z0), z1, z2, z3) → f68_out1(z0)
U28(z0, f100_out1(z1), z2, z3) → f68_out2(z1)
f70_in(z0, z1, z2) → U29(f72_in(z0, z1, z2), f73_in(z0, z1, z2), z0, z1, z2)
U29(f72_out1(z0), z1, z2, z3, z4) → f70_out1(z0)
U29(z0, f73_out1(z1), z2, z3, z4) → f70_out2(z1)

Tuples:

F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0))
F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c2(F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(F228_IN(z0, z1))
F29_IN(s(z0)) → c18(F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(F245_IN(z1, z0, z3))
F48_IN(z0) → c34(F27_IN(z0))
F49_IN(z0) → c36(F27_IN(z0))
F72_IN(z0, z1, z2) → c38(F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(F86_IN(z0, z2))
F23_IN(z0) → c42(F27_IN(z0))
F24_IN(z0) → c44(F27_IN(z0))
U16'(f29_out1, z0) → c47(F2_IN(z0, void))
U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))
U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))
U22'(f108_out1, z0, z1, z2) → c56(F2_IN(z0, z2))
U24'(f228_out1, z0, z1, z2) → c59(F2_IN(z1, z2))
F19_IN(z0) → c61(F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c

S tuples:

F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0))
F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c2(F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(F228_IN(z0, z1))
F29_IN(s(z0)) → c18(F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(F245_IN(z1, z0, z3))
F48_IN(z0) → c34(F27_IN(z0))
F49_IN(z0) → c36(F27_IN(z0))
F72_IN(z0, z1, z2) → c38(F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(F86_IN(z0, z2))
F23_IN(z0) → c42(F27_IN(z0))
F24_IN(z0) → c44(F27_IN(z0))
U22'(f108_out1, z0, z1, z2) → c56(F2_IN(z0, z2))
U24'(f228_out1, z0, z1, z2) → c59(F2_IN(z1, z2))
F19_IN(z0) → c61(F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c

K tuples:

U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))
U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))
U16'(f29_out1, z0) → c47(F2_IN(z0, void))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, f228_in, U5, f29_in, U6, f108_in, U7, f99_in, U8, f100_in, U9, f48_in, U10, f49_in, U11, f72_in, U12, f73_in, U13, f23_in, U14, f24_in, U15, f27_in, U16, U17, f76_in, U18, U19, f86_in, U20, U21, f105_in, U22, U23, f245_in, U24, U25, f19_in, U26, f20_in, U27, f68_in, U28, f70_in, U29

Defined Pair Symbols:

F27_IN, F76_IN, F86_IN, F105_IN, F245_IN, F108_IN, F2_IN, F228_IN, F29_IN, F99_IN, F100_IN, F48_IN, F49_IN, F72_IN, F73_IN, F23_IN, F24_IN, U16', U18', U20', U22', U24', F19_IN, F20_IN, F68_IN, F70_IN

Compound Symbols:

c46, c49, c52, c55, c58, c, c2, c3, c5, c6, c16, c18, c30, c32, c34, c36, c38, c40, c42, c44, c47, c50, c53, c56, c59, c61, c64, c67, c70, c

(15) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace F27_IN(z0) → c46(U16'(f29_in(z0), z0), F29_IN(z0)) by

F27_IN(s(z0)) → c46(U16'(U6(f29_in(z0), s(z0)), s(z0)), F29_IN(s(z0)))

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, void)) → f2_out1(void)
f2_in(z0, tree(z0, void, void)) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U1(f20_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f19_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U3(f70_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(z0, z1) → U4(f68_in(z0, z1), z0, z1)
U1(f20_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U1(f20_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U3(f70_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U3(f70_out2(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U4(f68_out1(z0), z1, z2) → f2_out1(z0)
U4(f68_out2(z0), z1, z2) → f2_out1(z0)
f228_in(0, s(z0)) → f228_out1
f228_in(s(z0), s(z1)) → U5(f228_in(z0, z1), s(z0), s(z1))
U5(f228_out1, s(z0), s(z1)) → f228_out1
f29_in(s(z0)) → U6(f29_in(z0), s(z0))
U6(f29_out1, s(z0)) → f29_out1
f108_in(0, s(z0)) → f108_out1
f108_in(s(0), s(s(z0))) → f108_out1
f108_in(s(s(0)), s(s(s(z0)))) → f108_out1
f108_in(s(s(s(0))), s(s(s(s(z0))))) → f108_out1
f108_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f108_out1
f108_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f108_out1
f108_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U7(f228_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U7(f228_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f108_out1
f99_in(z0, tree(z1, z2, z3)) → U8(f105_in(z0, z1, z2), z0, tree(z1, z2, z3))
U8(f105_out1(z0), z1, tree(z2, z3, z4)) → f99_out1(tree(z2, z0, z4))
f100_in(z0, tree(z1, z2, z3)) → U9(f245_in(z1, z0, z3), z0, tree(z1, z2, z3))
U9(f245_out1(z0), z1, tree(z2, z3, z4)) → f100_out1(tree(z2, z3, z0))
f48_in(z0) → U10(f27_in(z0), z0)
U10(f27_out1(z0), z1) → f48_out1(tree(z1, z0, void))
f49_in(z0) → U11(f27_in(z0), z0)
U11(f27_out1(z0), z1) → f49_out1(tree(z1, void, z0))
f72_in(z0, z1, z2) → U12(f76_in(z0, z1), z0, z1, z2)
U12(f76_out1(z0), z1, z2, z3) → f72_out1(tree(z1, z0, z3))
f73_in(z0, z1, z2) → U13(f86_in(z0, z2), z0, z1, z2)
U13(f86_out1(z0), z1, z2, z3) → f73_out1(tree(z1, z2, z0))
f23_in(z0) → U14(f27_in(z0), z0)
U14(f27_out1(z0), z1) → f23_out1(tree(z1, z0, void))
f24_in(z0) → U15(f27_in(z0), z0)
U15(f27_out1(z0), z1) → f24_out1(tree(z1, void, z0))
f27_in(z0) → U16(f29_in(z0), z0)
U16(f29_out1, z0) → U17(f2_in(z0, void), z0)
U17(f2_out1(z0), z1) → f27_out1(z0)
f76_in(z0, z1) → U18(f29_in(z0), z0, z1)
U18(f29_out1, z0, z1) → U19(f2_in(z0, z1), z0, z1)
U19(f2_out1(z0), z1, z2) → f76_out1(z0)
f86_in(z0, z1) → U20(f29_in(z0), z0, z1)
U20(f29_out1, z0, z1) → U21(f2_in(z0, z1), z0, z1)
U21(f2_out1(z0), z1, z2) → f86_out1(z0)
f105_in(z0, z1, z2) → U22(f108_in(z0, z1), z0, z1, z2)
U22(f108_out1, z0, z1, z2) → U23(f2_in(z0, z2), z0, z1, z2)
U23(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f245_in(z0, z1, z2) → U24(f228_in(z0, z1), z0, z1, z2)
U24(f228_out1, z0, z1, z2) → U25(f2_in(z1, z2), z0, z1, z2)
U25(f2_out1(z0), z1, z2, z3) → f245_out1(z0)
f19_in(z0) → U26(f48_in(z0), f49_in(z0), z0)
U26(f48_out1(z0), z1, z2) → f19_out1(z0)
U26(z0, f49_out1(z1), z2) → f19_out2(z1)
f20_in(z0) → U27(f23_in(z0), f24_in(z0), z0)
U27(f23_out1(z0), z1, z2) → f20_out1(z0)
U27(z0, f24_out1(z1), z2) → f20_out2(z1)
f68_in(z0, z1) → U28(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U28(f99_out1(z0), z1, z2, z3) → f68_out1(z0)
U28(z0, f100_out1(z1), z2, z3) → f68_out2(z1)
f70_in(z0, z1, z2) → U29(f72_in(z0, z1, z2), f73_in(z0, z1, z2), z0, z1, z2)
U29(f72_out1(z0), z1, z2, z3, z4) → f70_out1(z0)
U29(z0, f73_out1(z1), z2, z3, z4) → f70_out2(z1)

Tuples:

F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c2(F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(F228_IN(z0, z1))
F29_IN(s(z0)) → c18(F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(F245_IN(z1, z0, z3))
F48_IN(z0) → c34(F27_IN(z0))
F49_IN(z0) → c36(F27_IN(z0))
F72_IN(z0, z1, z2) → c38(F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(F86_IN(z0, z2))
F23_IN(z0) → c42(F27_IN(z0))
F24_IN(z0) → c44(F27_IN(z0))
U16'(f29_out1, z0) → c47(F2_IN(z0, void))
U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))
U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))
U22'(f108_out1, z0, z1, z2) → c56(F2_IN(z0, z2))
U24'(f228_out1, z0, z1, z2) → c59(F2_IN(z1, z2))
F19_IN(z0) → c61(F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F27_IN(s(z0)) → c46(U16'(U6(f29_in(z0), s(z0)), s(z0)), F29_IN(s(z0)))

S tuples:

F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c2(F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(F228_IN(z0, z1))
F29_IN(s(z0)) → c18(F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(F245_IN(z1, z0, z3))
F48_IN(z0) → c34(F27_IN(z0))
F49_IN(z0) → c36(F27_IN(z0))
F72_IN(z0, z1, z2) → c38(F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(F86_IN(z0, z2))
F23_IN(z0) → c42(F27_IN(z0))
F24_IN(z0) → c44(F27_IN(z0))
U22'(f108_out1, z0, z1, z2) → c56(F2_IN(z0, z2))
U24'(f228_out1, z0, z1, z2) → c59(F2_IN(z1, z2))
F19_IN(z0) → c61(F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F27_IN(s(z0)) → c46(U16'(U6(f29_in(z0), s(z0)), s(z0)), F29_IN(s(z0)))

K tuples:

U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))
U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))
U16'(f29_out1, z0) → c47(F2_IN(z0, void))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, f228_in, U5, f29_in, U6, f108_in, U7, f99_in, U8, f100_in, U9, f48_in, U10, f49_in, U11, f72_in, U12, f73_in, U13, f23_in, U14, f24_in, U15, f27_in, U16, U17, f76_in, U18, U19, f86_in, U20, U21, f105_in, U22, U23, f245_in, U24, U25, f19_in, U26, f20_in, U27, f68_in, U28, f70_in, U29

Defined Pair Symbols:

F76_IN, F86_IN, F105_IN, F245_IN, F108_IN, F2_IN, F228_IN, F29_IN, F99_IN, F100_IN, F48_IN, F49_IN, F72_IN, F73_IN, F23_IN, F24_IN, U16', U18', U20', U22', U24', F19_IN, F20_IN, F68_IN, F70_IN, F27_IN

Compound Symbols:

c49, c52, c55, c58, c, c2, c3, c5, c6, c16, c18, c30, c32, c34, c36, c38, c40, c42, c44, c47, c50, c53, c56, c59, c61, c64, c67, c70, c, c46

(17) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, void)) → f2_out1(void)
f2_in(z0, tree(z0, void, void)) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U1(f20_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f19_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U3(f70_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(z0, z1) → U4(f68_in(z0, z1), z0, z1)
U1(f20_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U1(f20_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out1(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U2(f19_out2(z0), z1, tree(z1, void, void)) → f2_out1(z0)
U3(f70_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U3(f70_out2(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U4(f68_out1(z0), z1, z2) → f2_out1(z0)
U4(f68_out2(z0), z1, z2) → f2_out1(z0)
f228_in(0, s(z0)) → f228_out1
f228_in(s(z0), s(z1)) → U5(f228_in(z0, z1), s(z0), s(z1))
U5(f228_out1, s(z0), s(z1)) → f228_out1
f29_in(s(z0)) → U6(f29_in(z0), s(z0))
U6(f29_out1, s(z0)) → f29_out1
f108_in(0, s(z0)) → f108_out1
f108_in(s(0), s(s(z0))) → f108_out1
f108_in(s(s(0)), s(s(s(z0)))) → f108_out1
f108_in(s(s(s(0))), s(s(s(s(z0))))) → f108_out1
f108_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f108_out1
f108_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f108_out1
f108_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f108_out1
f108_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U7(f228_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U7(f228_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f108_out1
f99_in(z0, tree(z1, z2, z3)) → U8(f105_in(z0, z1, z2), z0, tree(z1, z2, z3))
U8(f105_out1(z0), z1, tree(z2, z3, z4)) → f99_out1(tree(z2, z0, z4))
f100_in(z0, tree(z1, z2, z3)) → U9(f245_in(z1, z0, z3), z0, tree(z1, z2, z3))
U9(f245_out1(z0), z1, tree(z2, z3, z4)) → f100_out1(tree(z2, z3, z0))
f48_in(z0) → U10(f27_in(z0), z0)
U10(f27_out1(z0), z1) → f48_out1(tree(z1, z0, void))
f49_in(z0) → U11(f27_in(z0), z0)
U11(f27_out1(z0), z1) → f49_out1(tree(z1, void, z0))
f72_in(z0, z1, z2) → U12(f76_in(z0, z1), z0, z1, z2)
U12(f76_out1(z0), z1, z2, z3) → f72_out1(tree(z1, z0, z3))
f73_in(z0, z1, z2) → U13(f86_in(z0, z2), z0, z1, z2)
U13(f86_out1(z0), z1, z2, z3) → f73_out1(tree(z1, z2, z0))
f23_in(z0) → U14(f27_in(z0), z0)
U14(f27_out1(z0), z1) → f23_out1(tree(z1, z0, void))
f24_in(z0) → U15(f27_in(z0), z0)
U15(f27_out1(z0), z1) → f24_out1(tree(z1, void, z0))
f27_in(z0) → U16(f29_in(z0), z0)
U16(f29_out1, z0) → U17(f2_in(z0, void), z0)
U17(f2_out1(z0), z1) → f27_out1(z0)
f76_in(z0, z1) → U18(f29_in(z0), z0, z1)
U18(f29_out1, z0, z1) → U19(f2_in(z0, z1), z0, z1)
U19(f2_out1(z0), z1, z2) → f76_out1(z0)
f86_in(z0, z1) → U20(f29_in(z0), z0, z1)
U20(f29_out1, z0, z1) → U21(f2_in(z0, z1), z0, z1)
U21(f2_out1(z0), z1, z2) → f86_out1(z0)
f105_in(z0, z1, z2) → U22(f108_in(z0, z1), z0, z1, z2)
U22(f108_out1, z0, z1, z2) → U23(f2_in(z0, z2), z0, z1, z2)
U23(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f245_in(z0, z1, z2) → U24(f228_in(z0, z1), z0, z1, z2)
U24(f228_out1, z0, z1, z2) → U25(f2_in(z1, z2), z0, z1, z2)
U25(f2_out1(z0), z1, z2, z3) → f245_out1(z0)
f19_in(z0) → U26(f48_in(z0), f49_in(z0), z0)
U26(f48_out1(z0), z1, z2) → f19_out1(z0)
U26(z0, f49_out1(z1), z2) → f19_out2(z1)
f20_in(z0) → U27(f23_in(z0), f24_in(z0), z0)
U27(f23_out1(z0), z1, z2) → f20_out1(z0)
U27(z0, f24_out1(z1), z2) → f20_out2(z1)
f68_in(z0, z1) → U28(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U28(f99_out1(z0), z1, z2, z3) → f68_out1(z0)
U28(z0, f100_out1(z1), z2, z3) → f68_out2(z1)
f70_in(z0, z1, z2) → U29(f72_in(z0, z1, z2), f73_in(z0, z1, z2), z0, z1, z2)
U29(f72_out1(z0), z1, z2, z3, z4) → f70_out1(z0)
U29(z0, f73_out1(z1), z2, z3, z4) → f70_out2(z1)

Tuples:

F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c2(F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(F228_IN(z0, z1))
F29_IN(s(z0)) → c18(F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(F245_IN(z1, z0, z3))
F48_IN(z0) → c34(F27_IN(z0))
F49_IN(z0) → c36(F27_IN(z0))
F72_IN(z0, z1, z2) → c38(F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(F86_IN(z0, z2))
F23_IN(z0) → c42(F27_IN(z0))
F24_IN(z0) → c44(F27_IN(z0))
U16'(f29_out1, z0) → c47(F2_IN(z0, void))
U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))
U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))
U22'(f108_out1, z0, z1, z2) → c56(F2_IN(z0, z2))
U24'(f228_out1, z0, z1, z2) → c59(F2_IN(z1, z2))
F19_IN(z0) → c61(F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F27_IN(s(z0)) → c46(U16'(U6(f29_in(z0), s(z0)), s(z0)), F29_IN(s(z0)))

S tuples:

F76_IN(z0, z1) → c49(U18'(f29_in(z0), z0, z1), F29_IN(z0))
F86_IN(z0, z1) → c52(U20'(f29_in(z0), z0, z1), F29_IN(z0))
F105_IN(z0, z1, z2) → c55(U22'(f108_in(z0, z1), z0, z1, z2), F108_IN(z0, z1))
F245_IN(z0, z1, z2) → c58(U24'(f228_in(z0, z1), z0, z1, z2), F228_IN(z0, z1))
F108_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F228_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c2(F20_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(F19_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c5(F70_IN(z0, z1, z2))
F2_IN(z0, z1) → c6(F68_IN(z0, z1))
F228_IN(s(z0), s(z1)) → c16(F228_IN(z0, z1))
F29_IN(s(z0)) → c18(F29_IN(z0))
F99_IN(z0, tree(z1, z2, z3)) → c30(F105_IN(z0, z1, z2))
F100_IN(z0, tree(z1, z2, z3)) → c32(F245_IN(z1, z0, z3))
F48_IN(z0) → c34(F27_IN(z0))
F49_IN(z0) → c36(F27_IN(z0))
F72_IN(z0, z1, z2) → c38(F76_IN(z0, z1))
F73_IN(z0, z1, z2) → c40(F86_IN(z0, z2))
F23_IN(z0) → c42(F27_IN(z0))
F24_IN(z0) → c44(F27_IN(z0))
U22'(f108_out1, z0, z1, z2) → c56(F2_IN(z0, z2))
U24'(f228_out1, z0, z1, z2) → c59(F2_IN(z1, z2))
F19_IN(z0) → c61(F48_IN(z0), F49_IN(z0))
F20_IN(z0) → c64(F23_IN(z0), F24_IN(z0))
F68_IN(z0, z1) → c67(F99_IN(z0, z1), F100_IN(z0, z1))
F70_IN(z0, z1, z2) → c70(F72_IN(z0, z1, z2), F73_IN(z0, z1, z2))
F27_IN(s(z0)) → c46(U16'(U6(f29_in(z0), s(z0)), s(z0)), F29_IN(s(z0)))

K tuples:

U20'(f29_out1, z0, z1) → c53(F2_IN(z0, z1))
U18'(f29_out1, z0, z1) → c50(F2_IN(z0, z1))
U16'(f29_out1, z0) → c47(F2_IN(z0, void))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, f228_in, U5, f29_in, U6, f108_in, U7, f99_in, U8, f100_in, U9, f48_in, U10, f49_in, U11, f72_in, U12, f73_in, U13, f23_in, U14, f24_in, U15, f27_in, U16, U17, f76_in, U18, U19, f86_in, U20, U21, f105_in, U22, U23, f245_in, U24, U25, f19_in, U26, f20_in, U27, f68_in, U28, f70_in, U29

Defined Pair Symbols:

F76_IN, F86_IN, F105_IN, F245_IN, F108_IN, F2_IN, F228_IN, F29_IN, F99_IN, F100_IN, F48_IN, F49_IN, F72_IN, F73_IN, F23_IN, F24_IN, U16', U18', U20', U22', U24', F19_IN, F20_IN, F68_IN, F70_IN, F27_IN

Compound Symbols:

c49, c52, c55, c58, c, c2, c3, c5, c6, c16, c18, c30, c32, c34, c36, c38, c40, c42, c44, c47, c50, c53, c56, c59, c61, c64, c67, c70, c46

(19) PrologToCdtProblemTransformerProof (UPPER BOUND (ID) transformation)

Built complexity over-approximating cdt problems from derivation graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: insert(T1, T2, T3)\n\nT1 is ground\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
4 [label="4: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 0 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: true | insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 1 | insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 3 | insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 4\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT3 is ground\nX3 is free\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 1 | insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 3 | insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 4\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: true | insert(T9, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 3 | insert(T9, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 4\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 3 | insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 4\n\nT5 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T5, T2, tree(T5, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: insert(T9, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 3 | insert(T9, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 4\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: ','(less(T16, T16), insert(T16, T20, void)) | insert(T16, T2, tree(T16, void, void)), SCOPE: 1, CLAUSE: 4\n\nT16 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: insert(T9, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 4\n\nT9 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(T9, T2, tree(T9, void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: ','(less(T16, T16), insert(T16, T20, void)), SCOPE: 2, CLAUSE: 2 | ','(less(T16, T16), insert(T16, T20, void)), SCOPE: 2, CLAUSE: 5 | ?_2 | insert(T16, T2, tree(T16, void, void)), SCOPE: 1, CLAUSE: 4\n\nT16 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: ','(less(T16, T16), insert(T16, T20, void)), SCOPE: 2, CLAUSE: 5 | ?_2 | insert(T16, T2, tree(T16, void, void)), SCOPE: 1, CLAUSE: 4\n\nT16 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: ','(less(T16, T16), insert(T16, T20, void)), SCOPE: 2, CLAUSE: 5\n\nT16 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: ?_2 | insert(T16, T2, tree(T16, void, void)), SCOPE: 1, CLAUSE: 4\n\nT16 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: ','(less(T25, T25), insert(s(T25), T20, void))\n\nT25 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: less(T25, T25)\n\nT25 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: insert(s(T25), T20, void)\n\nT25 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: less(T25, T25), SCOPE: 3, CLAUSE: 2 | less(T25, T25), SCOPE: 3, CLAUSE: 5\n\nT25 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: less(T25, T25), SCOPE: 3, CLAUSE: 5\n\nT25 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: less(T28, T28)\n\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: insert(T16, T2, tree(T16, void, void)), SCOPE: 1, CLAUSE: 4\n\nT16 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: ','(less(T39, T39), insert(T39, T43, void))\n\nT39 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: less(T39, T39)\n\nT39 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: insert(T39, T43, void)\n\nT39 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(less(T50, T50), insert(T50, T54, void))\n\nT50 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(T50, T2, tree(T50, void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: ','(less(T50, T50), insert(T50, T54, void)), SCOPE: 4, CLAUSE: 2 | ','(less(T50, T50), insert(T50, T54, void)), SCOPE: 4, CLAUSE: 5\n\nT50 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(T50, T2, tree(T50, void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: ','(less(T50, T50), insert(T50, T54, void)), SCOPE: 4, CLAUSE: 5\n\nT50 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(T50, T2, tree(T50, void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: ','(less(T57, T57), insert(s(T57), T54, void))\n\nT57 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(s(T57), T2, tree(s(T57), void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: ','(less(T62, T62), insert(T62, T66, void)) | insert(T62, T2, tree(T62, void, void)), SCOPE: 1, CLAUSE: 4\n\nT62 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T62, T2, tree(T62, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: insert(T5, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 4\n\nT5 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T5, T2, tree(T5, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: ','(less(T62, T62), insert(T62, T66, void)), SCOPE: 5, CLAUSE: 2 | ','(less(T62, T62), insert(T62, T66, void)), SCOPE: 5, CLAUSE: 5 | ?_5 | insert(T62, T2, tree(T62, void, void)), SCOPE: 1, CLAUSE: 4\n\nT62 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T62, T2, tree(T62, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: ','(less(T62, T62), insert(T62, T66, void)), SCOPE: 5, CLAUSE: 5 | ?_5 | insert(T62, T2, tree(T62, void, void)), SCOPE: 1, CLAUSE: 4\n\nT62 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T62, T2, tree(T62, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: ','(less(T62, T62), insert(T62, T66, void)), SCOPE: 5, CLAUSE: 5\n\nT62 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T62, T2, tree(T62, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: ?_5 | insert(T62, T2, tree(T62, void, void)), SCOPE: 1, CLAUSE: 4\n\nT62 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T62, T2, tree(T62, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: ','(less(T71, T71), insert(s(T71), T66, void))\n\nT71 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(s(T71), T2, tree(s(T71), void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: insert(T62, T2, tree(T62, void, void)), SCOPE: 1, CLAUSE: 4\n\nT62 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T62, T2, tree(T62, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: ','(less(T80, T80), insert(T80, T84, void))\n\nT80 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T80, T2, tree(T80, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: ','(less(T89, T89), insert(T89, T93, void))\n\nT89 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T89, T2, tree(T89, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: ','(less(T89, T89), insert(T89, T93, void)), SCOPE: 6, CLAUSE: 2 | ','(less(T89, T89), insert(T89, T93, void)), SCOPE: 6, CLAUSE: 5\n\nT89 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T89, T2, tree(T89, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: ','(less(T89, T89), insert(T89, T93, void)), SCOPE: 6, CLAUSE: 5\n\nT89 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T89, T2, tree(T89, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: ','(less(T96, T96), insert(s(T96), T93, void))\n\nT96 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(s(T96), T2, tree(s(T96), void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: true | insert(T100, T2, tree(T100, T101, T102)), SCOPE: 1, CLAUSE: 3 | insert(T100, T2, tree(T100, T101, T102)), SCOPE: 1, CLAUSE: 4\n\nT100 is ground\nT101 is ground\nT102 is ground\nX3 is free\ninsert(T100, T2, tree(T100, T101, T102)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT3 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, T3) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: insert(T100, T2, tree(T100, T101, T102)), SCOPE: 1, CLAUSE: 3 | insert(T100, T2, tree(T100, T101, T102)), SCOPE: 1, CLAUSE: 4\n\nT100 is ground\nT101 is ground\nT102 is ground\nX3 is free\ninsert(T100, T2, tree(T100, T101, T102)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: ','(less(T108, T108), insert(T108, T113, T112)) | insert(T108, T2, tree(T108, T112, T111)), SCOPE: 1, CLAUSE: 4\n\nT108 is ground\nT112 is ground\nT111 is ground\nX3 is free\ninsert(T108, T2, tree(T108, T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: insert(T100, T2, tree(T100, T101, T102)), SCOPE: 1, CLAUSE: 4\n\nT100 is ground\nT101 is ground\nT102 is ground\nX3 is free\nX156 is free\nX157 is free\nX158 is free\nX159 is free\nX160 is free\ninsert(T100, T2, tree(T100, T101, T102)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T100, T2, tree(T100, T101, T102)) !=? insert(X156, tree(X157, X158, X159), tree(X157, X160, X159))", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: ','(less(T108, T108), insert(T108, T113, T112)), SCOPE: 7, CLAUSE: 2 | ','(less(T108, T108), insert(T108, T113, T112)), SCOPE: 7, CLAUSE: 5 | ?_7 | insert(T108, T2, tree(T108, T112, T111)), SCOPE: 1, CLAUSE: 4\n\nT108 is ground\nT112 is ground\nT111 is ground\nX3 is free\ninsert(T108, T2, tree(T108, T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: ','(less(T108, T108), insert(T108, T113, T112)), SCOPE: 7, CLAUSE: 5 | ?_7 | insert(T108, T2, tree(T108, T112, T111)), SCOPE: 1, CLAUSE: 4\n\nT108 is ground\nT112 is ground\nT111 is ground\nX3 is free\ninsert(T108, T2, tree(T108, T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: ','(less(T108, T108), insert(T108, T113, T112)), SCOPE: 7, CLAUSE: 5\n\nT108 is ground\nT112 is ground\nT111 is ground\nX3 is free\ninsert(T108, T2, tree(T108, T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: ?_7 | insert(T108, T2, tree(T108, T112, T111)), SCOPE: 1, CLAUSE: 4\n\nT108 is ground\nT112 is ground\nT111 is ground\nX3 is free\ninsert(T108, T2, tree(T108, T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: ','(less(T118, T118), insert(s(T118), T113, T112))\n\nT112 is ground\nT111 is ground\nT118 is ground\nX3 is free\ninsert(s(T118), T2, tree(s(T118), T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: less(T118, T118)\n\nT112 is ground\nT111 is ground\nT118 is ground\nX3 is free\ninsert(s(T118), T2, tree(s(T118), T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: insert(s(T118), T113, T112)\n\nT112 is ground\nT111 is ground\nT118 is ground\nX3 is free\ninsert(s(T118), T2, tree(s(T118), T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: insert(T108, T2, tree(T108, T112, T111)), SCOPE: 1, CLAUSE: 4\n\nT108 is ground\nT112 is ground\nT111 is ground\nX3 is free\ninsert(T108, T2, tree(T108, T112, T111)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: ','(less(T131, T131), insert(T131, T136, T135))\n\nT131 is ground\nT133 is ground\nT135 is ground\nX3 is free\ninsert(T131, T2, tree(T131, T133, T135)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: less(T131, T131)\n\nT131 is ground\nT133 is ground\nT135 is ground\nX3 is free\ninsert(T131, T2, tree(T131, T133, T135)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: insert(T131, T136, T135)\n\nT131 is ground\nT133 is ground\nT135 is ground\nX3 is free\ninsert(T131, T2, tree(T131, T133, T135)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: ','(less(T144, T144), insert(T144, T149, T148))\n\nT144 is ground\nT146 is ground\nT148 is ground\nX3 is free\nX156 is free\nX157 is free\nX158 is free\nX159 is free\nX160 is free\ninsert(T144, T2, tree(T144, T146, T148)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T144, T2, tree(T144, T146, T148)) !=? insert(X156, tree(X157, X158, X159), tree(X157, X160, X159))", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: ','(less(T144, T144), insert(T144, T149, T148)), SCOPE: 8, CLAUSE: 2 | ','(less(T144, T144), insert(T144, T149, T148)), SCOPE: 8, CLAUSE: 5\n\nT144 is ground\nT146 is ground\nT148 is ground\nX3 is free\nX156 is free\nX157 is free\nX158 is free\nX159 is free\nX160 is free\ninsert(T144, T2, tree(T144, T146, T148)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T144, T2, tree(T144, T146, T148)) !=? insert(X156, tree(X157, X158, X159), tree(X157, X160, X159))", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: ','(less(T144, T144), insert(T144, T149, T148)), SCOPE: 8, CLAUSE: 5\n\nT144 is ground\nT146 is ground\nT148 is ground\nX3 is free\nX156 is free\nX157 is free\nX158 is free\nX159 is free\nX160 is free\ninsert(T144, T2, tree(T144, T146, T148)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T144, T2, tree(T144, T146, T148)) !=? insert(X156, tree(X157, X158, X159), tree(X157, X160, X159))", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: ','(less(T152, T152), insert(s(T152), T149, T148))\n\nT146 is ground\nT148 is ground\nT152 is ground\nX3 is free\nX156 is free\nX157 is free\nX158 is free\nX159 is free\nX160 is free\ninsert(s(T152), T2, tree(s(T152), T146, T148)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T152), T2, tree(s(T152), T146, T148)) !=? insert(X156, tree(X157, X158, X159), tree(X157, X160, X159))", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: less(T152, T152)\n\nT146 is ground\nT148 is ground\nT152 is ground\nX3 is free\nX156 is free\nX157 is free\nX158 is free\nX159 is free\nX160 is free\ninsert(s(T152), T2, tree(s(T152), T146, T148)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T152), T2, tree(s(T152), T146, T148)) !=? insert(X156, tree(X157, X158, X159), tree(X157, X160, X159))", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: insert(s(T152), T149, T148)\n\nT146 is ground\nT148 is ground\nT152 is ground\nX3 is free\nX156 is free\nX157 is free\nX158 is free\nX159 is free\nX160 is free\ninsert(s(T152), T2, tree(s(T152), T146, T148)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T152), T2, tree(s(T152), T146, T148)) !=? insert(X156, tree(X157, X158, X159), tree(X157, X160, X159))", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: ','(less(T160, T161), insert(T160, T165, T164)) | insert(T160, T2, tree(T161, T164, T163)), SCOPE: 1, CLAUSE: 4\n\nT160 is ground\nT161 is ground\nT164 is ground\nT163 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT3 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, T3) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: ','(less(T160, T161), insert(T160, T165, T164)), SCOPE: 9, CLAUSE: 2 | ','(less(T160, T161), insert(T160, T165, T164)), SCOPE: 9, CLAUSE: 5 | ?_9 | insert(T160, T2, tree(T161, T164, T163)), SCOPE: 1, CLAUSE: 4\n\nT160 is ground\nT161 is ground\nT164 is ground\nT163 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: insert(0, T165, T164) | ','(less(0, s(T168)), insert(0, T165, T164)), SCOPE: 9, CLAUSE: 5 | ?_9 | insert(0, T2, tree(s(T168), T164, T163)), SCOPE: 1, CLAUSE: 4\n\nT164 is ground\nT163 is ground\nT168 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: ','(less(T160, T161), insert(T160, T165, T164)), SCOPE: 9, CLAUSE: 5 | ?_9 | insert(T160, T2, tree(T161, T164, T163)), SCOPE: 1, CLAUSE: 4\n\nT160 is ground\nT161 is ground\nT164 is ground\nT163 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\nX234 is free\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))\nless(T160, T161) !=? less(0, s(X234))", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: insert(0, T165, T164)\n\nT164 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: ','(less(0, s(T168)), insert(0, T165, T164)), SCOPE: 9, CLAUSE: 5 | ?_9 | insert(0, T2, tree(s(T168), T164, T163)), SCOPE: 1, CLAUSE: 4\n\nT164 is ground\nT163 is ground\nT168 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: ?_9 | insert(0, T2, tree(s(T168), T164, T163)), SCOPE: 1, CLAUSE: 4\n\nT164 is ground\nT163 is ground\nT168 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: insert(0, T2, tree(s(T168), T164, T163)), SCOPE: 1, CLAUSE: 4\n\nT164 is ground\nT163 is ground\nT168 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: ','(less(s(T182), 0), insert(0, T184, T183))\n\nT182 is ground\nT183 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: less(s(T182), 0)\n\nT182 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: insert(0, T184, T183)\n\nT183 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: less(s(T182), 0), SCOPE: 10, CLAUSE: 2 | less(s(T182), 0), SCOPE: 10, CLAUSE: 5\n\nT182 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: less(s(T182), 0), SCOPE: 10, CLAUSE: 5\n\nT182 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: ','(less(T160, T161), insert(T160, T165, T164)), SCOPE: 9, CLAUSE: 5\n\nT160 is ground\nT161 is ground\nT164 is ground\nT163 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\nX234 is free\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))\nless(T160, T161) !=? less(0, s(X234))", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: ?_9 | insert(T160, T2, tree(T161, T164, T163)), SCOPE: 1, CLAUSE: 4\n\nT160 is ground\nT161 is ground\nT164 is ground\nT163 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\nX234 is free\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))\nless(T160, T161) !=? less(0, s(X234))", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: ','(less(T194, T195), insert(s(T194), T165, T164))\n\nT164 is ground\nT163 is ground\nT194 is ground\nT195 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T194), T2, tree(s(T195), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T194), T2, tree(s(T195), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: less(T194, T195)\n\nT164 is ground\nT163 is ground\nT194 is ground\nT195 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T194), T2, tree(s(T195), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T194), T2, tree(s(T195), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: insert(s(T194), T165, T164)\n\nT164 is ground\nT163 is ground\nT194 is ground\nT195 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T194), T2, tree(s(T195), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T194), T2, tree(s(T195), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: less(T194, T195), SCOPE: 11, CLAUSE: 2 | less(T194, T195), SCOPE: 11, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT194 is ground\nT195 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T194), T2, tree(s(T195), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T194), T2, tree(s(T195), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: true | less(0, s(T202)), SCOPE: 11, CLAUSE: 5\n\nT202 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: less(T194, T195), SCOPE: 11, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT194 is ground\nT195 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\nX281 is free\ninsert(s(T194), T2, tree(s(T195), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T194), T2, tree(s(T195), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))\nless(T194, T195) !=? less(0, s(X281))", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: less(0, s(T202)), SCOPE: 11, CLAUSE: 5\n\nT202 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: less(T207, T208)\n\nT164 is ground\nT163 is ground\nT207 is ground\nT208 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(T207)), T2, tree(s(s(T208)), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(T207)), T2, tree(s(s(T208)), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: less(T207, T208), SCOPE: 12, CLAUSE: 2 | less(T207, T208), SCOPE: 12, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT207 is ground\nT208 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(T207)), T2, tree(s(s(T208)), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(T207)), T2, tree(s(s(T208)), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: true | less(0, s(T213)), SCOPE: 12, CLAUSE: 5\n\nT213 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: less(T207, T208), SCOPE: 12, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT207 is ground\nT208 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\nX294 is free\ninsert(s(s(T207)), T2, tree(s(s(T208)), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(T207)), T2, tree(s(s(T208)), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))\nless(T207, T208) !=? less(0, s(X294))", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: less(0, s(T213)), SCOPE: 12, CLAUSE: 5\n\nT213 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: less(T218, T219)\n\nT164 is ground\nT163 is ground\nT218 is ground\nT219 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(T218))), T2, tree(s(s(s(T219))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(T218))), T2, tree(s(s(s(T219))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: less(T218, T219), SCOPE: 13, CLAUSE: 2 | less(T218, T219), SCOPE: 13, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT218 is ground\nT219 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(T218))), T2, tree(s(s(s(T219))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(T218))), T2, tree(s(s(s(T219))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: true | less(0, s(T224)), SCOPE: 13, CLAUSE: 5\n\nT224 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: less(T218, T219), SCOPE: 13, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT218 is ground\nT219 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\nX307 is free\ninsert(s(s(s(T218))), T2, tree(s(s(s(T219))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(T218))), T2, tree(s(s(s(T219))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))\nless(T218, T219) !=? less(0, s(X307))", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: less(0, s(T224)), SCOPE: 13, CLAUSE: 5\n\nT224 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: less(T229, T230)\n\nT164 is ground\nT163 is ground\nT229 is ground\nT230 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(T229)))), T2, tree(s(s(s(s(T230)))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(T229)))), T2, tree(s(s(s(s(T230)))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: less(T229, T230), SCOPE: 14, CLAUSE: 2 | less(T229, T230), SCOPE: 14, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT229 is ground\nT230 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(T229)))), T2, tree(s(s(s(s(T230)))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(T229)))), T2, tree(s(s(s(s(T230)))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: true | less(0, s(T235)), SCOPE: 14, CLAUSE: 5\n\nT235 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: less(T229, T230), SCOPE: 14, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT229 is ground\nT230 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\nX320 is free\ninsert(s(s(s(s(T229)))), T2, tree(s(s(s(s(T230)))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(T229)))), T2, tree(s(s(s(s(T230)))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))\nless(T229, T230) !=? less(0, s(X320))", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: less(0, s(T235)), SCOPE: 14, CLAUSE: 5\n\nT235 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: less(T240, T241)\n\nT164 is ground\nT163 is ground\nT240 is ground\nT241 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(T240))))), T2, tree(s(s(s(s(s(T241))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(T240))))), T2, tree(s(s(s(s(s(T241))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
227 [label="227: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
229 [label="229: less(T240, T241), SCOPE: 15, CLAUSE: 2 | less(T240, T241), SCOPE: 15, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT240 is ground\nT241 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(T240))))), T2, tree(s(s(s(s(s(T241))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(T240))))), T2, tree(s(s(s(s(s(T241))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="230: true | less(0, s(T246)), SCOPE: 15, CLAUSE: 5\n\nT246 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
232 [label="232: less(T240, T241), SCOPE: 15, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT240 is ground\nT241 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\nX333 is free\ninsert(s(s(s(s(s(T240))))), T2, tree(s(s(s(s(s(T241))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(T240))))), T2, tree(s(s(s(s(s(T241))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))\nless(T240, T241) !=? less(0, s(X333))", fontsize=16, style=filled, fillcolor=lightyellow];
234 [label="234: less(0, s(T246)), SCOPE: 15, CLAUSE: 5\n\nT246 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
237 [label="237: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
241 [label="241: less(T251, T252)\n\nT164 is ground\nT163 is ground\nT251 is ground\nT252 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(s(T251)))))), T2, tree(s(s(s(s(s(s(T252)))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(T251)))))), T2, tree(s(s(s(s(s(s(T252)))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
242 [label="242: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
243 [label="243: less(T251, T252), SCOPE: 16, CLAUSE: 2 | less(T251, T252), SCOPE: 16, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT251 is ground\nT252 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(s(T251)))))), T2, tree(s(s(s(s(s(s(T252)))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(T251)))))), T2, tree(s(s(s(s(s(s(T252)))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
244 [label="244: true | less(0, s(T257)), SCOPE: 16, CLAUSE: 5\n\nT257 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
246 [label="246: less(T251, T252), SCOPE: 16, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT251 is ground\nT252 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\nX346 is free\ninsert(s(s(s(s(s(s(T251)))))), T2, tree(s(s(s(s(s(s(T252)))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(T251)))))), T2, tree(s(s(s(s(s(s(T252)))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))\nless(T251, T252) !=? less(0, s(X346))", fontsize=16, style=filled, fillcolor=lightyellow];
247 [label="247: less(0, s(T257)), SCOPE: 16, CLAUSE: 5\n\nT257 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
249 [label="249: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
251 [label="251: less(T262, T263)\n\nT164 is ground\nT163 is ground\nT262 is ground\nT263 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(s(s(T262))))))), T2, tree(s(s(s(s(s(s(s(T263))))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(s(T262))))))), T2, tree(s(s(s(s(s(s(s(T263))))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
253 [label="253: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
254 [label="254: less(T262, T263), SCOPE: 17, CLAUSE: 2 | less(T262, T263), SCOPE: 17, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT262 is ground\nT263 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(s(s(T262))))))), T2, tree(s(s(s(s(s(s(s(T263))))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(s(T262))))))), T2, tree(s(s(s(s(s(s(s(T263))))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
255 [label="255: true | less(0, s(T268)), SCOPE: 17, CLAUSE: 5\n\nT268 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
256 [label="256: less(T262, T263), SCOPE: 17, CLAUSE: 5\n\nT164 is ground\nT163 is ground\nT262 is ground\nT263 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\nX359 is free\ninsert(s(s(s(s(s(s(s(T262))))))), T2, tree(s(s(s(s(s(s(s(T263))))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(s(T262))))))), T2, tree(s(s(s(s(s(s(s(T263))))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))\nless(T262, T263) !=? less(0, s(X359))", fontsize=16, style=filled, fillcolor=lightyellow];
257 [label="257: less(0, s(T268)), SCOPE: 17, CLAUSE: 5\n\nT268 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
258 [label="258: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
259 [label="259: less(T273, T274)\n\nT164 is ground\nT163 is ground\nT273 is ground\nT274 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(s(s(s(s(s(s(s(T273)))))))), T2, tree(s(s(s(s(s(s(s(s(T274)))))))), T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(s(s(s(s(s(s(s(T273)))))))), T2, tree(s(s(s(s(s(s(s(s(T274)))))))), T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
260 [label="260: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
261 [label="261: less(T273, T274)\n\nT273 is ground\nT274 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
262 [label="262: less(T273, T274), SCOPE: 18, CLAUSE: 2 | less(T273, T274), SCOPE: 18, CLAUSE: 5\n\nT273 is ground\nT274 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
263 [label="263: true | less(0, s(T283)), SCOPE: 18, CLAUSE: 5\n\nT283 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
264 [label="264: less(T273, T274), SCOPE: 18, CLAUSE: 5\n\nT273 is ground\nT274 is ground\nX374 is free\nless(T273, T274) !=? less(0, s(X374))", fontsize=16, style=filled, fillcolor=lightyellow];
265 [label="265: less(0, s(T283)), SCOPE: 18, CLAUSE: 5\n\nT283 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
266 [label="266: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
267 [label="267: less(T288, T289)\n\nT288 is ground\nT289 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
268 [label="268: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
269 [label="269: insert(T160, T2, tree(T161, T164, T163)), SCOPE: 1, CLAUSE: 4\n\nT160 is ground\nT161 is ground\nT164 is ground\nT163 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\nX234 is free\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T160, T2, tree(T161, T164, T163)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))\nless(T160, T161) !=? less(0, s(X234))", fontsize=16, style=filled, fillcolor=lightyellow];
270 [label="270: ','(less(T305, T304), insert(T304, T309, T308))\n\nT304 is ground\nT305 is ground\nT306 is ground\nT308 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\nX234 is free\ninsert(T304, T2, tree(T305, T306, T308)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T304, T2, tree(T305, T306, T308)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))\nless(T304, T305) !=? less(0, s(X234))", fontsize=16, style=filled, fillcolor=lightyellow];
271 [label="271: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
272 [label="272: less(T305, T304)\n\nT304 is ground\nT305 is ground\nT306 is ground\nT308 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\nX234 is free\ninsert(T304, T2, tree(T305, T306, T308)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T304, T2, tree(T305, T306, T308)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))\nless(T304, T305) !=? less(0, s(X234))", fontsize=16, style=filled, fillcolor=lightyellow];
273 [label="273: insert(T304, T309, T308)\n\nT304 is ground\nT305 is ground\nT306 is ground\nT308 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\nX234 is free\ninsert(T304, T2, tree(T305, T306, T308)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T304, T2, tree(T305, T306, T308)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))\nless(T304, T305) !=? less(0, s(X234))", fontsize=16, style=filled, fillcolor=lightyellow];
274 [label="274: ','(less(T322, T321), insert(T321, T326, T325))\n\nT321 is ground\nT322 is ground\nT323 is ground\nT325 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T321, T2, tree(T322, T323, T325)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T321, T2, tree(T322, T323, T325)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
275 [label="275: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
276 [label="276: ','(less(T322, T321), insert(T321, T326, T325)), SCOPE: 19, CLAUSE: 2 | ','(less(T322, T321), insert(T321, T326, T325)), SCOPE: 19, CLAUSE: 5\n\nT321 is ground\nT322 is ground\nT323 is ground\nT325 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(T321, T2, tree(T322, T323, T325)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T321, T2, tree(T322, T323, T325)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
277 [label="277: insert(s(T329), T326, T325) | ','(less(0, s(T329)), insert(s(T329), T326, T325)), SCOPE: 19, CLAUSE: 5\n\nT325 is ground\nT329 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
278 [label="278: ','(less(T322, T321), insert(T321, T326, T325)), SCOPE: 19, CLAUSE: 5\n\nT321 is ground\nT322 is ground\nT323 is ground\nT325 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\nX420 is free\ninsert(T321, T2, tree(T322, T323, T325)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T321, T2, tree(T322, T323, T325)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))\nless(T322, T321) !=? less(0, s(X420))", fontsize=16, style=filled, fillcolor=lightyellow];
279 [label="279: insert(s(T329), T326, T325)\n\nT325 is ground\nT329 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
280 [label="280: ','(less(0, s(T329)), insert(s(T329), T326, T325)), SCOPE: 19, CLAUSE: 5\n\nT325 is ground\nT329 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
281 [label="281: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
282 [label="282: ','(less(T338, T339), insert(s(T339), T326, T325))\n\nT323 is ground\nT325 is ground\nT338 is ground\nT339 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T339), T2, tree(s(T338), T323, T325)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T339), T2, tree(s(T338), T323, T325)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
283 [label="283: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
284 [label="284: less(T338, T339)\n\nT323 is ground\nT325 is ground\nT338 is ground\nT339 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T339), T2, tree(s(T338), T323, T325)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T339), T2, tree(s(T338), T323, T325)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
285 [label="285: insert(s(T339), T326, T325)\n\nT323 is ground\nT325 is ground\nT338 is ground\nT339 is ground\nX3 is free\nX148 is free\nX149 is free\nX150 is free\ninsert(s(T339), T2, tree(s(T338), T323, T325)) !=? insert(X3, void, tree(X3, void, void))\ninsert(s(T339), T2, tree(s(T338), T323, T325)) !=? insert(X148, tree(X148, X149, X150), tree(X148, X149, X150))", fontsize=16, style=filled, fillcolor=lightyellow];
286 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 286 [arrowhead = none ];
286 -> 4;

287 [label="EVAL with clause\ninsert(X3, void, tree(X3, void, void)).\nand substitutionT1 -> T5,\nX3 -> T5,\nT2 -> void,\nT3 -> tree(T5, void, void)", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 287 [arrowhead = none ];
287 -> 5;

288 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 288 [arrowhead = none ];
288 -> 7;

289 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 289 [arrowhead = none ];
289 -> 9;

290 [label="EVAL with clause\ninsert(X148, tree(X148, X149, X150), tree(X148, X149, X150)).\nand substitutionT1 -> T100,\nX148 -> T100,\nX149 -> T101,\nX150 -> T102,\nT2 -> tree(T100, T101, T102),\nT3 -> tree(T100, T101, T102)", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 290 [arrowhead = none ];
290 -> 88;

291 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 291 [arrowhead = none ];
291 -> 89;

292 [label="EVAL with clause\ninsert(X7, tree(X7, X8, X9), tree(X7, X8, X9)).\nand substitutionT5 -> T9,\nX7 -> T9,\nX8 -> void,\nX9 -> void,\nT2 -> tree(T9, void, void),\nT10 -> void,\nT11 -> void", fontsize=14, style = filled, fillcolor = lightblue];
9 -> 292 [arrowhead = none ];
292 -> 11;

293 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
9 -> 293 [arrowhead = none ];
293 -> 12;

294 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 294 [arrowhead = none ];
294 -> 13;

295 [label="EVAL with clause\ninsert(X91, tree(X92, X93, X94), tree(X92, X95, X94)) :- ','(less(X91, X92), insert(X91, X93, X95)).\nand substitutionT5 -> T62,\nX91 -> T62,\nX92 -> T62,\nX93 -> T66,\nX94 -> void,\nT2 -> tree(T62, T66, void),\nT63 -> T62,\nX95 -> void,\nT65 -> void,\nT64 -> T66", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 295 [arrowhead = none ];
295 -> 58;

296 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 296 [arrowhead = none ];
296 -> 60;

297 [label="EVAL with clause\ninsert(X15, tree(X16, X17, X18), tree(X16, X19, X18)) :- ','(less(X15, X16), insert(X15, X17, X19)).\nand substitutionT9 -> T16,\nX15 -> T16,\nX16 -> T16,\nX17 -> T20,\nX18 -> void,\nT2 -> tree(T16, T20, void),\nT17 -> T16,\nX19 -> void,\nT19 -> void,\nT18 -> T20", fontsize=14, style = filled, fillcolor = lightblue];
13 -> 297 [arrowhead = none ];
297 -> 14;

298 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
13 -> 298 [arrowhead = none ];
298 -> 16;

299 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
14 -> 299 [arrowhead = none ];
299 -> 17;

300 [label="EVAL with clause\ninsert(X72, tree(X73, X74, X75), tree(X73, X74, X76)) :- ','(less(X73, X72), insert(X72, X75, X76)).\nand substitutionT9 -> T50,\nX72 -> T50,\nX73 -> T50,\nX74 -> void,\nX75 -> T54,\nT2 -> tree(T50, void, T54),\nT51 -> T50,\nT52 -> void,\nX76 -> void,\nT53 -> T54", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 300 [arrowhead = none ];
300 -> 50;

301 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 301 [arrowhead = none ];
301 -> 51;

302 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 302 [arrowhead = none ];
302 -> 18;

303 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
18 -> 303 [arrowhead = none ];
303 -> 21;

304 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
18 -> 304 [arrowhead = none ];
304 -> 22;

305 [label="EVAL with clause\nless(s(X29), s(X30)) :- less(X29, X30).\nand substitutionX29 -> T25,\nT16 -> s(T25),\nX30 -> T25", fontsize=14, style = filled, fillcolor = lightblue];
21 -> 305 [arrowhead = none ];
305 -> 25;

306 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
21 -> 306 [arrowhead = none ];
306 -> 26;

307 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
22 -> 307 [arrowhead = none ];
307 -> 41;

308 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
25 -> 308 [arrowhead = none ];
308 -> 30;

309 [label="SPLIT 2\nnew knowledge:\nT25 is ground", fontsize=14, style = filled, fillcolor = violet];
25 -> 309 [arrowhead = none ];
309 -> 32;

310 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
30 -> 310 [arrowhead = none ];
310 -> 33;

311 [label="INSTANCE with matching:\nT1 -> s(T25)\nT2 -> T20\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
32 -> 311 [arrowhead = none , style=dashed];
311 -> 1[style=dashed];

312 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
33 -> 312 [arrowhead = none ];
312 -> 35;

313 [label="EVAL with clause\nless(s(X40), s(X41)) :- less(X40, X41).\nand substitutionX40 -> T28,\nT25 -> s(T28),\nX41 -> T28", fontsize=14, style = filled, fillcolor = lightblue];
35 -> 313 [arrowhead = none ];
313 -> 37;

314 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
35 -> 314 [arrowhead = none ];
314 -> 38;

315 [label="INSTANCE with matching:\nT25 -> T28", fontsize=14, style = filled, fillcolor = lightgrey];
37 -> 315 [arrowhead = none , style=dashed];
315 -> 30[style=dashed];

316 [label="EVAL with clause\ninsert(X56, tree(X57, X58, X59), tree(X57, X58, X60)) :- ','(less(X57, X56), insert(X56, X59, X60)).\nand substitutionT16 -> T39,\nX56 -> T39,\nX57 -> T39,\nX58 -> void,\nX59 -> T43,\nT2 -> tree(T39, void, T43),\nT40 -> T39,\nT41 -> void,\nX60 -> void,\nT42 -> T43", fontsize=14, style = filled, fillcolor = lightblue];
41 -> 316 [arrowhead = none ];
316 -> 42;

317 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 317 [arrowhead = none ];
317 -> 44;

318 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
42 -> 318 [arrowhead = none ];
318 -> 46;

319 [label="SPLIT 2\nnew knowledge:\nT39 is ground", fontsize=14, style = filled, fillcolor = violet];
42 -> 319 [arrowhead = none ];
319 -> 47;

320 [label="INSTANCE with matching:\nT25 -> T39", fontsize=14, style = filled, fillcolor = lightgrey];
46 -> 320 [arrowhead = none , style=dashed];
320 -> 30[style=dashed];

321 [label="INSTANCE with matching:\nT1 -> T39\nT2 -> T43\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
47 -> 321 [arrowhead = none , style=dashed];
321 -> 1[style=dashed];

322 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
50 -> 322 [arrowhead = none ];
322 -> 52;

323 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
52 -> 323 [arrowhead = none ];
323 -> 53;

324 [label="EVAL with clause\nless(s(X82), s(X83)) :- less(X82, X83).\nand substitutionX82 -> T57,\nT50 -> s(T57),\nX83 -> T57", fontsize=14, style = filled, fillcolor = lightblue];
53 -> 324 [arrowhead = none ];
324 -> 55;

325 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
53 -> 325 [arrowhead = none ];
325 -> 57;

326 [label="INSTANCE with matching:\nT25 -> T57\nT20 -> T54", fontsize=14, style = filled, fillcolor = lightgrey];
55 -> 326 [arrowhead = none , style=dashed];
326 -> 25[style=dashed];

327 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
58 -> 327 [arrowhead = none ];
327 -> 62;

328 [label="EVAL with clause\ninsert(X131, tree(X132, X133, X134), tree(X132, X133, X135)) :- ','(less(X132, X131), insert(X131, X134, X135)).\nand substitutionT5 -> T89,\nX131 -> T89,\nX132 -> T89,\nX133 -> void,\nX134 -> T93,\nT2 -> tree(T89, void, T93),\nT90 -> T89,\nT91 -> void,\nX135 -> void,\nT92 -> T93", fontsize=14, style = filled, fillcolor = lightblue];
60 -> 328 [arrowhead = none ];
328 -> 79;

329 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
60 -> 329 [arrowhead = none ];
329 -> 81;

330 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
62 -> 330 [arrowhead = none ];
330 -> 63;

331 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
63 -> 331 [arrowhead = none ];
331 -> 64;

332 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
63 -> 332 [arrowhead = none ];
332 -> 65;

333 [label="EVAL with clause\nless(s(X105), s(X106)) :- less(X105, X106).\nand substitutionX105 -> T71,\nT62 -> s(T71),\nX106 -> T71", fontsize=14, style = filled, fillcolor = lightblue];
64 -> 333 [arrowhead = none ];
333 -> 67;

334 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
64 -> 334 [arrowhead = none ];
334 -> 69;

335 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
65 -> 335 [arrowhead = none ];
335 -> 71;

336 [label="INSTANCE with matching:\nT25 -> T71\nT20 -> T66", fontsize=14, style = filled, fillcolor = lightgrey];
67 -> 336 [arrowhead = none , style=dashed];
336 -> 25[style=dashed];

337 [label="EVAL with clause\ninsert(X119, tree(X120, X121, X122), tree(X120, X121, X123)) :- ','(less(X120, X119), insert(X119, X122, X123)).\nand substitutionT62 -> T80,\nX119 -> T80,\nX120 -> T80,\nX121 -> void,\nX122 -> T84,\nT2 -> tree(T80, void, T84),\nT81 -> T80,\nT82 -> void,\nX123 -> void,\nT83 -> T84", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 337 [arrowhead = none ];
337 -> 74;

338 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
71 -> 338 [arrowhead = none ];
338 -> 75;

339 [label="INSTANCE with matching:\nT39 -> T80\nT43 -> T84", fontsize=14, style = filled, fillcolor = lightgrey];
74 -> 339 [arrowhead = none , style=dashed];
339 -> 42[style=dashed];

340 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
79 -> 340 [arrowhead = none ];
340 -> 82;

341 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
82 -> 341 [arrowhead = none ];
341 -> 83;

342 [label="EVAL with clause\nless(s(X141), s(X142)) :- less(X141, X142).\nand substitutionX141 -> T96,\nT89 -> s(T96),\nX142 -> T96", fontsize=14, style = filled, fillcolor = lightblue];
83 -> 342 [arrowhead = none ];
342 -> 84;

343 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
83 -> 343 [arrowhead = none ];
343 -> 85;

344 [label="INSTANCE with matching:\nT25 -> T96\nT20 -> T93", fontsize=14, style = filled, fillcolor = lightgrey];
84 -> 344 [arrowhead = none , style=dashed];
344 -> 25[style=dashed];

345 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
88 -> 345 [arrowhead = none ];
345 -> 90;

346 [label="EVAL with clause\ninsert(X227, tree(X228, X229, X230), tree(X228, X231, X230)) :- ','(less(X227, X228), insert(X227, X229, X231)).\nand substitutionT1 -> T160,\nX227 -> T160,\nX228 -> T161,\nX229 -> T165,\nX230 -> T163,\nT2 -> tree(T161, T165, T163),\nX231 -> T164,\nT3 -> tree(T161, T164, T163),\nT162 -> T165", fontsize=14, style = filled, fillcolor = lightblue];
89 -> 346 [arrowhead = none ];
346 -> 140;

347 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
89 -> 347 [arrowhead = none ];
347 -> 142;

348 [label="EVAL with clause\ninsert(X156, tree(X157, X158, X159), tree(X157, X160, X159)) :- ','(less(X156, X157), insert(X156, X158, X160)).\nand substitutionT100 -> T108,\nX156 -> T108,\nX157 -> T108,\nX158 -> T113,\nX159 -> T111,\nT2 -> tree(T108, T113, T111),\nT109 -> T108,\nT101 -> T112,\nX160 -> T112,\nT102 -> T111,\nT110 -> T113", fontsize=14, style = filled, fillcolor = lightblue];
90 -> 348 [arrowhead = none ];
348 -> 93;

349 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
90 -> 349 [arrowhead = none ];
349 -> 94;

350 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
93 -> 350 [arrowhead = none ];
350 -> 95;

351 [label="EVAL with clause\ninsert(X204, tree(X205, X206, X207), tree(X205, X206, X208)) :- ','(less(X205, X204), insert(X204, X207, X208)).\nand substitutionT100 -> T144,\nX204 -> T144,\nX205 -> T144,\nX206 -> T146,\nX207 -> T149,\nT2 -> tree(T144, T146, T149),\nT145 -> T144,\nT101 -> T146,\nT102 -> T148,\nX208 -> T148,\nT147 -> T149", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 351 [arrowhead = none ];
351 -> 121;

352 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
94 -> 352 [arrowhead = none ];
352 -> 122;

353 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
95 -> 353 [arrowhead = none ];
353 -> 96;

354 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
96 -> 354 [arrowhead = none ];
354 -> 97;

355 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
96 -> 355 [arrowhead = none ];
355 -> 98;

356 [label="EVAL with clause\nless(s(X170), s(X171)) :- less(X170, X171).\nand substitutionX170 -> T118,\nT108 -> s(T118),\nX171 -> T118", fontsize=14, style = filled, fillcolor = lightblue];
97 -> 356 [arrowhead = none ];
356 -> 101;

357 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
97 -> 357 [arrowhead = none ];
357 -> 102;

358 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
98 -> 358 [arrowhead = none ];
358 -> 107;

359 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
101 -> 359 [arrowhead = none ];
359 -> 103;

360 [label="SPLIT 2\nnew knowledge:\nT118 is ground", fontsize=14, style = filled, fillcolor = violet];
101 -> 360 [arrowhead = none ];
360 -> 104;

361 [label="INSTANCE with matching:\nT25 -> T118", fontsize=14, style = filled, fillcolor = lightgrey];
103 -> 361 [arrowhead = none , style=dashed];
361 -> 30[style=dashed];

362 [label="INSTANCE with matching:\nT1 -> s(T118)\nT2 -> T113\nT3 -> T112", fontsize=14, style = filled, fillcolor = lightgrey];
104 -> 362 [arrowhead = none , style=dashed];
362 -> 1[style=dashed];

363 [label="EVAL with clause\ninsert(X188, tree(X189, X190, X191), tree(X189, X190, X192)) :- ','(less(X189, X188), insert(X188, X191, X192)).\nand substitutionT108 -> T131,\nX188 -> T131,\nX189 -> T131,\nX190 -> T133,\nX191 -> T136,\nT2 -> tree(T131, T133, T136),\nT132 -> T131,\nT112 -> T133,\nT111 -> T135,\nX192 -> T135,\nT134 -> T136", fontsize=14, style = filled, fillcolor = lightblue];
107 -> 363 [arrowhead = none ];
363 -> 110;

364 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
107 -> 364 [arrowhead = none ];
364 -> 111;

365 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
110 -> 365 [arrowhead = none ];
365 -> 114;

366 [label="SPLIT 2\nnew knowledge:\nT131 is ground", fontsize=14, style = filled, fillcolor = violet];
110 -> 366 [arrowhead = none ];
366 -> 115;

367 [label="INSTANCE with matching:\nT25 -> T131", fontsize=14, style = filled, fillcolor = lightgrey];
114 -> 367 [arrowhead = none , style=dashed];
367 -> 30[style=dashed];

368 [label="INSTANCE with matching:\nT1 -> T131\nT2 -> T136\nT3 -> T135", fontsize=14, style = filled, fillcolor = lightgrey];
115 -> 368 [arrowhead = none , style=dashed];
368 -> 1[style=dashed];

369 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
121 -> 369 [arrowhead = none ];
369 -> 123;

370 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
123 -> 370 [arrowhead = none ];
370 -> 125;

371 [label="EVAL with clause\nless(s(X214), s(X215)) :- less(X214, X215).\nand substitutionX214 -> T152,\nT144 -> s(T152),\nX215 -> T152", fontsize=14, style = filled, fillcolor = lightblue];
125 -> 371 [arrowhead = none ];
371 -> 127;

372 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
125 -> 372 [arrowhead = none ];
372 -> 131;

373 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
127 -> 373 [arrowhead = none ];
373 -> 133;

374 [label="SPLIT 2\nnew knowledge:\nT152 is ground", fontsize=14, style = filled, fillcolor = violet];
127 -> 374 [arrowhead = none ];
374 -> 135;

375 [label="INSTANCE with matching:\nT25 -> T152", fontsize=14, style = filled, fillcolor = lightgrey];
133 -> 375 [arrowhead = none , style=dashed];
375 -> 30[style=dashed];

376 [label="INSTANCE with matching:\nT1 -> s(T152)\nT2 -> T149\nT3 -> T148", fontsize=14, style = filled, fillcolor = lightgrey];
135 -> 376 [arrowhead = none , style=dashed];
376 -> 1[style=dashed];

377 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
140 -> 377 [arrowhead = none ];
377 -> 143;

378 [label="EVAL with clause\ninsert(X413, tree(X414, X415, X416), tree(X414, X415, X417)) :- ','(less(X414, X413), insert(X413, X416, X417)).\nand substitutionT1 -> T321,\nX413 -> T321,\nX414 -> T322,\nX415 -> T323,\nX416 -> T326,\nT2 -> tree(T322, T323, T326),\nX417 -> T325,\nT3 -> tree(T322, T323, T325),\nT324 -> T326", fontsize=14, style = filled, fillcolor = lightblue];
142 -> 378 [arrowhead = none ];
378 -> 274;

379 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
142 -> 379 [arrowhead = none ];
379 -> 275;

380 [label="EVAL with clause\nless(0, s(X234)).\nand substitutionT160 -> 0,\nX234 -> T168,\nT161 -> s(T168)", fontsize=14, style = filled, fillcolor = lightblue];
143 -> 380 [arrowhead = none ];
380 -> 144;

381 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
143 -> 381 [arrowhead = none ];
381 -> 147;

382 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
144 -> 382 [arrowhead = none ];
382 -> 148;

383 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
144 -> 383 [arrowhead = none ];
383 -> 149;

384 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
147 -> 384 [arrowhead = none ];
384 -> 167;

385 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
147 -> 385 [arrowhead = none ];
385 -> 168;

386 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T165\nT3 -> T164", fontsize=14, style = filled, fillcolor = lightgrey];
148 -> 386 [arrowhead = none , style=dashed];
386 -> 1[style=dashed];

387 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
149 -> 387 [arrowhead = none ];
387 -> 150;

388 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
150 -> 388 [arrowhead = none ];
388 -> 151;

389 [label="EVAL with clause\ninsert(X251, tree(X252, X253, X254), tree(X252, X253, X255)) :- ','(less(X252, X251), insert(X251, X254, X255)).\nand substitutionX251 -> 0,\nX252 -> s(T182),\nX253 -> T180,\nX254 -> T184,\nT2 -> tree(s(T182), T180, T184),\nT168 -> T182,\nT179 -> s(T182),\nT164 -> T180,\nT163 -> T183,\nX255 -> T183,\nT181 -> T184", fontsize=14, style = filled, fillcolor = lightblue];
151 -> 389 [arrowhead = none ];
389 -> 154;

390 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
151 -> 390 [arrowhead = none ];
390 -> 157;

391 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
154 -> 391 [arrowhead = none ];
391 -> 159;

392 [label="SPLIT 2\nnew knowledge:\nT182 is ground", fontsize=14, style = filled, fillcolor = violet];
154 -> 392 [arrowhead = none ];
392 -> 160;

393 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
159 -> 393 [arrowhead = none ];
393 -> 163;

394 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T184\nT3 -> T183", fontsize=14, style = filled, fillcolor = lightgrey];
160 -> 394 [arrowhead = none , style=dashed];
394 -> 1[style=dashed];

395 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
163 -> 395 [arrowhead = none ];
395 -> 164;

396 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
164 -> 396 [arrowhead = none ];
396 -> 165;

397 [label="EVAL with clause\nless(s(X273), s(X274)) :- less(X273, X274).\nand substitutionX273 -> T194,\nT160 -> s(T194),\nX274 -> T195,\nT161 -> s(T195)", fontsize=14, style = filled, fillcolor = lightblue];
167 -> 397 [arrowhead = none ];
397 -> 173;

398 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
167 -> 398 [arrowhead = none ];
398 -> 174;

399 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
168 -> 399 [arrowhead = none ];
399 -> 269;

400 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
173 -> 400 [arrowhead = none ];
400 -> 177;

401 [label="SPLIT 2\nnew knowledge:\nT194 is ground\nT195 is ground", fontsize=14, style = filled, fillcolor = violet];
173 -> 401 [arrowhead = none ];
401 -> 178;

402 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
177 -> 402 [arrowhead = none ];
402 -> 180;

403 [label="INSTANCE with matching:\nT1 -> s(T194)\nT2 -> T165\nT3 -> T164", fontsize=14, style = filled, fillcolor = lightgrey];
178 -> 403 [arrowhead = none , style=dashed];
403 -> 1[style=dashed];

404 [label="EVAL with clause\nless(0, s(X281)).\nand substitutionT194 -> 0,\nX281 -> T202,\nT195 -> s(T202)", fontsize=14, style = filled, fillcolor = lightblue];
180 -> 404 [arrowhead = none ];
404 -> 182;

405 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
180 -> 405 [arrowhead = none ];
405 -> 183;

406 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
182 -> 406 [arrowhead = none ];
406 -> 184;

407 [label="EVAL with clause\nless(s(X288), s(X289)) :- less(X288, X289).\nand substitutionX288 -> T207,\nT194 -> s(T207),\nX289 -> T208,\nT195 -> s(T208)", fontsize=14, style = filled, fillcolor = lightblue];
183 -> 407 [arrowhead = none ];
407 -> 189;

408 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
183 -> 408 [arrowhead = none ];
408 -> 190;

409 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
184 -> 409 [arrowhead = none ];
409 -> 187;

410 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
189 -> 410 [arrowhead = none ];
410 -> 193;

411 [label="EVAL with clause\nless(0, s(X294)).\nand substitutionT207 -> 0,\nX294 -> T213,\nT208 -> s(T213)", fontsize=14, style = filled, fillcolor = lightblue];
193 -> 411 [arrowhead = none ];
411 -> 194;

412 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
193 -> 412 [arrowhead = none ];
412 -> 195;

413 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
194 -> 413 [arrowhead = none ];
413 -> 196;

414 [label="EVAL with clause\nless(s(X301), s(X302)) :- less(X301, X302).\nand substitutionX301 -> T218,\nT207 -> s(T218),\nX302 -> T219,\nT208 -> s(T219)", fontsize=14, style = filled, fillcolor = lightblue];
195 -> 414 [arrowhead = none ];
414 -> 200;

415 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
195 -> 415 [arrowhead = none ];
415 -> 203;

416 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
196 -> 416 [arrowhead = none ];
416 -> 198;

417 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
200 -> 417 [arrowhead = none ];
417 -> 206;

418 [label="EVAL with clause\nless(0, s(X307)).\nand substitutionT218 -> 0,\nX307 -> T224,\nT219 -> s(T224)", fontsize=14, style = filled, fillcolor = lightblue];
206 -> 418 [arrowhead = none ];
418 -> 208;

419 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
206 -> 419 [arrowhead = none ];
419 -> 209;

420 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
208 -> 420 [arrowhead = none ];
420 -> 210;

421 [label="EVAL with clause\nless(s(X314), s(X315)) :- less(X314, X315).\nand substitutionX314 -> T229,\nT218 -> s(T229),\nX315 -> T230,\nT219 -> s(T230)", fontsize=14, style = filled, fillcolor = lightblue];
209 -> 421 [arrowhead = none ];
421 -> 213;

422 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
209 -> 422 [arrowhead = none ];
422 -> 214;

423 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
210 -> 423 [arrowhead = none ];
423 -> 211;

424 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
213 -> 424 [arrowhead = none ];
424 -> 219;

425 [label="EVAL with clause\nless(0, s(X320)).\nand substitutionT229 -> 0,\nX320 -> T235,\nT230 -> s(T235)", fontsize=14, style = filled, fillcolor = lightblue];
219 -> 425 [arrowhead = none ];
425 -> 220;

426 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
219 -> 426 [arrowhead = none ];
426 -> 223;

427 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
220 -> 427 [arrowhead = none ];
427 -> 224;

428 [label="EVAL with clause\nless(s(X327), s(X328)) :- less(X327, X328).\nand substitutionX327 -> T240,\nT229 -> s(T240),\nX328 -> T241,\nT230 -> s(T241)", fontsize=14, style = filled, fillcolor = lightblue];
223 -> 428 [arrowhead = none ];
428 -> 226;

429 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
223 -> 429 [arrowhead = none ];
429 -> 227;

430 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
224 -> 430 [arrowhead = none ];
430 -> 225;

431 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
226 -> 431 [arrowhead = none ];
431 -> 229;

432 [label="EVAL with clause\nless(0, s(X333)).\nand substitutionT240 -> 0,\nX333 -> T246,\nT241 -> s(T246)", fontsize=14, style = filled, fillcolor = lightblue];
229 -> 432 [arrowhead = none ];
432 -> 230;

433 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
229 -> 433 [arrowhead = none ];
433 -> 232;

434 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
230 -> 434 [arrowhead = none ];
434 -> 234;

435 [label="EVAL with clause\nless(s(X340), s(X341)) :- less(X340, X341).\nand substitutionX340 -> T251,\nT240 -> s(T251),\nX341 -> T252,\nT241 -> s(T252)", fontsize=14, style = filled, fillcolor = lightblue];
232 -> 435 [arrowhead = none ];
435 -> 241;

436 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
232 -> 436 [arrowhead = none ];
436 -> 242;

437 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
234 -> 437 [arrowhead = none ];
437 -> 237;

438 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
241 -> 438 [arrowhead = none ];
438 -> 243;

439 [label="EVAL with clause\nless(0, s(X346)).\nand substitutionT251 -> 0,\nX346 -> T257,\nT252 -> s(T257)", fontsize=14, style = filled, fillcolor = lightblue];
243 -> 439 [arrowhead = none ];
439 -> 244;

440 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
243 -> 440 [arrowhead = none ];
440 -> 246;

441 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
244 -> 441 [arrowhead = none ];
441 -> 247;

442 [label="EVAL with clause\nless(s(X353), s(X354)) :- less(X353, X354).\nand substitutionX353 -> T262,\nT251 -> s(T262),\nX354 -> T263,\nT252 -> s(T263)", fontsize=14, style = filled, fillcolor = lightblue];
246 -> 442 [arrowhead = none ];
442 -> 251;

443 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
246 -> 443 [arrowhead = none ];
443 -> 253;

444 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
247 -> 444 [arrowhead = none ];
444 -> 249;

445 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
251 -> 445 [arrowhead = none ];
445 -> 254;

446 [label="EVAL with clause\nless(0, s(X359)).\nand substitutionT262 -> 0,\nX359 -> T268,\nT263 -> s(T268)", fontsize=14, style = filled, fillcolor = lightblue];
254 -> 446 [arrowhead = none ];
446 -> 255;

447 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
254 -> 447 [arrowhead = none ];
447 -> 256;

448 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
255 -> 448 [arrowhead = none ];
448 -> 257;

449 [label="EVAL with clause\nless(s(X366), s(X367)) :- less(X366, X367).\nand substitutionX366 -> T273,\nT262 -> s(T273),\nX367 -> T274,\nT263 -> s(T274)", fontsize=14, style = filled, fillcolor = lightblue];
256 -> 449 [arrowhead = none ];
449 -> 259;

450 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
256 -> 450 [arrowhead = none ];
450 -> 260;

451 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
257 -> 451 [arrowhead = none ];
451 -> 258;

452 [label="GENERALIZATION\nT277 <-- s(s(s(s(s(s(s(T273)))))))\nT278 <-- s(s(s(s(s(s(s(T274)))))))\n\nNew Knowledge:\nT277 is ground\nT278 is ground", fontsize=14, style = filled, fillcolor = violet];
259 -> 452 [arrowhead = none ];
452 -> 261;

453 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
261 -> 453 [arrowhead = none ];
453 -> 262;

454 [label="EVAL with clause\nless(0, s(X374)).\nand substitutionT273 -> 0,\nX374 -> T283,\nT274 -> s(T283)", fontsize=14, style = filled, fillcolor = lightblue];
262 -> 454 [arrowhead = none ];
454 -> 263;

455 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
262 -> 455 [arrowhead = none ];
455 -> 264;

456 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
263 -> 456 [arrowhead = none ];
456 -> 265;

457 [label="EVAL with clause\nless(s(X381), s(X382)) :- less(X381, X382).\nand substitutionX381 -> T288,\nT273 -> s(T288),\nX382 -> T289,\nT274 -> s(T289)", fontsize=14, style = filled, fillcolor = lightblue];
264 -> 457 [arrowhead = none ];
457 -> 267;

458 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
264 -> 458 [arrowhead = none ];
458 -> 268;

459 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
265 -> 459 [arrowhead = none ];
459 -> 266;

460 [label="INSTANCE with matching:\nT273 -> T288\nT274 -> T289", fontsize=14, style = filled, fillcolor = lightgrey];
267 -> 460 [arrowhead = none , style=dashed];
460 -> 261[style=dashed];

461 [label="EVAL with clause\ninsert(X397, tree(X398, X399, X400), tree(X398, X399, X401)) :- ','(less(X398, X397), insert(X397, X400, X401)).\nand substitutionT160 -> T304,\nX397 -> T304,\nX398 -> T305,\nX399 -> T306,\nX400 -> T309,\nT2 -> tree(T305, T306, T309),\nT161 -> T305,\nT164 -> T306,\nT163 -> T308,\nX401 -> T308,\nT307 -> T309", fontsize=14, style = filled, fillcolor = lightblue];
269 -> 461 [arrowhead = none ];
461 -> 270;

462 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
269 -> 462 [arrowhead = none ];
462 -> 271;

463 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
270 -> 463 [arrowhead = none ];
463 -> 272;

464 [label="SPLIT 2\nnew knowledge:\nT305 is ground\nT304 is ground", fontsize=14, style = filled, fillcolor = violet];
270 -> 464 [arrowhead = none ];
464 -> 273;

465 [label="INSTANCE with matching:\nT273 -> T305\nT274 -> T304", fontsize=14, style = filled, fillcolor = lightgrey];
272 -> 465 [arrowhead = none , style=dashed];
465 -> 261[style=dashed];

466 [label="INSTANCE with matching:\nT1 -> T304\nT2 -> T309\nT3 -> T308", fontsize=14, style = filled, fillcolor = lightgrey];
273 -> 466 [arrowhead = none , style=dashed];
466 -> 1[style=dashed];

467 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
274 -> 467 [arrowhead = none ];
467 -> 276;

468 [label="EVAL with clause\nless(0, s(X420)).\nand substitutionT322 -> 0,\nX420 -> T329,\nT321 -> s(T329)", fontsize=14, style = filled, fillcolor = lightblue];
276 -> 468 [arrowhead = none ];
468 -> 277;

469 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
276 -> 469 [arrowhead = none ];
469 -> 278;

470 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
277 -> 470 [arrowhead = none ];
470 -> 279;

471 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
277 -> 471 [arrowhead = none ];
471 -> 280;

472 [label="EVAL with clause\nless(s(X431), s(X432)) :- less(X431, X432).\nand substitutionX431 -> T338,\nT322 -> s(T338),\nX432 -> T339,\nT321 -> s(T339)", fontsize=14, style = filled, fillcolor = lightblue];
278 -> 472 [arrowhead = none ];
472 -> 282;

473 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
278 -> 473 [arrowhead = none ];
473 -> 283;

474 [label="INSTANCE with matching:\nT1 -> s(T329)\nT2 -> T326\nT3 -> T325", fontsize=14, style = filled, fillcolor = lightgrey];
279 -> 474 [arrowhead = none , style=dashed];
474 -> 1[style=dashed];

475 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
280 -> 475 [arrowhead = none ];
475 -> 281;

476 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
282 -> 476 [arrowhead = none ];
476 -> 284;

477 [label="SPLIT 2\nnew knowledge:\nT338 is ground\nT339 is ground", fontsize=14, style = filled, fillcolor = violet];
282 -> 477 [arrowhead = none ];
477 -> 285;

478 [label="INSTANCE with matching:\nT273 -> T338\nT274 -> T339", fontsize=14, style = filled, fillcolor = lightgrey];
284 -> 478 [arrowhead = none , style=dashed];
478 -> 261[style=dashed];

479 [label="INSTANCE with matching:\nT1 -> s(T339)\nT2 -> T326\nT3 -> T325", fontsize=14, style = filled, fillcolor = lightgrey];
285 -> 479 [arrowhead = none , style=dashed];
479 -> 1[style=dashed];

}

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, void)) → f1_out1(void)
f1_in(z0, tree(z0, void, void)) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, void, void)) → U1(f18_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U2(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, void, void)) → U3(f63_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U4(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U5(f96_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(s(z0), tree(s(z0), z1, z2)) → U6(f127_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f1_in(0, tree(s(z0), z1, z2)) → U7(f144_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f1_in(z0, tree(z1, z2, z3)) → U8(f147_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f1_in(s(z0), tree(0, z1, z2)) → U9(f277_in(z0, z2), s(z0), tree(0, z1, z2))
f1_in(s(z0), tree(s(z1), z2, z3)) → U10(f282_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f18_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U1(f18_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U2(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U3(f63_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U3(f63_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U4(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U5(f96_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(tree(z1, z0, z3))
U5(f96_out3(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U6(f127_out1(z0), s(z1), tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z2, z0))
U7(f144_out1(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out2(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out4(z0), 0, tree(s(z1), z2, z3)) → f1_out1(z0)
U8(f147_out1(z0), z1, tree(z2, z3, z4)) → f1_out1(tree(z2, z0, z4))
U8(f147_out3(z0), z1, tree(z2, z3, z4)) → f1_out1(z0)
U9(f277_out1(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U9(f277_out2(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U10(f282_out1(z0), s(z1), tree(s(z2), z3, z4)) → f1_out1(tree(s(z2), z3, z0))
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1
f149_in(z0, z1, z2) → U14(f154_in(z0, z2), z0, z1, z2)
U14(f154_out1(z0), z1, z2, z3) → f149_out3(tree(s(z1), z2, z0))
f167_in(s(z0), s(z1), z2) → U15(f173_in(z0, z1, z2), s(z0), s(z1), z2)
U15(f173_out1(z0), s(z1), s(z2), z3) → f167_out1(z0)
f168_in(z0, z1, z2, z3) → U16(f270_in(z1, z0, z3), z0, z1, z2, z3)
U16(f270_out1(z0), z1, z2, z3, z4) → f168_out2(tree(z2, z3, z0))
f64_in(s(z0)) → U17(f25_in(z0), s(z0))
U17(f25_out1(z0), s(z1)) → f64_out1(z0)
f65_in(z0) → U18(f42_in(z0), z0)
U18(f42_out1(z0), z1) → f65_out2(tree(z1, void, z0))
f97_in(s(z0), z1) → U19(f101_in(z0, z1), s(z0), z1)
U19(f101_out1(z0), s(z1), z2) → f97_out1(z0)
f98_in(z0, z1, z2) → U20(f110_in(z0, z2), z0, z1, z2)
U20(f110_out1(z0), z1, z2, z3) → f98_out2(tree(z1, z2, z0))
f21_in(s(z0)) → U21(f25_in(z0), s(z0))
U21(f25_out1(z0), s(z1)) → f21_out1(z0)
f22_in(z0) → U22(f42_in(z0), z0)
U22(f42_out1(z0), z1) → f22_out2(tree(z1, void, z0))
f25_in(z0) → U23(f30_in(z0), z0)
U23(f30_out1, z0) → U24(f1_in(s(z0), void), z0)
U24(f1_out1(z0), z1) → f25_out1(z0)
f42_in(z0) → U25(f30_in(z0), z0)
U25(f30_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1(z0), z1) → f42_out1(z0)
f101_in(z0, z1) → U27(f30_in(z0), z0, z1)
U27(f30_out1, z0, z1) → U28(f1_in(s(z0), z1), z0, z1)
U28(f1_out1(z0), z1, z2) → f101_out1(z0)
f110_in(z0, z1) → U29(f30_in(z0), z0, z1)
U29(f30_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1(z0), z1, z2) → f110_out1(z0)
f127_in(z0, z1) → U31(f30_in(z0), z0, z1)
U31(f30_out1, z0, z1) → U32(f1_in(s(z0), z1), z0, z1)
U32(f1_out1(z0), z1, z2) → f127_out1(z0)
f154_in(z0, z1) → U33(f159_in(z0), z0, z1)
U33(f159_out1, z0, z1) → U34(f1_in(0, z1), z0, z1)
U34(f1_out1(z0), z1, z2) → f154_out1(z0)
f173_in(z0, z1, z2) → U35(f177_in(z0, z1), z0, z1, z2)
U35(f177_out1, z0, z1, z2) → U36(f1_in(s(z0), z2), z0, z1, z2)
U36(f1_out1(z0), z1, z2, z3) → f173_out1(z0)
f270_in(z0, z1, z2) → U37(f261_in(z0, z1), z0, z1, z2)
U37(f261_out1, z0, z1, z2) → U38(f1_in(z1, z2), z0, z1, z2)
U38(f1_out1(z0), z1, z2, z3) → f270_out1(z0)
f282_in(z0, z1, z2) → U39(f261_in(z0, z1), z0, z1, z2)
U39(f261_out1, z0, z1, z2) → U40(f1_in(s(z1), z2), z0, z1, z2)
U40(f1_out1(z0), z1, z2, z3) → f282_out1(z0)
f18_in(z0) → U41(f21_in(z0), f22_in(z0), z0)
U41(f21_out1(z0), z1, z2) → f18_out1(z0)
U41(z0, f22_out2(z1), z2) → f18_out3(z1)
f63_in(z0) → U42(f64_in(z0), f65_in(z0), z0)
U42(f64_out1(z0), z1, z2) → f63_out1(z0)
U42(z0, f65_out2(z1), z2) → f63_out3(z1)
f96_in(z0, z1, z2) → U43(f97_in(z0, z1), f98_in(z0, z1, z2), z0, z1, z2)
U43(f97_out1(z0), z1, z2, z3, z4) → f96_out1(z0)
U43(z0, f98_out2(z1), z2, z3, z4) → f96_out3(z1)
f144_in(z0, z1, z2) → U44(f1_in(0, z0), f149_in(z1, z0, z2), z0, z1, z2)
U44(f1_out1(z0), z1, z2, z3, z4) → f144_out1(z0)
U44(z0, f149_out1(z1), z2, z3, z4) → f144_out2(z1)
U44(z0, f149_out3(z1), z2, z3, z4) → f144_out4(z1)
f147_in(z0, z1, z2, z3) → U45(f167_in(z0, z1, z2), f168_in(z0, z1, z2, z3), z0, z1, z2, z3)
U45(f167_out1(z0), z1, z2, z3, z4, z5) → f147_out1(z0)
U45(z0, f168_out2(z1), z2, z3, z4, z5) → f147_out3(z1)
f277_in(z0, z1) → U46(f1_in(s(z0), z1), f280_in(z0, z1), z0, z1)
U46(f1_out1(z0), z1, z2, z3) → f277_out1(z0)
U46(z0, f280_out1(z1), z2, z3) → f277_out2(z1)

Tuples:

F1_IN(z0, tree(z0, void, void)) → c2(U1'(f18_in(z0), z0, tree(z0, void, void)), F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c3(U2'(f25_in(z0), s(z0), tree(s(z0), void, void)), F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c4(U3'(f63_in(z0), z0, tree(z0, void, void)), F63_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c5(U4'(f25_in(z0), s(z0), tree(s(z0), void, void)), F25_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(U5'(f96_in(z0, z1, z2), z0, tree(z0, z1, z2)), F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(U6'(f127_in(z0, z2), s(z0), tree(s(z0), z1, z2)), F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(U7'(f144_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(U8'(f147_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(U9'(f277_in(z0, z2), s(z0), tree(0, z1, z2)), F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(U10'(f282_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(U11'(f261_in(z0, z1), s(z0), s(z1)), F261_IN(z0, z1))
F30_IN(s(z0)) → c33(U12'(f30_in(z0), s(z0)), F30_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c42(U13'(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))), F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c44(U14'(f154_in(z0, z2), z0, z1, z2), F154_IN(z0, z2))
F167_IN(s(z0), s(z1), z2) → c46(U15'(f173_in(z0, z1, z2), s(z0), s(z1), z2), F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(U16'(f270_in(z1, z0, z3), z0, z1, z2, z3), F270_IN(z1, z0, z3))
F64_IN(s(z0)) → c50(U17'(f25_in(z0), s(z0)), F25_IN(z0))
F65_IN(z0) → c52(U18'(f42_in(z0), z0), F42_IN(z0))
F97_IN(s(z0), z1) → c54(U19'(f101_in(z0, z1), s(z0), z1), F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(U20'(f110_in(z0, z2), z0, z1, z2), F110_IN(z0, z2))
F21_IN(s(z0)) → c58(U21'(f25_in(z0), s(z0)), F25_IN(z0))
F22_IN(z0) → c60(U22'(f42_in(z0), z0), F42_IN(z0))
F25_IN(z0) → c62(U23'(f30_in(z0), z0), F30_IN(z0))
U23'(f30_out1, z0) → c63(U24'(f1_in(s(z0), void), z0), F1_IN(s(z0), void))
F42_IN(z0) → c65(U25'(f30_in(z0), z0), F30_IN(z0))
U25'(f30_out1, z0) → c66(U26'(f1_in(z0, void), z0), F1_IN(z0, void))
F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
U27'(f30_out1, z0, z1) → c69(U28'(f1_in(s(z0), z1), z0, z1), F1_IN(s(z0), z1))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
U29'(f30_out1, z0, z1) → c72(U30'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
U31'(f30_out1, z0, z1) → c75(U32'(f1_in(s(z0), z1), z0, z1), F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77(U33'(f159_in(z0), z0, z1))
U33'(f159_out1, z0, z1) → c78(U34'(f1_in(0, z1), z0, z1), F1_IN(0, z1))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
U35'(f177_out1, z0, z1, z2) → c81(U36'(f1_in(s(z0), z2), z0, z1, z2), F1_IN(s(z0), z2))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
U37'(f261_out1, z0, z1, z2) → c84(U38'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
U39'(f261_out1, z0, z1, z2) → c87(U40'(f1_in(s(z1), z2), z0, z1, z2), F1_IN(s(z1), z2))
F18_IN(z0) → c89(U41'(f21_in(z0), f22_in(z0), z0), F21_IN(z0), F22_IN(z0))
F63_IN(z0) → c92(U42'(f64_in(z0), f65_in(z0), z0), F64_IN(z0), F65_IN(z0))
F96_IN(z0, z1, z2) → c95(U43'(f97_in(z0, z1), f98_in(z0, z1, z2), z0, z1, z2), F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(U44'(f1_in(0, z0), f149_in(z1, z0, z2), z0, z1, z2), F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(U45'(f167_in(z0, z1, z2), f168_in(z0, z1, z2, z3), z0, z1, z2, z3), F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(U46'(f1_in(s(z0), z1), f280_in(z0, z1), z0, z1), F1_IN(s(z0), z1))

S tuples:

F1_IN(z0, tree(z0, void, void)) → c2(U1'(f18_in(z0), z0, tree(z0, void, void)), F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c3(U2'(f25_in(z0), s(z0), tree(s(z0), void, void)), F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c4(U3'(f63_in(z0), z0, tree(z0, void, void)), F63_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c5(U4'(f25_in(z0), s(z0), tree(s(z0), void, void)), F25_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(U5'(f96_in(z0, z1, z2), z0, tree(z0, z1, z2)), F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(U6'(f127_in(z0, z2), s(z0), tree(s(z0), z1, z2)), F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(U7'(f144_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(U8'(f147_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(U9'(f277_in(z0, z2), s(z0), tree(0, z1, z2)), F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(U10'(f282_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(U11'(f261_in(z0, z1), s(z0), s(z1)), F261_IN(z0, z1))
F30_IN(s(z0)) → c33(U12'(f30_in(z0), s(z0)), F30_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c42(U13'(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))), F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c44(U14'(f154_in(z0, z2), z0, z1, z2), F154_IN(z0, z2))
F167_IN(s(z0), s(z1), z2) → c46(U15'(f173_in(z0, z1, z2), s(z0), s(z1), z2), F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(U16'(f270_in(z1, z0, z3), z0, z1, z2, z3), F270_IN(z1, z0, z3))
F64_IN(s(z0)) → c50(U17'(f25_in(z0), s(z0)), F25_IN(z0))
F65_IN(z0) → c52(U18'(f42_in(z0), z0), F42_IN(z0))
F97_IN(s(z0), z1) → c54(U19'(f101_in(z0, z1), s(z0), z1), F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(U20'(f110_in(z0, z2), z0, z1, z2), F110_IN(z0, z2))
F21_IN(s(z0)) → c58(U21'(f25_in(z0), s(z0)), F25_IN(z0))
F22_IN(z0) → c60(U22'(f42_in(z0), z0), F42_IN(z0))
F25_IN(z0) → c62(U23'(f30_in(z0), z0), F30_IN(z0))
U23'(f30_out1, z0) → c63(U24'(f1_in(s(z0), void), z0), F1_IN(s(z0), void))
F42_IN(z0) → c65(U25'(f30_in(z0), z0), F30_IN(z0))
U25'(f30_out1, z0) → c66(U26'(f1_in(z0, void), z0), F1_IN(z0, void))
F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
U27'(f30_out1, z0, z1) → c69(U28'(f1_in(s(z0), z1), z0, z1), F1_IN(s(z0), z1))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
U29'(f30_out1, z0, z1) → c72(U30'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
U31'(f30_out1, z0, z1) → c75(U32'(f1_in(s(z0), z1), z0, z1), F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77(U33'(f159_in(z0), z0, z1))
U33'(f159_out1, z0, z1) → c78(U34'(f1_in(0, z1), z0, z1), F1_IN(0, z1))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
U35'(f177_out1, z0, z1, z2) → c81(U36'(f1_in(s(z0), z2), z0, z1, z2), F1_IN(s(z0), z2))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
U37'(f261_out1, z0, z1, z2) → c84(U38'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
U39'(f261_out1, z0, z1, z2) → c87(U40'(f1_in(s(z1), z2), z0, z1, z2), F1_IN(s(z1), z2))
F18_IN(z0) → c89(U41'(f21_in(z0), f22_in(z0), z0), F21_IN(z0), F22_IN(z0))
F63_IN(z0) → c92(U42'(f64_in(z0), f65_in(z0), z0), F64_IN(z0), F65_IN(z0))
F96_IN(z0, z1, z2) → c95(U43'(f97_in(z0, z1), f98_in(z0, z1, z2), z0, z1, z2), F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(U44'(f1_in(0, z0), f149_in(z1, z0, z2), z0, z1, z2), F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(U45'(f167_in(z0, z1, z2), f168_in(z0, z1, z2, z3), z0, z1, z2, z3), F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(U46'(f1_in(s(z0), z1), f280_in(z0, z1), z0, z1), F1_IN(s(z0), z1))

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, f261_in, U11, f30_in, U12, f177_in, U13, f149_in, U14, f167_in, U15, f168_in, U16, f64_in, U17, f65_in, U18, f97_in, U19, f98_in, U20, f21_in, U21, f22_in, U22, f25_in, U23, U24, f42_in, U25, U26, f101_in, U27, U28, f110_in, U29, U30, f127_in, U31, U32, f154_in, U33, U34, f173_in, U35, U36, f270_in, U37, U38, f282_in, U39, U40, f18_in, U41, f63_in, U42, f96_in, U43, f144_in, U44, f147_in, U45, f277_in, U46

Defined Pair Symbols:

F1_IN, F261_IN, F30_IN, F177_IN, F149_IN, F167_IN, F168_IN, F64_IN, F65_IN, F97_IN, F98_IN, F21_IN, F22_IN, F25_IN, U23', F42_IN, U25', F101_IN, U27', F110_IN, U29', F127_IN, U31', F154_IN, U33', F173_IN, U35', F270_IN, U37', F282_IN, U39', F18_IN, F63_IN, F96_IN, F144_IN, F147_IN, F277_IN

Compound Symbols:

c2, c3, c4, c5, c7, c8, c9, c10, c11, c12, c31, c33, c42, c44, c46, c48, c50, c52, c54, c56, c58, c60, c62, c63, c65, c66, c68, c69, c71, c72, c74, c75, c77, c78, c80, c81, c83, c84, c86, c87, c89, c92, c95, c98, c102, c105

(21) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, void)) → f1_out1(void)
f1_in(z0, tree(z0, void, void)) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, void, void)) → U1(f18_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U2(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, void, void)) → U3(f63_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U4(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U5(f96_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(s(z0), tree(s(z0), z1, z2)) → U6(f127_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f1_in(0, tree(s(z0), z1, z2)) → U7(f144_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f1_in(z0, tree(z1, z2, z3)) → U8(f147_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f1_in(s(z0), tree(0, z1, z2)) → U9(f277_in(z0, z2), s(z0), tree(0, z1, z2))
f1_in(s(z0), tree(s(z1), z2, z3)) → U10(f282_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f18_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U1(f18_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U2(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U3(f63_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U3(f63_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U4(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U5(f96_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(tree(z1, z0, z3))
U5(f96_out3(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U6(f127_out1(z0), s(z1), tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z2, z0))
U7(f144_out1(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out2(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out4(z0), 0, tree(s(z1), z2, z3)) → f1_out1(z0)
U8(f147_out1(z0), z1, tree(z2, z3, z4)) → f1_out1(tree(z2, z0, z4))
U8(f147_out3(z0), z1, tree(z2, z3, z4)) → f1_out1(z0)
U9(f277_out1(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U9(f277_out2(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U10(f282_out1(z0), s(z1), tree(s(z2), z3, z4)) → f1_out1(tree(s(z2), z3, z0))
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1
f149_in(z0, z1, z2) → U14(f154_in(z0, z2), z0, z1, z2)
U14(f154_out1(z0), z1, z2, z3) → f149_out3(tree(s(z1), z2, z0))
f167_in(s(z0), s(z1), z2) → U15(f173_in(z0, z1, z2), s(z0), s(z1), z2)
U15(f173_out1(z0), s(z1), s(z2), z3) → f167_out1(z0)
f168_in(z0, z1, z2, z3) → U16(f270_in(z1, z0, z3), z0, z1, z2, z3)
U16(f270_out1(z0), z1, z2, z3, z4) → f168_out2(tree(z2, z3, z0))
f64_in(s(z0)) → U17(f25_in(z0), s(z0))
U17(f25_out1(z0), s(z1)) → f64_out1(z0)
f65_in(z0) → U18(f42_in(z0), z0)
U18(f42_out1(z0), z1) → f65_out2(tree(z1, void, z0))
f97_in(s(z0), z1) → U19(f101_in(z0, z1), s(z0), z1)
U19(f101_out1(z0), s(z1), z2) → f97_out1(z0)
f98_in(z0, z1, z2) → U20(f110_in(z0, z2), z0, z1, z2)
U20(f110_out1(z0), z1, z2, z3) → f98_out2(tree(z1, z2, z0))
f21_in(s(z0)) → U21(f25_in(z0), s(z0))
U21(f25_out1(z0), s(z1)) → f21_out1(z0)
f22_in(z0) → U22(f42_in(z0), z0)
U22(f42_out1(z0), z1) → f22_out2(tree(z1, void, z0))
f25_in(z0) → U23(f30_in(z0), z0)
U23(f30_out1, z0) → U24(f1_in(s(z0), void), z0)
U24(f1_out1(z0), z1) → f25_out1(z0)
f42_in(z0) → U25(f30_in(z0), z0)
U25(f30_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1(z0), z1) → f42_out1(z0)
f101_in(z0, z1) → U27(f30_in(z0), z0, z1)
U27(f30_out1, z0, z1) → U28(f1_in(s(z0), z1), z0, z1)
U28(f1_out1(z0), z1, z2) → f101_out1(z0)
f110_in(z0, z1) → U29(f30_in(z0), z0, z1)
U29(f30_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1(z0), z1, z2) → f110_out1(z0)
f127_in(z0, z1) → U31(f30_in(z0), z0, z1)
U31(f30_out1, z0, z1) → U32(f1_in(s(z0), z1), z0, z1)
U32(f1_out1(z0), z1, z2) → f127_out1(z0)
f154_in(z0, z1) → U33(f159_in(z0), z0, z1)
U33(f159_out1, z0, z1) → U34(f1_in(0, z1), z0, z1)
U34(f1_out1(z0), z1, z2) → f154_out1(z0)
f173_in(z0, z1, z2) → U35(f177_in(z0, z1), z0, z1, z2)
U35(f177_out1, z0, z1, z2) → U36(f1_in(s(z0), z2), z0, z1, z2)
U36(f1_out1(z0), z1, z2, z3) → f173_out1(z0)
f270_in(z0, z1, z2) → U37(f261_in(z0, z1), z0, z1, z2)
U37(f261_out1, z0, z1, z2) → U38(f1_in(z1, z2), z0, z1, z2)
U38(f1_out1(z0), z1, z2, z3) → f270_out1(z0)
f282_in(z0, z1, z2) → U39(f261_in(z0, z1), z0, z1, z2)
U39(f261_out1, z0, z1, z2) → U40(f1_in(s(z1), z2), z0, z1, z2)
U40(f1_out1(z0), z1, z2, z3) → f282_out1(z0)
f18_in(z0) → U41(f21_in(z0), f22_in(z0), z0)
U41(f21_out1(z0), z1, z2) → f18_out1(z0)
U41(z0, f22_out2(z1), z2) → f18_out3(z1)
f63_in(z0) → U42(f64_in(z0), f65_in(z0), z0)
U42(f64_out1(z0), z1, z2) → f63_out1(z0)
U42(z0, f65_out2(z1), z2) → f63_out3(z1)
f96_in(z0, z1, z2) → U43(f97_in(z0, z1), f98_in(z0, z1, z2), z0, z1, z2)
U43(f97_out1(z0), z1, z2, z3, z4) → f96_out1(z0)
U43(z0, f98_out2(z1), z2, z3, z4) → f96_out3(z1)
f144_in(z0, z1, z2) → U44(f1_in(0, z0), f149_in(z1, z0, z2), z0, z1, z2)
U44(f1_out1(z0), z1, z2, z3, z4) → f144_out1(z0)
U44(z0, f149_out1(z1), z2, z3, z4) → f144_out2(z1)
U44(z0, f149_out3(z1), z2, z3, z4) → f144_out4(z1)
f147_in(z0, z1, z2, z3) → U45(f167_in(z0, z1, z2), f168_in(z0, z1, z2, z3), z0, z1, z2, z3)
U45(f167_out1(z0), z1, z2, z3, z4, z5) → f147_out1(z0)
U45(z0, f168_out2(z1), z2, z3, z4, z5) → f147_out3(z1)
f277_in(z0, z1) → U46(f1_in(s(z0), z1), f280_in(z0, z1), z0, z1)
U46(f1_out1(z0), z1, z2, z3) → f277_out1(z0)
U46(z0, f280_out1(z1), z2, z3) → f277_out2(z1)

Tuples:

F1_IN(z0, tree(z0, z1, z2)) → c7(U5'(f96_in(z0, z1, z2), z0, tree(z0, z1, z2)), F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(U6'(f127_in(z0, z2), s(z0), tree(s(z0), z1, z2)), F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(U7'(f144_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(U8'(f147_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(U9'(f277_in(z0, z2), s(z0), tree(0, z1, z2)), F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(U10'(f282_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(U11'(f261_in(z0, z1), s(z0), s(z1)), F261_IN(z0, z1))
F30_IN(s(z0)) → c33(U12'(f30_in(z0), s(z0)), F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(U15'(f173_in(z0, z1, z2), s(z0), s(z1), z2), F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(U16'(f270_in(z1, z0, z3), z0, z1, z2, z3), F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(U19'(f101_in(z0, z1), s(z0), z1), F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(U20'(f110_in(z0, z2), z0, z1, z2), F110_IN(z0, z2))
F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
U27'(f30_out1, z0, z1) → c69(U28'(f1_in(s(z0), z1), z0, z1), F1_IN(s(z0), z1))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
U29'(f30_out1, z0, z1) → c72(U30'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
U31'(f30_out1, z0, z1) → c75(U32'(f1_in(s(z0), z1), z0, z1), F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77(U33'(f159_in(z0), z0, z1))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
U35'(f177_out1, z0, z1, z2) → c81(U36'(f1_in(s(z0), z2), z0, z1, z2), F1_IN(s(z0), z2))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
U37'(f261_out1, z0, z1, z2) → c84(U38'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
U39'(f261_out1, z0, z1, z2) → c87(U40'(f1_in(s(z1), z2), z0, z1, z2), F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(U43'(f97_in(z0, z1), f98_in(z0, z1, z2), z0, z1, z2), F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(U44'(f1_in(0, z0), f149_in(z1, z0, z2), z0, z1, z2), F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(U45'(f167_in(z0, z1, z2), f168_in(z0, z1, z2, z3), z0, z1, z2, z3), F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(U46'(f1_in(s(z0), z1), f280_in(z0, z1), z0, z1), F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c(U1'(f18_in(z0), z0, tree(z0, void, void)))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(U2'(f25_in(z0), s(z0), tree(s(z0), void, void)))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(U3'(f63_in(z0), z0, tree(z0, void, void)))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(U4'(f25_in(z0), s(z0), tree(s(z0), void, void)))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(U13'(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(U14'(f154_in(z0, z2), z0, z1, z2))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(U17'(f25_in(z0), s(z0)))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(U18'(f42_in(z0), z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(U21'(f25_in(z0), s(z0)))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(U22'(f42_in(z0), z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
U23'(f30_out1, z0) → c(U24'(f1_in(s(z0), void), z0))
U23'(f30_out1, z0) → c(F1_IN(s(z0), void))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U25'(f30_out1, z0) → c(U26'(f1_in(z0, void), z0))
U25'(f30_out1, z0) → c(F1_IN(z0, void))
U33'(f159_out1, z0, z1) → c(U34'(f1_in(0, z1), z0, z1))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(U41'(f21_in(z0), f22_in(z0), z0))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(U42'(f64_in(z0), f65_in(z0), z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))

S tuples:

F1_IN(z0, tree(z0, z1, z2)) → c7(U5'(f96_in(z0, z1, z2), z0, tree(z0, z1, z2)), F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(U6'(f127_in(z0, z2), s(z0), tree(s(z0), z1, z2)), F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(U7'(f144_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(U8'(f147_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(U9'(f277_in(z0, z2), s(z0), tree(0, z1, z2)), F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(U10'(f282_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(U11'(f261_in(z0, z1), s(z0), s(z1)), F261_IN(z0, z1))
F30_IN(s(z0)) → c33(U12'(f30_in(z0), s(z0)), F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(U15'(f173_in(z0, z1, z2), s(z0), s(z1), z2), F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(U16'(f270_in(z1, z0, z3), z0, z1, z2, z3), F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(U19'(f101_in(z0, z1), s(z0), z1), F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(U20'(f110_in(z0, z2), z0, z1, z2), F110_IN(z0, z2))
F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
U27'(f30_out1, z0, z1) → c69(U28'(f1_in(s(z0), z1), z0, z1), F1_IN(s(z0), z1))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
U29'(f30_out1, z0, z1) → c72(U30'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
U31'(f30_out1, z0, z1) → c75(U32'(f1_in(s(z0), z1), z0, z1), F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77(U33'(f159_in(z0), z0, z1))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
U35'(f177_out1, z0, z1, z2) → c81(U36'(f1_in(s(z0), z2), z0, z1, z2), F1_IN(s(z0), z2))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
U37'(f261_out1, z0, z1, z2) → c84(U38'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
U39'(f261_out1, z0, z1, z2) → c87(U40'(f1_in(s(z1), z2), z0, z1, z2), F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(U43'(f97_in(z0, z1), f98_in(z0, z1, z2), z0, z1, z2), F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(U44'(f1_in(0, z0), f149_in(z1, z0, z2), z0, z1, z2), F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(U45'(f167_in(z0, z1, z2), f168_in(z0, z1, z2, z3), z0, z1, z2, z3), F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(U46'(f1_in(s(z0), z1), f280_in(z0, z1), z0, z1), F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c(U1'(f18_in(z0), z0, tree(z0, void, void)))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(U2'(f25_in(z0), s(z0), tree(s(z0), void, void)))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(U3'(f63_in(z0), z0, tree(z0, void, void)))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(U4'(f25_in(z0), s(z0), tree(s(z0), void, void)))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(U13'(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(U14'(f154_in(z0, z2), z0, z1, z2))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(U17'(f25_in(z0), s(z0)))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(U18'(f42_in(z0), z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(U21'(f25_in(z0), s(z0)))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(U22'(f42_in(z0), z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
U23'(f30_out1, z0) → c(U24'(f1_in(s(z0), void), z0))
U23'(f30_out1, z0) → c(F1_IN(s(z0), void))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U25'(f30_out1, z0) → c(U26'(f1_in(z0, void), z0))
U25'(f30_out1, z0) → c(F1_IN(z0, void))
U33'(f159_out1, z0, z1) → c(U34'(f1_in(0, z1), z0, z1))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(U41'(f21_in(z0), f22_in(z0), z0))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(U42'(f64_in(z0), f65_in(z0), z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, f261_in, U11, f30_in, U12, f177_in, U13, f149_in, U14, f167_in, U15, f168_in, U16, f64_in, U17, f65_in, U18, f97_in, U19, f98_in, U20, f21_in, U21, f22_in, U22, f25_in, U23, U24, f42_in, U25, U26, f101_in, U27, U28, f110_in, U29, U30, f127_in, U31, U32, f154_in, U33, U34, f173_in, U35, U36, f270_in, U37, U38, f282_in, U39, U40, f18_in, U41, f63_in, U42, f96_in, U43, f144_in, U44, f147_in, U45, f277_in, U46

Defined Pair Symbols:

F1_IN, F261_IN, F30_IN, F167_IN, F168_IN, F97_IN, F98_IN, F101_IN, U27', F110_IN, U29', F127_IN, U31', F154_IN, F173_IN, U35', F270_IN, U37', F282_IN, U39', F96_IN, F144_IN, F147_IN, F277_IN, F177_IN, F149_IN, F64_IN, F65_IN, F21_IN, F22_IN, F25_IN, U23', F42_IN, U25', U33', F18_IN, F63_IN

Compound Symbols:

c7, c8, c9, c10, c11, c12, c31, c33, c46, c48, c54, c56, c68, c69, c71, c72, c74, c75, c77, c80, c81, c83, c84, c86, c87, c95, c98, c102, c105, c

(23) CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID) transformation)

Removed 40 trailing tuple parts

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, void)) → f1_out1(void)
f1_in(z0, tree(z0, void, void)) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, void, void)) → U1(f18_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U2(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, void, void)) → U3(f63_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U4(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U5(f96_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(s(z0), tree(s(z0), z1, z2)) → U6(f127_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f1_in(0, tree(s(z0), z1, z2)) → U7(f144_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f1_in(z0, tree(z1, z2, z3)) → U8(f147_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f1_in(s(z0), tree(0, z1, z2)) → U9(f277_in(z0, z2), s(z0), tree(0, z1, z2))
f1_in(s(z0), tree(s(z1), z2, z3)) → U10(f282_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f18_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U1(f18_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U2(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U3(f63_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U3(f63_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U4(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U5(f96_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(tree(z1, z0, z3))
U5(f96_out3(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U6(f127_out1(z0), s(z1), tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z2, z0))
U7(f144_out1(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out2(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out4(z0), 0, tree(s(z1), z2, z3)) → f1_out1(z0)
U8(f147_out1(z0), z1, tree(z2, z3, z4)) → f1_out1(tree(z2, z0, z4))
U8(f147_out3(z0), z1, tree(z2, z3, z4)) → f1_out1(z0)
U9(f277_out1(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U9(f277_out2(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U10(f282_out1(z0), s(z1), tree(s(z2), z3, z4)) → f1_out1(tree(s(z2), z3, z0))
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1
f149_in(z0, z1, z2) → U14(f154_in(z0, z2), z0, z1, z2)
U14(f154_out1(z0), z1, z2, z3) → f149_out3(tree(s(z1), z2, z0))
f167_in(s(z0), s(z1), z2) → U15(f173_in(z0, z1, z2), s(z0), s(z1), z2)
U15(f173_out1(z0), s(z1), s(z2), z3) → f167_out1(z0)
f168_in(z0, z1, z2, z3) → U16(f270_in(z1, z0, z3), z0, z1, z2, z3)
U16(f270_out1(z0), z1, z2, z3, z4) → f168_out2(tree(z2, z3, z0))
f64_in(s(z0)) → U17(f25_in(z0), s(z0))
U17(f25_out1(z0), s(z1)) → f64_out1(z0)
f65_in(z0) → U18(f42_in(z0), z0)
U18(f42_out1(z0), z1) → f65_out2(tree(z1, void, z0))
f97_in(s(z0), z1) → U19(f101_in(z0, z1), s(z0), z1)
U19(f101_out1(z0), s(z1), z2) → f97_out1(z0)
f98_in(z0, z1, z2) → U20(f110_in(z0, z2), z0, z1, z2)
U20(f110_out1(z0), z1, z2, z3) → f98_out2(tree(z1, z2, z0))
f21_in(s(z0)) → U21(f25_in(z0), s(z0))
U21(f25_out1(z0), s(z1)) → f21_out1(z0)
f22_in(z0) → U22(f42_in(z0), z0)
U22(f42_out1(z0), z1) → f22_out2(tree(z1, void, z0))
f25_in(z0) → U23(f30_in(z0), z0)
U23(f30_out1, z0) → U24(f1_in(s(z0), void), z0)
U24(f1_out1(z0), z1) → f25_out1(z0)
f42_in(z0) → U25(f30_in(z0), z0)
U25(f30_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1(z0), z1) → f42_out1(z0)
f101_in(z0, z1) → U27(f30_in(z0), z0, z1)
U27(f30_out1, z0, z1) → U28(f1_in(s(z0), z1), z0, z1)
U28(f1_out1(z0), z1, z2) → f101_out1(z0)
f110_in(z0, z1) → U29(f30_in(z0), z0, z1)
U29(f30_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1(z0), z1, z2) → f110_out1(z0)
f127_in(z0, z1) → U31(f30_in(z0), z0, z1)
U31(f30_out1, z0, z1) → U32(f1_in(s(z0), z1), z0, z1)
U32(f1_out1(z0), z1, z2) → f127_out1(z0)
f154_in(z0, z1) → U33(f159_in(z0), z0, z1)
U33(f159_out1, z0, z1) → U34(f1_in(0, z1), z0, z1)
U34(f1_out1(z0), z1, z2) → f154_out1(z0)
f173_in(z0, z1, z2) → U35(f177_in(z0, z1), z0, z1, z2)
U35(f177_out1, z0, z1, z2) → U36(f1_in(s(z0), z2), z0, z1, z2)
U36(f1_out1(z0), z1, z2, z3) → f173_out1(z0)
f270_in(z0, z1, z2) → U37(f261_in(z0, z1), z0, z1, z2)
U37(f261_out1, z0, z1, z2) → U38(f1_in(z1, z2), z0, z1, z2)
U38(f1_out1(z0), z1, z2, z3) → f270_out1(z0)
f282_in(z0, z1, z2) → U39(f261_in(z0, z1), z0, z1, z2)
U39(f261_out1, z0, z1, z2) → U40(f1_in(s(z1), z2), z0, z1, z2)
U40(f1_out1(z0), z1, z2, z3) → f282_out1(z0)
f18_in(z0) → U41(f21_in(z0), f22_in(z0), z0)
U41(f21_out1(z0), z1, z2) → f18_out1(z0)
U41(z0, f22_out2(z1), z2) → f18_out3(z1)
f63_in(z0) → U42(f64_in(z0), f65_in(z0), z0)
U42(f64_out1(z0), z1, z2) → f63_out1(z0)
U42(z0, f65_out2(z1), z2) → f63_out3(z1)
f96_in(z0, z1, z2) → U43(f97_in(z0, z1), f98_in(z0, z1, z2), z0, z1, z2)
U43(f97_out1(z0), z1, z2, z3, z4) → f96_out1(z0)
U43(z0, f98_out2(z1), z2, z3, z4) → f96_out3(z1)
f144_in(z0, z1, z2) → U44(f1_in(0, z0), f149_in(z1, z0, z2), z0, z1, z2)
U44(f1_out1(z0), z1, z2, z3, z4) → f144_out1(z0)
U44(z0, f149_out1(z1), z2, z3, z4) → f144_out2(z1)
U44(z0, f149_out3(z1), z2, z3, z4) → f144_out4(z1)
f147_in(z0, z1, z2, z3) → U45(f167_in(z0, z1, z2), f168_in(z0, z1, z2, z3), z0, z1, z2, z3)
U45(f167_out1(z0), z1, z2, z3, z4, z5) → f147_out1(z0)
U45(z0, f168_out2(z1), z2, z3, z4, z5) → f147_out3(z1)
f277_in(z0, z1) → U46(f1_in(s(z0), z1), f280_in(z0, z1), z0, z1)
U46(f1_out1(z0), z1, z2, z3) → f277_out1(z0)
U46(z0, f280_out1(z1), z2, z3) → f277_out2(z1)

Tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U33'(f159_out1, z0, z1) → c
F18_IN(z0) → c
F63_IN(z0) → c

S tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U33'(f159_out1, z0, z1) → c
F18_IN(z0) → c
F63_IN(z0) → c

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, f261_in, U11, f30_in, U12, f177_in, U13, f149_in, U14, f167_in, U15, f168_in, U16, f64_in, U17, f65_in, U18, f97_in, U19, f98_in, U20, f21_in, U21, f22_in, U22, f25_in, U23, U24, f42_in, U25, U26, f101_in, U27, U28, f110_in, U29, U30, f127_in, U31, U32, f154_in, U33, U34, f173_in, U35, U36, f270_in, U37, U38, f282_in, U39, U40, f18_in, U41, f63_in, U42, f96_in, U43, f144_in, U44, f147_in, U45, f277_in, U46

Defined Pair Symbols:

F101_IN, F110_IN, F127_IN, F173_IN, F270_IN, F282_IN, F1_IN, F177_IN, F149_IN, F64_IN, F65_IN, F21_IN, F22_IN, F25_IN, F42_IN, U33', F18_IN, F63_IN, F261_IN, F30_IN, F167_IN, F168_IN, F97_IN, F98_IN, U27', U29', U31', F154_IN, U35', U37', U39', F96_IN, F144_IN, F147_IN, F277_IN, U23', U25'

Compound Symbols:

c68, c71, c74, c80, c83, c86, c, c7, c8, c9, c10, c11, c12, c31, c33, c46, c48, c54, c56, c69, c72, c75, c77, c81, c84, c87, c95, c98, c102, c105, c

(25) CdtKnowledgeProof (EQUIVALENT transformation)

The following tuples could be moved from S to K by knowledge propagation:

U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
U33'(f159_out1, z0, z1) → c

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, void)) → f1_out1(void)
f1_in(z0, tree(z0, void, void)) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, void, void)) → U1(f18_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U2(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, void, void)) → U3(f63_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U4(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U5(f96_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(s(z0), tree(s(z0), z1, z2)) → U6(f127_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f1_in(0, tree(s(z0), z1, z2)) → U7(f144_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f1_in(z0, tree(z1, z2, z3)) → U8(f147_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f1_in(s(z0), tree(0, z1, z2)) → U9(f277_in(z0, z2), s(z0), tree(0, z1, z2))
f1_in(s(z0), tree(s(z1), z2, z3)) → U10(f282_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f18_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U1(f18_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U2(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U3(f63_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U3(f63_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U4(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U5(f96_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(tree(z1, z0, z3))
U5(f96_out3(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U6(f127_out1(z0), s(z1), tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z2, z0))
U7(f144_out1(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out2(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out4(z0), 0, tree(s(z1), z2, z3)) → f1_out1(z0)
U8(f147_out1(z0), z1, tree(z2, z3, z4)) → f1_out1(tree(z2, z0, z4))
U8(f147_out3(z0), z1, tree(z2, z3, z4)) → f1_out1(z0)
U9(f277_out1(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U9(f277_out2(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U10(f282_out1(z0), s(z1), tree(s(z2), z3, z4)) → f1_out1(tree(s(z2), z3, z0))
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1
f149_in(z0, z1, z2) → U14(f154_in(z0, z2), z0, z1, z2)
U14(f154_out1(z0), z1, z2, z3) → f149_out3(tree(s(z1), z2, z0))
f167_in(s(z0), s(z1), z2) → U15(f173_in(z0, z1, z2), s(z0), s(z1), z2)
U15(f173_out1(z0), s(z1), s(z2), z3) → f167_out1(z0)
f168_in(z0, z1, z2, z3) → U16(f270_in(z1, z0, z3), z0, z1, z2, z3)
U16(f270_out1(z0), z1, z2, z3, z4) → f168_out2(tree(z2, z3, z0))
f64_in(s(z0)) → U17(f25_in(z0), s(z0))
U17(f25_out1(z0), s(z1)) → f64_out1(z0)
f65_in(z0) → U18(f42_in(z0), z0)
U18(f42_out1(z0), z1) → f65_out2(tree(z1, void, z0))
f97_in(s(z0), z1) → U19(f101_in(z0, z1), s(z0), z1)
U19(f101_out1(z0), s(z1), z2) → f97_out1(z0)
f98_in(z0, z1, z2) → U20(f110_in(z0, z2), z0, z1, z2)
U20(f110_out1(z0), z1, z2, z3) → f98_out2(tree(z1, z2, z0))
f21_in(s(z0)) → U21(f25_in(z0), s(z0))
U21(f25_out1(z0), s(z1)) → f21_out1(z0)
f22_in(z0) → U22(f42_in(z0), z0)
U22(f42_out1(z0), z1) → f22_out2(tree(z1, void, z0))
f25_in(z0) → U23(f30_in(z0), z0)
U23(f30_out1, z0) → U24(f1_in(s(z0), void), z0)
U24(f1_out1(z0), z1) → f25_out1(z0)
f42_in(z0) → U25(f30_in(z0), z0)
U25(f30_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1(z0), z1) → f42_out1(z0)
f101_in(z0, z1) → U27(f30_in(z0), z0, z1)
U27(f30_out1, z0, z1) → U28(f1_in(s(z0), z1), z0, z1)
U28(f1_out1(z0), z1, z2) → f101_out1(z0)
f110_in(z0, z1) → U29(f30_in(z0), z0, z1)
U29(f30_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1(z0), z1, z2) → f110_out1(z0)
f127_in(z0, z1) → U31(f30_in(z0), z0, z1)
U31(f30_out1, z0, z1) → U32(f1_in(s(z0), z1), z0, z1)
U32(f1_out1(z0), z1, z2) → f127_out1(z0)
f154_in(z0, z1) → U33(f159_in(z0), z0, z1)
U33(f159_out1, z0, z1) → U34(f1_in(0, z1), z0, z1)
U34(f1_out1(z0), z1, z2) → f154_out1(z0)
f173_in(z0, z1, z2) → U35(f177_in(z0, z1), z0, z1, z2)
U35(f177_out1, z0, z1, z2) → U36(f1_in(s(z0), z2), z0, z1, z2)
U36(f1_out1(z0), z1, z2, z3) → f173_out1(z0)
f270_in(z0, z1, z2) → U37(f261_in(z0, z1), z0, z1, z2)
U37(f261_out1, z0, z1, z2) → U38(f1_in(z1, z2), z0, z1, z2)
U38(f1_out1(z0), z1, z2, z3) → f270_out1(z0)
f282_in(z0, z1, z2) → U39(f261_in(z0, z1), z0, z1, z2)
U39(f261_out1, z0, z1, z2) → U40(f1_in(s(z1), z2), z0, z1, z2)
U40(f1_out1(z0), z1, z2, z3) → f282_out1(z0)
f18_in(z0) → U41(f21_in(z0), f22_in(z0), z0)
U41(f21_out1(z0), z1, z2) → f18_out1(z0)
U41(z0, f22_out2(z1), z2) → f18_out3(z1)
f63_in(z0) → U42(f64_in(z0), f65_in(z0), z0)
U42(f64_out1(z0), z1, z2) → f63_out1(z0)
U42(z0, f65_out2(z1), z2) → f63_out3(z1)
f96_in(z0, z1, z2) → U43(f97_in(z0, z1), f98_in(z0, z1, z2), z0, z1, z2)
U43(f97_out1(z0), z1, z2, z3, z4) → f96_out1(z0)
U43(z0, f98_out2(z1), z2, z3, z4) → f96_out3(z1)
f144_in(z0, z1, z2) → U44(f1_in(0, z0), f149_in(z1, z0, z2), z0, z1, z2)
U44(f1_out1(z0), z1, z2, z3, z4) → f144_out1(z0)
U44(z0, f149_out1(z1), z2, z3, z4) → f144_out2(z1)
U44(z0, f149_out3(z1), z2, z3, z4) → f144_out4(z1)
f147_in(z0, z1, z2, z3) → U45(f167_in(z0, z1, z2), f168_in(z0, z1, z2, z3), z0, z1, z2, z3)
U45(f167_out1(z0), z1, z2, z3, z4, z5) → f147_out1(z0)
U45(z0, f168_out2(z1), z2, z3, z4, z5) → f147_out3(z1)
f277_in(z0, z1) → U46(f1_in(s(z0), z1), f280_in(z0, z1), z0, z1)
U46(f1_out1(z0), z1, z2, z3) → f277_out1(z0)
U46(z0, f280_out1(z1), z2, z3) → f277_out2(z1)

Tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U33'(f159_out1, z0, z1) → c
F18_IN(z0) → c
F63_IN(z0) → c

S tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
F18_IN(z0) → c
F63_IN(z0) → c

K tuples:

U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
U33'(f159_out1, z0, z1) → c

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, f261_in, U11, f30_in, U12, f177_in, U13, f149_in, U14, f167_in, U15, f168_in, U16, f64_in, U17, f65_in, U18, f97_in, U19, f98_in, U20, f21_in, U21, f22_in, U22, f25_in, U23, U24, f42_in, U25, U26, f101_in, U27, U28, f110_in, U29, U30, f127_in, U31, U32, f154_in, U33, U34, f173_in, U35, U36, f270_in, U37, U38, f282_in, U39, U40, f18_in, U41, f63_in, U42, f96_in, U43, f144_in, U44, f147_in, U45, f277_in, U46

Defined Pair Symbols:

F101_IN, F110_IN, F127_IN, F173_IN, F270_IN, F282_IN, F1_IN, F177_IN, F149_IN, F64_IN, F65_IN, F21_IN, F22_IN, F25_IN, F42_IN, U33', F18_IN, F63_IN, F261_IN, F30_IN, F167_IN, F168_IN, F97_IN, F98_IN, U27', U29', U31', F154_IN, U35', U37', U39', F96_IN, F144_IN, F147_IN, F277_IN, U23', U25'

Compound Symbols:

c68, c71, c74, c80, c83, c86, c, c7, c8, c9, c10, c11, c12, c31, c33, c46, c48, c54, c56, c69, c72, c75, c77, c81, c84, c87, c95, c98, c102, c105, c

(27) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F65_IN(z0) → c
F63_IN(z0) → c

We considered the (Usable) Rules:

f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1

And the Tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U33'(f159_out1, z0, z1) → c
F18_IN(z0) → c
F63_IN(z0) → c

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(0) = 0
POL(F101_IN(x₁, x₂)) = x₂
POL(F110_IN(x₁, x₂)) = x₂
POL(F127_IN(x₁, x₂)) = x₂
POL(F144_IN(x₁, x₂, x₃)) = x₁ + x₃
POL(F147_IN(x₁, x₂, x₃, x₄)) = x₃ + x₄
POL(F149_IN(x₁, x₂, x₃)) = 0
POL(F154_IN(x₁, x₂)) = 0
POL(F167_IN(x₁, x₂, x₃)) = x₃
POL(F168_IN(x₁, x₂, x₃, x₄)) = x₄
POL(F173_IN(x₁, x₂, x₃)) = x₃
POL(F177_IN(x₁, x₂)) = 0
POL(F18_IN(x₁)) = 0
POL(F1_IN(x₁, x₂)) = x₂
POL(F21_IN(x₁)) = 0
POL(F22_IN(x₁)) = 0
POL(F25_IN(x₁)) = 0
POL(F261_IN(x₁, x₂)) = 0
POL(F270_IN(x₁, x₂, x₃)) = x₃
POL(F277_IN(x₁, x₂)) = x₂
POL(F282_IN(x₁, x₂, x₃)) = x₃
POL(F30_IN(x₁)) = 0
POL(F42_IN(x₁)) = 0
POL(F63_IN(x₁)) = [1]
POL(F64_IN(x₁)) = 0
POL(F65_IN(x₁)) = [1]
POL(F96_IN(x₁, x₂, x₃)) = x₂ + x₃
POL(F97_IN(x₁, x₂)) = x₂
POL(F98_IN(x₁, x₂, x₃)) = x₃
POL(U11(x₁, x₂, x₃)) = 0
POL(U12(x₁, x₂)) = 0
POL(U13(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U27'(x₁, x₂, x₃)) = x₃
POL(U29'(x₁, x₂, x₃)) = x₃
POL(U31'(x₁, x₂, x₃)) = x₃
POL(U33'(x₁, x₂, x₃)) = x₃
POL(U35'(x₁, x₂, x₃, x₄)) = x₄
POL(U37'(x₁, x₂, x₃, x₄)) = x₄
POL(U39'(x₁, x₂, x₃, x₄)) = x₄
POL(c) = 0
POL(c(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c102(x₁, x₂)) = x₁ + x₂
POL(c105(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c68(x₁, x₂)) = x₁ + x₂
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c71(x₁, x₂)) = x₁ + x₂
POL(c72(x₁)) = x₁
POL(c74(x₁, x₂)) = x₁ + x₂
POL(c75(x₁)) = x₁
POL(c77) = 0
POL(c8(x₁)) = x₁
POL(c80(x₁, x₂)) = x₁ + x₂
POL(c81(x₁)) = x₁
POL(c83(x₁, x₂)) = x₁ + x₂
POL(c84(x₁)) = x₁
POL(c86(x₁, x₂)) = x₁ + x₂
POL(c87(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(c95(x₁, x₂)) = x₁ + x₂
POL(c98(x₁, x₂)) = x₁ + x₂
POL(f159_out1) = 0
POL(f177_in(x₁, x₂)) = 0
POL(f177_out1) = 0
POL(f261_in(x₁, x₂)) = 0
POL(f261_out1) = 0
POL(f30_in(x₁)) = 0
POL(f30_out1) = 0
POL(s(x₁)) = 0
POL(tree(x₁, x₂, x₃)) = x₂ + x₃
POL(void) = [2]

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, void)) → f1_out1(void)
f1_in(z0, tree(z0, void, void)) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, void, void)) → U1(f18_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U2(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, void, void)) → U3(f63_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U4(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U5(f96_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(s(z0), tree(s(z0), z1, z2)) → U6(f127_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f1_in(0, tree(s(z0), z1, z2)) → U7(f144_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f1_in(z0, tree(z1, z2, z3)) → U8(f147_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f1_in(s(z0), tree(0, z1, z2)) → U9(f277_in(z0, z2), s(z0), tree(0, z1, z2))
f1_in(s(z0), tree(s(z1), z2, z3)) → U10(f282_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f18_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U1(f18_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U2(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U3(f63_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U3(f63_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U4(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U5(f96_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(tree(z1, z0, z3))
U5(f96_out3(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U6(f127_out1(z0), s(z1), tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z2, z0))
U7(f144_out1(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out2(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out4(z0), 0, tree(s(z1), z2, z3)) → f1_out1(z0)
U8(f147_out1(z0), z1, tree(z2, z3, z4)) → f1_out1(tree(z2, z0, z4))
U8(f147_out3(z0), z1, tree(z2, z3, z4)) → f1_out1(z0)
U9(f277_out1(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U9(f277_out2(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U10(f282_out1(z0), s(z1), tree(s(z2), z3, z4)) → f1_out1(tree(s(z2), z3, z0))
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1
f149_in(z0, z1, z2) → U14(f154_in(z0, z2), z0, z1, z2)
U14(f154_out1(z0), z1, z2, z3) → f149_out3(tree(s(z1), z2, z0))
f167_in(s(z0), s(z1), z2) → U15(f173_in(z0, z1, z2), s(z0), s(z1), z2)
U15(f173_out1(z0), s(z1), s(z2), z3) → f167_out1(z0)
f168_in(z0, z1, z2, z3) → U16(f270_in(z1, z0, z3), z0, z1, z2, z3)
U16(f270_out1(z0), z1, z2, z3, z4) → f168_out2(tree(z2, z3, z0))
f64_in(s(z0)) → U17(f25_in(z0), s(z0))
U17(f25_out1(z0), s(z1)) → f64_out1(z0)
f65_in(z0) → U18(f42_in(z0), z0)
U18(f42_out1(z0), z1) → f65_out2(tree(z1, void, z0))
f97_in(s(z0), z1) → U19(f101_in(z0, z1), s(z0), z1)
U19(f101_out1(z0), s(z1), z2) → f97_out1(z0)
f98_in(z0, z1, z2) → U20(f110_in(z0, z2), z0, z1, z2)
U20(f110_out1(z0), z1, z2, z3) → f98_out2(tree(z1, z2, z0))
f21_in(s(z0)) → U21(f25_in(z0), s(z0))
U21(f25_out1(z0), s(z1)) → f21_out1(z0)
f22_in(z0) → U22(f42_in(z0), z0)
U22(f42_out1(z0), z1) → f22_out2(tree(z1, void, z0))
f25_in(z0) → U23(f30_in(z0), z0)
U23(f30_out1, z0) → U24(f1_in(s(z0), void), z0)
U24(f1_out1(z0), z1) → f25_out1(z0)
f42_in(z0) → U25(f30_in(z0), z0)
U25(f30_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1(z0), z1) → f42_out1(z0)
f101_in(z0, z1) → U27(f30_in(z0), z0, z1)
U27(f30_out1, z0, z1) → U28(f1_in(s(z0), z1), z0, z1)
U28(f1_out1(z0), z1, z2) → f101_out1(z0)
f110_in(z0, z1) → U29(f30_in(z0), z0, z1)
U29(f30_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1(z0), z1, z2) → f110_out1(z0)
f127_in(z0, z1) → U31(f30_in(z0), z0, z1)
U31(f30_out1, z0, z1) → U32(f1_in(s(z0), z1), z0, z1)
U32(f1_out1(z0), z1, z2) → f127_out1(z0)
f154_in(z0, z1) → U33(f159_in(z0), z0, z1)
U33(f159_out1, z0, z1) → U34(f1_in(0, z1), z0, z1)
U34(f1_out1(z0), z1, z2) → f154_out1(z0)
f173_in(z0, z1, z2) → U35(f177_in(z0, z1), z0, z1, z2)
U35(f177_out1, z0, z1, z2) → U36(f1_in(s(z0), z2), z0, z1, z2)
U36(f1_out1(z0), z1, z2, z3) → f173_out1(z0)
f270_in(z0, z1, z2) → U37(f261_in(z0, z1), z0, z1, z2)
U37(f261_out1, z0, z1, z2) → U38(f1_in(z1, z2), z0, z1, z2)
U38(f1_out1(z0), z1, z2, z3) → f270_out1(z0)
f282_in(z0, z1, z2) → U39(f261_in(z0, z1), z0, z1, z2)
U39(f261_out1, z0, z1, z2) → U40(f1_in(s(z1), z2), z0, z1, z2)
U40(f1_out1(z0), z1, z2, z3) → f282_out1(z0)
f18_in(z0) → U41(f21_in(z0), f22_in(z0), z0)
U41(f21_out1(z0), z1, z2) → f18_out1(z0)
U41(z0, f22_out2(z1), z2) → f18_out3(z1)
f63_in(z0) → U42(f64_in(z0), f65_in(z0), z0)
U42(f64_out1(z0), z1, z2) → f63_out1(z0)
U42(z0, f65_out2(z1), z2) → f63_out3(z1)
f96_in(z0, z1, z2) → U43(f97_in(z0, z1), f98_in(z0, z1, z2), z0, z1, z2)
U43(f97_out1(z0), z1, z2, z3, z4) → f96_out1(z0)
U43(z0, f98_out2(z1), z2, z3, z4) → f96_out3(z1)
f144_in(z0, z1, z2) → U44(f1_in(0, z0), f149_in(z1, z0, z2), z0, z1, z2)
U44(f1_out1(z0), z1, z2, z3, z4) → f144_out1(z0)
U44(z0, f149_out1(z1), z2, z3, z4) → f144_out2(z1)
U44(z0, f149_out3(z1), z2, z3, z4) → f144_out4(z1)
f147_in(z0, z1, z2, z3) → U45(f167_in(z0, z1, z2), f168_in(z0, z1, z2, z3), z0, z1, z2, z3)
U45(f167_out1(z0), z1, z2, z3, z4, z5) → f147_out1(z0)
U45(z0, f168_out2(z1), z2, z3, z4, z5) → f147_out3(z1)
f277_in(z0, z1) → U46(f1_in(s(z0), z1), f280_in(z0, z1), z0, z1)
U46(f1_out1(z0), z1, z2, z3) → f277_out1(z0)
U46(z0, f280_out1(z1), z2, z3) → f277_out2(z1)

Tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U33'(f159_out1, z0, z1) → c
F18_IN(z0) → c
F63_IN(z0) → c

S tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
F18_IN(z0) → c

K tuples:

U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
U33'(f159_out1, z0, z1) → c
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F65_IN(z0) → c
F63_IN(z0) → c

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, f261_in, U11, f30_in, U12, f177_in, U13, f149_in, U14, f167_in, U15, f168_in, U16, f64_in, U17, f65_in, U18, f97_in, U19, f98_in, U20, f21_in, U21, f22_in, U22, f25_in, U23, U24, f42_in, U25, U26, f101_in, U27, U28, f110_in, U29, U30, f127_in, U31, U32, f154_in, U33, U34, f173_in, U35, U36, f270_in, U37, U38, f282_in, U39, U40, f18_in, U41, f63_in, U42, f96_in, U43, f144_in, U44, f147_in, U45, f277_in, U46

Defined Pair Symbols:

F101_IN, F110_IN, F127_IN, F173_IN, F270_IN, F282_IN, F1_IN, F177_IN, F149_IN, F64_IN, F65_IN, F21_IN, F22_IN, F25_IN, F42_IN, U33', F18_IN, F63_IN, F261_IN, F30_IN, F167_IN, F168_IN, F97_IN, F98_IN, U27', U29', U31', F154_IN, U35', U37', U39', F96_IN, F144_IN, F147_IN, F277_IN, U23', U25'

Compound Symbols:

c68, c71, c74, c80, c83, c86, c, c7, c8, c9, c10, c11, c12, c31, c33, c46, c48, c54, c56, c69, c72, c75, c77, c81, c84, c87, c95, c98, c102, c105, c

(29) CdtKnowledgeProof (EQUIVALENT transformation)

The following tuples could be moved from S to K by knowledge propagation:

F64_IN(s(z0)) → c(F25_IN(z0))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F64_IN(s(z0)) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
F18_IN(z0) → c
F21_IN(s(z0)) → c(F25_IN(z0))
F21_IN(s(z0)) → c
F22_IN(z0) → c(F42_IN(z0))
F22_IN(z0) → c
F65_IN(z0) → c(F42_IN(z0))
F65_IN(z0) → c
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U23'(f30_out1, z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U25'(f30_out1, z0) → c

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, void)) → f1_out1(void)
f1_in(z0, tree(z0, void, void)) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, void, void)) → U1(f18_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U2(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, void, void)) → U3(f63_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U4(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U5(f96_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(s(z0), tree(s(z0), z1, z2)) → U6(f127_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f1_in(0, tree(s(z0), z1, z2)) → U7(f144_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f1_in(z0, tree(z1, z2, z3)) → U8(f147_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f1_in(s(z0), tree(0, z1, z2)) → U9(f277_in(z0, z2), s(z0), tree(0, z1, z2))
f1_in(s(z0), tree(s(z1), z2, z3)) → U10(f282_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f18_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U1(f18_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U2(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U3(f63_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U3(f63_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U4(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U5(f96_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(tree(z1, z0, z3))
U5(f96_out3(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U6(f127_out1(z0), s(z1), tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z2, z0))
U7(f144_out1(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out2(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out4(z0), 0, tree(s(z1), z2, z3)) → f1_out1(z0)
U8(f147_out1(z0), z1, tree(z2, z3, z4)) → f1_out1(tree(z2, z0, z4))
U8(f147_out3(z0), z1, tree(z2, z3, z4)) → f1_out1(z0)
U9(f277_out1(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U9(f277_out2(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U10(f282_out1(z0), s(z1), tree(s(z2), z3, z4)) → f1_out1(tree(s(z2), z3, z0))
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1
f149_in(z0, z1, z2) → U14(f154_in(z0, z2), z0, z1, z2)
U14(f154_out1(z0), z1, z2, z3) → f149_out3(tree(s(z1), z2, z0))
f167_in(s(z0), s(z1), z2) → U15(f173_in(z0, z1, z2), s(z0), s(z1), z2)
U15(f173_out1(z0), s(z1), s(z2), z3) → f167_out1(z0)
f168_in(z0, z1, z2, z3) → U16(f270_in(z1, z0, z3), z0, z1, z2, z3)
U16(f270_out1(z0), z1, z2, z3, z4) → f168_out2(tree(z2, z3, z0))
f64_in(s(z0)) → U17(f25_in(z0), s(z0))
U17(f25_out1(z0), s(z1)) → f64_out1(z0)
f65_in(z0) → U18(f42_in(z0), z0)
U18(f42_out1(z0), z1) → f65_out2(tree(z1, void, z0))
f97_in(s(z0), z1) → U19(f101_in(z0, z1), s(z0), z1)
U19(f101_out1(z0), s(z1), z2) → f97_out1(z0)
f98_in(z0, z1, z2) → U20(f110_in(z0, z2), z0, z1, z2)
U20(f110_out1(z0), z1, z2, z3) → f98_out2(tree(z1, z2, z0))
f21_in(s(z0)) → U21(f25_in(z0), s(z0))
U21(f25_out1(z0), s(z1)) → f21_out1(z0)
f22_in(z0) → U22(f42_in(z0), z0)
U22(f42_out1(z0), z1) → f22_out2(tree(z1, void, z0))
f25_in(z0) → U23(f30_in(z0), z0)
U23(f30_out1, z0) → U24(f1_in(s(z0), void), z0)
U24(f1_out1(z0), z1) → f25_out1(z0)
f42_in(z0) → U25(f30_in(z0), z0)
U25(f30_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1(z0), z1) → f42_out1(z0)
f101_in(z0, z1) → U27(f30_in(z0), z0, z1)
U27(f30_out1, z0, z1) → U28(f1_in(s(z0), z1), z0, z1)
U28(f1_out1(z0), z1, z2) → f101_out1(z0)
f110_in(z0, z1) → U29(f30_in(z0), z0, z1)
U29(f30_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1(z0), z1, z2) → f110_out1(z0)
f127_in(z0, z1) → U31(f30_in(z0), z0, z1)
U31(f30_out1, z0, z1) → U32(f1_in(s(z0), z1), z0, z1)
U32(f1_out1(z0), z1, z2) → f127_out1(z0)
f154_in(z0, z1) → U33(f159_in(z0), z0, z1)
U33(f159_out1, z0, z1) → U34(f1_in(0, z1), z0, z1)
U34(f1_out1(z0), z1, z2) → f154_out1(z0)
f173_in(z0, z1, z2) → U35(f177_in(z0, z1), z0, z1, z2)
U35(f177_out1, z0, z1, z2) → U36(f1_in(s(z0), z2), z0, z1, z2)
U36(f1_out1(z0), z1, z2, z3) → f173_out1(z0)
f270_in(z0, z1, z2) → U37(f261_in(z0, z1), z0, z1, z2)
U37(f261_out1, z0, z1, z2) → U38(f1_in(z1, z2), z0, z1, z2)
U38(f1_out1(z0), z1, z2, z3) → f270_out1(z0)
f282_in(z0, z1, z2) → U39(f261_in(z0, z1), z0, z1, z2)
U39(f261_out1, z0, z1, z2) → U40(f1_in(s(z1), z2), z0, z1, z2)
U40(f1_out1(z0), z1, z2, z3) → f282_out1(z0)
f18_in(z0) → U41(f21_in(z0), f22_in(z0), z0)
U41(f21_out1(z0), z1, z2) → f18_out1(z0)
U41(z0, f22_out2(z1), z2) → f18_out3(z1)
f63_in(z0) → U42(f64_in(z0), f65_in(z0), z0)
U42(f64_out1(z0), z1, z2) → f63_out1(z0)
U42(z0, f65_out2(z1), z2) → f63_out3(z1)
f96_in(z0, z1, z2) → U43(f97_in(z0, z1), f98_in(z0, z1, z2), z0, z1, z2)
U43(f97_out1(z0), z1, z2, z3, z4) → f96_out1(z0)
U43(z0, f98_out2(z1), z2, z3, z4) → f96_out3(z1)
f144_in(z0, z1, z2) → U44(f1_in(0, z0), f149_in(z1, z0, z2), z0, z1, z2)
U44(f1_out1(z0), z1, z2, z3, z4) → f144_out1(z0)
U44(z0, f149_out1(z1), z2, z3, z4) → f144_out2(z1)
U44(z0, f149_out3(z1), z2, z3, z4) → f144_out4(z1)
f147_in(z0, z1, z2, z3) → U45(f167_in(z0, z1, z2), f168_in(z0, z1, z2, z3), z0, z1, z2, z3)
U45(f167_out1(z0), z1, z2, z3, z4, z5) → f147_out1(z0)
U45(z0, f168_out2(z1), z2, z3, z4, z5) → f147_out3(z1)
f277_in(z0, z1) → U46(f1_in(s(z0), z1), f280_in(z0, z1), z0, z1)
U46(f1_out1(z0), z1, z2, z3) → f277_out1(z0)
U46(z0, f280_out1(z1), z2, z3) → f277_out2(z1)

Tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U33'(f159_out1, z0, z1) → c
F18_IN(z0) → c
F63_IN(z0) → c

S tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c

K tuples:

U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
U33'(f159_out1, z0, z1) → c
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F65_IN(z0) → c
F63_IN(z0) → c
F64_IN(s(z0)) → c(F25_IN(z0))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F64_IN(s(z0)) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
F18_IN(z0) → c
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, f261_in, U11, f30_in, U12, f177_in, U13, f149_in, U14, f167_in, U15, f168_in, U16, f64_in, U17, f65_in, U18, f97_in, U19, f98_in, U20, f21_in, U21, f22_in, U22, f25_in, U23, U24, f42_in, U25, U26, f101_in, U27, U28, f110_in, U29, U30, f127_in, U31, U32, f154_in, U33, U34, f173_in, U35, U36, f270_in, U37, U38, f282_in, U39, U40, f18_in, U41, f63_in, U42, f96_in, U43, f144_in, U44, f147_in, U45, f277_in, U46

Defined Pair Symbols:

F101_IN, F110_IN, F127_IN, F173_IN, F270_IN, F282_IN, F1_IN, F177_IN, F149_IN, F64_IN, F65_IN, F21_IN, F22_IN, F25_IN, F42_IN, U33', F18_IN, F63_IN, F261_IN, F30_IN, F167_IN, F168_IN, F97_IN, F98_IN, U27', U29', U31', F154_IN, U35', U37', U39', F96_IN, F144_IN, F147_IN, F277_IN, U23', U25'

Compound Symbols:

c68, c71, c74, c80, c83, c86, c, c7, c8, c9, c10, c11, c12, c31, c33, c46, c48, c54, c56, c69, c72, c75, c77, c81, c84, c87, c95, c98, c102, c105, c

(31) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))

We considered the (Usable) Rules:

f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1

And the Tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U33'(f159_out1, z0, z1) → c
F18_IN(z0) → c
F63_IN(z0) → c

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(0) = 0
POL(F101_IN(x₁, x₂)) = 0
POL(F110_IN(x₁, x₂)) = 0
POL(F127_IN(x₁, x₂)) = 0
POL(F144_IN(x₁, x₂, x₃)) = 0
POL(F147_IN(x₁, x₂, x₃, x₄)) = 0
POL(F149_IN(x₁, x₂, x₃)) = 0
POL(F154_IN(x₁, x₂)) = 0
POL(F167_IN(x₁, x₂, x₃)) = 0
POL(F168_IN(x₁, x₂, x₃, x₄)) = 0
POL(F173_IN(x₁, x₂, x₃)) = 0
POL(F177_IN(x₁, x₂)) = 0
POL(F18_IN(x₁)) = 0
POL(F1_IN(x₁, x₂)) = 0
POL(F21_IN(x₁)) = 0
POL(F22_IN(x₁)) = 0
POL(F25_IN(x₁)) = 0
POL(F261_IN(x₁, x₂)) = 0
POL(F270_IN(x₁, x₂, x₃)) = 0
POL(F277_IN(x₁, x₂)) = 0
POL(F282_IN(x₁, x₂, x₃)) = 0
POL(F30_IN(x₁)) = 0
POL(F42_IN(x₁)) = 0
POL(F63_IN(x₁)) = 0
POL(F64_IN(x₁)) = 0
POL(F65_IN(x₁)) = 0
POL(F96_IN(x₁, x₂, x₃)) = 0
POL(F97_IN(x₁, x₂)) = 0
POL(F98_IN(x₁, x₂, x₃)) = 0
POL(U11(x₁, x₂, x₃)) = 0
POL(U12(x₁, x₂)) = [2]x₁
POL(U13(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U27'(x₁, x₂, x₃)) = [3]x₁
POL(U29'(x₁, x₂, x₃)) = x₁
POL(U31'(x₁, x₂, x₃)) = x₁
POL(U33'(x₁, x₂, x₃)) = [2]x₁
POL(U35'(x₁, x₂, x₃, x₄)) = 0
POL(U37'(x₁, x₂, x₃, x₄)) = 0
POL(U39'(x₁, x₂, x₃, x₄)) = 0
POL(c) = 0
POL(c(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c102(x₁, x₂)) = x₁ + x₂
POL(c105(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c68(x₁, x₂)) = x₁ + x₂
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c71(x₁, x₂)) = x₁ + x₂
POL(c72(x₁)) = x₁
POL(c74(x₁, x₂)) = x₁ + x₂
POL(c75(x₁)) = x₁
POL(c77) = 0
POL(c8(x₁)) = x₁
POL(c80(x₁, x₂)) = x₁ + x₂
POL(c81(x₁)) = x₁
POL(c83(x₁, x₂)) = x₁ + x₂
POL(c84(x₁)) = x₁
POL(c86(x₁, x₂)) = x₁ + x₂
POL(c87(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(c95(x₁, x₂)) = x₁ + x₂
POL(c98(x₁, x₂)) = x₁ + x₂
POL(f159_out1) = [2]
POL(f177_in(x₁, x₂)) = 0
POL(f177_out1) = 0
POL(f261_in(x₁, x₂)) = 0
POL(f261_out1) = 0
POL(f30_in(x₁)) = 0
POL(f30_out1) = [1]
POL(s(x₁)) = 0
POL(tree(x₁, x₂, x₃)) = 0
POL(void) = 0

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, void)) → f1_out1(void)
f1_in(z0, tree(z0, void, void)) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, void, void)) → U1(f18_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U2(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, void, void)) → U3(f63_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U4(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U5(f96_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(s(z0), tree(s(z0), z1, z2)) → U6(f127_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f1_in(0, tree(s(z0), z1, z2)) → U7(f144_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f1_in(z0, tree(z1, z2, z3)) → U8(f147_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f1_in(s(z0), tree(0, z1, z2)) → U9(f277_in(z0, z2), s(z0), tree(0, z1, z2))
f1_in(s(z0), tree(s(z1), z2, z3)) → U10(f282_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f18_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U1(f18_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U2(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U3(f63_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U3(f63_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U4(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U5(f96_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(tree(z1, z0, z3))
U5(f96_out3(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U6(f127_out1(z0), s(z1), tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z2, z0))
U7(f144_out1(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out2(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out4(z0), 0, tree(s(z1), z2, z3)) → f1_out1(z0)
U8(f147_out1(z0), z1, tree(z2, z3, z4)) → f1_out1(tree(z2, z0, z4))
U8(f147_out3(z0), z1, tree(z2, z3, z4)) → f1_out1(z0)
U9(f277_out1(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U9(f277_out2(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U10(f282_out1(z0), s(z1), tree(s(z2), z3, z4)) → f1_out1(tree(s(z2), z3, z0))
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1
f149_in(z0, z1, z2) → U14(f154_in(z0, z2), z0, z1, z2)
U14(f154_out1(z0), z1, z2, z3) → f149_out3(tree(s(z1), z2, z0))
f167_in(s(z0), s(z1), z2) → U15(f173_in(z0, z1, z2), s(z0), s(z1), z2)
U15(f173_out1(z0), s(z1), s(z2), z3) → f167_out1(z0)
f168_in(z0, z1, z2, z3) → U16(f270_in(z1, z0, z3), z0, z1, z2, z3)
U16(f270_out1(z0), z1, z2, z3, z4) → f168_out2(tree(z2, z3, z0))
f64_in(s(z0)) → U17(f25_in(z0), s(z0))
U17(f25_out1(z0), s(z1)) → f64_out1(z0)
f65_in(z0) → U18(f42_in(z0), z0)
U18(f42_out1(z0), z1) → f65_out2(tree(z1, void, z0))
f97_in(s(z0), z1) → U19(f101_in(z0, z1), s(z0), z1)
U19(f101_out1(z0), s(z1), z2) → f97_out1(z0)
f98_in(z0, z1, z2) → U20(f110_in(z0, z2), z0, z1, z2)
U20(f110_out1(z0), z1, z2, z3) → f98_out2(tree(z1, z2, z0))
f21_in(s(z0)) → U21(f25_in(z0), s(z0))
U21(f25_out1(z0), s(z1)) → f21_out1(z0)
f22_in(z0) → U22(f42_in(z0), z0)
U22(f42_out1(z0), z1) → f22_out2(tree(z1, void, z0))
f25_in(z0) → U23(f30_in(z0), z0)
U23(f30_out1, z0) → U24(f1_in(s(z0), void), z0)
U24(f1_out1(z0), z1) → f25_out1(z0)
f42_in(z0) → U25(f30_in(z0), z0)
U25(f30_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1(z0), z1) → f42_out1(z0)
f101_in(z0, z1) → U27(f30_in(z0), z0, z1)
U27(f30_out1, z0, z1) → U28(f1_in(s(z0), z1), z0, z1)
U28(f1_out1(z0), z1, z2) → f101_out1(z0)
f110_in(z0, z1) → U29(f30_in(z0), z0, z1)
U29(f30_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1(z0), z1, z2) → f110_out1(z0)
f127_in(z0, z1) → U31(f30_in(z0), z0, z1)
U31(f30_out1, z0, z1) → U32(f1_in(s(z0), z1), z0, z1)
U32(f1_out1(z0), z1, z2) → f127_out1(z0)
f154_in(z0, z1) → U33(f159_in(z0), z0, z1)
U33(f159_out1, z0, z1) → U34(f1_in(0, z1), z0, z1)
U34(f1_out1(z0), z1, z2) → f154_out1(z0)
f173_in(z0, z1, z2) → U35(f177_in(z0, z1), z0, z1, z2)
U35(f177_out1, z0, z1, z2) → U36(f1_in(s(z0), z2), z0, z1, z2)
U36(f1_out1(z0), z1, z2, z3) → f173_out1(z0)
f270_in(z0, z1, z2) → U37(f261_in(z0, z1), z0, z1, z2)
U37(f261_out1, z0, z1, z2) → U38(f1_in(z1, z2), z0, z1, z2)
U38(f1_out1(z0), z1, z2, z3) → f270_out1(z0)
f282_in(z0, z1, z2) → U39(f261_in(z0, z1), z0, z1, z2)
U39(f261_out1, z0, z1, z2) → U40(f1_in(s(z1), z2), z0, z1, z2)
U40(f1_out1(z0), z1, z2, z3) → f282_out1(z0)
f18_in(z0) → U41(f21_in(z0), f22_in(z0), z0)
U41(f21_out1(z0), z1, z2) → f18_out1(z0)
U41(z0, f22_out2(z1), z2) → f18_out3(z1)
f63_in(z0) → U42(f64_in(z0), f65_in(z0), z0)
U42(f64_out1(z0), z1, z2) → f63_out1(z0)
U42(z0, f65_out2(z1), z2) → f63_out3(z1)
f96_in(z0, z1, z2) → U43(f97_in(z0, z1), f98_in(z0, z1, z2), z0, z1, z2)
U43(f97_out1(z0), z1, z2, z3, z4) → f96_out1(z0)
U43(z0, f98_out2(z1), z2, z3, z4) → f96_out3(z1)
f144_in(z0, z1, z2) → U44(f1_in(0, z0), f149_in(z1, z0, z2), z0, z1, z2)
U44(f1_out1(z0), z1, z2, z3, z4) → f144_out1(z0)
U44(z0, f149_out1(z1), z2, z3, z4) → f144_out2(z1)
U44(z0, f149_out3(z1), z2, z3, z4) → f144_out4(z1)
f147_in(z0, z1, z2, z3) → U45(f167_in(z0, z1, z2), f168_in(z0, z1, z2, z3), z0, z1, z2, z3)
U45(f167_out1(z0), z1, z2, z3, z4, z5) → f147_out1(z0)
U45(z0, f168_out2(z1), z2, z3, z4, z5) → f147_out3(z1)
f277_in(z0, z1) → U46(f1_in(s(z0), z1), f280_in(z0, z1), z0, z1)
U46(f1_out1(z0), z1, z2, z3) → f277_out1(z0)
U46(z0, f280_out1(z1), z2, z3) → f277_out2(z1)

Tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U33'(f159_out1, z0, z1) → c
F18_IN(z0) → c
F63_IN(z0) → c

S tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c

K tuples:

U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
U33'(f159_out1, z0, z1) → c
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F65_IN(z0) → c
F63_IN(z0) → c
F64_IN(s(z0)) → c(F25_IN(z0))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F64_IN(s(z0)) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
F18_IN(z0) → c
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, f261_in, U11, f30_in, U12, f177_in, U13, f149_in, U14, f167_in, U15, f168_in, U16, f64_in, U17, f65_in, U18, f97_in, U19, f98_in, U20, f21_in, U21, f22_in, U22, f25_in, U23, U24, f42_in, U25, U26, f101_in, U27, U28, f110_in, U29, U30, f127_in, U31, U32, f154_in, U33, U34, f173_in, U35, U36, f270_in, U37, U38, f282_in, U39, U40, f18_in, U41, f63_in, U42, f96_in, U43, f144_in, U44, f147_in, U45, f277_in, U46

Defined Pair Symbols:

F101_IN, F110_IN, F127_IN, F173_IN, F270_IN, F282_IN, F1_IN, F177_IN, F149_IN, F64_IN, F65_IN, F21_IN, F22_IN, F25_IN, F42_IN, U33', F18_IN, F63_IN, F261_IN, F30_IN, F167_IN, F168_IN, F97_IN, F98_IN, U27', U29', U31', F154_IN, U35', U37', U39', F96_IN, F144_IN, F147_IN, F277_IN, U23', U25'

Compound Symbols:

c68, c71, c74, c80, c83, c86, c, c7, c8, c9, c10, c11, c12, c31, c33, c46, c48, c54, c56, c69, c72, c75, c77, c81, c84, c87, c95, c98, c102, c105, c

(33) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))

We considered the (Usable) Rules:

f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1

And the Tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U33'(f159_out1, z0, z1) → c
F18_IN(z0) → c
F63_IN(z0) → c

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(0) = [1]
POL(F101_IN(x₁, x₂)) = [2]x₂
POL(F110_IN(x₁, x₂)) = [2]x₂
POL(F127_IN(x₁, x₂)) = [2]x₂
POL(F144_IN(x₁, x₂, x₃)) = [2]x₁
POL(F147_IN(x₁, x₂, x₃, x₄)) = x₂ + [2]x₃ + [2]x₄
POL(F149_IN(x₁, x₂, x₃)) = 0
POL(F154_IN(x₁, x₂)) = 0
POL(F167_IN(x₁, x₂, x₃)) = [2]x₃
POL(F168_IN(x₁, x₂, x₃, x₄)) = [2]x₄
POL(F173_IN(x₁, x₂, x₃)) = [2]x₃
POL(F177_IN(x₁, x₂)) = 0
POL(F18_IN(x₁)) = [1] + [2]x₁
POL(F1_IN(x₁, x₂)) = [2]x₂
POL(F21_IN(x₁)) = 0
POL(F22_IN(x₁)) = [2]x₁
POL(F25_IN(x₁)) = 0
POL(F261_IN(x₁, x₂)) = 0
POL(F270_IN(x₁, x₂, x₃)) = [2]x₃
POL(F277_IN(x₁, x₂)) = [2]x₂
POL(F282_IN(x₁, x₂, x₃)) = [2] + [2]x₃
POL(F30_IN(x₁)) = 0
POL(F42_IN(x₁)) = 0
POL(F63_IN(x₁)) = [1] + [2]x₁
POL(F64_IN(x₁)) = [1] + [2]x₁
POL(F65_IN(x₁)) = [1] + x₁
POL(F96_IN(x₁, x₂, x₃)) = [2]x₂ + [2]x₃
POL(F97_IN(x₁, x₂)) = [2]x₂
POL(F98_IN(x₁, x₂, x₃)) = [2]x₃
POL(U11(x₁, x₂, x₃)) = 0
POL(U12(x₁, x₂)) = 0
POL(U13(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U27'(x₁, x₂, x₃)) = [2]x₃
POL(U29'(x₁, x₂, x₃)) = [2]x₃
POL(U31'(x₁, x₂, x₃)) = [2]x₃
POL(U33'(x₁, x₂, x₃)) = [2]x₁ + [2]x₃
POL(U35'(x₁, x₂, x₃, x₄)) = [2]x₄
POL(U37'(x₁, x₂, x₃, x₄)) = [2]x₄
POL(U39'(x₁, x₂, x₃, x₄)) = [2]x₄
POL(c) = 0
POL(c(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c102(x₁, x₂)) = x₁ + x₂
POL(c105(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c68(x₁, x₂)) = x₁ + x₂
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c71(x₁, x₂)) = x₁ + x₂
POL(c72(x₁)) = x₁
POL(c74(x₁, x₂)) = x₁ + x₂
POL(c75(x₁)) = x₁
POL(c77) = 0
POL(c8(x₁)) = x₁
POL(c80(x₁, x₂)) = x₁ + x₂
POL(c81(x₁)) = x₁
POL(c83(x₁, x₂)) = x₁ + x₂
POL(c84(x₁)) = x₁
POL(c86(x₁, x₂)) = x₁ + x₂
POL(c87(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(c95(x₁, x₂)) = x₁ + x₂
POL(c98(x₁, x₂)) = x₁ + x₂
POL(f159_out1) = [2]
POL(f177_in(x₁, x₂)) = x₁
POL(f177_out1) = 0
POL(f261_in(x₁, x₂)) = 0
POL(f261_out1) = 0
POL(f30_in(x₁)) = 0
POL(f30_out1) = 0
POL(s(x₁)) = 0
POL(tree(x₁, x₂, x₃)) = [1] + x₁ + x₂ + x₃
POL(void) = 0

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, void)) → f1_out1(void)
f1_in(z0, tree(z0, void, void)) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, void, void)) → U1(f18_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U2(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, void, void)) → U3(f63_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U4(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U5(f96_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(s(z0), tree(s(z0), z1, z2)) → U6(f127_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f1_in(0, tree(s(z0), z1, z2)) → U7(f144_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f1_in(z0, tree(z1, z2, z3)) → U8(f147_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f1_in(s(z0), tree(0, z1, z2)) → U9(f277_in(z0, z2), s(z0), tree(0, z1, z2))
f1_in(s(z0), tree(s(z1), z2, z3)) → U10(f282_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f18_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U1(f18_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U2(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U3(f63_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U3(f63_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U4(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U5(f96_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(tree(z1, z0, z3))
U5(f96_out3(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U6(f127_out1(z0), s(z1), tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z2, z0))
U7(f144_out1(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out2(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out4(z0), 0, tree(s(z1), z2, z3)) → f1_out1(z0)
U8(f147_out1(z0), z1, tree(z2, z3, z4)) → f1_out1(tree(z2, z0, z4))
U8(f147_out3(z0), z1, tree(z2, z3, z4)) → f1_out1(z0)
U9(f277_out1(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U9(f277_out2(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U10(f282_out1(z0), s(z1), tree(s(z2), z3, z4)) → f1_out1(tree(s(z2), z3, z0))
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1
f149_in(z0, z1, z2) → U14(f154_in(z0, z2), z0, z1, z2)
U14(f154_out1(z0), z1, z2, z3) → f149_out3(tree(s(z1), z2, z0))
f167_in(s(z0), s(z1), z2) → U15(f173_in(z0, z1, z2), s(z0), s(z1), z2)
U15(f173_out1(z0), s(z1), s(z2), z3) → f167_out1(z0)
f168_in(z0, z1, z2, z3) → U16(f270_in(z1, z0, z3), z0, z1, z2, z3)
U16(f270_out1(z0), z1, z2, z3, z4) → f168_out2(tree(z2, z3, z0))
f64_in(s(z0)) → U17(f25_in(z0), s(z0))
U17(f25_out1(z0), s(z1)) → f64_out1(z0)
f65_in(z0) → U18(f42_in(z0), z0)
U18(f42_out1(z0), z1) → f65_out2(tree(z1, void, z0))
f97_in(s(z0), z1) → U19(f101_in(z0, z1), s(z0), z1)
U19(f101_out1(z0), s(z1), z2) → f97_out1(z0)
f98_in(z0, z1, z2) → U20(f110_in(z0, z2), z0, z1, z2)
U20(f110_out1(z0), z1, z2, z3) → f98_out2(tree(z1, z2, z0))
f21_in(s(z0)) → U21(f25_in(z0), s(z0))
U21(f25_out1(z0), s(z1)) → f21_out1(z0)
f22_in(z0) → U22(f42_in(z0), z0)
U22(f42_out1(z0), z1) → f22_out2(tree(z1, void, z0))
f25_in(z0) → U23(f30_in(z0), z0)
U23(f30_out1, z0) → U24(f1_in(s(z0), void), z0)
U24(f1_out1(z0), z1) → f25_out1(z0)
f42_in(z0) → U25(f30_in(z0), z0)
U25(f30_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1(z0), z1) → f42_out1(z0)
f101_in(z0, z1) → U27(f30_in(z0), z0, z1)
U27(f30_out1, z0, z1) → U28(f1_in(s(z0), z1), z0, z1)
U28(f1_out1(z0), z1, z2) → f101_out1(z0)
f110_in(z0, z1) → U29(f30_in(z0), z0, z1)
U29(f30_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1(z0), z1, z2) → f110_out1(z0)
f127_in(z0, z1) → U31(f30_in(z0), z0, z1)
U31(f30_out1, z0, z1) → U32(f1_in(s(z0), z1), z0, z1)
U32(f1_out1(z0), z1, z2) → f127_out1(z0)
f154_in(z0, z1) → U33(f159_in(z0), z0, z1)
U33(f159_out1, z0, z1) → U34(f1_in(0, z1), z0, z1)
U34(f1_out1(z0), z1, z2) → f154_out1(z0)
f173_in(z0, z1, z2) → U35(f177_in(z0, z1), z0, z1, z2)
U35(f177_out1, z0, z1, z2) → U36(f1_in(s(z0), z2), z0, z1, z2)
U36(f1_out1(z0), z1, z2, z3) → f173_out1(z0)
f270_in(z0, z1, z2) → U37(f261_in(z0, z1), z0, z1, z2)
U37(f261_out1, z0, z1, z2) → U38(f1_in(z1, z2), z0, z1, z2)
U38(f1_out1(z0), z1, z2, z3) → f270_out1(z0)
f282_in(z0, z1, z2) → U39(f261_in(z0, z1), z0, z1, z2)
U39(f261_out1, z0, z1, z2) → U40(f1_in(s(z1), z2), z0, z1, z2)
U40(f1_out1(z0), z1, z2, z3) → f282_out1(z0)
f18_in(z0) → U41(f21_in(z0), f22_in(z0), z0)
U41(f21_out1(z0), z1, z2) → f18_out1(z0)
U41(z0, f22_out2(z1), z2) → f18_out3(z1)
f63_in(z0) → U42(f64_in(z0), f65_in(z0), z0)
U42(f64_out1(z0), z1, z2) → f63_out1(z0)
U42(z0, f65_out2(z1), z2) → f63_out3(z1)
f96_in(z0, z1, z2) → U43(f97_in(z0, z1), f98_in(z0, z1, z2), z0, z1, z2)
U43(f97_out1(z0), z1, z2, z3, z4) → f96_out1(z0)
U43(z0, f98_out2(z1), z2, z3, z4) → f96_out3(z1)
f144_in(z0, z1, z2) → U44(f1_in(0, z0), f149_in(z1, z0, z2), z0, z1, z2)
U44(f1_out1(z0), z1, z2, z3, z4) → f144_out1(z0)
U44(z0, f149_out1(z1), z2, z3, z4) → f144_out2(z1)
U44(z0, f149_out3(z1), z2, z3, z4) → f144_out4(z1)
f147_in(z0, z1, z2, z3) → U45(f167_in(z0, z1, z2), f168_in(z0, z1, z2, z3), z0, z1, z2, z3)
U45(f167_out1(z0), z1, z2, z3, z4, z5) → f147_out1(z0)
U45(z0, f168_out2(z1), z2, z3, z4, z5) → f147_out3(z1)
f277_in(z0, z1) → U46(f1_in(s(z0), z1), f280_in(z0, z1), z0, z1)
U46(f1_out1(z0), z1, z2, z3) → f277_out1(z0)
U46(z0, f280_out1(z1), z2, z3) → f277_out2(z1)

Tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U33'(f159_out1, z0, z1) → c
F18_IN(z0) → c
F63_IN(z0) → c

S tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c

K tuples:

U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
U33'(f159_out1, z0, z1) → c
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F65_IN(z0) → c
F63_IN(z0) → c
F64_IN(s(z0)) → c(F25_IN(z0))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F64_IN(s(z0)) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
F18_IN(z0) → c
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, f261_in, U11, f30_in, U12, f177_in, U13, f149_in, U14, f167_in, U15, f168_in, U16, f64_in, U17, f65_in, U18, f97_in, U19, f98_in, U20, f21_in, U21, f22_in, U22, f25_in, U23, U24, f42_in, U25, U26, f101_in, U27, U28, f110_in, U29, U30, f127_in, U31, U32, f154_in, U33, U34, f173_in, U35, U36, f270_in, U37, U38, f282_in, U39, U40, f18_in, U41, f63_in, U42, f96_in, U43, f144_in, U44, f147_in, U45, f277_in, U46

Defined Pair Symbols:

F101_IN, F110_IN, F127_IN, F173_IN, F270_IN, F282_IN, F1_IN, F177_IN, F149_IN, F64_IN, F65_IN, F21_IN, F22_IN, F25_IN, F42_IN, U33', F18_IN, F63_IN, F261_IN, F30_IN, F167_IN, F168_IN, F97_IN, F98_IN, U27', U29', U31', F154_IN, U35', U37', U39', F96_IN, F144_IN, F147_IN, F277_IN, U23', U25'

Compound Symbols:

c68, c71, c74, c80, c83, c86, c, c7, c8, c9, c10, c11, c12, c31, c33, c46, c48, c54, c56, c69, c72, c75, c77, c81, c84, c87, c95, c98, c102, c105, c

(35) CdtKnowledgeProof (EQUIVALENT transformation)

The following tuples could be moved from S to K by knowledge propagation:

F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F149_IN(z0, z1, z2) → c
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(z0, tree(z0, void, void)) → c
F149_IN(z0, z1, z2) → c
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F154_IN(z0, z1) → c77
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, void)) → f1_out1(void)
f1_in(z0, tree(z0, void, void)) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, void, void)) → U1(f18_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U2(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, void, void)) → U3(f63_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U4(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U5(f96_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(s(z0), tree(s(z0), z1, z2)) → U6(f127_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f1_in(0, tree(s(z0), z1, z2)) → U7(f144_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f1_in(z0, tree(z1, z2, z3)) → U8(f147_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f1_in(s(z0), tree(0, z1, z2)) → U9(f277_in(z0, z2), s(z0), tree(0, z1, z2))
f1_in(s(z0), tree(s(z1), z2, z3)) → U10(f282_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f18_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U1(f18_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U2(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U3(f63_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U3(f63_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U4(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U5(f96_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(tree(z1, z0, z3))
U5(f96_out3(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U6(f127_out1(z0), s(z1), tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z2, z0))
U7(f144_out1(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out2(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out4(z0), 0, tree(s(z1), z2, z3)) → f1_out1(z0)
U8(f147_out1(z0), z1, tree(z2, z3, z4)) → f1_out1(tree(z2, z0, z4))
U8(f147_out3(z0), z1, tree(z2, z3, z4)) → f1_out1(z0)
U9(f277_out1(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U9(f277_out2(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U10(f282_out1(z0), s(z1), tree(s(z2), z3, z4)) → f1_out1(tree(s(z2), z3, z0))
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1
f149_in(z0, z1, z2) → U14(f154_in(z0, z2), z0, z1, z2)
U14(f154_out1(z0), z1, z2, z3) → f149_out3(tree(s(z1), z2, z0))
f167_in(s(z0), s(z1), z2) → U15(f173_in(z0, z1, z2), s(z0), s(z1), z2)
U15(f173_out1(z0), s(z1), s(z2), z3) → f167_out1(z0)
f168_in(z0, z1, z2, z3) → U16(f270_in(z1, z0, z3), z0, z1, z2, z3)
U16(f270_out1(z0), z1, z2, z3, z4) → f168_out2(tree(z2, z3, z0))
f64_in(s(z0)) → U17(f25_in(z0), s(z0))
U17(f25_out1(z0), s(z1)) → f64_out1(z0)
f65_in(z0) → U18(f42_in(z0), z0)
U18(f42_out1(z0), z1) → f65_out2(tree(z1, void, z0))
f97_in(s(z0), z1) → U19(f101_in(z0, z1), s(z0), z1)
U19(f101_out1(z0), s(z1), z2) → f97_out1(z0)
f98_in(z0, z1, z2) → U20(f110_in(z0, z2), z0, z1, z2)
U20(f110_out1(z0), z1, z2, z3) → f98_out2(tree(z1, z2, z0))
f21_in(s(z0)) → U21(f25_in(z0), s(z0))
U21(f25_out1(z0), s(z1)) → f21_out1(z0)
f22_in(z0) → U22(f42_in(z0), z0)
U22(f42_out1(z0), z1) → f22_out2(tree(z1, void, z0))
f25_in(z0) → U23(f30_in(z0), z0)
U23(f30_out1, z0) → U24(f1_in(s(z0), void), z0)
U24(f1_out1(z0), z1) → f25_out1(z0)
f42_in(z0) → U25(f30_in(z0), z0)
U25(f30_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1(z0), z1) → f42_out1(z0)
f101_in(z0, z1) → U27(f30_in(z0), z0, z1)
U27(f30_out1, z0, z1) → U28(f1_in(s(z0), z1), z0, z1)
U28(f1_out1(z0), z1, z2) → f101_out1(z0)
f110_in(z0, z1) → U29(f30_in(z0), z0, z1)
U29(f30_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1(z0), z1, z2) → f110_out1(z0)
f127_in(z0, z1) → U31(f30_in(z0), z0, z1)
U31(f30_out1, z0, z1) → U32(f1_in(s(z0), z1), z0, z1)
U32(f1_out1(z0), z1, z2) → f127_out1(z0)
f154_in(z0, z1) → U33(f159_in(z0), z0, z1)
U33(f159_out1, z0, z1) → U34(f1_in(0, z1), z0, z1)
U34(f1_out1(z0), z1, z2) → f154_out1(z0)
f173_in(z0, z1, z2) → U35(f177_in(z0, z1), z0, z1, z2)
U35(f177_out1, z0, z1, z2) → U36(f1_in(s(z0), z2), z0, z1, z2)
U36(f1_out1(z0), z1, z2, z3) → f173_out1(z0)
f270_in(z0, z1, z2) → U37(f261_in(z0, z1), z0, z1, z2)
U37(f261_out1, z0, z1, z2) → U38(f1_in(z1, z2), z0, z1, z2)
U38(f1_out1(z0), z1, z2, z3) → f270_out1(z0)
f282_in(z0, z1, z2) → U39(f261_in(z0, z1), z0, z1, z2)
U39(f261_out1, z0, z1, z2) → U40(f1_in(s(z1), z2), z0, z1, z2)
U40(f1_out1(z0), z1, z2, z3) → f282_out1(z0)
f18_in(z0) → U41(f21_in(z0), f22_in(z0), z0)
U41(f21_out1(z0), z1, z2) → f18_out1(z0)
U41(z0, f22_out2(z1), z2) → f18_out3(z1)
f63_in(z0) → U42(f64_in(z0), f65_in(z0), z0)
U42(f64_out1(z0), z1, z2) → f63_out1(z0)
U42(z0, f65_out2(z1), z2) → f63_out3(z1)
f96_in(z0, z1, z2) → U43(f97_in(z0, z1), f98_in(z0, z1, z2), z0, z1, z2)
U43(f97_out1(z0), z1, z2, z3, z4) → f96_out1(z0)
U43(z0, f98_out2(z1), z2, z3, z4) → f96_out3(z1)
f144_in(z0, z1, z2) → U44(f1_in(0, z0), f149_in(z1, z0, z2), z0, z1, z2)
U44(f1_out1(z0), z1, z2, z3, z4) → f144_out1(z0)
U44(z0, f149_out1(z1), z2, z3, z4) → f144_out2(z1)
U44(z0, f149_out3(z1), z2, z3, z4) → f144_out4(z1)
f147_in(z0, z1, z2, z3) → U45(f167_in(z0, z1, z2), f168_in(z0, z1, z2, z3), z0, z1, z2, z3)
U45(f167_out1(z0), z1, z2, z3, z4, z5) → f147_out1(z0)
U45(z0, f168_out2(z1), z2, z3, z4, z5) → f147_out3(z1)
f277_in(z0, z1) → U46(f1_in(s(z0), z1), f280_in(z0, z1), z0, z1)
U46(f1_out1(z0), z1, z2, z3) → f277_out1(z0)
U46(z0, f280_out1(z1), z2, z3) → f277_out2(z1)

Tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U33'(f159_out1, z0, z1) → c
F18_IN(z0) → c
F63_IN(z0) → c

S tuples:

F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))

K tuples:

U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
U33'(f159_out1, z0, z1) → c
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F65_IN(z0) → c
F63_IN(z0) → c
F64_IN(s(z0)) → c(F25_IN(z0))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F64_IN(s(z0)) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
F18_IN(z0) → c
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F149_IN(z0, z1, z2) → c
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F154_IN(z0, z1) → c77
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, f261_in, U11, f30_in, U12, f177_in, U13, f149_in, U14, f167_in, U15, f168_in, U16, f64_in, U17, f65_in, U18, f97_in, U19, f98_in, U20, f21_in, U21, f22_in, U22, f25_in, U23, U24, f42_in, U25, U26, f101_in, U27, U28, f110_in, U29, U30, f127_in, U31, U32, f154_in, U33, U34, f173_in, U35, U36, f270_in, U37, U38, f282_in, U39, U40, f18_in, U41, f63_in, U42, f96_in, U43, f144_in, U44, f147_in, U45, f277_in, U46

Defined Pair Symbols:

F101_IN, F110_IN, F127_IN, F173_IN, F270_IN, F282_IN, F1_IN, F177_IN, F149_IN, F64_IN, F65_IN, F21_IN, F22_IN, F25_IN, F42_IN, U33', F18_IN, F63_IN, F261_IN, F30_IN, F167_IN, F168_IN, F97_IN, F98_IN, U27', U29', U31', F154_IN, U35', U37', U39', F96_IN, F144_IN, F147_IN, F277_IN, U23', U25'

Compound Symbols:

c68, c71, c74, c80, c83, c86, c, c7, c8, c9, c10, c11, c12, c31, c33, c46, c48, c54, c56, c69, c72, c75, c77, c81, c84, c87, c95, c98, c102, c105, c

(37) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

F30_IN(s(z0)) → c33(F30_IN(z0))

We considered the (Usable) Rules:

f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1

And the Tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U33'(f159_out1, z0, z1) → c
F18_IN(z0) → c
F63_IN(z0) → c

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(0) = 0
POL(F101_IN(x₁, x₂)) = [2] + x₁ + [3]x₂
POL(F110_IN(x₁, x₂)) = [2]x₁ + [3]x₂
POL(F127_IN(x₁, x₂)) = [3] + [2]x₁ + [3]x₂
POL(F144_IN(x₁, x₂, x₃)) = [3]x₁ + [2]x₂ + [3]x₃
POL(F147_IN(x₁, x₂, x₃, x₄)) = x₂ + [3]x₃ + [3]x₄
POL(F149_IN(x₁, x₂, x₃)) = x₁ + [2]x₃
POL(F154_IN(x₁, x₂)) = x₂
POL(F167_IN(x₁, x₂, x₃)) = [3]x₃
POL(F168_IN(x₁, x₂, x₃, x₄)) = x₂ + [3]x₄
POL(F173_IN(x₁, x₂, x₃)) = [3]x₃
POL(F177_IN(x₁, x₂)) = 0
POL(F18_IN(x₁)) = x₁
POL(F1_IN(x₁, x₂)) = [3]x₂
POL(F21_IN(x₁)) = x₁
POL(F22_IN(x₁)) = x₁
POL(F25_IN(x₁)) = [3] + x₁
POL(F261_IN(x₁, x₂)) = 0
POL(F270_IN(x₁, x₂, x₃)) = x₁ + [3]x₃
POL(F277_IN(x₁, x₂)) = [3]x₂
POL(F282_IN(x₁, x₂, x₃)) = [2] + [3]x₁ + [3]x₃
POL(F30_IN(x₁)) = x₁
POL(F42_IN(x₁)) = x₁
POL(F63_IN(x₁)) = [2]x₁
POL(F64_IN(x₁)) = x₁
POL(F65_IN(x₁)) = x₁
POL(F96_IN(x₁, x₂, x₃)) = [3]x₁ + [3]x₂ + [3]x₃
POL(F97_IN(x₁, x₂)) = x₁ + [3]x₂
POL(F98_IN(x₁, x₂, x₃)) = [2]x₁ + [3]x₃
POL(U11(x₁, x₂, x₃)) = 0
POL(U12(x₁, x₂)) = 0
POL(U13(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂)) = 0
POL(U25'(x₁, x₂)) = x₂
POL(U27'(x₁, x₂, x₃)) = [1] + [3]x₃
POL(U29'(x₁, x₂, x₃)) = [3]x₃
POL(U31'(x₁, x₂, x₃)) = [1] + [3]x₃
POL(U33'(x₁, x₂, x₃)) = [3]x₃
POL(U35'(x₁, x₂, x₃, x₄)) = [3]x₄
POL(U37'(x₁, x₂, x₃, x₄)) = [3]x₄
POL(U39'(x₁, x₂, x₃, x₄)) = [2] + [3]x₄
POL(c) = 0
POL(c(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c102(x₁, x₂)) = x₁ + x₂
POL(c105(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c68(x₁, x₂)) = x₁ + x₂
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c71(x₁, x₂)) = x₁ + x₂
POL(c72(x₁)) = x₁
POL(c74(x₁, x₂)) = x₁ + x₂
POL(c75(x₁)) = x₁
POL(c77) = 0
POL(c8(x₁)) = x₁
POL(c80(x₁, x₂)) = x₁ + x₂
POL(c81(x₁)) = x₁
POL(c83(x₁, x₂)) = x₁ + x₂
POL(c84(x₁)) = x₁
POL(c86(x₁, x₂)) = x₁ + x₂
POL(c87(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(c95(x₁, x₂)) = x₁ + x₂
POL(c98(x₁, x₂)) = x₁ + x₂
POL(f159_out1) = 0
POL(f177_in(x₁, x₂)) = 0
POL(f177_out1) = 0
POL(f261_in(x₁, x₂)) = 0
POL(f261_out1) = 0
POL(f30_in(x₁)) = 0
POL(f30_out1) = 0
POL(s(x₁)) = [3] + x₁
POL(tree(x₁, x₂, x₃)) = x₁ + x₂ + x₃
POL(void) = 0

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, void)) → f1_out1(void)
f1_in(z0, tree(z0, void, void)) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, void, void)) → U1(f18_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U2(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, void, void)) → U3(f63_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U4(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U5(f96_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(s(z0), tree(s(z0), z1, z2)) → U6(f127_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f1_in(0, tree(s(z0), z1, z2)) → U7(f144_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f1_in(z0, tree(z1, z2, z3)) → U8(f147_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f1_in(s(z0), tree(0, z1, z2)) → U9(f277_in(z0, z2), s(z0), tree(0, z1, z2))
f1_in(s(z0), tree(s(z1), z2, z3)) → U10(f282_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f18_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U1(f18_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U2(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U3(f63_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U3(f63_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U4(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U5(f96_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(tree(z1, z0, z3))
U5(f96_out3(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U6(f127_out1(z0), s(z1), tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z2, z0))
U7(f144_out1(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out2(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out4(z0), 0, tree(s(z1), z2, z3)) → f1_out1(z0)
U8(f147_out1(z0), z1, tree(z2, z3, z4)) → f1_out1(tree(z2, z0, z4))
U8(f147_out3(z0), z1, tree(z2, z3, z4)) → f1_out1(z0)
U9(f277_out1(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U9(f277_out2(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U10(f282_out1(z0), s(z1), tree(s(z2), z3, z4)) → f1_out1(tree(s(z2), z3, z0))
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1
f149_in(z0, z1, z2) → U14(f154_in(z0, z2), z0, z1, z2)
U14(f154_out1(z0), z1, z2, z3) → f149_out3(tree(s(z1), z2, z0))
f167_in(s(z0), s(z1), z2) → U15(f173_in(z0, z1, z2), s(z0), s(z1), z2)
U15(f173_out1(z0), s(z1), s(z2), z3) → f167_out1(z0)
f168_in(z0, z1, z2, z3) → U16(f270_in(z1, z0, z3), z0, z1, z2, z3)
U16(f270_out1(z0), z1, z2, z3, z4) → f168_out2(tree(z2, z3, z0))
f64_in(s(z0)) → U17(f25_in(z0), s(z0))
U17(f25_out1(z0), s(z1)) → f64_out1(z0)
f65_in(z0) → U18(f42_in(z0), z0)
U18(f42_out1(z0), z1) → f65_out2(tree(z1, void, z0))
f97_in(s(z0), z1) → U19(f101_in(z0, z1), s(z0), z1)
U19(f101_out1(z0), s(z1), z2) → f97_out1(z0)
f98_in(z0, z1, z2) → U20(f110_in(z0, z2), z0, z1, z2)
U20(f110_out1(z0), z1, z2, z3) → f98_out2(tree(z1, z2, z0))
f21_in(s(z0)) → U21(f25_in(z0), s(z0))
U21(f25_out1(z0), s(z1)) → f21_out1(z0)
f22_in(z0) → U22(f42_in(z0), z0)
U22(f42_out1(z0), z1) → f22_out2(tree(z1, void, z0))
f25_in(z0) → U23(f30_in(z0), z0)
U23(f30_out1, z0) → U24(f1_in(s(z0), void), z0)
U24(f1_out1(z0), z1) → f25_out1(z0)
f42_in(z0) → U25(f30_in(z0), z0)
U25(f30_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1(z0), z1) → f42_out1(z0)
f101_in(z0, z1) → U27(f30_in(z0), z0, z1)
U27(f30_out1, z0, z1) → U28(f1_in(s(z0), z1), z0, z1)
U28(f1_out1(z0), z1, z2) → f101_out1(z0)
f110_in(z0, z1) → U29(f30_in(z0), z0, z1)
U29(f30_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1(z0), z1, z2) → f110_out1(z0)
f127_in(z0, z1) → U31(f30_in(z0), z0, z1)
U31(f30_out1, z0, z1) → U32(f1_in(s(z0), z1), z0, z1)
U32(f1_out1(z0), z1, z2) → f127_out1(z0)
f154_in(z0, z1) → U33(f159_in(z0), z0, z1)
U33(f159_out1, z0, z1) → U34(f1_in(0, z1), z0, z1)
U34(f1_out1(z0), z1, z2) → f154_out1(z0)
f173_in(z0, z1, z2) → U35(f177_in(z0, z1), z0, z1, z2)
U35(f177_out1, z0, z1, z2) → U36(f1_in(s(z0), z2), z0, z1, z2)
U36(f1_out1(z0), z1, z2, z3) → f173_out1(z0)
f270_in(z0, z1, z2) → U37(f261_in(z0, z1), z0, z1, z2)
U37(f261_out1, z0, z1, z2) → U38(f1_in(z1, z2), z0, z1, z2)
U38(f1_out1(z0), z1, z2, z3) → f270_out1(z0)
f282_in(z0, z1, z2) → U39(f261_in(z0, z1), z0, z1, z2)
U39(f261_out1, z0, z1, z2) → U40(f1_in(s(z1), z2), z0, z1, z2)
U40(f1_out1(z0), z1, z2, z3) → f282_out1(z0)
f18_in(z0) → U41(f21_in(z0), f22_in(z0), z0)
U41(f21_out1(z0), z1, z2) → f18_out1(z0)
U41(z0, f22_out2(z1), z2) → f18_out3(z1)
f63_in(z0) → U42(f64_in(z0), f65_in(z0), z0)
U42(f64_out1(z0), z1, z2) → f63_out1(z0)
U42(z0, f65_out2(z1), z2) → f63_out3(z1)
f96_in(z0, z1, z2) → U43(f97_in(z0, z1), f98_in(z0, z1, z2), z0, z1, z2)
U43(f97_out1(z0), z1, z2, z3, z4) → f96_out1(z0)
U43(z0, f98_out2(z1), z2, z3, z4) → f96_out3(z1)
f144_in(z0, z1, z2) → U44(f1_in(0, z0), f149_in(z1, z0, z2), z0, z1, z2)
U44(f1_out1(z0), z1, z2, z3, z4) → f144_out1(z0)
U44(z0, f149_out1(z1), z2, z3, z4) → f144_out2(z1)
U44(z0, f149_out3(z1), z2, z3, z4) → f144_out4(z1)
f147_in(z0, z1, z2, z3) → U45(f167_in(z0, z1, z2), f168_in(z0, z1, z2, z3), z0, z1, z2, z3)
U45(f167_out1(z0), z1, z2, z3, z4, z5) → f147_out1(z0)
U45(z0, f168_out2(z1), z2, z3, z4, z5) → f147_out3(z1)
f277_in(z0, z1) → U46(f1_in(s(z0), z1), f280_in(z0, z1), z0, z1)
U46(f1_out1(z0), z1, z2, z3) → f277_out1(z0)
U46(z0, f280_out1(z1), z2, z3) → f277_out2(z1)

Tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U33'(f159_out1, z0, z1) → c
F18_IN(z0) → c
F63_IN(z0) → c

S tuples:

F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))

K tuples:

U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
U33'(f159_out1, z0, z1) → c
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F65_IN(z0) → c
F63_IN(z0) → c
F64_IN(s(z0)) → c(F25_IN(z0))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F64_IN(s(z0)) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
F18_IN(z0) → c
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F149_IN(z0, z1, z2) → c
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F154_IN(z0, z1) → c77
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F30_IN(s(z0)) → c33(F30_IN(z0))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, f261_in, U11, f30_in, U12, f177_in, U13, f149_in, U14, f167_in, U15, f168_in, U16, f64_in, U17, f65_in, U18, f97_in, U19, f98_in, U20, f21_in, U21, f22_in, U22, f25_in, U23, U24, f42_in, U25, U26, f101_in, U27, U28, f110_in, U29, U30, f127_in, U31, U32, f154_in, U33, U34, f173_in, U35, U36, f270_in, U37, U38, f282_in, U39, U40, f18_in, U41, f63_in, U42, f96_in, U43, f144_in, U44, f147_in, U45, f277_in, U46

Defined Pair Symbols:

F101_IN, F110_IN, F127_IN, F173_IN, F270_IN, F282_IN, F1_IN, F177_IN, F149_IN, F64_IN, F65_IN, F21_IN, F22_IN, F25_IN, F42_IN, U33', F18_IN, F63_IN, F261_IN, F30_IN, F167_IN, F168_IN, F97_IN, F98_IN, U27', U29', U31', F154_IN, U35', U37', U39', F96_IN, F144_IN, F147_IN, F277_IN, U23', U25'

Compound Symbols:

c68, c71, c74, c80, c83, c86, c, c7, c8, c9, c10, c11, c12, c31, c33, c46, c48, c54, c56, c69, c72, c75, c77, c81, c84, c87, c95, c98, c102, c105, c

(39) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))

We considered the (Usable) Rules:

f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1

And the Tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U33'(f159_out1, z0, z1) → c
F18_IN(z0) → c
F63_IN(z0) → c

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(0) = 0
POL(F101_IN(x₁, x₂)) = x₂ + x₂² + x₁·x₂
POL(F110_IN(x₁, x₂)) = x₂² + x₁·x₂ + x₁²
POL(F127_IN(x₁, x₂)) = [1] + x₁ + x₂ + x₂² + x₁·x₂ + x₁²
POL(F144_IN(x₁, x₂, x₃)) = x₁ + x₃ + x₃² + x₂·x₃ + x₁·x₃ + x₁² + x₁·x₂
POL(F147_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₄ + x₄² + x₃·x₄ + x₂·x₄ + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂·x₃ + x₂²
POL(F149_IN(x₁, x₂, x₃)) = x₂·x₃ + x₁·x₂
POL(F154_IN(x₁, x₂)) = 0
POL(F167_IN(x₁, x₂, x₃)) = x₂ + x₃² + x₂·x₃ + x₁·x₃
POL(F168_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₄ + x₄² + x₃·x₄ + x₁·x₄
POL(F173_IN(x₁, x₂, x₃)) = x₂ + x₃ + x₃² + x₁·x₃
POL(F177_IN(x₁, x₂)) = x₂
POL(F18_IN(x₁)) = x₁ + x₁²
POL(F1_IN(x₁, x₂)) = x₂² + x₁·x₂
POL(F21_IN(x₁)) = x₁ + x₁²
POL(F22_IN(x₁)) = 0
POL(F25_IN(x₁)) = 0
POL(F261_IN(x₁, x₂)) = x₂
POL(F270_IN(x₁, x₂, x₃)) = [1] + x₂ + x₃ + x₃² + x₂·x₃
POL(F277_IN(x₁, x₂)) = x₂ + x₂² + x₁·x₂
POL(F282_IN(x₁, x₂, x₃)) = [1] + x₁ + x₂ + x₃ + x₃² + x₂·x₃
POL(F30_IN(x₁)) = 0
POL(F42_IN(x₁)) = 0
POL(F63_IN(x₁)) = [1] + x₁ + x₁²
POL(F64_IN(x₁)) = x₁ + x₁²
POL(F65_IN(x₁)) = 0
POL(F96_IN(x₁, x₂, x₃)) = [1] + x₁ + x₂ + x₃ + x₃² + x₂·x₃ + x₁·x₃ + x₁² + x₁·x₂ + x₂²
POL(F97_IN(x₁, x₂)) = x₂ + x₂² + x₁·x₂
POL(F98_IN(x₁, x₂, x₃)) = [1] + x₁ + x₃² + x₂·x₃ + x₁·x₃ + x₁²
POL(U11(x₁, x₂, x₃)) = x₁²
POL(U12(x₁, x₂)) = 0
POL(U13(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U27'(x₁, x₂, x₃)) = x₃ + x₃² + x₂·x₃
POL(U29'(x₁, x₂, x₃)) = x₃² + x₂·x₃ + x₂²
POL(U31'(x₁, x₂, x₃)) = x₃ + x₃² + x₂·x₃ + x₂²
POL(U33'(x₁, x₂, x₃)) = x₃²
POL(U35'(x₁, x₂, x₃, x₄)) = x₄ + x₄² + x₂·x₄
POL(U37'(x₁, x₂, x₃, x₄)) = x₄² + x₃·x₄ + x₁·x₄ + x₁²
POL(U39'(x₁, x₂, x₃, x₄)) = x₄ + x₄² + x₃·x₄
POL(c) = 0
POL(c(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c102(x₁, x₂)) = x₁ + x₂
POL(c105(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c68(x₁, x₂)) = x₁ + x₂
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c71(x₁, x₂)) = x₁ + x₂
POL(c72(x₁)) = x₁
POL(c74(x₁, x₂)) = x₁ + x₂
POL(c75(x₁)) = x₁
POL(c77) = 0
POL(c8(x₁)) = x₁
POL(c80(x₁, x₂)) = x₁ + x₂
POL(c81(x₁)) = x₁
POL(c83(x₁, x₂)) = x₁ + x₂
POL(c84(x₁)) = x₁
POL(c86(x₁, x₂)) = x₁ + x₂
POL(c87(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(c95(x₁, x₂)) = x₁ + x₂
POL(c98(x₁, x₂)) = x₁ + x₂
POL(f159_out1) = [1]
POL(f177_in(x₁, x₂)) = [1] + x₁²
POL(f177_out1) = [1]
POL(f261_in(x₁, x₂)) = [1]
POL(f261_out1) = 0
POL(f30_in(x₁)) = 0
POL(f30_out1) = 0
POL(s(x₁)) = [1] + x₁
POL(tree(x₁, x₂, x₃)) = [1] + x₁ + x₂ + x₃
POL(void) = 0

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, void)) → f1_out1(void)
f1_in(z0, tree(z0, void, void)) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, void, void)) → U1(f18_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U2(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, void, void)) → U3(f63_in(z0), z0, tree(z0, void, void))
f1_in(s(z0), tree(s(z0), void, void)) → U4(f25_in(z0), s(z0), tree(s(z0), void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U5(f96_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(s(z0), tree(s(z0), z1, z2)) → U6(f127_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f1_in(0, tree(s(z0), z1, z2)) → U7(f144_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f1_in(z0, tree(z1, z2, z3)) → U8(f147_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f1_in(s(z0), tree(0, z1, z2)) → U9(f277_in(z0, z2), s(z0), tree(0, z1, z2))
f1_in(s(z0), tree(s(z1), z2, z3)) → U10(f282_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f18_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U1(f18_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U2(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U3(f63_out1(z0), z1, tree(z1, void, void)) → f1_out1(tree(z1, z0, void))
U3(f63_out3(z0), z1, tree(z1, void, void)) → f1_out1(z0)
U4(f25_out1(z0), s(z1), tree(s(z1), void, void)) → f1_out1(tree(s(z1), void, z0))
U5(f96_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(tree(z1, z0, z3))
U5(f96_out3(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U6(f127_out1(z0), s(z1), tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z2, z0))
U7(f144_out1(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out2(z0), 0, tree(s(z1), z2, z3)) → f1_out1(tree(s(z1), z0, z3))
U7(f144_out4(z0), 0, tree(s(z1), z2, z3)) → f1_out1(z0)
U8(f147_out1(z0), z1, tree(z2, z3, z4)) → f1_out1(tree(z2, z0, z4))
U8(f147_out3(z0), z1, tree(z2, z3, z4)) → f1_out1(z0)
U9(f277_out1(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U9(f277_out2(z0), s(z1), tree(0, z2, z3)) → f1_out1(tree(0, z2, z0))
U10(f282_out1(z0), s(z1), tree(s(z2), z3, z4)) → f1_out1(tree(s(z2), z3, z0))
f261_in(0, s(z0)) → f261_out1
f261_in(s(z0), s(z1)) → U11(f261_in(z0, z1), s(z0), s(z1))
U11(f261_out1, s(z0), s(z1)) → f261_out1
f30_in(s(z0)) → U12(f30_in(z0), s(z0))
U12(f30_out1, s(z0)) → f30_out1
f177_in(0, s(z0)) → f177_out1
f177_in(s(0), s(s(z0))) → f177_out1
f177_in(s(s(0)), s(s(s(z0)))) → f177_out1
f177_in(s(s(s(0))), s(s(s(s(z0))))) → f177_out1
f177_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f177_out1
f177_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f177_out1
f177_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f177_out1
f177_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U13(f261_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U13(f261_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f177_out1
f149_in(z0, z1, z2) → U14(f154_in(z0, z2), z0, z1, z2)
U14(f154_out1(z0), z1, z2, z3) → f149_out3(tree(s(z1), z2, z0))
f167_in(s(z0), s(z1), z2) → U15(f173_in(z0, z1, z2), s(z0), s(z1), z2)
U15(f173_out1(z0), s(z1), s(z2), z3) → f167_out1(z0)
f168_in(z0, z1, z2, z3) → U16(f270_in(z1, z0, z3), z0, z1, z2, z3)
U16(f270_out1(z0), z1, z2, z3, z4) → f168_out2(tree(z2, z3, z0))
f64_in(s(z0)) → U17(f25_in(z0), s(z0))
U17(f25_out1(z0), s(z1)) → f64_out1(z0)
f65_in(z0) → U18(f42_in(z0), z0)
U18(f42_out1(z0), z1) → f65_out2(tree(z1, void, z0))
f97_in(s(z0), z1) → U19(f101_in(z0, z1), s(z0), z1)
U19(f101_out1(z0), s(z1), z2) → f97_out1(z0)
f98_in(z0, z1, z2) → U20(f110_in(z0, z2), z0, z1, z2)
U20(f110_out1(z0), z1, z2, z3) → f98_out2(tree(z1, z2, z0))
f21_in(s(z0)) → U21(f25_in(z0), s(z0))
U21(f25_out1(z0), s(z1)) → f21_out1(z0)
f22_in(z0) → U22(f42_in(z0), z0)
U22(f42_out1(z0), z1) → f22_out2(tree(z1, void, z0))
f25_in(z0) → U23(f30_in(z0), z0)
U23(f30_out1, z0) → U24(f1_in(s(z0), void), z0)
U24(f1_out1(z0), z1) → f25_out1(z0)
f42_in(z0) → U25(f30_in(z0), z0)
U25(f30_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1(z0), z1) → f42_out1(z0)
f101_in(z0, z1) → U27(f30_in(z0), z0, z1)
U27(f30_out1, z0, z1) → U28(f1_in(s(z0), z1), z0, z1)
U28(f1_out1(z0), z1, z2) → f101_out1(z0)
f110_in(z0, z1) → U29(f30_in(z0), z0, z1)
U29(f30_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1(z0), z1, z2) → f110_out1(z0)
f127_in(z0, z1) → U31(f30_in(z0), z0, z1)
U31(f30_out1, z0, z1) → U32(f1_in(s(z0), z1), z0, z1)
U32(f1_out1(z0), z1, z2) → f127_out1(z0)
f154_in(z0, z1) → U33(f159_in(z0), z0, z1)
U33(f159_out1, z0, z1) → U34(f1_in(0, z1), z0, z1)
U34(f1_out1(z0), z1, z2) → f154_out1(z0)
f173_in(z0, z1, z2) → U35(f177_in(z0, z1), z0, z1, z2)
U35(f177_out1, z0, z1, z2) → U36(f1_in(s(z0), z2), z0, z1, z2)
U36(f1_out1(z0), z1, z2, z3) → f173_out1(z0)
f270_in(z0, z1, z2) → U37(f261_in(z0, z1), z0, z1, z2)
U37(f261_out1, z0, z1, z2) → U38(f1_in(z1, z2), z0, z1, z2)
U38(f1_out1(z0), z1, z2, z3) → f270_out1(z0)
f282_in(z0, z1, z2) → U39(f261_in(z0, z1), z0, z1, z2)
U39(f261_out1, z0, z1, z2) → U40(f1_in(s(z1), z2), z0, z1, z2)
U40(f1_out1(z0), z1, z2, z3) → f282_out1(z0)
f18_in(z0) → U41(f21_in(z0), f22_in(z0), z0)
U41(f21_out1(z0), z1, z2) → f18_out1(z0)
U41(z0, f22_out2(z1), z2) → f18_out3(z1)
f63_in(z0) → U42(f64_in(z0), f65_in(z0), z0)
U42(f64_out1(z0), z1, z2) → f63_out1(z0)
U42(z0, f65_out2(z1), z2) → f63_out3(z1)
f96_in(z0, z1, z2) → U43(f97_in(z0, z1), f98_in(z0, z1, z2), z0, z1, z2)
U43(f97_out1(z0), z1, z2, z3, z4) → f96_out1(z0)
U43(z0, f98_out2(z1), z2, z3, z4) → f96_out3(z1)
f144_in(z0, z1, z2) → U44(f1_in(0, z0), f149_in(z1, z0, z2), z0, z1, z2)
U44(f1_out1(z0), z1, z2, z3, z4) → f144_out1(z0)
U44(z0, f149_out1(z1), z2, z3, z4) → f144_out2(z1)
U44(z0, f149_out3(z1), z2, z3, z4) → f144_out4(z1)
f147_in(z0, z1, z2, z3) → U45(f167_in(z0, z1, z2), f168_in(z0, z1, z2, z3), z0, z1, z2, z3)
U45(f167_out1(z0), z1, z2, z3, z4, z5) → f147_out1(z0)
U45(z0, f168_out2(z1), z2, z3, z4, z5) → f147_out3(z1)
f277_in(z0, z1) → U46(f1_in(s(z0), z1), f280_in(z0, z1), z0, z1)
U46(f1_out1(z0), z1, z2, z3) → f277_out1(z0)
U46(z0, f280_out1(z1), z2, z3) → f277_out2(z1)

Tuples:

F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F64_IN(s(z0)) → c(F25_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))
F30_IN(s(z0)) → c33(F30_IN(z0))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F154_IN(z0, z1) → c77
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F149_IN(z0, z1, z2) → c
F64_IN(s(z0)) → c
F65_IN(z0) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U33'(f159_out1, z0, z1) → c
F18_IN(z0) → c
F63_IN(z0) → c

S tuples:none
K tuples:

U33'(f159_out1, z0, z1) → c(F1_IN(0, z1))
U33'(f159_out1, z0, z1) → c
F1_IN(z0, tree(z0, void, void)) → c(F18_IN(z0))
F1_IN(s(z0), tree(s(z0), void, void)) → c(F25_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F65_IN(z0) → c(F42_IN(z0))
F63_IN(z0) → c(F64_IN(z0))
F1_IN(z0, tree(z0, void, void)) → c
F1_IN(s(z0), tree(s(z0), void, void)) → c
F65_IN(z0) → c
F63_IN(z0) → c
F64_IN(s(z0)) → c(F25_IN(z0))
F18_IN(z0) → c(F21_IN(z0))
F18_IN(z0) → c(F22_IN(z0))
F63_IN(z0) → c(F65_IN(z0))
F64_IN(s(z0)) → c
F21_IN(s(z0)) → c
F22_IN(z0) → c
F18_IN(z0) → c
F21_IN(s(z0)) → c(F25_IN(z0))
F22_IN(z0) → c(F42_IN(z0))
F25_IN(z0) → c(U23'(f30_in(z0), z0))
F25_IN(z0) → c(F30_IN(z0))
F42_IN(z0) → c(U25'(f30_in(z0), z0))
F42_IN(z0) → c(F30_IN(z0))
U23'(f30_out1, z0) → c
U25'(f30_out1, z0) → c
U27'(f30_out1, z0, z1) → c69(F1_IN(s(z0), z1))
U29'(f30_out1, z0, z1) → c72(F1_IN(z0, z1))
U31'(f30_out1, z0, z1) → c75(F1_IN(s(z0), z1))
F282_IN(z0, z1, z2) → c86(U39'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c7(F96_IN(z0, z1, z2))
F1_IN(s(z0), tree(s(z0), z1, z2)) → c8(F127_IN(z0, z2))
F1_IN(0, tree(s(z0), z1, z2)) → c9(F144_IN(z1, z0, z2))
F1_IN(z0, tree(z1, z2, z3)) → c10(F147_IN(z0, z1, z2, z3))
F1_IN(s(z0), tree(0, z1, z2)) → c11(F277_IN(z0, z2))
F127_IN(z0, z1) → c74(U31'(f30_in(z0), z0, z1), F30_IN(z0))
U39'(f261_out1, z0, z1, z2) → c87(F1_IN(s(z1), z2))
F96_IN(z0, z1, z2) → c95(F97_IN(z0, z1), F98_IN(z0, z1, z2))
F144_IN(z0, z1, z2) → c98(F1_IN(0, z0), F149_IN(z1, z0, z2))
F147_IN(z0, z1, z2, z3) → c102(F167_IN(z0, z1, z2), F168_IN(z0, z1, z2, z3))
F277_IN(z0, z1) → c105(F1_IN(s(z0), z1))
F149_IN(z0, z1, z2) → c
F97_IN(s(z0), z1) → c54(F101_IN(z0, z1))
F98_IN(z0, z1, z2) → c56(F110_IN(z0, z2))
F149_IN(z0, z1, z2) → c(F154_IN(z0, z2))
F167_IN(s(z0), s(z1), z2) → c46(F173_IN(z0, z1, z2))
F168_IN(z0, z1, z2, z3) → c48(F270_IN(z1, z0, z3))
F101_IN(z0, z1) → c68(U27'(f30_in(z0), z0, z1), F30_IN(z0))
F110_IN(z0, z1) → c71(U29'(f30_in(z0), z0, z1), F30_IN(z0))
F154_IN(z0, z1) → c77
F173_IN(z0, z1, z2) → c80(U35'(f177_in(z0, z1), z0, z1, z2), F177_IN(z0, z1))
F270_IN(z0, z1, z2) → c83(U37'(f261_in(z0, z1), z0, z1, z2), F261_IN(z0, z1))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F261_IN(z0, z1))
U35'(f177_out1, z0, z1, z2) → c81(F1_IN(s(z0), z2))
F177_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
U37'(f261_out1, z0, z1, z2) → c84(F1_IN(z1, z2))
F1_IN(s(z0), tree(s(z1), z2, z3)) → c12(F282_IN(z1, z0, z3))
F30_IN(s(z0)) → c33(F30_IN(z0))
F261_IN(s(z0), s(z1)) → c31(F261_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, f261_in, U11, f30_in, U12, f177_in, U13, f149_in, U14, f167_in, U15, f168_in, U16, f64_in, U17, f65_in, U18, f97_in, U19, f98_in, U20, f21_in, U21, f22_in, U22, f25_in, U23, U24, f42_in, U25, U26, f101_in, U27, U28, f110_in, U29, U30, f127_in, U31, U32, f154_in, U33, U34, f173_in, U35, U36, f270_in, U37, U38, f282_in, U39, U40, f18_in, U41, f63_in, U42, f96_in, U43, f144_in, U44, f147_in, U45, f277_in, U46

Defined Pair Symbols:

F101_IN, F110_IN, F127_IN, F173_IN, F270_IN, F282_IN, F1_IN, F177_IN, F149_IN, F64_IN, F65_IN, F21_IN, F22_IN, F25_IN, F42_IN, U33', F18_IN, F63_IN, F261_IN, F30_IN, F167_IN, F168_IN, F97_IN, F98_IN, U27', U29', U31', F154_IN, U35', U37', U39', F96_IN, F144_IN, F147_IN, F277_IN, U23', U25'

Compound Symbols:

c68, c71, c74, c80, c83, c86, c, c7, c8, c9, c10, c11, c12, c31, c33, c46, c48, c54, c56, c69, c72, c75, c77, c81, c84, c87, c95, c98, c102, c105, c

(41) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

(0) Obligation:

(1) LPReorderTransformerProof (EQUIVALENT transformation)

(2) Obligation:

(3) PrologToCdtProblemTransformerProof (UPPER BOUND (ID) transformation)

(4) Obligation:

(5) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

(6) Obligation:

(7) CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID) transformation)

(8) Obligation:

(9) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

(10) Obligation:

(11) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

(12) Obligation:

(13) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

(14) Obligation:

(15) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(16) Obligation:

(17) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

(18) Obligation:

(19) PrologToCdtProblemTransformerProof (UPPER BOUND (ID) transformation)

(20) Obligation:

(21) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

(22) Obligation:

(23) CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID) transformation)

(24) Obligation:

(25) CdtKnowledgeProof (EQUIVALENT transformation)

(26) Obligation:

(27) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

(28) Obligation:

(29) CdtKnowledgeProof (EQUIVALENT transformation)

(30) Obligation:

(31) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

(32) Obligation:

(33) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

(34) Obligation:

(35) CdtKnowledgeProof (EQUIVALENT transformation)

(36) Obligation:

(37) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

(38) Obligation:

(39) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))) transformation)

(40) Obligation:

(41) SIsEmptyProof (EQUIVALENT transformation)

(42) BOUNDS(O(1), O(1))