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

(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,g,a)

(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,g,a)

(3) 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\nT2 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\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: true | insert(T6, void, T3), SCOPE: 1, CLAUSE: 1 | insert(T6, void, T3), SCOPE: 1, CLAUSE: 3 | insert(T6, void, T3), 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\nT2 is ground\nX4 is free\ninsert(T1, T2, T3) !=? insert(X4, void, tree(X4, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: insert(T6, void, T3), SCOPE: 1, CLAUSE: 1 | insert(T6, void, T3), SCOPE: 1, CLAUSE: 3 | insert(T6, void, T3), SCOPE: 1, CLAUSE: 4\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: insert(T6, void, T3), SCOPE: 1, CLAUSE: 3 | insert(T6, void, T3), SCOPE: 1, CLAUSE: 4\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: insert(T6, void, T3), SCOPE: 1, CLAUSE: 4\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: true | insert(T16, tree(T16, T17, T18), T3), SCOPE: 1, CLAUSE: 3 | insert(T16, tree(T16, T17, T18), T3), SCOPE: 1, CLAUSE: 4\n\nT16 is ground\nT17 is ground\nT18 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT2 is ground\nX4 is free\nX24 is free\nX25 is free\nX26 is free\ninsert(T1, T2, T3) !=? insert(X4, void, tree(X4, void, void))\ninsert(T1, T2, T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: insert(T16, tree(T16, T17, T18), T3), SCOPE: 1, CLAUSE: 3 | insert(T16, tree(T16, T17, T18), T3), SCOPE: 1, CLAUSE: 4\n\nT16 is ground\nT17 is ground\nT18 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: insert(T16, tree(T16, T17, T18), T3), SCOPE: 1, CLAUSE: 3\n\nT16 is ground\nT17 is ground\nT18 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: insert(T16, tree(T16, T17, T18), T3), SCOPE: 1, CLAUSE: 4\n\nT16 is ground\nT17 is ground\nT18 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: ','(less(T35, T35), insert(T35, T36, T39))\n\nT35 is ground\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: less(T35, T35)\n\nT35 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: insert(T35, T36, T39)\n\nT35 is ground\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: less(T35, T35), SCOPE: 2, CLAUSE: 2 | less(T35, T35), SCOPE: 2, CLAUSE: 5\n\nT35 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: less(T35, T35), SCOPE: 2, CLAUSE: 5\n\nT35 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: less(T42, T42)\n\nT42 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: ','(less(T53, T53), insert(T53, T55, T57))\n\nT53 is ground\nT55 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT1 is ground\nT2 is ground\nX4 is free\nX24 is free\nX25 is free\nX26 is free\ninsert(T1, T2, T3) !=? insert(X4, void, tree(X4, void, void))\ninsert(T1, T2, T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT2 is ground\nX4 is free\nX24 is free\nX25 is free\nX26 is free\ninsert(T1, T2, T3) !=? insert(X4, void, tree(X4, void, void))\ninsert(T1, T2, T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ','(less(T78, T79), insert(T78, T80, T83))\n\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(T78, tree(T79, T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: less(T78, T79)\n\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(T78, tree(T79, T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: insert(T78, T80, T83)\n\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(T78, tree(T79, T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: less(T78, T79), SCOPE: 3, CLAUSE: 2 | less(T78, T79), SCOPE: 3, CLAUSE: 5\n\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(T78, tree(T79, T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: true | less(0, s(T90)), SCOPE: 3, CLAUSE: 5\n\nT90 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: less(T78, T79), SCOPE: 3, CLAUSE: 5\n\nT78 is ground\nT79 is ground\nT80 is ground\nT81 is ground\nX24 is free\nX25 is free\nX26 is free\nX115 is free\ninsert(T78, tree(T79, T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))\nless(T78, T79) !=? less(0, s(X115))", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: less(0, s(T90)), SCOPE: 3, CLAUSE: 5\n\nT90 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: less(T95, T96)\n\nT80 is ground\nT81 is ground\nT95 is ground\nT96 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(s(T95), tree(s(T96), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: less(T95, T96), SCOPE: 4, CLAUSE: 2 | less(T95, T96), SCOPE: 4, CLAUSE: 5\n\nT80 is ground\nT81 is ground\nT95 is ground\nT96 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(s(T95), tree(s(T96), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: true | less(0, s(T101)), SCOPE: 4, CLAUSE: 5\n\nT101 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: less(T95, T96), SCOPE: 4, CLAUSE: 5\n\nT80 is ground\nT81 is ground\nT95 is ground\nT96 is ground\nX24 is free\nX25 is free\nX26 is free\nX128 is free\ninsert(s(T95), tree(s(T96), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))\nless(T95, T96) !=? less(0, s(X128))", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: less(0, s(T101)), SCOPE: 4, CLAUSE: 5\n\nT101 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: less(T106, T107)\n\nT80 is ground\nT81 is ground\nT106 is ground\nT107 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(s(s(T106)), tree(s(s(T107)), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: less(T106, T107), SCOPE: 5, CLAUSE: 2 | less(T106, T107), SCOPE: 5, CLAUSE: 5\n\nT80 is ground\nT81 is ground\nT106 is ground\nT107 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(s(s(T106)), tree(s(s(T107)), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: true | less(0, s(T112)), SCOPE: 5, CLAUSE: 5\n\nT112 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: less(T106, T107), SCOPE: 5, CLAUSE: 5\n\nT80 is ground\nT81 is ground\nT106 is ground\nT107 is ground\nX24 is free\nX25 is free\nX26 is free\nX141 is free\ninsert(s(s(T106)), tree(s(s(T107)), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))\nless(T106, T107) !=? less(0, s(X141))", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: less(0, s(T112)), SCOPE: 5, CLAUSE: 5\n\nT112 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: less(T117, T118)\n\nT80 is ground\nT81 is ground\nT117 is ground\nT118 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(s(s(s(T117))), tree(s(s(s(T118))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: less(T117, T118), SCOPE: 6, CLAUSE: 2 | less(T117, T118), SCOPE: 6, CLAUSE: 5\n\nT80 is ground\nT81 is ground\nT117 is ground\nT118 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(s(s(s(T117))), tree(s(s(s(T118))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: true | less(0, s(T123)), SCOPE: 6, CLAUSE: 5\n\nT123 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: less(T117, T118), SCOPE: 6, CLAUSE: 5\n\nT80 is ground\nT81 is ground\nT117 is ground\nT118 is ground\nX24 is free\nX25 is free\nX26 is free\nX154 is free\ninsert(s(s(s(T117))), tree(s(s(s(T118))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))\nless(T117, T118) !=? less(0, s(X154))", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: less(0, s(T123)), SCOPE: 6, CLAUSE: 5\n\nT123 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: less(T128, T129)\n\nT80 is ground\nT81 is ground\nT128 is ground\nT129 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(s(s(s(s(T128)))), tree(s(s(s(s(T129)))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: less(T128, T129), SCOPE: 7, CLAUSE: 2 | less(T128, T129), SCOPE: 7, CLAUSE: 5\n\nT80 is ground\nT81 is ground\nT128 is ground\nT129 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(s(s(s(s(T128)))), tree(s(s(s(s(T129)))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: true | less(0, s(T134)), SCOPE: 7, CLAUSE: 5\n\nT134 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: less(T128, T129), SCOPE: 7, CLAUSE: 5\n\nT80 is ground\nT81 is ground\nT128 is ground\nT129 is ground\nX24 is free\nX25 is free\nX26 is free\nX167 is free\ninsert(s(s(s(s(T128)))), tree(s(s(s(s(T129)))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))\nless(T128, T129) !=? less(0, s(X167))", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: less(0, s(T134)), SCOPE: 7, CLAUSE: 5\n\nT134 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: less(T139, T140)\n\nT80 is ground\nT81 is ground\nT139 is ground\nT140 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(s(s(s(s(s(T139))))), tree(s(s(s(s(s(T140))))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: less(T139, T140), SCOPE: 8, CLAUSE: 2 | less(T139, T140), SCOPE: 8, CLAUSE: 5\n\nT80 is ground\nT81 is ground\nT139 is ground\nT140 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(s(s(s(s(s(T139))))), tree(s(s(s(s(s(T140))))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: true | less(0, s(T145)), SCOPE: 8, CLAUSE: 5\n\nT145 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: less(T139, T140), SCOPE: 8, CLAUSE: 5\n\nT80 is ground\nT81 is ground\nT139 is ground\nT140 is ground\nX24 is free\nX25 is free\nX26 is free\nX180 is free\ninsert(s(s(s(s(s(T139))))), tree(s(s(s(s(s(T140))))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))\nless(T139, T140) !=? less(0, s(X180))", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: less(0, s(T145)), SCOPE: 8, CLAUSE: 5\n\nT145 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: less(T150, T151)\n\nT80 is ground\nT81 is ground\nT150 is ground\nT151 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(s(s(s(s(s(s(T150)))))), tree(s(s(s(s(s(s(T151)))))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: less(T150, T151), SCOPE: 9, CLAUSE: 2 | less(T150, T151), SCOPE: 9, CLAUSE: 5\n\nT80 is ground\nT81 is ground\nT150 is ground\nT151 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(s(s(s(s(s(s(T150)))))), tree(s(s(s(s(s(s(T151)))))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: true | less(0, s(T156)), SCOPE: 9, CLAUSE: 5\n\nT156 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: less(T150, T151), SCOPE: 9, CLAUSE: 5\n\nT80 is ground\nT81 is ground\nT150 is ground\nT151 is ground\nX24 is free\nX25 is free\nX26 is free\nX193 is free\ninsert(s(s(s(s(s(s(T150)))))), tree(s(s(s(s(s(s(T151)))))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))\nless(T150, T151) !=? less(0, s(X193))", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: less(0, s(T156)), SCOPE: 9, CLAUSE: 5\n\nT156 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: less(T161, T162)\n\nT80 is ground\nT81 is ground\nT161 is ground\nT162 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(s(s(s(s(s(s(s(T161))))))), tree(s(s(s(s(s(s(s(T162))))))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: less(T161, T162), SCOPE: 10, CLAUSE: 2 | less(T161, T162), SCOPE: 10, CLAUSE: 5\n\nT80 is ground\nT81 is ground\nT161 is ground\nT162 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(s(s(s(s(s(s(s(T161))))))), tree(s(s(s(s(s(s(s(T162))))))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: true | less(0, s(T167)), SCOPE: 10, CLAUSE: 5\n\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: less(T161, T162), SCOPE: 10, CLAUSE: 5\n\nT80 is ground\nT81 is ground\nT161 is ground\nT162 is ground\nX24 is free\nX25 is free\nX26 is free\nX206 is free\ninsert(s(s(s(s(s(s(s(T161))))))), tree(s(s(s(s(s(s(s(T162))))))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))\nless(T161, T162) !=? less(0, s(X206))", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: less(0, s(T167)), SCOPE: 10, CLAUSE: 5\n\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: less(T172, T173)\n\nT80 is ground\nT81 is ground\nT172 is ground\nT173 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(s(s(s(s(s(s(s(s(T172)))))))), tree(s(s(s(s(s(s(s(s(T173)))))))), T80, T81), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: less(T172, T173)\n\nT172 is ground\nT173 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: less(T172, T173), SCOPE: 11, CLAUSE: 2 | less(T172, T173), SCOPE: 11, CLAUSE: 5\n\nT172 is ground\nT173 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: true | less(0, s(T182)), SCOPE: 11, CLAUSE: 5\n\nT182 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: less(T172, T173), SCOPE: 11, CLAUSE: 5\n\nT172 is ground\nT173 is ground\nX221 is free\nless(T172, T173) !=? less(0, s(X221))", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: less(0, s(T182)), SCOPE: 11, CLAUSE: 5\n\nT182 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: less(T187, T188)\n\nT187 is ground\nT188 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: ','(less(T204, T203), insert(T203, T206, T208))\n\nT203 is ground\nT204 is ground\nT205 is ground\nT206 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(T203, tree(T204, T205, T206), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: less(T204, T203)\n\nT203 is ground\nT204 is ground\nT205 is ground\nT206 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(T203, tree(T204, T205, T206), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: insert(T203, T206, T208)\n\nT203 is ground\nT204 is ground\nT205 is ground\nT206 is ground\nX24 is free\nX25 is free\nX26 is free\ninsert(T203, tree(T204, T205, T206), T3) !=? insert(X24, tree(X24, X25, X26), tree(X24, X25, X26))", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 205 [arrowhead = none ];
205 -> 3;

206 [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 -> 206 [arrowhead = none ];
206 -> 6;

207 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 207 [arrowhead = none ];
207 -> 8;

208 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 208 [arrowhead = none ];
208 -> 9;

209 [label="EVAL with clause\ninsert(X24, tree(X24, X25, X26), tree(X24, X25, X26)).\nand substitutionT1 -> T16,\nX24 -> T16,\nX25 -> T17,\nX26 -> T18,\nT2 -> tree(T16, T17, T18),\nT3 -> tree(T16, T17, T18)", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 209 [arrowhead = none ];
209 -> 20;

210 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 210 [arrowhead = none ];
210 -> 21;

211 [label="BACKTRACK\nfor clause: insert(X, tree(X, Left, Right), tree(X, Left, Right))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
9 -> 211 [arrowhead = none ];
211 -> 11;

212 [label="BACKTRACK\nfor clause: insert(X, tree(Y, Left, Right), tree(Y, Left1, Right)) :- ','(less(X, Y), insert(X, Left, Left1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 212 [arrowhead = none ];
212 -> 14;

213 [label="BACKTRACK\nfor clause: insert(X, tree(Y, Left, Right), tree(Y, Left, Right1)) :- ','(less(Y, X), insert(X, Right, Right1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
14 -> 213 [arrowhead = none ];
213 -> 16;

214 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
20 -> 214 [arrowhead = none ];
214 -> 22;

215 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 215 [arrowhead = none ];
215 -> 54;

216 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 216 [arrowhead = none ];
216 -> 55;

217 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
22 -> 217 [arrowhead = none ];
217 -> 27;

218 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
22 -> 218 [arrowhead = none ];
218 -> 29;

219 [label="EVAL with clause\ninsert(X47, tree(X48, X49, X50), tree(X48, X51, X50)) :- ','(less(X47, X48), insert(X47, X49, X51)).\nand substitutionT16 -> T35,\nX47 -> T35,\nX48 -> T35,\nT17 -> T36,\nX49 -> T36,\nT18 -> T37,\nX50 -> T37,\nX51 -> T39,\nT3 -> tree(T35, T39, T37),\nT38 -> T39", fontsize=14, style = filled, fillcolor = lightblue];
27 -> 219 [arrowhead = none ];
219 -> 33;

220 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
27 -> 220 [arrowhead = none ];
220 -> 34;

221 [label="EVAL with clause\ninsert(X77, tree(X78, X79, X80), tree(X78, X79, X81)) :- ','(less(X78, X77), insert(X77, X80, X81)).\nand substitutionT16 -> T53,\nX77 -> T53,\nX78 -> T53,\nT17 -> T54,\nX79 -> T54,\nT18 -> T55,\nX80 -> T55,\nX81 -> T57,\nT3 -> tree(T53, T54, T57),\nT56 -> T57", fontsize=14, style = filled, fillcolor = lightblue];
29 -> 221 [arrowhead = none ];
221 -> 48;

222 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
29 -> 222 [arrowhead = none ];
222 -> 49;

223 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
33 -> 223 [arrowhead = none ];
223 -> 35;

224 [label="SPLIT 2\nnew knowledge:\nT35 is ground", fontsize=14, style = filled, fillcolor = violet];
33 -> 224 [arrowhead = none ];
224 -> 37;

225 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
35 -> 225 [arrowhead = none ];
225 -> 40;

226 [label="INSTANCE with matching:\nT1 -> T35\nT2 -> T36\nT3 -> T39", fontsize=14, style = filled, fillcolor = lightgrey];
37 -> 226 [arrowhead = none , style=dashed];
226 -> 1[style=dashed];

227 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
40 -> 227 [arrowhead = none ];
227 -> 42;

228 [label="EVAL with clause\nless(s(X61), s(X62)) :- less(X61, X62).\nand substitutionX61 -> T42,\nT35 -> s(T42),\nX62 -> T42", fontsize=14, style = filled, fillcolor = lightblue];
42 -> 228 [arrowhead = none ];
228 -> 44;

229 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
42 -> 229 [arrowhead = none ];
229 -> 46;

230 [label="INSTANCE with matching:\nT35 -> T42", fontsize=14, style = filled, fillcolor = lightgrey];
44 -> 230 [arrowhead = none , style=dashed];
230 -> 35[style=dashed];

231 [label="INSTANCE with matching:\nT35 -> T53\nT36 -> T55\nT39 -> T57", fontsize=14, style = filled, fillcolor = lightgrey];
48 -> 231 [arrowhead = none , style=dashed];
231 -> 33[style=dashed];

232 [label="EVAL with clause\ninsert(X104, tree(X105, X106, X107), tree(X105, X108, X107)) :- ','(less(X104, X105), insert(X104, X106, X108)).\nand substitutionT1 -> T78,\nX104 -> T78,\nX105 -> T79,\nX106 -> T80,\nX107 -> T81,\nT2 -> tree(T79, T80, T81),\nX108 -> T83,\nT3 -> tree(T79, T83, T81),\nT82 -> T83", fontsize=14, style = filled, fillcolor = lightblue];
54 -> 232 [arrowhead = none ];
232 -> 59;

233 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
54 -> 233 [arrowhead = none ];
233 -> 61;

234 [label="EVAL with clause\ninsert(X244, tree(X245, X246, X247), tree(X245, X246, X248)) :- ','(less(X245, X244), insert(X244, X247, X248)).\nand substitutionT1 -> T203,\nX244 -> T203,\nX245 -> T204,\nX246 -> T205,\nX247 -> T206,\nT2 -> tree(T204, T205, T206),\nX248 -> T208,\nT3 -> tree(T204, T205, T208),\nT207 -> T208", fontsize=14, style = filled, fillcolor = lightblue];
55 -> 234 [arrowhead = none ];
234 -> 200;

235 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
55 -> 235 [arrowhead = none ];
235 -> 202;

236 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
59 -> 236 [arrowhead = none ];
236 -> 64;

237 [label="SPLIT 2\nnew knowledge:\nT78 is ground\nT79 is ground", fontsize=14, style = filled, fillcolor = violet];
59 -> 237 [arrowhead = none ];
237 -> 65;

238 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
64 -> 238 [arrowhead = none ];
238 -> 66;

239 [label="INSTANCE with matching:\nT1 -> T78\nT2 -> T80\nT3 -> T83", fontsize=14, style = filled, fillcolor = lightgrey];
65 -> 239 [arrowhead = none , style=dashed];
239 -> 1[style=dashed];

240 [label="EVAL with clause\nless(0, s(X115)).\nand substitutionT78 -> 0,\nX115 -> T90,\nT79 -> s(T90)", fontsize=14, style = filled, fillcolor = lightblue];
66 -> 240 [arrowhead = none ];
240 -> 67;

241 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
66 -> 241 [arrowhead = none ];
241 -> 69;

242 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
67 -> 242 [arrowhead = none ];
242 -> 70;

243 [label="EVAL with clause\nless(s(X122), s(X123)) :- less(X122, X123).\nand substitutionX122 -> T95,\nT78 -> s(T95),\nX123 -> T96,\nT79 -> s(T96)", fontsize=14, style = filled, fillcolor = lightblue];
69 -> 243 [arrowhead = none ];
243 -> 75;

244 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
69 -> 244 [arrowhead = none ];
244 -> 76;

245 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
70 -> 245 [arrowhead = none ];
245 -> 71;

246 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
75 -> 246 [arrowhead = none ];
246 -> 80;

247 [label="EVAL with clause\nless(0, s(X128)).\nand substitutionT95 -> 0,\nX128 -> T101,\nT96 -> s(T101)", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 247 [arrowhead = none ];
247 -> 83;

248 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
80 -> 248 [arrowhead = none ];
248 -> 84;

249 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
83 -> 249 [arrowhead = none ];
249 -> 85;

250 [label="EVAL with clause\nless(s(X135), s(X136)) :- less(X135, X136).\nand substitutionX135 -> T106,\nT95 -> s(T106),\nX136 -> T107,\nT96 -> s(T107)", fontsize=14, style = filled, fillcolor = lightblue];
84 -> 250 [arrowhead = none ];
250 -> 89;

251 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
84 -> 251 [arrowhead = none ];
251 -> 90;

252 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
85 -> 252 [arrowhead = none ];
252 -> 86;

253 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
89 -> 253 [arrowhead = none ];
253 -> 96;

254 [label="EVAL with clause\nless(0, s(X141)).\nand substitutionT106 -> 0,\nX141 -> T112,\nT107 -> s(T112)", fontsize=14, style = filled, fillcolor = lightblue];
96 -> 254 [arrowhead = none ];
254 -> 97;

255 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
96 -> 255 [arrowhead = none ];
255 -> 98;

256 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
97 -> 256 [arrowhead = none ];
256 -> 99;

257 [label="EVAL with clause\nless(s(X148), s(X149)) :- less(X148, X149).\nand substitutionX148 -> T117,\nT106 -> s(T117),\nX149 -> T118,\nT107 -> s(T118)", fontsize=14, style = filled, fillcolor = lightblue];
98 -> 257 [arrowhead = none ];
257 -> 103;

258 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
98 -> 258 [arrowhead = none ];
258 -> 104;

259 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
99 -> 259 [arrowhead = none ];
259 -> 100;

260 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
103 -> 260 [arrowhead = none ];
260 -> 109;

261 [label="EVAL with clause\nless(0, s(X154)).\nand substitutionT117 -> 0,\nX154 -> T123,\nT118 -> s(T123)", fontsize=14, style = filled, fillcolor = lightblue];
109 -> 261 [arrowhead = none ];
261 -> 110;

262 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
109 -> 262 [arrowhead = none ];
262 -> 112;

263 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
110 -> 263 [arrowhead = none ];
263 -> 113;

264 [label="EVAL with clause\nless(s(X161), s(X162)) :- less(X161, X162).\nand substitutionX161 -> T128,\nT117 -> s(T128),\nX162 -> T129,\nT118 -> s(T129)", fontsize=14, style = filled, fillcolor = lightblue];
112 -> 264 [arrowhead = none ];
264 -> 119;

265 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
112 -> 265 [arrowhead = none ];
265 -> 120;

266 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
113 -> 266 [arrowhead = none ];
266 -> 114;

267 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
119 -> 267 [arrowhead = none ];
267 -> 123;

268 [label="EVAL with clause\nless(0, s(X167)).\nand substitutionT128 -> 0,\nX167 -> T134,\nT129 -> s(T134)", fontsize=14, style = filled, fillcolor = lightblue];
123 -> 268 [arrowhead = none ];
268 -> 125;

269 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
123 -> 269 [arrowhead = none ];
269 -> 127;

270 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
125 -> 270 [arrowhead = none ];
270 -> 128;

271 [label="EVAL with clause\nless(s(X174), s(X175)) :- less(X174, X175).\nand substitutionX174 -> T139,\nT128 -> s(T139),\nX175 -> T140,\nT129 -> s(T140)", fontsize=14, style = filled, fillcolor = lightblue];
127 -> 271 [arrowhead = none ];
271 -> 133;

272 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
127 -> 272 [arrowhead = none ];
272 -> 135;

273 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
128 -> 273 [arrowhead = none ];
273 -> 129;

274 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
133 -> 274 [arrowhead = none ];
274 -> 137;

275 [label="EVAL with clause\nless(0, s(X180)).\nand substitutionT139 -> 0,\nX180 -> T145,\nT140 -> s(T145)", fontsize=14, style = filled, fillcolor = lightblue];
137 -> 275 [arrowhead = none ];
275 -> 140;

276 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
137 -> 276 [arrowhead = none ];
276 -> 143;

277 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
140 -> 277 [arrowhead = none ];
277 -> 144;

278 [label="EVAL with clause\nless(s(X187), s(X188)) :- less(X187, X188).\nand substitutionX187 -> T150,\nT139 -> s(T150),\nX188 -> T151,\nT140 -> s(T151)", fontsize=14, style = filled, fillcolor = lightblue];
143 -> 278 [arrowhead = none ];
278 -> 148;

279 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
143 -> 279 [arrowhead = none ];
279 -> 150;

280 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
144 -> 280 [arrowhead = none ];
280 -> 146;

281 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
148 -> 281 [arrowhead = none ];
281 -> 152;

282 [label="EVAL with clause\nless(0, s(X193)).\nand substitutionT150 -> 0,\nX193 -> T156,\nT151 -> s(T156)", fontsize=14, style = filled, fillcolor = lightblue];
152 -> 282 [arrowhead = none ];
282 -> 154;

283 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
152 -> 283 [arrowhead = none ];
283 -> 158;

284 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
154 -> 284 [arrowhead = none ];
284 -> 159;

285 [label="EVAL with clause\nless(s(X200), s(X201)) :- less(X200, X201).\nand substitutionX200 -> T161,\nT150 -> s(T161),\nX201 -> T162,\nT151 -> s(T162)", fontsize=14, style = filled, fillcolor = lightblue];
158 -> 285 [arrowhead = none ];
285 -> 163;

286 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
158 -> 286 [arrowhead = none ];
286 -> 164;

287 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
159 -> 287 [arrowhead = none ];
287 -> 160;

288 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
163 -> 288 [arrowhead = none ];
288 -> 167;

289 [label="EVAL with clause\nless(0, s(X206)).\nand substitutionT161 -> 0,\nX206 -> T167,\nT162 -> s(T167)", fontsize=14, style = filled, fillcolor = lightblue];
167 -> 289 [arrowhead = none ];
289 -> 171;

290 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
167 -> 290 [arrowhead = none ];
290 -> 172;

291 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
171 -> 291 [arrowhead = none ];
291 -> 173;

292 [label="EVAL with clause\nless(s(X213), s(X214)) :- less(X213, X214).\nand substitutionX213 -> T172,\nT161 -> s(T172),\nX214 -> T173,\nT162 -> s(T173)", fontsize=14, style = filled, fillcolor = lightblue];
172 -> 292 [arrowhead = none ];
292 -> 177;

293 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
172 -> 293 [arrowhead = none ];
293 -> 178;

294 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
173 -> 294 [arrowhead = none ];
294 -> 174;

295 [label="GENERALIZATION\nT176 <-- s(s(s(s(s(s(s(T172)))))))\nT177 <-- s(s(s(s(s(s(s(T173)))))))\n\nNew Knowledge:\nT176 is ground\nT177 is ground", fontsize=14, style = filled, fillcolor = violet];
177 -> 295 [arrowhead = none ];
295 -> 182;

296 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
182 -> 296 [arrowhead = none ];
296 -> 185;

297 [label="EVAL with clause\nless(0, s(X221)).\nand substitutionT172 -> 0,\nX221 -> T182,\nT173 -> s(T182)", fontsize=14, style = filled, fillcolor = lightblue];
185 -> 297 [arrowhead = none ];
297 -> 187;

298 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
185 -> 298 [arrowhead = none ];
298 -> 188;

299 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
187 -> 299 [arrowhead = none ];
299 -> 189;

300 [label="EVAL with clause\nless(s(X228), s(X229)) :- less(X228, X229).\nand substitutionX228 -> T187,\nT172 -> s(T187),\nX229 -> T188,\nT173 -> s(T188)", fontsize=14, style = filled, fillcolor = lightblue];
188 -> 300 [arrowhead = none ];
300 -> 192;

301 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
188 -> 301 [arrowhead = none ];
301 -> 193;

302 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
189 -> 302 [arrowhead = none ];
302 -> 191;

303 [label="INSTANCE with matching:\nT172 -> T187\nT173 -> T188", fontsize=14, style = filled, fillcolor = lightgrey];
192 -> 303 [arrowhead = none , style=dashed];
303 -> 182[style=dashed];

304 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
200 -> 304 [arrowhead = none ];
304 -> 203;

305 [label="SPLIT 2\nnew knowledge:\nT204 is ground\nT203 is ground", fontsize=14, style = filled, fillcolor = violet];
200 -> 305 [arrowhead = none ];
305 -> 204;

306 [label="INSTANCE with matching:\nT172 -> T204\nT173 -> T203", fontsize=14, style = filled, fillcolor = lightgrey];
203 -> 306 [arrowhead = none , style=dashed];
306 -> 182[style=dashed];

307 [label="INSTANCE with matching:\nT1 -> T203\nT2 -> T206\nT3 -> T208", fontsize=14, style = filled, fillcolor = lightgrey];
204 -> 307 [arrowhead = none , style=dashed];
307 -> 1[style=dashed];

}

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, void) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U1(f22_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(z0, z1) → U2(f21_in(z0, z1), z0, z1)
U1(f22_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U1(f22_out2(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U2(f21_out1(z0), z1, z2) → f1_out1(z0)
U2(f21_out2(z0), z1, z2) → f1_out1(z0)
f182_in(0, s(z0)) → f182_out1
f182_in(s(z0), s(z1)) → U3(f182_in(z0, z1), s(z0), s(z1))
U3(f182_out1, s(z0), s(z1)) → f182_out1
f35_in(s(z0)) → U4(f35_in(z0), s(z0))
U4(f35_out1, s(z0)) → f35_out1
f64_in(0, s(z0)) → f64_out1
f64_in(s(0), s(s(z0))) → f64_out1
f64_in(s(s(0)), s(s(s(z0)))) → f64_out1
f64_in(s(s(s(0))), s(s(s(s(z0))))) → f64_out1
f64_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f64_out1
f64_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f64_out1
f64_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U5(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U5(f182_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f64_out1
f54_in(z0, tree(z1, z2, z3)) → U6(f59_in(z0, z1, z2), z0, tree(z1, z2, z3))
U6(f59_out1(z0), z1, tree(z2, z3, z4)) → f54_out1(tree(z2, z0, z4))
f55_in(z0, tree(z1, z2, z3)) → U7(f200_in(z1, z0, z3), z0, tree(z1, z2, z3))
U7(f200_out1(z0), z1, tree(z2, z3, z4)) → f55_out1(tree(z2, z3, z0))
f27_in(z0, z1, z2) → U8(f33_in(z0, z1), z0, z1, z2)
U8(f33_out1(z0), z1, z2, z3) → f27_out1(tree(z1, z0, z3))
f29_in(z0, z1, z2) → U9(f33_in(z0, z2), z0, z1, z2)
U9(f33_out1(z0), z1, z2, z3) → f29_out1(tree(z1, z2, z0))
f33_in(z0, z1) → U10(f35_in(z0), z0, z1)
U10(f35_out1, z0, z1) → U11(f1_in(z0, z1), z0, z1)
U11(f1_out1(z0), z1, z2) → f33_out1(z0)
f59_in(z0, z1, z2) → U12(f64_in(z0, z1), z0, z1, z2)
U12(f64_out1, z0, z1, z2) → U13(f1_in(z0, z2), z0, z1, z2)
U13(f1_out1(z0), z1, z2, z3) → f59_out1(z0)
f200_in(z0, z1, z2) → U14(f182_in(z0, z1), z0, z1, z2)
U14(f182_out1, z0, z1, z2) → U15(f1_in(z1, z2), z0, z1, z2)
U15(f1_out1(z0), z1, z2, z3) → f200_out1(z0)
f21_in(z0, z1) → U16(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U16(f54_out1(z0), z1, z2, z3) → f21_out1(z0)
U16(z0, f55_out1(z1), z2, z3) → f21_out2(z1)
f22_in(z0, z1, z2) → U17(f27_in(z0, z1, z2), f29_in(z0, z1, z2), z0, z1, z2)
U17(f27_out1(z0), z1, z2, z3, z4) → f22_out1(z0)
U17(z0, f29_out1(z1), z2, z3, z4) → f22_out2(z1)

Tuples:

F1_IN(z0, tree(z0, z1, z2)) → c2(U1'(f22_in(z0, z1, z2), z0, tree(z0, z1, z2)), F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(U2'(f21_in(z0, z1), z0, z1), F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(U3'(f182_in(z0, z1), s(z0), s(z1)), F182_IN(z0, z1))
F35_IN(s(z0)) → c11(U4'(f35_in(z0), s(z0)), F35_IN(z0))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c21(U5'(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))), F182_IN(z0, z1))
F54_IN(z0, tree(z1, z2, z3)) → c23(U6'(f59_in(z0, z1, z2), z0, tree(z1, z2, z3)), F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(U7'(f200_in(z1, z0, z3), z0, tree(z1, z2, z3)), F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(U8'(f33_in(z0, z1), z0, z1, z2), F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(U9'(f33_in(z0, z2), z0, z1, z2), F33_IN(z0, z2))
F33_IN(z0, z1) → c31(U10'(f35_in(z0), z0, z1), F35_IN(z0))
U10'(f35_out1, z0, z1) → c32(U11'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F59_IN(z0, z1, z2) → c34(U12'(f64_in(z0, z1), z0, z1, z2), F64_IN(z0, z1))
U12'(f64_out1, z0, z1, z2) → c35(U13'(f1_in(z0, z2), z0, z1, z2), F1_IN(z0, z2))
F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
U14'(f182_out1, z0, z1, z2) → c38(U15'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F21_IN(z0, z1) → c40(U16'(f54_in(z0, z1), f55_in(z0, z1), z0, z1), F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(U17'(f27_in(z0, z1, z2), f29_in(z0, z1, z2), z0, z1, z2), F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))

S tuples:

F1_IN(z0, tree(z0, z1, z2)) → c2(U1'(f22_in(z0, z1, z2), z0, tree(z0, z1, z2)), F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(U2'(f21_in(z0, z1), z0, z1), F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(U3'(f182_in(z0, z1), s(z0), s(z1)), F182_IN(z0, z1))
F35_IN(s(z0)) → c11(U4'(f35_in(z0), s(z0)), F35_IN(z0))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c21(U5'(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))), F182_IN(z0, z1))
F54_IN(z0, tree(z1, z2, z3)) → c23(U6'(f59_in(z0, z1, z2), z0, tree(z1, z2, z3)), F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(U7'(f200_in(z1, z0, z3), z0, tree(z1, z2, z3)), F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(U8'(f33_in(z0, z1), z0, z1, z2), F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(U9'(f33_in(z0, z2), z0, z1, z2), F33_IN(z0, z2))
F33_IN(z0, z1) → c31(U10'(f35_in(z0), z0, z1), F35_IN(z0))
U10'(f35_out1, z0, z1) → c32(U11'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F59_IN(z0, z1, z2) → c34(U12'(f64_in(z0, z1), z0, z1, z2), F64_IN(z0, z1))
U12'(f64_out1, z0, z1, z2) → c35(U13'(f1_in(z0, z2), z0, z1, z2), F1_IN(z0, z2))
F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
U14'(f182_out1, z0, z1, z2) → c38(U15'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F21_IN(z0, z1) → c40(U16'(f54_in(z0, z1), f55_in(z0, z1), z0, z1), F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(U17'(f27_in(z0, z1, z2), f29_in(z0, z1, z2), z0, z1, z2), F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, f182_in, U3, f35_in, U4, f64_in, U5, f54_in, U6, f55_in, U7, f27_in, U8, f29_in, U9, f33_in, U10, U11, f59_in, U12, U13, f200_in, U14, U15, f21_in, U16, f22_in, U17

Defined Pair Symbols:

F1_IN, F182_IN, F35_IN, F64_IN, F54_IN, F55_IN, F27_IN, F29_IN, F33_IN, U10', F59_IN, U12', F200_IN, U14', F21_IN, F22_IN

Compound Symbols:

c2, c3, c9, c11, c21, c23, c25, c27, c29, c31, c32, c34, c35, c37, c38, c40, c43

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

Split RHS of tuples not part of any SCC

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, void) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U1(f22_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(z0, z1) → U2(f21_in(z0, z1), z0, z1)
U1(f22_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U1(f22_out2(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U2(f21_out1(z0), z1, z2) → f1_out1(z0)
U2(f21_out2(z0), z1, z2) → f1_out1(z0)
f182_in(0, s(z0)) → f182_out1
f182_in(s(z0), s(z1)) → U3(f182_in(z0, z1), s(z0), s(z1))
U3(f182_out1, s(z0), s(z1)) → f182_out1
f35_in(s(z0)) → U4(f35_in(z0), s(z0))
U4(f35_out1, s(z0)) → f35_out1
f64_in(0, s(z0)) → f64_out1
f64_in(s(0), s(s(z0))) → f64_out1
f64_in(s(s(0)), s(s(s(z0)))) → f64_out1
f64_in(s(s(s(0))), s(s(s(s(z0))))) → f64_out1
f64_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f64_out1
f64_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f64_out1
f64_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U5(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U5(f182_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f64_out1
f54_in(z0, tree(z1, z2, z3)) → U6(f59_in(z0, z1, z2), z0, tree(z1, z2, z3))
U6(f59_out1(z0), z1, tree(z2, z3, z4)) → f54_out1(tree(z2, z0, z4))
f55_in(z0, tree(z1, z2, z3)) → U7(f200_in(z1, z0, z3), z0, tree(z1, z2, z3))
U7(f200_out1(z0), z1, tree(z2, z3, z4)) → f55_out1(tree(z2, z3, z0))
f27_in(z0, z1, z2) → U8(f33_in(z0, z1), z0, z1, z2)
U8(f33_out1(z0), z1, z2, z3) → f27_out1(tree(z1, z0, z3))
f29_in(z0, z1, z2) → U9(f33_in(z0, z2), z0, z1, z2)
U9(f33_out1(z0), z1, z2, z3) → f29_out1(tree(z1, z2, z0))
f33_in(z0, z1) → U10(f35_in(z0), z0, z1)
U10(f35_out1, z0, z1) → U11(f1_in(z0, z1), z0, z1)
U11(f1_out1(z0), z1, z2) → f33_out1(z0)
f59_in(z0, z1, z2) → U12(f64_in(z0, z1), z0, z1, z2)
U12(f64_out1, z0, z1, z2) → U13(f1_in(z0, z2), z0, z1, z2)
U13(f1_out1(z0), z1, z2, z3) → f59_out1(z0)
f200_in(z0, z1, z2) → U14(f182_in(z0, z1), z0, z1, z2)
U14(f182_out1, z0, z1, z2) → U15(f1_in(z1, z2), z0, z1, z2)
U15(f1_out1(z0), z1, z2, z3) → f200_out1(z0)
f21_in(z0, z1) → U16(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U16(f54_out1(z0), z1, z2, z3) → f21_out1(z0)
U16(z0, f55_out1(z1), z2, z3) → f21_out2(z1)
f22_in(z0, z1, z2) → U17(f27_in(z0, z1, z2), f29_in(z0, z1, z2), z0, z1, z2)
U17(f27_out1(z0), z1, z2, z3, z4) → f22_out1(z0)
U17(z0, f29_out1(z1), z2, z3, z4) → f22_out2(z1)

Tuples:

F1_IN(z0, tree(z0, z1, z2)) → c2(U1'(f22_in(z0, z1, z2), z0, tree(z0, z1, z2)), F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(U2'(f21_in(z0, z1), z0, z1), F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(U3'(f182_in(z0, z1), s(z0), s(z1)), F182_IN(z0, z1))
F35_IN(s(z0)) → c11(U4'(f35_in(z0), s(z0)), F35_IN(z0))
F54_IN(z0, tree(z1, z2, z3)) → c23(U6'(f59_in(z0, z1, z2), z0, tree(z1, z2, z3)), F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(U7'(f200_in(z1, z0, z3), z0, tree(z1, z2, z3)), F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(U8'(f33_in(z0, z1), z0, z1, z2), F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(U9'(f33_in(z0, z2), z0, z1, z2), F33_IN(z0, z2))
F33_IN(z0, z1) → c31(U10'(f35_in(z0), z0, z1), F35_IN(z0))
U10'(f35_out1, z0, z1) → c32(U11'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F59_IN(z0, z1, z2) → c34(U12'(f64_in(z0, z1), z0, z1, z2), F64_IN(z0, z1))
U12'(f64_out1, z0, z1, z2) → c35(U13'(f1_in(z0, z2), z0, z1, z2), F1_IN(z0, z2))
F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
U14'(f182_out1, z0, z1, z2) → c38(U15'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F21_IN(z0, z1) → c40(U16'(f54_in(z0, z1), f55_in(z0, z1), z0, z1), F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(U17'(f27_in(z0, z1, z2), f29_in(z0, z1, z2), z0, z1, z2), F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(U5'(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F182_IN(z0, z1))

S tuples:

F1_IN(z0, tree(z0, z1, z2)) → c2(U1'(f22_in(z0, z1, z2), z0, tree(z0, z1, z2)), F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(U2'(f21_in(z0, z1), z0, z1), F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(U3'(f182_in(z0, z1), s(z0), s(z1)), F182_IN(z0, z1))
F35_IN(s(z0)) → c11(U4'(f35_in(z0), s(z0)), F35_IN(z0))
F54_IN(z0, tree(z1, z2, z3)) → c23(U6'(f59_in(z0, z1, z2), z0, tree(z1, z2, z3)), F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(U7'(f200_in(z1, z0, z3), z0, tree(z1, z2, z3)), F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(U8'(f33_in(z0, z1), z0, z1, z2), F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(U9'(f33_in(z0, z2), z0, z1, z2), F33_IN(z0, z2))
F33_IN(z0, z1) → c31(U10'(f35_in(z0), z0, z1), F35_IN(z0))
U10'(f35_out1, z0, z1) → c32(U11'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F59_IN(z0, z1, z2) → c34(U12'(f64_in(z0, z1), z0, z1, z2), F64_IN(z0, z1))
U12'(f64_out1, z0, z1, z2) → c35(U13'(f1_in(z0, z2), z0, z1, z2), F1_IN(z0, z2))
F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
U14'(f182_out1, z0, z1, z2) → c38(U15'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F21_IN(z0, z1) → c40(U16'(f54_in(z0, z1), f55_in(z0, z1), z0, z1), F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(U17'(f27_in(z0, z1, z2), f29_in(z0, z1, z2), z0, z1, z2), F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(U5'(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F182_IN(z0, z1))

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, f182_in, U3, f35_in, U4, f64_in, U5, f54_in, U6, f55_in, U7, f27_in, U8, f29_in, U9, f33_in, U10, U11, f59_in, U12, U13, f200_in, U14, U15, f21_in, U16, f22_in, U17

Defined Pair Symbols:

F1_IN, F182_IN, F35_IN, F54_IN, F55_IN, F27_IN, F29_IN, F33_IN, U10', F59_IN, U12', F200_IN, U14', F21_IN, F22_IN, F64_IN

Compound Symbols:

c2, c3, c9, c11, c23, c25, c27, c29, c31, c32, c34, c35, c37, c38, c40, c43, c

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

Removed 14 trailing tuple parts

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, void) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U1(f22_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(z0, z1) → U2(f21_in(z0, z1), z0, z1)
U1(f22_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U1(f22_out2(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U2(f21_out1(z0), z1, z2) → f1_out1(z0)
U2(f21_out2(z0), z1, z2) → f1_out1(z0)
f182_in(0, s(z0)) → f182_out1
f182_in(s(z0), s(z1)) → U3(f182_in(z0, z1), s(z0), s(z1))
U3(f182_out1, s(z0), s(z1)) → f182_out1
f35_in(s(z0)) → U4(f35_in(z0), s(z0))
U4(f35_out1, s(z0)) → f35_out1
f64_in(0, s(z0)) → f64_out1
f64_in(s(0), s(s(z0))) → f64_out1
f64_in(s(s(0)), s(s(s(z0)))) → f64_out1
f64_in(s(s(s(0))), s(s(s(s(z0))))) → f64_out1
f64_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f64_out1
f64_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f64_out1
f64_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U5(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U5(f182_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f64_out1
f54_in(z0, tree(z1, z2, z3)) → U6(f59_in(z0, z1, z2), z0, tree(z1, z2, z3))
U6(f59_out1(z0), z1, tree(z2, z3, z4)) → f54_out1(tree(z2, z0, z4))
f55_in(z0, tree(z1, z2, z3)) → U7(f200_in(z1, z0, z3), z0, tree(z1, z2, z3))
U7(f200_out1(z0), z1, tree(z2, z3, z4)) → f55_out1(tree(z2, z3, z0))
f27_in(z0, z1, z2) → U8(f33_in(z0, z1), z0, z1, z2)
U8(f33_out1(z0), z1, z2, z3) → f27_out1(tree(z1, z0, z3))
f29_in(z0, z1, z2) → U9(f33_in(z0, z2), z0, z1, z2)
U9(f33_out1(z0), z1, z2, z3) → f29_out1(tree(z1, z2, z0))
f33_in(z0, z1) → U10(f35_in(z0), z0, z1)
U10(f35_out1, z0, z1) → U11(f1_in(z0, z1), z0, z1)
U11(f1_out1(z0), z1, z2) → f33_out1(z0)
f59_in(z0, z1, z2) → U12(f64_in(z0, z1), z0, z1, z2)
U12(f64_out1, z0, z1, z2) → U13(f1_in(z0, z2), z0, z1, z2)
U13(f1_out1(z0), z1, z2, z3) → f59_out1(z0)
f200_in(z0, z1, z2) → U14(f182_in(z0, z1), z0, z1, z2)
U14(f182_out1, z0, z1, z2) → U15(f1_in(z1, z2), z0, z1, z2)
U15(f1_out1(z0), z1, z2, z3) → f200_out1(z0)
f21_in(z0, z1) → U16(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U16(f54_out1(z0), z1, z2, z3) → f21_out1(z0)
U16(z0, f55_out1(z1), z2, z3) → f21_out2(z1)
f22_in(z0, z1, z2) → U17(f27_in(z0, z1, z2), f29_in(z0, z1, z2), z0, z1, z2)
U17(f27_out1(z0), z1, z2, z3, z4) → f22_out1(z0)
U17(z0, f29_out1(z1), z2, z3, z4) → f22_out2(z1)

Tuples:

F33_IN(z0, z1) → c31(U10'(f35_in(z0), z0, z1), F35_IN(z0))
F59_IN(z0, z1, z2) → c34(U12'(f64_in(z0, z1), z0, z1, z2), F64_IN(z0, z1))
F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F182_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c2(F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(F182_IN(z0, z1))
F35_IN(s(z0)) → c11(F35_IN(z0))
F54_IN(z0, tree(z1, z2, z3)) → c23(F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(F33_IN(z0, z2))
U10'(f35_out1, z0, z1) → c32(F1_IN(z0, z1))
U12'(f64_out1, z0, z1, z2) → c35(F1_IN(z0, z2))
U14'(f182_out1, z0, z1, z2) → c38(F1_IN(z1, z2))
F21_IN(z0, z1) → c40(F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c

S tuples:

F33_IN(z0, z1) → c31(U10'(f35_in(z0), z0, z1), F35_IN(z0))
F59_IN(z0, z1, z2) → c34(U12'(f64_in(z0, z1), z0, z1, z2), F64_IN(z0, z1))
F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F182_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c2(F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(F182_IN(z0, z1))
F35_IN(s(z0)) → c11(F35_IN(z0))
F54_IN(z0, tree(z1, z2, z3)) → c23(F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(F33_IN(z0, z2))
U10'(f35_out1, z0, z1) → c32(F1_IN(z0, z1))
U12'(f64_out1, z0, z1, z2) → c35(F1_IN(z0, z2))
U14'(f182_out1, z0, z1, z2) → c38(F1_IN(z1, z2))
F21_IN(z0, z1) → c40(F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))
F64_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:

f1_in, U1, U2, f182_in, U3, f35_in, U4, f64_in, U5, f54_in, U6, f55_in, U7, f27_in, U8, f29_in, U9, f33_in, U10, U11, f59_in, U12, U13, f200_in, U14, U15, f21_in, U16, f22_in, U17

Defined Pair Symbols:

F33_IN, F59_IN, F200_IN, F64_IN, F1_IN, F182_IN, F35_IN, F54_IN, F55_IN, F27_IN, F29_IN, U10', U12', U14', F21_IN, F22_IN

Compound Symbols:

c31, c34, c37, c, c2, c3, c9, c11, c23, c25, c27, c29, c32, c35, c38, c40, c43, 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.

U10'(f35_out1, z0, z1) → c32(F1_IN(z0, z1))

We considered the (Usable) Rules:

f182_in(0, s(z0)) → f182_out1
f182_in(s(z0), s(z1)) → U3(f182_in(z0, z1), s(z0), s(z1))
U3(f182_out1, s(z0), s(z1)) → f182_out1
f64_in(0, s(z0)) → f64_out1
f64_in(s(0), s(s(z0))) → f64_out1
f64_in(s(s(0)), s(s(s(z0)))) → f64_out1
f64_in(s(s(s(0))), s(s(s(s(z0))))) → f64_out1
f64_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f64_out1
f64_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f64_out1
f64_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U5(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U5(f182_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f64_out1
f35_in(s(z0)) → U4(f35_in(z0), s(z0))
U4(f35_out1, s(z0)) → f35_out1

And the Tuples:

F33_IN(z0, z1) → c31(U10'(f35_in(z0), z0, z1), F35_IN(z0))
F59_IN(z0, z1, z2) → c34(U12'(f64_in(z0, z1), z0, z1, z2), F64_IN(z0, z1))
F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F182_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c2(F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(F182_IN(z0, z1))
F35_IN(s(z0)) → c11(F35_IN(z0))
F54_IN(z0, tree(z1, z2, z3)) → c23(F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(F33_IN(z0, z2))
U10'(f35_out1, z0, z1) → c32(F1_IN(z0, z1))
U12'(f64_out1, z0, z1, z2) → c35(F1_IN(z0, z2))
U14'(f182_out1, z0, z1, z2) → c38(F1_IN(z1, z2))
F21_IN(z0, z1) → c40(F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))
F64_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(F182_IN(x₁, x₂)) = 0   
POL(F1_IN(x₁, x₂)) = 0   
POL(F200_IN(x₁, x₂, x₃)) = 0   
POL(F21_IN(x₁, x₂)) = 0   
POL(F22_IN(x₁, x₂, x₃)) = 0   
POL(F27_IN(x₁, x₂, x₃)) = 0   
POL(F29_IN(x₁, x₂, x₃)) = 0   
POL(F33_IN(x₁, x₂)) = 0   
POL(F35_IN(x₁)) = 0   
POL(F54_IN(x₁, x₂)) = 0   
POL(F55_IN(x₁, x₂)) = 0   
POL(F59_IN(x₁, x₂, x₃)) = 0   
POL(F64_IN(x₁, x₂)) = 0   
POL(U10'(x₁, x₂, x₃)) = [2]x₁   
POL(U12'(x₁, x₂, x₃, x₄)) = 0   
POL(U14'(x₁, x₂, x₃, x₄)) = 0   
POL(U3(x₁, x₂, x₃)) = 0   
POL(U4(x₁, x₂)) = x₁   
POL(U5(x₁, x₂, x₃)) = 0   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c2(x₁)) = x₁   
POL(c23(x₁)) = x₁   
POL(c25(x₁)) = x₁   
POL(c27(x₁)) = x₁   
POL(c29(x₁)) = x₁   
POL(c3(x₁)) = x₁   
POL(c31(x₁, x₂)) = x₁ + x₂   
POL(c32(x₁)) = x₁   
POL(c34(x₁, x₂)) = x₁ + x₂   
POL(c35(x₁)) = x₁   
POL(c37(x₁, x₂)) = x₁ + x₂   
POL(c38(x₁)) = x₁   
POL(c40(x₁, x₂)) = x₁ + x₂   
POL(c43(x₁, x₂)) = x₁ + x₂   
POL(c9(x₁)) = x₁   
POL(f182_in(x₁, x₂)) = 0   
POL(f182_out1) = 0   
POL(f35_in(x₁)) = 0   
POL(f35_out1) = [2]   
POL(f64_in(x₁, x₂)) = 0   
POL(f64_out1) = 0   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = 0   

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, void) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U1(f22_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(z0, z1) → U2(f21_in(z0, z1), z0, z1)
U1(f22_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U1(f22_out2(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U2(f21_out1(z0), z1, z2) → f1_out1(z0)
U2(f21_out2(z0), z1, z2) → f1_out1(z0)
f182_in(0, s(z0)) → f182_out1
f182_in(s(z0), s(z1)) → U3(f182_in(z0, z1), s(z0), s(z1))
U3(f182_out1, s(z0), s(z1)) → f182_out1
f35_in(s(z0)) → U4(f35_in(z0), s(z0))
U4(f35_out1, s(z0)) → f35_out1
f64_in(0, s(z0)) → f64_out1
f64_in(s(0), s(s(z0))) → f64_out1
f64_in(s(s(0)), s(s(s(z0)))) → f64_out1
f64_in(s(s(s(0))), s(s(s(s(z0))))) → f64_out1
f64_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f64_out1
f64_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f64_out1
f64_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U5(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U5(f182_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f64_out1
f54_in(z0, tree(z1, z2, z3)) → U6(f59_in(z0, z1, z2), z0, tree(z1, z2, z3))
U6(f59_out1(z0), z1, tree(z2, z3, z4)) → f54_out1(tree(z2, z0, z4))
f55_in(z0, tree(z1, z2, z3)) → U7(f200_in(z1, z0, z3), z0, tree(z1, z2, z3))
U7(f200_out1(z0), z1, tree(z2, z3, z4)) → f55_out1(tree(z2, z3, z0))
f27_in(z0, z1, z2) → U8(f33_in(z0, z1), z0, z1, z2)
U8(f33_out1(z0), z1, z2, z3) → f27_out1(tree(z1, z0, z3))
f29_in(z0, z1, z2) → U9(f33_in(z0, z2), z0, z1, z2)
U9(f33_out1(z0), z1, z2, z3) → f29_out1(tree(z1, z2, z0))
f33_in(z0, z1) → U10(f35_in(z0), z0, z1)
U10(f35_out1, z0, z1) → U11(f1_in(z0, z1), z0, z1)
U11(f1_out1(z0), z1, z2) → f33_out1(z0)
f59_in(z0, z1, z2) → U12(f64_in(z0, z1), z0, z1, z2)
U12(f64_out1, z0, z1, z2) → U13(f1_in(z0, z2), z0, z1, z2)
U13(f1_out1(z0), z1, z2, z3) → f59_out1(z0)
f200_in(z0, z1, z2) → U14(f182_in(z0, z1), z0, z1, z2)
U14(f182_out1, z0, z1, z2) → U15(f1_in(z1, z2), z0, z1, z2)
U15(f1_out1(z0), z1, z2, z3) → f200_out1(z0)
f21_in(z0, z1) → U16(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U16(f54_out1(z0), z1, z2, z3) → f21_out1(z0)
U16(z0, f55_out1(z1), z2, z3) → f21_out2(z1)
f22_in(z0, z1, z2) → U17(f27_in(z0, z1, z2), f29_in(z0, z1, z2), z0, z1, z2)
U17(f27_out1(z0), z1, z2, z3, z4) → f22_out1(z0)
U17(z0, f29_out1(z1), z2, z3, z4) → f22_out2(z1)

Tuples:

F33_IN(z0, z1) → c31(U10'(f35_in(z0), z0, z1), F35_IN(z0))
F59_IN(z0, z1, z2) → c34(U12'(f64_in(z0, z1), z0, z1, z2), F64_IN(z0, z1))
F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F182_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c2(F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(F182_IN(z0, z1))
F35_IN(s(z0)) → c11(F35_IN(z0))
F54_IN(z0, tree(z1, z2, z3)) → c23(F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(F33_IN(z0, z2))
U10'(f35_out1, z0, z1) → c32(F1_IN(z0, z1))
U12'(f64_out1, z0, z1, z2) → c35(F1_IN(z0, z2))
U14'(f182_out1, z0, z1, z2) → c38(F1_IN(z1, z2))
F21_IN(z0, z1) → c40(F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c

S tuples:

F33_IN(z0, z1) → c31(U10'(f35_in(z0), z0, z1), F35_IN(z0))
F59_IN(z0, z1, z2) → c34(U12'(f64_in(z0, z1), z0, z1, z2), F64_IN(z0, z1))
F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F182_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c2(F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(F182_IN(z0, z1))
F35_IN(s(z0)) → c11(F35_IN(z0))
F54_IN(z0, tree(z1, z2, z3)) → c23(F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(F33_IN(z0, z2))
U12'(f64_out1, z0, z1, z2) → c35(F1_IN(z0, z2))
U14'(f182_out1, z0, z1, z2) → c38(F1_IN(z1, z2))
F21_IN(z0, z1) → c40(F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c

K tuples:

U10'(f35_out1, z0, z1) → c32(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, f182_in, U3, f35_in, U4, f64_in, U5, f54_in, U6, f55_in, U7, f27_in, U8, f29_in, U9, f33_in, U10, U11, f59_in, U12, U13, f200_in, U14, U15, f21_in, U16, f22_in, U17

Defined Pair Symbols:

F33_IN, F59_IN, F200_IN, F64_IN, F1_IN, F182_IN, F35_IN, F54_IN, F55_IN, F27_IN, F29_IN, U10', U12', U14', F21_IN, F22_IN

Compound Symbols:

c31, c34, c37, c, c2, c3, c9, c11, c23, c25, c27, c29, c32, c35, c38, c40, c43, c

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

Use narrowing to replace F33_IN(z0, z1) → c31(U10'(f35_in(z0), z0, z1), F35_IN(z0)) by

F33_IN(s(z0), x1) → c31(U10'(U4(f35_in(z0), s(z0)), s(z0), x1), F35_IN(s(z0)))

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, void) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U1(f22_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(z0, z1) → U2(f21_in(z0, z1), z0, z1)
U1(f22_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U1(f22_out2(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U2(f21_out1(z0), z1, z2) → f1_out1(z0)
U2(f21_out2(z0), z1, z2) → f1_out1(z0)
f182_in(0, s(z0)) → f182_out1
f182_in(s(z0), s(z1)) → U3(f182_in(z0, z1), s(z0), s(z1))
U3(f182_out1, s(z0), s(z1)) → f182_out1
f35_in(s(z0)) → U4(f35_in(z0), s(z0))
U4(f35_out1, s(z0)) → f35_out1
f64_in(0, s(z0)) → f64_out1
f64_in(s(0), s(s(z0))) → f64_out1
f64_in(s(s(0)), s(s(s(z0)))) → f64_out1
f64_in(s(s(s(0))), s(s(s(s(z0))))) → f64_out1
f64_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f64_out1
f64_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f64_out1
f64_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U5(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U5(f182_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f64_out1
f54_in(z0, tree(z1, z2, z3)) → U6(f59_in(z0, z1, z2), z0, tree(z1, z2, z3))
U6(f59_out1(z0), z1, tree(z2, z3, z4)) → f54_out1(tree(z2, z0, z4))
f55_in(z0, tree(z1, z2, z3)) → U7(f200_in(z1, z0, z3), z0, tree(z1, z2, z3))
U7(f200_out1(z0), z1, tree(z2, z3, z4)) → f55_out1(tree(z2, z3, z0))
f27_in(z0, z1, z2) → U8(f33_in(z0, z1), z0, z1, z2)
U8(f33_out1(z0), z1, z2, z3) → f27_out1(tree(z1, z0, z3))
f29_in(z0, z1, z2) → U9(f33_in(z0, z2), z0, z1, z2)
U9(f33_out1(z0), z1, z2, z3) → f29_out1(tree(z1, z2, z0))
f33_in(z0, z1) → U10(f35_in(z0), z0, z1)
U10(f35_out1, z0, z1) → U11(f1_in(z0, z1), z0, z1)
U11(f1_out1(z0), z1, z2) → f33_out1(z0)
f59_in(z0, z1, z2) → U12(f64_in(z0, z1), z0, z1, z2)
U12(f64_out1, z0, z1, z2) → U13(f1_in(z0, z2), z0, z1, z2)
U13(f1_out1(z0), z1, z2, z3) → f59_out1(z0)
f200_in(z0, z1, z2) → U14(f182_in(z0, z1), z0, z1, z2)
U14(f182_out1, z0, z1, z2) → U15(f1_in(z1, z2), z0, z1, z2)
U15(f1_out1(z0), z1, z2, z3) → f200_out1(z0)
f21_in(z0, z1) → U16(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U16(f54_out1(z0), z1, z2, z3) → f21_out1(z0)
U16(z0, f55_out1(z1), z2, z3) → f21_out2(z1)
f22_in(z0, z1, z2) → U17(f27_in(z0, z1, z2), f29_in(z0, z1, z2), z0, z1, z2)
U17(f27_out1(z0), z1, z2, z3, z4) → f22_out1(z0)
U17(z0, f29_out1(z1), z2, z3, z4) → f22_out2(z1)

Tuples:

F59_IN(z0, z1, z2) → c34(U12'(f64_in(z0, z1), z0, z1, z2), F64_IN(z0, z1))
F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F182_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c2(F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(F182_IN(z0, z1))
F35_IN(s(z0)) → c11(F35_IN(z0))
F54_IN(z0, tree(z1, z2, z3)) → c23(F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(F33_IN(z0, z2))
U10'(f35_out1, z0, z1) → c32(F1_IN(z0, z1))
U12'(f64_out1, z0, z1, z2) → c35(F1_IN(z0, z2))
U14'(f182_out1, z0, z1, z2) → c38(F1_IN(z1, z2))
F21_IN(z0, z1) → c40(F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F33_IN(s(z0), x1) → c31(U10'(U4(f35_in(z0), s(z0)), s(z0), x1), F35_IN(s(z0)))

S tuples:

F59_IN(z0, z1, z2) → c34(U12'(f64_in(z0, z1), z0, z1, z2), F64_IN(z0, z1))
F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F182_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c2(F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(F182_IN(z0, z1))
F35_IN(s(z0)) → c11(F35_IN(z0))
F54_IN(z0, tree(z1, z2, z3)) → c23(F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(F33_IN(z0, z2))
U12'(f64_out1, z0, z1, z2) → c35(F1_IN(z0, z2))
U14'(f182_out1, z0, z1, z2) → c38(F1_IN(z1, z2))
F21_IN(z0, z1) → c40(F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F33_IN(s(z0), x1) → c31(U10'(U4(f35_in(z0), s(z0)), s(z0), x1), F35_IN(s(z0)))

K tuples:

U10'(f35_out1, z0, z1) → c32(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, f182_in, U3, f35_in, U4, f64_in, U5, f54_in, U6, f55_in, U7, f27_in, U8, f29_in, U9, f33_in, U10, U11, f59_in, U12, U13, f200_in, U14, U15, f21_in, U16, f22_in, U17

Defined Pair Symbols:

F59_IN, F200_IN, F64_IN, F1_IN, F182_IN, F35_IN, F54_IN, F55_IN, F27_IN, F29_IN, U10', U12', U14', F21_IN, F22_IN, F33_IN

Compound Symbols:

c34, c37, c, c2, c3, c9, c11, c23, c25, c27, c29, c32, c35, c38, c40, c43, c, c31

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

Split RHS of tuples not part of any SCC

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, void) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U1(f22_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(z0, z1) → U2(f21_in(z0, z1), z0, z1)
U1(f22_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U1(f22_out2(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U2(f21_out1(z0), z1, z2) → f1_out1(z0)
U2(f21_out2(z0), z1, z2) → f1_out1(z0)
f182_in(0, s(z0)) → f182_out1
f182_in(s(z0), s(z1)) → U3(f182_in(z0, z1), s(z0), s(z1))
U3(f182_out1, s(z0), s(z1)) → f182_out1
f35_in(s(z0)) → U4(f35_in(z0), s(z0))
U4(f35_out1, s(z0)) → f35_out1
f64_in(0, s(z0)) → f64_out1
f64_in(s(0), s(s(z0))) → f64_out1
f64_in(s(s(0)), s(s(s(z0)))) → f64_out1
f64_in(s(s(s(0))), s(s(s(s(z0))))) → f64_out1
f64_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f64_out1
f64_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f64_out1
f64_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U5(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U5(f182_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f64_out1
f54_in(z0, tree(z1, z2, z3)) → U6(f59_in(z0, z1, z2), z0, tree(z1, z2, z3))
U6(f59_out1(z0), z1, tree(z2, z3, z4)) → f54_out1(tree(z2, z0, z4))
f55_in(z0, tree(z1, z2, z3)) → U7(f200_in(z1, z0, z3), z0, tree(z1, z2, z3))
U7(f200_out1(z0), z1, tree(z2, z3, z4)) → f55_out1(tree(z2, z3, z0))
f27_in(z0, z1, z2) → U8(f33_in(z0, z1), z0, z1, z2)
U8(f33_out1(z0), z1, z2, z3) → f27_out1(tree(z1, z0, z3))
f29_in(z0, z1, z2) → U9(f33_in(z0, z2), z0, z1, z2)
U9(f33_out1(z0), z1, z2, z3) → f29_out1(tree(z1, z2, z0))
f33_in(z0, z1) → U10(f35_in(z0), z0, z1)
U10(f35_out1, z0, z1) → U11(f1_in(z0, z1), z0, z1)
U11(f1_out1(z0), z1, z2) → f33_out1(z0)
f59_in(z0, z1, z2) → U12(f64_in(z0, z1), z0, z1, z2)
U12(f64_out1, z0, z1, z2) → U13(f1_in(z0, z2), z0, z1, z2)
U13(f1_out1(z0), z1, z2, z3) → f59_out1(z0)
f200_in(z0, z1, z2) → U14(f182_in(z0, z1), z0, z1, z2)
U14(f182_out1, z0, z1, z2) → U15(f1_in(z1, z2), z0, z1, z2)
U15(f1_out1(z0), z1, z2, z3) → f200_out1(z0)
f21_in(z0, z1) → U16(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U16(f54_out1(z0), z1, z2, z3) → f21_out1(z0)
U16(z0, f55_out1(z1), z2, z3) → f21_out2(z1)
f22_in(z0, z1, z2) → U17(f27_in(z0, z1, z2), f29_in(z0, z1, z2), z0, z1, z2)
U17(f27_out1(z0), z1, z2, z3, z4) → f22_out1(z0)
U17(z0, f29_out1(z1), z2, z3, z4) → f22_out2(z1)

Tuples:

F59_IN(z0, z1, z2) → c34(U12'(f64_in(z0, z1), z0, z1, z2), F64_IN(z0, z1))
F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F182_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c2(F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(F182_IN(z0, z1))
F35_IN(s(z0)) → c11(F35_IN(z0))
F54_IN(z0, tree(z1, z2, z3)) → c23(F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(F33_IN(z0, z2))
U10'(f35_out1, z0, z1) → c32(F1_IN(z0, z1))
U12'(f64_out1, z0, z1, z2) → c35(F1_IN(z0, z2))
U14'(f182_out1, z0, z1, z2) → c38(F1_IN(z1, z2))
F21_IN(z0, z1) → c40(F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))
F33_IN(s(z0), x1) → c31(U10'(U4(f35_in(z0), s(z0)), s(z0), x1), F35_IN(s(z0)))

S tuples:

F59_IN(z0, z1, z2) → c34(U12'(f64_in(z0, z1), z0, z1, z2), F64_IN(z0, z1))
F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F182_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c2(F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(F182_IN(z0, z1))
F35_IN(s(z0)) → c11(F35_IN(z0))
F54_IN(z0, tree(z1, z2, z3)) → c23(F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(F33_IN(z0, z2))
U12'(f64_out1, z0, z1, z2) → c35(F1_IN(z0, z2))
U14'(f182_out1, z0, z1, z2) → c38(F1_IN(z1, z2))
F21_IN(z0, z1) → c40(F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))
F33_IN(s(z0), x1) → c31(U10'(U4(f35_in(z0), s(z0)), s(z0), x1), F35_IN(s(z0)))

K tuples:

U10'(f35_out1, z0, z1) → c32(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, f182_in, U3, f35_in, U4, f64_in, U5, f54_in, U6, f55_in, U7, f27_in, U8, f29_in, U9, f33_in, U10, U11, f59_in, U12, U13, f200_in, U14, U15, f21_in, U16, f22_in, U17

Defined Pair Symbols:

F59_IN, F200_IN, F64_IN, F1_IN, F182_IN, F35_IN, F54_IN, F55_IN, F27_IN, F29_IN, U10', U12', U14', F21_IN, F22_IN, F33_IN

Compound Symbols:

c34, c37, c, c2, c3, c9, c11, c23, c25, c27, c29, c32, c35, c38, c40, c43, c31

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

Use narrowing to replace F59_IN(z0, z1, z2) → c34(U12'(f64_in(z0, z1), z0, z1, z2), F64_IN(z0, z1)) by

F59_IN(0, s(z0), x2) → c34(U12'(f64_out1, 0, s(z0), x2), F64_IN(0, s(z0)))
F59_IN(s(0), s(s(z0)), x2) → c34(U12'(f64_out1, s(0), s(s(z0)), x2), F64_IN(s(0), s(s(z0))))
F59_IN(s(s(0)), s(s(s(z0))), x2) → c34(U12'(f64_out1, s(s(0)), s(s(s(z0))), x2), F64_IN(s(s(0)), s(s(s(z0)))))
F59_IN(s(s(s(0))), s(s(s(s(z0)))), x2) → c34(U12'(f64_out1, s(s(s(0))), s(s(s(s(z0)))), x2), F64_IN(s(s(s(0))), s(s(s(s(z0))))))
F59_IN(s(s(s(s(0)))), s(s(s(s(s(z0))))), x2) → c34(U12'(f64_out1, s(s(s(s(0)))), s(s(s(s(s(z0))))), x2), F64_IN(s(s(s(s(0)))), s(s(s(s(s(z0)))))))
F59_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2) → c34(U12'(f64_out1, s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2), F64_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))))
F59_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2) → c34(U12'(f64_out1, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2), F64_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))))
F59_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2) → c34(U12'(f64_out1, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2), F64_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))))
F59_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2) → c34(U12'(U5(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2), F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, void) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U1(f22_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(z0, z1) → U2(f21_in(z0, z1), z0, z1)
U1(f22_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U1(f22_out2(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U2(f21_out1(z0), z1, z2) → f1_out1(z0)
U2(f21_out2(z0), z1, z2) → f1_out1(z0)
f182_in(0, s(z0)) → f182_out1
f182_in(s(z0), s(z1)) → U3(f182_in(z0, z1), s(z0), s(z1))
U3(f182_out1, s(z0), s(z1)) → f182_out1
f35_in(s(z0)) → U4(f35_in(z0), s(z0))
U4(f35_out1, s(z0)) → f35_out1
f64_in(0, s(z0)) → f64_out1
f64_in(s(0), s(s(z0))) → f64_out1
f64_in(s(s(0)), s(s(s(z0)))) → f64_out1
f64_in(s(s(s(0))), s(s(s(s(z0))))) → f64_out1
f64_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f64_out1
f64_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f64_out1
f64_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U5(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U5(f182_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f64_out1
f54_in(z0, tree(z1, z2, z3)) → U6(f59_in(z0, z1, z2), z0, tree(z1, z2, z3))
U6(f59_out1(z0), z1, tree(z2, z3, z4)) → f54_out1(tree(z2, z0, z4))
f55_in(z0, tree(z1, z2, z3)) → U7(f200_in(z1, z0, z3), z0, tree(z1, z2, z3))
U7(f200_out1(z0), z1, tree(z2, z3, z4)) → f55_out1(tree(z2, z3, z0))
f27_in(z0, z1, z2) → U8(f33_in(z0, z1), z0, z1, z2)
U8(f33_out1(z0), z1, z2, z3) → f27_out1(tree(z1, z0, z3))
f29_in(z0, z1, z2) → U9(f33_in(z0, z2), z0, z1, z2)
U9(f33_out1(z0), z1, z2, z3) → f29_out1(tree(z1, z2, z0))
f33_in(z0, z1) → U10(f35_in(z0), z0, z1)
U10(f35_out1, z0, z1) → U11(f1_in(z0, z1), z0, z1)
U11(f1_out1(z0), z1, z2) → f33_out1(z0)
f59_in(z0, z1, z2) → U12(f64_in(z0, z1), z0, z1, z2)
U12(f64_out1, z0, z1, z2) → U13(f1_in(z0, z2), z0, z1, z2)
U13(f1_out1(z0), z1, z2, z3) → f59_out1(z0)
f200_in(z0, z1, z2) → U14(f182_in(z0, z1), z0, z1, z2)
U14(f182_out1, z0, z1, z2) → U15(f1_in(z1, z2), z0, z1, z2)
U15(f1_out1(z0), z1, z2, z3) → f200_out1(z0)
f21_in(z0, z1) → U16(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U16(f54_out1(z0), z1, z2, z3) → f21_out1(z0)
U16(z0, f55_out1(z1), z2, z3) → f21_out2(z1)
f22_in(z0, z1, z2) → U17(f27_in(z0, z1, z2), f29_in(z0, z1, z2), z0, z1, z2)
U17(f27_out1(z0), z1, z2, z3, z4) → f22_out1(z0)
U17(z0, f29_out1(z1), z2, z3, z4) → f22_out2(z1)

Tuples:

F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F182_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c2(F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(F182_IN(z0, z1))
F35_IN(s(z0)) → c11(F35_IN(z0))
F54_IN(z0, tree(z1, z2, z3)) → c23(F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(F33_IN(z0, z2))
U10'(f35_out1, z0, z1) → c32(F1_IN(z0, z1))
U12'(f64_out1, z0, z1, z2) → c35(F1_IN(z0, z2))
U14'(f182_out1, z0, z1, z2) → c38(F1_IN(z1, z2))
F21_IN(z0, z1) → c40(F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))
F33_IN(s(z0), x1) → c31(U10'(U4(f35_in(z0), s(z0)), s(z0), x1), F35_IN(s(z0)))
F59_IN(0, s(z0), x2) → c34(U12'(f64_out1, 0, s(z0), x2), F64_IN(0, s(z0)))
F59_IN(s(0), s(s(z0)), x2) → c34(U12'(f64_out1, s(0), s(s(z0)), x2), F64_IN(s(0), s(s(z0))))
F59_IN(s(s(0)), s(s(s(z0))), x2) → c34(U12'(f64_out1, s(s(0)), s(s(s(z0))), x2), F64_IN(s(s(0)), s(s(s(z0)))))
F59_IN(s(s(s(0))), s(s(s(s(z0)))), x2) → c34(U12'(f64_out1, s(s(s(0))), s(s(s(s(z0)))), x2), F64_IN(s(s(s(0))), s(s(s(s(z0))))))
F59_IN(s(s(s(s(0)))), s(s(s(s(s(z0))))), x2) → c34(U12'(f64_out1, s(s(s(s(0)))), s(s(s(s(s(z0))))), x2), F64_IN(s(s(s(s(0)))), s(s(s(s(s(z0)))))))
F59_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2) → c34(U12'(f64_out1, s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2), F64_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))))
F59_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2) → c34(U12'(f64_out1, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2), F64_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))))
F59_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2) → c34(U12'(f64_out1, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2), F64_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))))
F59_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2) → c34(U12'(U5(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2), F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))

S tuples:

F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F182_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c2(F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(F182_IN(z0, z1))
F35_IN(s(z0)) → c11(F35_IN(z0))
F54_IN(z0, tree(z1, z2, z3)) → c23(F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(F33_IN(z0, z2))
U12'(f64_out1, z0, z1, z2) → c35(F1_IN(z0, z2))
U14'(f182_out1, z0, z1, z2) → c38(F1_IN(z1, z2))
F21_IN(z0, z1) → c40(F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))
F33_IN(s(z0), x1) → c31(U10'(U4(f35_in(z0), s(z0)), s(z0), x1), F35_IN(s(z0)))
F59_IN(0, s(z0), x2) → c34(U12'(f64_out1, 0, s(z0), x2), F64_IN(0, s(z0)))
F59_IN(s(0), s(s(z0)), x2) → c34(U12'(f64_out1, s(0), s(s(z0)), x2), F64_IN(s(0), s(s(z0))))
F59_IN(s(s(0)), s(s(s(z0))), x2) → c34(U12'(f64_out1, s(s(0)), s(s(s(z0))), x2), F64_IN(s(s(0)), s(s(s(z0)))))
F59_IN(s(s(s(0))), s(s(s(s(z0)))), x2) → c34(U12'(f64_out1, s(s(s(0))), s(s(s(s(z0)))), x2), F64_IN(s(s(s(0))), s(s(s(s(z0))))))
F59_IN(s(s(s(s(0)))), s(s(s(s(s(z0))))), x2) → c34(U12'(f64_out1, s(s(s(s(0)))), s(s(s(s(s(z0))))), x2), F64_IN(s(s(s(s(0)))), s(s(s(s(s(z0)))))))
F59_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2) → c34(U12'(f64_out1, s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2), F64_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))))
F59_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2) → c34(U12'(f64_out1, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2), F64_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))))
F59_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2) → c34(U12'(f64_out1, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2), F64_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))))
F59_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2) → c34(U12'(U5(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2), F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))

K tuples:

U10'(f35_out1, z0, z1) → c32(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, f182_in, U3, f35_in, U4, f64_in, U5, f54_in, U6, f55_in, U7, f27_in, U8, f29_in, U9, f33_in, U10, U11, f59_in, U12, U13, f200_in, U14, U15, f21_in, U16, f22_in, U17

Defined Pair Symbols:

F200_IN, F64_IN, F1_IN, F182_IN, F35_IN, F54_IN, F55_IN, F27_IN, F29_IN, U10', U12', U14', F21_IN, F22_IN, F33_IN, F59_IN

Compound Symbols:

c37, c, c2, c3, c9, c11, c23, c25, c27, c29, c32, c35, c38, c40, c43, c31, c34

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

Removed 8 trailing tuple parts

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, void) → f1_out1(tree(z0, void, void))
f1_in(z0, tree(z0, z1, z2)) → f1_out1(tree(z0, z1, z2))
f1_in(z0, tree(z0, z1, z2)) → U1(f22_in(z0, z1, z2), z0, tree(z0, z1, z2))
f1_in(z0, z1) → U2(f21_in(z0, z1), z0, z1)
U1(f22_out1(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U1(f22_out2(z0), z1, tree(z1, z2, z3)) → f1_out1(z0)
U2(f21_out1(z0), z1, z2) → f1_out1(z0)
U2(f21_out2(z0), z1, z2) → f1_out1(z0)
f182_in(0, s(z0)) → f182_out1
f182_in(s(z0), s(z1)) → U3(f182_in(z0, z1), s(z0), s(z1))
U3(f182_out1, s(z0), s(z1)) → f182_out1
f35_in(s(z0)) → U4(f35_in(z0), s(z0))
U4(f35_out1, s(z0)) → f35_out1
f64_in(0, s(z0)) → f64_out1
f64_in(s(0), s(s(z0))) → f64_out1
f64_in(s(s(0)), s(s(s(z0)))) → f64_out1
f64_in(s(s(s(0))), s(s(s(s(z0))))) → f64_out1
f64_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f64_out1
f64_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f64_out1
f64_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f64_out1
f64_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U5(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U5(f182_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f64_out1
f54_in(z0, tree(z1, z2, z3)) → U6(f59_in(z0, z1, z2), z0, tree(z1, z2, z3))
U6(f59_out1(z0), z1, tree(z2, z3, z4)) → f54_out1(tree(z2, z0, z4))
f55_in(z0, tree(z1, z2, z3)) → U7(f200_in(z1, z0, z3), z0, tree(z1, z2, z3))
U7(f200_out1(z0), z1, tree(z2, z3, z4)) → f55_out1(tree(z2, z3, z0))
f27_in(z0, z1, z2) → U8(f33_in(z0, z1), z0, z1, z2)
U8(f33_out1(z0), z1, z2, z3) → f27_out1(tree(z1, z0, z3))
f29_in(z0, z1, z2) → U9(f33_in(z0, z2), z0, z1, z2)
U9(f33_out1(z0), z1, z2, z3) → f29_out1(tree(z1, z2, z0))
f33_in(z0, z1) → U10(f35_in(z0), z0, z1)
U10(f35_out1, z0, z1) → U11(f1_in(z0, z1), z0, z1)
U11(f1_out1(z0), z1, z2) → f33_out1(z0)
f59_in(z0, z1, z2) → U12(f64_in(z0, z1), z0, z1, z2)
U12(f64_out1, z0, z1, z2) → U13(f1_in(z0, z2), z0, z1, z2)
U13(f1_out1(z0), z1, z2, z3) → f59_out1(z0)
f200_in(z0, z1, z2) → U14(f182_in(z0, z1), z0, z1, z2)
U14(f182_out1, z0, z1, z2) → U15(f1_in(z1, z2), z0, z1, z2)
U15(f1_out1(z0), z1, z2, z3) → f200_out1(z0)
f21_in(z0, z1) → U16(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U16(f54_out1(z0), z1, z2, z3) → f21_out1(z0)
U16(z0, f55_out1(z1), z2, z3) → f21_out2(z1)
f22_in(z0, z1, z2) → U17(f27_in(z0, z1, z2), f29_in(z0, z1, z2), z0, z1, z2)
U17(f27_out1(z0), z1, z2, z3, z4) → f22_out1(z0)
U17(z0, f29_out1(z1), z2, z3, z4) → f22_out2(z1)

Tuples:

F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F182_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c2(F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(F182_IN(z0, z1))
F35_IN(s(z0)) → c11(F35_IN(z0))
F54_IN(z0, tree(z1, z2, z3)) → c23(F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(F33_IN(z0, z2))
U10'(f35_out1, z0, z1) → c32(F1_IN(z0, z1))
U12'(f64_out1, z0, z1, z2) → c35(F1_IN(z0, z2))
U14'(f182_out1, z0, z1, z2) → c38(F1_IN(z1, z2))
F21_IN(z0, z1) → c40(F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))
F33_IN(s(z0), x1) → c31(U10'(U4(f35_in(z0), s(z0)), s(z0), x1), F35_IN(s(z0)))
F59_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2) → c34(U12'(U5(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2), F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))
F59_IN(0, s(z0), x2) → c34(U12'(f64_out1, 0, s(z0), x2))
F59_IN(s(0), s(s(z0)), x2) → c34(U12'(f64_out1, s(0), s(s(z0)), x2))
F59_IN(s(s(0)), s(s(s(z0))), x2) → c34(U12'(f64_out1, s(s(0)), s(s(s(z0))), x2))
F59_IN(s(s(s(0))), s(s(s(s(z0)))), x2) → c34(U12'(f64_out1, s(s(s(0))), s(s(s(s(z0)))), x2))
F59_IN(s(s(s(s(0)))), s(s(s(s(s(z0))))), x2) → c34(U12'(f64_out1, s(s(s(s(0)))), s(s(s(s(s(z0))))), x2))
F59_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2) → c34(U12'(f64_out1, s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2))
F59_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2) → c34(U12'(f64_out1, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2))
F59_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2) → c34(U12'(f64_out1, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2))

S tuples:

F200_IN(z0, z1, z2) → c37(U14'(f182_in(z0, z1), z0, z1, z2), F182_IN(z0, z1))
F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F182_IN(z0, z1))
F1_IN(z0, tree(z0, z1, z2)) → c2(F22_IN(z0, z1, z2))
F1_IN(z0, z1) → c3(F21_IN(z0, z1))
F182_IN(s(z0), s(z1)) → c9(F182_IN(z0, z1))
F35_IN(s(z0)) → c11(F35_IN(z0))
F54_IN(z0, tree(z1, z2, z3)) → c23(F59_IN(z0, z1, z2))
F55_IN(z0, tree(z1, z2, z3)) → c25(F200_IN(z1, z0, z3))
F27_IN(z0, z1, z2) → c27(F33_IN(z0, z1))
F29_IN(z0, z1, z2) → c29(F33_IN(z0, z2))
U12'(f64_out1, z0, z1, z2) → c35(F1_IN(z0, z2))
U14'(f182_out1, z0, z1, z2) → c38(F1_IN(z1, z2))
F21_IN(z0, z1) → c40(F54_IN(z0, z1), F55_IN(z0, z1))
F22_IN(z0, z1, z2) → c43(F27_IN(z0, z1, z2), F29_IN(z0, z1, z2))
F33_IN(s(z0), x1) → c31(U10'(U4(f35_in(z0), s(z0)), s(z0), x1), F35_IN(s(z0)))
F59_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2) → c34(U12'(U5(f182_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2), F64_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))
F59_IN(0, s(z0), x2) → c34(U12'(f64_out1, 0, s(z0), x2))
F59_IN(s(0), s(s(z0)), x2) → c34(U12'(f64_out1, s(0), s(s(z0)), x2))
F59_IN(s(s(0)), s(s(s(z0))), x2) → c34(U12'(f64_out1, s(s(0)), s(s(s(z0))), x2))
F59_IN(s(s(s(0))), s(s(s(s(z0)))), x2) → c34(U12'(f64_out1, s(s(s(0))), s(s(s(s(z0)))), x2))
F59_IN(s(s(s(s(0)))), s(s(s(s(s(z0))))), x2) → c34(U12'(f64_out1, s(s(s(s(0)))), s(s(s(s(s(z0))))), x2))
F59_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2) → c34(U12'(f64_out1, s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2))
F59_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2) → c34(U12'(f64_out1, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2))
F59_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2) → c34(U12'(f64_out1, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2))

K tuples:

U10'(f35_out1, z0, z1) → c32(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, f182_in, U3, f35_in, U4, f64_in, U5, f54_in, U6, f55_in, U7, f27_in, U8, f29_in, U9, f33_in, U10, U11, f59_in, U12, U13, f200_in, U14, U15, f21_in, U16, f22_in, U17

Defined Pair Symbols:

F200_IN, F64_IN, F1_IN, F182_IN, F35_IN, F54_IN, F55_IN, F27_IN, F29_IN, U10', U12', U14', F21_IN, F22_IN, F33_IN, F59_IN

Compound Symbols:

c37, c, c2, c3, c9, c11, c23, c25, c27, c29, c32, c35, c38, c40, c43, c31, c34, c34

(19) 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\nT2 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\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: true | insert(T5, void, T3), SCOPE: 1, CLAUSE: 1 | insert(T5, void, T3), SCOPE: 1, CLAUSE: 3 | insert(T5, void, T3), 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\nT2 is ground\nX3 is free\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: insert(T5, void, T3), SCOPE: 1, CLAUSE: 1 | insert(T5, void, T3), SCOPE: 1, CLAUSE: 3 | insert(T5, void, T3), SCOPE: 1, CLAUSE: 4\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: insert(T5, void, T3), SCOPE: 1, CLAUSE: 3 | insert(T5, void, T3), SCOPE: 1, CLAUSE: 4\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: insert(T5, void, T3), SCOPE: 1, CLAUSE: 4\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: true | insert(T12, tree(T12, T13, T14), T3), SCOPE: 1, CLAUSE: 3 | insert(T12, tree(T12, T13, T14), T3), SCOPE: 1, CLAUSE: 4\n\nT12 is ground\nT13 is ground\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT2 is ground\nX3 is free\nX20 is free\nX21 is free\nX22 is free\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: insert(T12, tree(T12, T13, T14), T3), SCOPE: 1, CLAUSE: 3 | insert(T12, tree(T12, T13, T14), T3), SCOPE: 1, CLAUSE: 4\n\nT12 is ground\nT13 is ground\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: ','(less(T19, T19), insert(T19, T20, T23)) | insert(T19, tree(T19, T20, T21), T3), SCOPE: 1, CLAUSE: 4\n\nT19 is ground\nT20 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: insert(T12, tree(T12, T13, T14), T3), SCOPE: 1, CLAUSE: 4\n\nT12 is ground\nT13 is ground\nT14 is ground\nX28 is free\nX29 is free\nX30 is free\nX31 is free\nX32 is free\ninsert(T12, tree(T12, T13, T14), T3) !=? insert(X28, tree(X29, X30, X31), tree(X29, X32, X31))", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: ','(less(T19, T19), insert(T19, T20, T23)), SCOPE: 2, CLAUSE: 2 | ','(less(T19, T19), insert(T19, T20, T23)), SCOPE: 2, CLAUSE: 5 | ?_2 | insert(T19, tree(T19, T20, T21), T3), SCOPE: 1, CLAUSE: 4\n\nT19 is ground\nT20 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: ','(less(T19, T19), insert(T19, T20, T23)), SCOPE: 2, CLAUSE: 5 | ?_2 | insert(T19, tree(T19, T20, T21), T3), SCOPE: 1, CLAUSE: 4\n\nT19 is ground\nT20 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: ','(less(T19, T19), insert(T19, T20, T23)), SCOPE: 2, CLAUSE: 5\n\nT19 is ground\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: ?_2 | insert(T19, tree(T19, T20, T21), T3), SCOPE: 1, CLAUSE: 4\n\nT19 is ground\nT20 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ','(less(T28, T28), insert(s(T28), T20, T23))\n\nT20 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: less(T28, T28)\n\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: insert(s(T28), T20, T23)\n\nT20 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: less(T28, T28), SCOPE: 3, CLAUSE: 2 | less(T28, T28), SCOPE: 3, CLAUSE: 5\n\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: less(T28, T28), SCOPE: 3, CLAUSE: 5\n\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: less(T31, T31)\n\nT31 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: insert(T19, tree(T19, T20, T21), T3), SCOPE: 1, CLAUSE: 4\n\nT19 is ground\nT20 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(less(T42, T42), insert(T42, T44, T46))\n\nT42 is ground\nT44 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: less(T42, T42)\n\nT42 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: insert(T42, T44, T46)\n\nT42 is ground\nT44 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: ','(less(T53, T53), insert(T53, T55, T57))\n\nT53 is ground\nT54 is ground\nT55 is ground\nX28 is free\nX29 is free\nX30 is free\nX31 is free\nX32 is free\ninsert(T53, tree(T53, T54, T55), T3) !=? insert(X28, tree(X29, X30, X31), tree(X29, X32, X31))", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: ','(less(T53, T53), insert(T53, T55, T57)), SCOPE: 4, CLAUSE: 2 | ','(less(T53, T53), insert(T53, T55, T57)), SCOPE: 4, CLAUSE: 5\n\nT53 is ground\nT54 is ground\nT55 is ground\nX28 is free\nX29 is free\nX30 is free\nX31 is free\nX32 is free\ninsert(T53, tree(T53, T54, T55), T3) !=? insert(X28, tree(X29, X30, X31), tree(X29, X32, X31))", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: ','(less(T53, T53), insert(T53, T55, T57)), SCOPE: 4, CLAUSE: 5\n\nT53 is ground\nT54 is ground\nT55 is ground\nX28 is free\nX29 is free\nX30 is free\nX31 is free\nX32 is free\ninsert(T53, tree(T53, T54, T55), T3) !=? insert(X28, tree(X29, X30, X31), tree(X29, X32, X31))", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: ','(less(T60, T60), insert(s(T60), T55, T57))\n\nT54 is ground\nT55 is ground\nT60 is ground\nX28 is free\nX29 is free\nX30 is free\nX31 is free\nX32 is free\ninsert(s(T60), tree(s(T60), T54, T55), T3) !=? insert(X28, tree(X29, X30, X31), tree(X29, X32, X31))", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: ','(less(T66, T67), insert(T66, T68, T71)) | insert(T66, tree(T67, T68, T69), T3), SCOPE: 1, CLAUSE: 4\n\nT66 is ground\nT67 is ground\nT68 is ground\nT69 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(T66, tree(T67, T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT2 is ground\nX3 is free\nX20 is free\nX21 is free\nX22 is free\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: ','(less(T66, T67), insert(T66, T68, T71)), SCOPE: 5, CLAUSE: 2 | ','(less(T66, T67), insert(T66, T68, T71)), SCOPE: 5, CLAUSE: 5 | ?_5 | insert(T66, tree(T67, T68, T69), T3), SCOPE: 1, CLAUSE: 4\n\nT66 is ground\nT67 is ground\nT68 is ground\nT69 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(T66, tree(T67, T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: insert(0, T68, T71) | ','(less(0, s(T74)), insert(0, T68, T71)), SCOPE: 5, CLAUSE: 5 | ?_5 | insert(0, tree(s(T74), T68, T69), T3), SCOPE: 1, CLAUSE: 4\n\nT68 is ground\nT69 is ground\nT74 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: ','(less(T66, T67), insert(T66, T68, T71)), SCOPE: 5, CLAUSE: 5 | ?_5 | insert(T66, tree(T67, T68, T69), T3), SCOPE: 1, CLAUSE: 4\n\nT66 is ground\nT67 is ground\nT68 is ground\nT69 is ground\nX20 is free\nX21 is free\nX22 is free\nX111 is free\ninsert(T66, tree(T67, T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))\nless(T66, T67) !=? less(0, s(X111))", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: insert(0, T68, T71)\n\nT68 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: ','(less(0, s(T74)), insert(0, T68, T71)), SCOPE: 5, CLAUSE: 5 | ?_5 | insert(0, tree(s(T74), T68, T69), T3), SCOPE: 1, CLAUSE: 4\n\nT68 is ground\nT69 is ground\nT74 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: ?_5 | insert(0, tree(s(T74), T68, T69), T3), SCOPE: 1, CLAUSE: 4\n\nT68 is ground\nT69 is ground\nT74 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: insert(0, tree(s(T74), T68, T69), T3), SCOPE: 1, CLAUSE: 4\n\nT68 is ground\nT69 is ground\nT74 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: ','(less(s(T83), 0), insert(0, T85, T87))\n\nT83 is ground\nT85 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: less(s(T83), 0)\n\nT83 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: insert(0, T85, T87)\n\nT85 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: less(s(T83), 0), SCOPE: 6, CLAUSE: 2 | less(s(T83), 0), SCOPE: 6, CLAUSE: 5\n\nT83 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: less(s(T83), 0), SCOPE: 6, CLAUSE: 5\n\nT83 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: ','(less(T66, T67), insert(T66, T68, T71)), SCOPE: 5, CLAUSE: 5\n\nT66 is ground\nT67 is ground\nT68 is ground\nT69 is ground\nX20 is free\nX21 is free\nX22 is free\nX111 is free\ninsert(T66, tree(T67, T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))\nless(T66, T67) !=? less(0, s(X111))", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: ?_5 | insert(T66, tree(T67, T68, T69), T3), SCOPE: 1, CLAUSE: 4\n\nT66 is ground\nT67 is ground\nT68 is ground\nT69 is ground\nX20 is free\nX21 is free\nX22 is free\nX111 is free\ninsert(T66, tree(T67, T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))\nless(T66, T67) !=? less(0, s(X111))", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: ','(less(T97, T98), insert(s(T97), T68, T71))\n\nT68 is ground\nT69 is ground\nT97 is ground\nT98 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(T97), tree(s(T98), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: less(T97, T98)\n\nT68 is ground\nT69 is ground\nT97 is ground\nT98 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(T97), tree(s(T98), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: insert(s(T97), T68, T71)\n\nT68 is ground\nT69 is ground\nT97 is ground\nT98 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(T97), tree(s(T98), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: less(T97, T98), SCOPE: 7, CLAUSE: 2 | less(T97, T98), SCOPE: 7, CLAUSE: 5\n\nT68 is ground\nT69 is ground\nT97 is ground\nT98 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(T97), tree(s(T98), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: true | less(0, s(T105)), SCOPE: 7, CLAUSE: 5\n\nT105 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: less(T97, T98), SCOPE: 7, CLAUSE: 5\n\nT68 is ground\nT69 is ground\nT97 is ground\nT98 is ground\nX20 is free\nX21 is free\nX22 is free\nX158 is free\ninsert(s(T97), tree(s(T98), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))\nless(T97, T98) !=? less(0, s(X158))", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: less(0, s(T105)), SCOPE: 7, CLAUSE: 5\n\nT105 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: less(T110, T111)\n\nT68 is ground\nT69 is ground\nT110 is ground\nT111 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(s(T110)), tree(s(s(T111)), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: less(T110, T111), SCOPE: 8, CLAUSE: 2 | less(T110, T111), SCOPE: 8, CLAUSE: 5\n\nT68 is ground\nT69 is ground\nT110 is ground\nT111 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(s(T110)), tree(s(s(T111)), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: true | less(0, s(T116)), SCOPE: 8, CLAUSE: 5\n\nT116 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: less(T110, T111), SCOPE: 8, CLAUSE: 5\n\nT68 is ground\nT69 is ground\nT110 is ground\nT111 is ground\nX20 is free\nX21 is free\nX22 is free\nX171 is free\ninsert(s(s(T110)), tree(s(s(T111)), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))\nless(T110, T111) !=? less(0, s(X171))", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: less(0, s(T116)), SCOPE: 8, CLAUSE: 5\n\nT116 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: less(T121, T122)\n\nT68 is ground\nT69 is ground\nT121 is ground\nT122 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(s(s(T121))), tree(s(s(s(T122))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: less(T121, T122), SCOPE: 9, CLAUSE: 2 | less(T121, T122), SCOPE: 9, CLAUSE: 5\n\nT68 is ground\nT69 is ground\nT121 is ground\nT122 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(s(s(T121))), tree(s(s(s(T122))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: true | less(0, s(T127)), SCOPE: 9, CLAUSE: 5\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: less(T121, T122), SCOPE: 9, CLAUSE: 5\n\nT68 is ground\nT69 is ground\nT121 is ground\nT122 is ground\nX20 is free\nX21 is free\nX22 is free\nX184 is free\ninsert(s(s(s(T121))), tree(s(s(s(T122))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))\nless(T121, T122) !=? less(0, s(X184))", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: less(0, s(T127)), SCOPE: 9, CLAUSE: 5\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: less(T132, T133)\n\nT68 is ground\nT69 is ground\nT132 is ground\nT133 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(s(s(s(T132)))), tree(s(s(s(s(T133)))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: less(T132, T133), SCOPE: 10, CLAUSE: 2 | less(T132, T133), SCOPE: 10, CLAUSE: 5\n\nT68 is ground\nT69 is ground\nT132 is ground\nT133 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(s(s(s(T132)))), tree(s(s(s(s(T133)))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: true | less(0, s(T138)), SCOPE: 10, CLAUSE: 5\n\nT138 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: less(T132, T133), SCOPE: 10, CLAUSE: 5\n\nT68 is ground\nT69 is ground\nT132 is ground\nT133 is ground\nX20 is free\nX21 is free\nX22 is free\nX197 is free\ninsert(s(s(s(s(T132)))), tree(s(s(s(s(T133)))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))\nless(T132, T133) !=? less(0, s(X197))", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: less(0, s(T138)), SCOPE: 10, CLAUSE: 5\n\nT138 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: less(T143, T144)\n\nT68 is ground\nT69 is ground\nT143 is ground\nT144 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(s(s(s(s(T143))))), tree(s(s(s(s(s(T144))))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: less(T143, T144), SCOPE: 11, CLAUSE: 2 | less(T143, T144), SCOPE: 11, CLAUSE: 5\n\nT68 is ground\nT69 is ground\nT143 is ground\nT144 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(s(s(s(s(T143))))), tree(s(s(s(s(s(T144))))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: true | less(0, s(T149)), SCOPE: 11, CLAUSE: 5\n\nT149 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: less(T143, T144), SCOPE: 11, CLAUSE: 5\n\nT68 is ground\nT69 is ground\nT143 is ground\nT144 is ground\nX20 is free\nX21 is free\nX22 is free\nX210 is free\ninsert(s(s(s(s(s(T143))))), tree(s(s(s(s(s(T144))))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))\nless(T143, T144) !=? less(0, s(X210))", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: less(0, s(T149)), SCOPE: 11, CLAUSE: 5\n\nT149 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: less(T154, T155)\n\nT68 is ground\nT69 is ground\nT154 is ground\nT155 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(s(s(s(s(s(T154)))))), tree(s(s(s(s(s(s(T155)))))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: less(T154, T155), SCOPE: 12, CLAUSE: 2 | less(T154, T155), SCOPE: 12, CLAUSE: 5\n\nT68 is ground\nT69 is ground\nT154 is ground\nT155 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(s(s(s(s(s(T154)))))), tree(s(s(s(s(s(s(T155)))))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: true | less(0, s(T160)), SCOPE: 12, CLAUSE: 5\n\nT160 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: less(T154, T155), SCOPE: 12, CLAUSE: 5\n\nT68 is ground\nT69 is ground\nT154 is ground\nT155 is ground\nX20 is free\nX21 is free\nX22 is free\nX223 is free\ninsert(s(s(s(s(s(s(T154)))))), tree(s(s(s(s(s(s(T155)))))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))\nless(T154, T155) !=? less(0, s(X223))", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: less(0, s(T160)), SCOPE: 12, CLAUSE: 5\n\nT160 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: less(T165, T166)\n\nT68 is ground\nT69 is ground\nT165 is ground\nT166 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(s(s(s(s(s(s(T165))))))), tree(s(s(s(s(s(s(s(T166))))))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: less(T165, T166), SCOPE: 13, CLAUSE: 2 | less(T165, T166), SCOPE: 13, CLAUSE: 5\n\nT68 is ground\nT69 is ground\nT165 is ground\nT166 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(s(s(s(s(s(s(T165))))))), tree(s(s(s(s(s(s(s(T166))))))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: true | less(0, s(T171)), SCOPE: 13, CLAUSE: 5\n\nT171 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: less(T165, T166), SCOPE: 13, CLAUSE: 5\n\nT68 is ground\nT69 is ground\nT165 is ground\nT166 is ground\nX20 is free\nX21 is free\nX22 is free\nX236 is free\ninsert(s(s(s(s(s(s(s(T165))))))), tree(s(s(s(s(s(s(s(T166))))))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))\nless(T165, T166) !=? less(0, s(X236))", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: less(0, s(T171)), SCOPE: 13, CLAUSE: 5\n\nT171 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: less(T176, T177)\n\nT68 is ground\nT69 is ground\nT176 is ground\nT177 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(s(s(s(s(s(s(s(T176)))))))), tree(s(s(s(s(s(s(s(s(T177)))))))), T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: less(T176, T177)\n\nT176 is ground\nT177 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: less(T176, T177), SCOPE: 14, CLAUSE: 2 | less(T176, T177), SCOPE: 14, CLAUSE: 5\n\nT176 is ground\nT177 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: true | less(0, s(T186)), SCOPE: 14, CLAUSE: 5\n\nT186 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: less(T176, T177), SCOPE: 14, CLAUSE: 5\n\nT176 is ground\nT177 is ground\nX251 is free\nless(T176, T177) !=? less(0, s(X251))", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: less(0, s(T186)), SCOPE: 14, CLAUSE: 5\n\nT186 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: less(T191, T192)\n\nT191 is ground\nT192 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: insert(T66, tree(T67, T68, T69), T3), SCOPE: 1, CLAUSE: 4\n\nT66 is ground\nT67 is ground\nT68 is ground\nT69 is ground\nX20 is free\nX21 is free\nX22 is free\nX111 is free\ninsert(T66, tree(T67, T68, T69), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))\nless(T66, T67) !=? less(0, s(X111))", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: ','(less(T208, T207), insert(T207, T210, T212))\n\nT207 is ground\nT208 is ground\nT209 is ground\nT210 is ground\nX20 is free\nX21 is free\nX22 is free\nX111 is free\ninsert(T207, tree(T208, T209, T210), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))\nless(T207, T208) !=? less(0, s(X111))", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: less(T208, T207)\n\nT207 is ground\nT208 is ground\nT209 is ground\nT210 is ground\nX20 is free\nX21 is free\nX22 is free\nX111 is free\ninsert(T207, tree(T208, T209, T210), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))\nless(T207, T208) !=? less(0, s(X111))", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: insert(T207, T210, T212)\n\nT207 is ground\nT208 is ground\nT209 is ground\nT210 is ground\nX20 is free\nX21 is free\nX22 is free\nX111 is free\ninsert(T207, tree(T208, T209, T210), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))\nless(T207, T208) !=? less(0, s(X111))", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: ','(less(T225, T224), insert(T224, T227, T229))\n\nT224 is ground\nT225 is ground\nT226 is ground\nT227 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(T224, tree(T225, T226, T227), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: ','(less(T225, T224), insert(T224, T227, T229)), SCOPE: 15, CLAUSE: 2 | ','(less(T225, T224), insert(T224, T227, T229)), SCOPE: 15, CLAUSE: 5\n\nT224 is ground\nT225 is ground\nT226 is ground\nT227 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(T224, tree(T225, T226, T227), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: insert(s(T232), T227, T229) | ','(less(0, s(T232)), insert(s(T232), T227, T229)), SCOPE: 15, CLAUSE: 5\n\nT227 is ground\nT232 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: ','(less(T225, T224), insert(T224, T227, T229)), SCOPE: 15, CLAUSE: 5\n\nT224 is ground\nT225 is ground\nT226 is ground\nT227 is ground\nX20 is free\nX21 is free\nX22 is free\nX297 is free\ninsert(T224, tree(T225, T226, T227), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))\nless(T225, T224) !=? less(0, s(X297))", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: insert(s(T232), T227, T229)\n\nT227 is ground\nT232 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: ','(less(0, s(T232)), insert(s(T232), T227, T229)), SCOPE: 15, CLAUSE: 5\n\nT227 is ground\nT232 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: ','(less(T241, T242), insert(s(T242), T227, T229))\n\nT226 is ground\nT227 is ground\nT241 is ground\nT242 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(T242), tree(s(T241), T226, T227), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
227 [label="227: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
228 [label="228: less(T241, T242)\n\nT226 is ground\nT227 is ground\nT241 is ground\nT242 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(T242), tree(s(T241), T226, T227), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
229 [label="229: insert(s(T242), T227, T229)\n\nT226 is ground\nT227 is ground\nT241 is ground\nT242 is ground\nX20 is free\nX21 is free\nX22 is free\ninsert(s(T242), tree(s(T241), T226, T227), T3) !=? insert(X20, tree(X20, X21, X22), tree(X20, X21, X22))", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2 -> 230 [arrowhead = none ];
230 -> 4;

231 [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 -> 231 [arrowhead = none ];
231 -> 5;

232 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 232 [arrowhead = none ];
232 -> 7;

233 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 233 [arrowhead = none ];
233 -> 10;

234 [label="EVAL with clause\ninsert(X20, tree(X20, X21, X22), tree(X20, X21, X22)).\nand substitutionT1 -> T12,\nX20 -> T12,\nX21 -> T13,\nX22 -> T14,\nT2 -> tree(T12, T13, T14),\nT3 -> tree(T12, T13, T14)", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 234 [arrowhead = none ];
234 -> 17;

235 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 235 [arrowhead = none ];
235 -> 18;

236 [label="BACKTRACK\nfor clause: insert(X, tree(X, Left, Right), tree(X, Left, Right))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
10 -> 236 [arrowhead = none ];
236 -> 12;

237 [label="BACKTRACK\nfor clause: insert(X, tree(Y, Left, Right), tree(Y, Left1, Right)) :- ','(less(X, Y), insert(X, Left, Left1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 237 [arrowhead = none ];
237 -> 13;

238 [label="BACKTRACK\nfor clause: insert(X, tree(Y, Left, Right), tree(Y, Left, Right1)) :- ','(less(Y, X), insert(X, Right, Right1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
13 -> 238 [arrowhead = none ];
238 -> 15;

239 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 239 [arrowhead = none ];
239 -> 19;

240 [label="EVAL with clause\ninsert(X104, tree(X105, X106, X107), tree(X105, X108, X107)) :- ','(less(X104, X105), insert(X104, X106, X108)).\nand substitutionT1 -> T66,\nX104 -> T66,\nX105 -> T67,\nX106 -> T68,\nX107 -> T69,\nT2 -> tree(T67, T68, T69),\nX108 -> T71,\nT3 -> tree(T67, T71, T69),\nT70 -> T71", fontsize=14, style = filled, fillcolor = lightblue];
18 -> 240 [arrowhead = none ];
240 -> 68;

241 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
18 -> 241 [arrowhead = none ];
241 -> 72;

242 [label="EVAL with clause\ninsert(X28, tree(X29, X30, X31), tree(X29, X32, X31)) :- ','(less(X28, X29), insert(X28, X30, X32)).\nand substitutionT12 -> T19,\nX28 -> T19,\nX29 -> T19,\nT13 -> T20,\nX30 -> T20,\nT14 -> T21,\nX31 -> T21,\nX32 -> T23,\nT3 -> tree(T19, T23, T21),\nT22 -> T23", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 242 [arrowhead = none ];
242 -> 23;

243 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
19 -> 243 [arrowhead = none ];
243 -> 24;

244 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
23 -> 244 [arrowhead = none ];
244 -> 25;

245 [label="EVAL with clause\ninsert(X85, tree(X86, X87, X88), tree(X86, X87, X89)) :- ','(less(X86, X85), insert(X85, X88, X89)).\nand substitutionT12 -> T53,\nX85 -> T53,\nX86 -> T53,\nT13 -> T54,\nX87 -> T54,\nT14 -> T55,\nX88 -> T55,\nX89 -> T57,\nT3 -> tree(T53, T54, T57),\nT56 -> T57", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 245 [arrowhead = none ];
245 -> 56;

246 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
24 -> 246 [arrowhead = none ];
246 -> 57;

247 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
25 -> 247 [arrowhead = none ];
247 -> 26;

248 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
26 -> 248 [arrowhead = none ];
248 -> 28;

249 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
26 -> 249 [arrowhead = none ];
249 -> 30;

250 [label="EVAL with clause\nless(s(X42), s(X43)) :- less(X42, X43).\nand substitutionX42 -> T28,\nT19 -> s(T28),\nX43 -> T28", fontsize=14, style = filled, fillcolor = lightblue];
28 -> 250 [arrowhead = none ];
250 -> 31;

251 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
28 -> 251 [arrowhead = none ];
251 -> 32;

252 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 252 [arrowhead = none ];
252 -> 47;

253 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
31 -> 253 [arrowhead = none ];
253 -> 36;

254 [label="SPLIT 2\nnew knowledge:\nT28 is ground", fontsize=14, style = filled, fillcolor = violet];
31 -> 254 [arrowhead = none ];
254 -> 38;

255 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
36 -> 255 [arrowhead = none ];
255 -> 39;

256 [label="INSTANCE with matching:\nT1 -> s(T28)\nT2 -> T20\nT3 -> T23", fontsize=14, style = filled, fillcolor = lightgrey];
38 -> 256 [arrowhead = none , style=dashed];
256 -> 2[style=dashed];

257 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
39 -> 257 [arrowhead = none ];
257 -> 41;

258 [label="EVAL with clause\nless(s(X53), s(X54)) :- less(X53, X54).\nand substitutionX53 -> T31,\nT28 -> s(T31),\nX54 -> T31", fontsize=14, style = filled, fillcolor = lightblue];
41 -> 258 [arrowhead = none ];
258 -> 43;

259 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 259 [arrowhead = none ];
259 -> 45;

260 [label="INSTANCE with matching:\nT28 -> T31", fontsize=14, style = filled, fillcolor = lightgrey];
43 -> 260 [arrowhead = none , style=dashed];
260 -> 36[style=dashed];

261 [label="EVAL with clause\ninsert(X69, tree(X70, X71, X72), tree(X70, X71, X73)) :- ','(less(X70, X69), insert(X69, X72, X73)).\nand substitutionT19 -> T42,\nX69 -> T42,\nX70 -> T42,\nT20 -> T43,\nX71 -> T43,\nT21 -> T44,\nX72 -> T44,\nX73 -> T46,\nT3 -> tree(T42, T43, T46),\nT45 -> T46", fontsize=14, style = filled, fillcolor = lightblue];
47 -> 261 [arrowhead = none ];
261 -> 50;

262 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
47 -> 262 [arrowhead = none ];
262 -> 51;

263 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
50 -> 263 [arrowhead = none ];
263 -> 52;

264 [label="SPLIT 2\nnew knowledge:\nT42 is ground", fontsize=14, style = filled, fillcolor = violet];
50 -> 264 [arrowhead = none ];
264 -> 53;

265 [label="INSTANCE with matching:\nT28 -> T42", fontsize=14, style = filled, fillcolor = lightgrey];
52 -> 265 [arrowhead = none , style=dashed];
265 -> 36[style=dashed];

266 [label="INSTANCE with matching:\nT1 -> T42\nT2 -> T44\nT3 -> T46", fontsize=14, style = filled, fillcolor = lightgrey];
53 -> 266 [arrowhead = none , style=dashed];
266 -> 2[style=dashed];

267 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
56 -> 267 [arrowhead = none ];
267 -> 58;

268 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
58 -> 268 [arrowhead = none ];
268 -> 60;

269 [label="EVAL with clause\nless(s(X95), s(X96)) :- less(X95, X96).\nand substitutionX95 -> T60,\nT53 -> s(T60),\nX96 -> T60", fontsize=14, style = filled, fillcolor = lightblue];
60 -> 269 [arrowhead = none ];
269 -> 62;

270 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
60 -> 270 [arrowhead = none ];
270 -> 63;

271 [label="INSTANCE with matching:\nT28 -> T60\nT20 -> T55\nT23 -> T57", fontsize=14, style = filled, fillcolor = lightgrey];
62 -> 271 [arrowhead = none , style=dashed];
271 -> 31[style=dashed];

272 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
68 -> 272 [arrowhead = none ];
272 -> 73;

273 [label="EVAL with clause\ninsert(X290, tree(X291, X292, X293), tree(X291, X292, X294)) :- ','(less(X291, X290), insert(X290, X293, X294)).\nand substitutionT1 -> T224,\nX290 -> T224,\nX291 -> T225,\nX292 -> T226,\nX293 -> T227,\nT2 -> tree(T225, T226, T227),\nX294 -> T229,\nT3 -> tree(T225, T226, T229),\nT228 -> T229", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 273 [arrowhead = none ];
273 -> 218;

274 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
72 -> 274 [arrowhead = none ];
274 -> 219;

275 [label="EVAL with clause\nless(0, s(X111)).\nand substitutionT66 -> 0,\nX111 -> T74,\nT67 -> s(T74)", fontsize=14, style = filled, fillcolor = lightblue];
73 -> 275 [arrowhead = none ];
275 -> 74;

276 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
73 -> 276 [arrowhead = none ];
276 -> 77;

277 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
74 -> 277 [arrowhead = none ];
277 -> 78;

278 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
74 -> 278 [arrowhead = none ];
278 -> 79;

279 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
77 -> 279 [arrowhead = none ];
279 -> 101;

280 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
77 -> 280 [arrowhead = none ];
280 -> 102;

281 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T68\nT3 -> T71", fontsize=14, style = filled, fillcolor = lightgrey];
78 -> 281 [arrowhead = none , style=dashed];
281 -> 2[style=dashed];

282 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
79 -> 282 [arrowhead = none ];
282 -> 81;

283 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
81 -> 283 [arrowhead = none ];
283 -> 82;

284 [label="EVAL with clause\ninsert(X128, tree(X129, X130, X131), tree(X129, X130, X132)) :- ','(less(X129, X128), insert(X128, X131, X132)).\nand substitutionX128 -> 0,\nT74 -> T83,\nX129 -> s(T83),\nT68 -> T84,\nX130 -> T84,\nT69 -> T85,\nX131 -> T85,\nX132 -> T87,\nT3 -> tree(s(T83), T84, T87),\nT86 -> T87", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 284 [arrowhead = none ];
284 -> 87;

285 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
82 -> 285 [arrowhead = none ];
285 -> 88;

286 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
87 -> 286 [arrowhead = none ];
286 -> 91;

287 [label="SPLIT 2\nnew knowledge:\nT83 is ground", fontsize=14, style = filled, fillcolor = violet];
87 -> 287 [arrowhead = none ];
287 -> 92;

288 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
91 -> 288 [arrowhead = none ];
288 -> 93;

289 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T85\nT3 -> T87", fontsize=14, style = filled, fillcolor = lightgrey];
92 -> 289 [arrowhead = none , style=dashed];
289 -> 2[style=dashed];

290 [label="BACKTRACK\nfor clause: less(0, s(X1))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
93 -> 290 [arrowhead = none ];
290 -> 94;

291 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
94 -> 291 [arrowhead = none ];
291 -> 95;

292 [label="EVAL with clause\nless(s(X150), s(X151)) :- less(X150, X151).\nand substitutionX150 -> T97,\nT66 -> s(T97),\nX151 -> T98,\nT67 -> s(T98)", fontsize=14, style = filled, fillcolor = lightblue];
101 -> 292 [arrowhead = none ];
292 -> 105;

293 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
101 -> 293 [arrowhead = none ];
293 -> 106;

294 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
102 -> 294 [arrowhead = none ];
294 -> 213;

295 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
105 -> 295 [arrowhead = none ];
295 -> 107;

296 [label="SPLIT 2\nnew knowledge:\nT97 is ground\nT98 is ground", fontsize=14, style = filled, fillcolor = violet];
105 -> 296 [arrowhead = none ];
296 -> 108;

297 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
107 -> 297 [arrowhead = none ];
297 -> 111;

298 [label="INSTANCE with matching:\nT1 -> s(T97)\nT2 -> T68\nT3 -> T71", fontsize=14, style = filled, fillcolor = lightgrey];
108 -> 298 [arrowhead = none , style=dashed];
298 -> 2[style=dashed];

299 [label="EVAL with clause\nless(0, s(X158)).\nand substitutionT97 -> 0,\nX158 -> T105,\nT98 -> s(T105)", fontsize=14, style = filled, fillcolor = lightblue];
111 -> 299 [arrowhead = none ];
299 -> 115;

300 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
111 -> 300 [arrowhead = none ];
300 -> 116;

301 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
115 -> 301 [arrowhead = none ];
301 -> 117;

302 [label="EVAL with clause\nless(s(X165), s(X166)) :- less(X165, X166).\nand substitutionX165 -> T110,\nT97 -> s(T110),\nX166 -> T111,\nT98 -> s(T111)", fontsize=14, style = filled, fillcolor = lightblue];
116 -> 302 [arrowhead = none ];
302 -> 121;

303 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
116 -> 303 [arrowhead = none ];
303 -> 122;

304 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
117 -> 304 [arrowhead = none ];
304 -> 118;

305 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
121 -> 305 [arrowhead = none ];
305 -> 124;

306 [label="EVAL with clause\nless(0, s(X171)).\nand substitutionT110 -> 0,\nX171 -> T116,\nT111 -> s(T116)", fontsize=14, style = filled, fillcolor = lightblue];
124 -> 306 [arrowhead = none ];
306 -> 126;

307 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
124 -> 307 [arrowhead = none ];
307 -> 130;

308 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
126 -> 308 [arrowhead = none ];
308 -> 131;

309 [label="EVAL with clause\nless(s(X178), s(X179)) :- less(X178, X179).\nand substitutionX178 -> T121,\nT110 -> s(T121),\nX179 -> T122,\nT111 -> s(T122)", fontsize=14, style = filled, fillcolor = lightblue];
130 -> 309 [arrowhead = none ];
309 -> 134;

310 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
130 -> 310 [arrowhead = none ];
310 -> 136;

311 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
131 -> 311 [arrowhead = none ];
311 -> 132;

312 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
134 -> 312 [arrowhead = none ];
312 -> 138;

313 [label="EVAL with clause\nless(0, s(X184)).\nand substitutionT121 -> 0,\nX184 -> T127,\nT122 -> s(T127)", fontsize=14, style = filled, fillcolor = lightblue];
138 -> 313 [arrowhead = none ];
313 -> 139;

314 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
138 -> 314 [arrowhead = none ];
314 -> 141;

315 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
139 -> 315 [arrowhead = none ];
315 -> 142;

316 [label="EVAL with clause\nless(s(X191), s(X192)) :- less(X191, X192).\nand substitutionX191 -> T132,\nT121 -> s(T132),\nX192 -> T133,\nT122 -> s(T133)", fontsize=14, style = filled, fillcolor = lightblue];
141 -> 316 [arrowhead = none ];
316 -> 147;

317 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
141 -> 317 [arrowhead = none ];
317 -> 149;

318 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
142 -> 318 [arrowhead = none ];
318 -> 145;

319 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
147 -> 319 [arrowhead = none ];
319 -> 151;

320 [label="EVAL with clause\nless(0, s(X197)).\nand substitutionT132 -> 0,\nX197 -> T138,\nT133 -> s(T138)", fontsize=14, style = filled, fillcolor = lightblue];
151 -> 320 [arrowhead = none ];
320 -> 153;

321 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
151 -> 321 [arrowhead = none ];
321 -> 155;

322 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
153 -> 322 [arrowhead = none ];
322 -> 156;

323 [label="EVAL with clause\nless(s(X204), s(X205)) :- less(X204, X205).\nand substitutionX204 -> T143,\nT132 -> s(T143),\nX205 -> T144,\nT133 -> s(T144)", fontsize=14, style = filled, fillcolor = lightblue];
155 -> 323 [arrowhead = none ];
323 -> 161;

324 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
155 -> 324 [arrowhead = none ];
324 -> 162;

325 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
156 -> 325 [arrowhead = none ];
325 -> 157;

326 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
161 -> 326 [arrowhead = none ];
326 -> 165;

327 [label="EVAL with clause\nless(0, s(X210)).\nand substitutionT143 -> 0,\nX210 -> T149,\nT144 -> s(T149)", fontsize=14, style = filled, fillcolor = lightblue];
165 -> 327 [arrowhead = none ];
327 -> 166;

328 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
165 -> 328 [arrowhead = none ];
328 -> 168;

329 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
166 -> 329 [arrowhead = none ];
329 -> 169;

330 [label="EVAL with clause\nless(s(X217), s(X218)) :- less(X217, X218).\nand substitutionX217 -> T154,\nT143 -> s(T154),\nX218 -> T155,\nT144 -> s(T155)", fontsize=14, style = filled, fillcolor = lightblue];
168 -> 330 [arrowhead = none ];
330 -> 175;

331 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
168 -> 331 [arrowhead = none ];
331 -> 176;

332 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
169 -> 332 [arrowhead = none ];
332 -> 170;

333 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
175 -> 333 [arrowhead = none ];
333 -> 179;

334 [label="EVAL with clause\nless(0, s(X223)).\nand substitutionT154 -> 0,\nX223 -> T160,\nT155 -> s(T160)", fontsize=14, style = filled, fillcolor = lightblue];
179 -> 334 [arrowhead = none ];
334 -> 180;

335 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
179 -> 335 [arrowhead = none ];
335 -> 181;

336 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
180 -> 336 [arrowhead = none ];
336 -> 183;

337 [label="EVAL with clause\nless(s(X230), s(X231)) :- less(X230, X231).\nand substitutionX230 -> T165,\nT154 -> s(T165),\nX231 -> T166,\nT155 -> s(T166)", fontsize=14, style = filled, fillcolor = lightblue];
181 -> 337 [arrowhead = none ];
337 -> 186;

338 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
181 -> 338 [arrowhead = none ];
338 -> 190;

339 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
183 -> 339 [arrowhead = none ];
339 -> 184;

340 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
186 -> 340 [arrowhead = none ];
340 -> 194;

341 [label="EVAL with clause\nless(0, s(X236)).\nand substitutionT165 -> 0,\nX236 -> T171,\nT166 -> s(T171)", fontsize=14, style = filled, fillcolor = lightblue];
194 -> 341 [arrowhead = none ];
341 -> 195;

342 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
194 -> 342 [arrowhead = none ];
342 -> 196;

343 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
195 -> 343 [arrowhead = none ];
343 -> 197;

344 [label="EVAL with clause\nless(s(X243), s(X244)) :- less(X243, X244).\nand substitutionX243 -> T176,\nT165 -> s(T176),\nX244 -> T177,\nT166 -> s(T177)", fontsize=14, style = filled, fillcolor = lightblue];
196 -> 344 [arrowhead = none ];
344 -> 199;

345 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
196 -> 345 [arrowhead = none ];
345 -> 201;

346 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
197 -> 346 [arrowhead = none ];
346 -> 198;

347 [label="GENERALIZATION\nT180 <-- s(s(s(s(s(s(s(T176)))))))\nT181 <-- s(s(s(s(s(s(s(T177)))))))\n\nNew Knowledge:\nT180 is ground\nT181 is ground", fontsize=14, style = filled, fillcolor = violet];
199 -> 347 [arrowhead = none ];
347 -> 205;

348 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
205 -> 348 [arrowhead = none ];
348 -> 206;

349 [label="EVAL with clause\nless(0, s(X251)).\nand substitutionT176 -> 0,\nX251 -> T186,\nT177 -> s(T186)", fontsize=14, style = filled, fillcolor = lightblue];
206 -> 349 [arrowhead = none ];
349 -> 207;

350 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
206 -> 350 [arrowhead = none ];
350 -> 208;

351 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
207 -> 351 [arrowhead = none ];
351 -> 209;

352 [label="EVAL with clause\nless(s(X258), s(X259)) :- less(X258, X259).\nand substitutionX258 -> T191,\nT176 -> s(T191),\nX259 -> T192,\nT177 -> s(T192)", fontsize=14, style = filled, fillcolor = lightblue];
208 -> 352 [arrowhead = none ];
352 -> 211;

353 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
208 -> 353 [arrowhead = none ];
353 -> 212;

354 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
209 -> 354 [arrowhead = none ];
354 -> 210;

355 [label="INSTANCE with matching:\nT176 -> T191\nT177 -> T192", fontsize=14, style = filled, fillcolor = lightgrey];
211 -> 355 [arrowhead = none , style=dashed];
355 -> 205[style=dashed];

356 [label="EVAL with clause\ninsert(X274, tree(X275, X276, X277), tree(X275, X276, X278)) :- ','(less(X275, X274), insert(X274, X277, X278)).\nand substitutionT66 -> T207,\nX274 -> T207,\nT67 -> T208,\nX275 -> T208,\nT68 -> T209,\nX276 -> T209,\nT69 -> T210,\nX277 -> T210,\nX278 -> T212,\nT3 -> tree(T208, T209, T212),\nT211 -> T212", fontsize=14, style = filled, fillcolor = lightblue];
213 -> 356 [arrowhead = none ];
356 -> 214;

357 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
213 -> 357 [arrowhead = none ];
357 -> 215;

358 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
214 -> 358 [arrowhead = none ];
358 -> 216;

359 [label="SPLIT 2\nnew knowledge:\nT208 is ground\nT207 is ground", fontsize=14, style = filled, fillcolor = violet];
214 -> 359 [arrowhead = none ];
359 -> 217;

360 [label="INSTANCE with matching:\nT176 -> T208\nT177 -> T207", fontsize=14, style = filled, fillcolor = lightgrey];
216 -> 360 [arrowhead = none , style=dashed];
360 -> 205[style=dashed];

361 [label="INSTANCE with matching:\nT1 -> T207\nT2 -> T210\nT3 -> T212", fontsize=14, style = filled, fillcolor = lightgrey];
217 -> 361 [arrowhead = none , style=dashed];
361 -> 2[style=dashed];

362 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
218 -> 362 [arrowhead = none ];
362 -> 220;

363 [label="EVAL with clause\nless(0, s(X297)).\nand substitutionT225 -> 0,\nX297 -> T232,\nT224 -> s(T232)", fontsize=14, style = filled, fillcolor = lightblue];
220 -> 363 [arrowhead = none ];
363 -> 221;

364 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
220 -> 364 [arrowhead = none ];
364 -> 222;

365 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
221 -> 365 [arrowhead = none ];
365 -> 223;

366 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
221 -> 366 [arrowhead = none ];
366 -> 224;

367 [label="EVAL with clause\nless(s(X308), s(X309)) :- less(X308, X309).\nand substitutionX308 -> T241,\nT225 -> s(T241),\nX309 -> T242,\nT224 -> s(T242)", fontsize=14, style = filled, fillcolor = lightblue];
222 -> 367 [arrowhead = none ];
367 -> 226;

368 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
222 -> 368 [arrowhead = none ];
368 -> 227;

369 [label="INSTANCE with matching:\nT1 -> s(T232)\nT2 -> T227\nT3 -> T229", fontsize=14, style = filled, fillcolor = lightgrey];
223 -> 369 [arrowhead = none , style=dashed];
369 -> 2[style=dashed];

370 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
224 -> 370 [arrowhead = none ];
370 -> 225;

371 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
226 -> 371 [arrowhead = none ];
371 -> 228;

372 [label="SPLIT 2\nnew knowledge:\nT241 is ground\nT242 is ground", fontsize=14, style = filled, fillcolor = violet];
226 -> 372 [arrowhead = none ];
372 -> 229;

373 [label="INSTANCE with matching:\nT176 -> T241\nT177 -> T242", fontsize=14, style = filled, fillcolor = lightgrey];
228 -> 373 [arrowhead = none , style=dashed];
373 -> 205[style=dashed];

374 [label="INSTANCE with matching:\nT1 -> s(T242)\nT2 -> T227\nT3 -> T229", fontsize=14, style = filled, fillcolor = lightgrey];
229 -> 374 [arrowhead = none , style=dashed];
374 -> 2[style=dashed];

}

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, void) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U1(f26_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(s(z0), tree(s(z0), z1, z2)) → U2(f31_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U3(f74_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f77_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f221_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f226_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f26_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(tree(z1, z0, z3))
U1(f26_out3(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U2(f31_out1(z0), s(z1), tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z2, z0))
U3(f74_out1(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out2(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out4(z0), 0, tree(s(z1), z2, z3)) → f2_out1(z0)
U4(f77_out1(z0), z1, tree(z2, z3, z4)) → f2_out1(tree(z2, z0, z4))
U4(f77_out3(z0), z1, tree(z2, z3, z4)) → f2_out1(z0)
U5(f221_out1(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U5(f221_out2(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U6(f226_out1(z0), s(z1), tree(s(z2), z3, z4)) → f2_out1(tree(s(z2), z3, z0))
f205_in(0, s(z0)) → f205_out1
f205_in(s(z0), s(z1)) → U7(f205_in(z0, z1), s(z0), s(z1))
U7(f205_out1, s(z0), s(z1)) → f205_out1
f36_in(s(z0)) → U8(f36_in(z0), s(z0))
U8(f36_out1, s(z0)) → f36_out1
f107_in(0, s(z0)) → f107_out1
f107_in(s(0), s(s(z0))) → f107_out1
f107_in(s(s(0)), s(s(s(z0)))) → f107_out1
f107_in(s(s(s(0))), s(s(s(s(z0))))) → f107_out1
f107_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f107_out1
f107_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f107_out1
f107_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f107_out1
f107_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U9(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U9(f205_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f107_out1
f79_in(z0, z1, z2) → U10(f87_in(z0, z2), z0, z1, z2)
U10(f87_out1(z0), z1, z2, z3) → f79_out3(tree(s(z1), z2, z0))
f101_in(s(z0), s(z1), z2) → U11(f105_in(z0, z1, z2), s(z0), s(z1), z2)
U11(f105_out1(z0), s(z1), s(z2), z3) → f101_out1(z0)
f102_in(z0, z1, z2, z3) → U12(f214_in(z1, z0, z3), z0, z1, z2, z3)
U12(f214_out1(z0), z1, z2, z3, z4) → f102_out2(tree(z2, z3, z0))
f28_in(s(z0), z1) → U13(f31_in(z0, z1), s(z0), z1)
U13(f31_out1(z0), s(z1), z2) → f28_out1(z0)
f30_in(z0, z1, z2) → U14(f50_in(z0, z2), z0, z1, z2)
U14(f50_out1(z0), z1, z2, z3) → f30_out2(tree(z1, z2, z0))
f31_in(z0, z1) → U15(f36_in(z0), z0, z1)
U15(f36_out1, z0, z1) → U16(f2_in(s(z0), z1), z0, z1)
U16(f2_out1(z0), z1, z2) → f31_out1(z0)
f50_in(z0, z1) → U17(f36_in(z0), z0, z1)
U17(f36_out1, z0, z1) → U18(f2_in(z0, z1), z0, z1)
U18(f2_out1(z0), z1, z2) → f50_out1(z0)
f87_in(z0, z1) → U19(f91_in(z0), z0, z1)
U19(f91_out1, z0, z1) → U20(f2_in(0, z1), z0, z1)
U20(f2_out1(z0), z1, z2) → f87_out1(z0)
f105_in(z0, z1, z2) → U21(f107_in(z0, z1), z0, z1, z2)
U21(f107_out1, z0, z1, z2) → U22(f2_in(s(z0), z2), z0, z1, z2)
U22(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f214_in(z0, z1, z2) → U23(f205_in(z0, z1), z0, z1, z2)
U23(f205_out1, z0, z1, z2) → U24(f2_in(z1, z2), z0, z1, z2)
U24(f2_out1(z0), z1, z2, z3) → f214_out1(z0)
f226_in(z0, z1, z2) → U25(f205_in(z0, z1), z0, z1, z2)
U25(f205_out1, z0, z1, z2) → U26(f2_in(s(z1), z2), z0, z1, z2)
U26(f2_out1(z0), z1, z2, z3) → f226_out1(z0)
f26_in(z0, z1, z2) → U27(f28_in(z0, z1), f30_in(z0, z1, z2), z0, z1, z2)
U27(f28_out1(z0), z1, z2, z3, z4) → f26_out1(z0)
U27(z0, f30_out2(z1), z2, z3, z4) → f26_out3(z1)
f74_in(z0, z1, z2) → U28(f2_in(0, z0), f79_in(z1, z0, z2), z0, z1, z2)
U28(f2_out1(z0), z1, z2, z3, z4) → f74_out1(z0)
U28(z0, f79_out1(z1), z2, z3, z4) → f74_out2(z1)
U28(z0, f79_out3(z1), z2, z3, z4) → f74_out4(z1)
f77_in(z0, z1, z2, z3) → U29(f101_in(z0, z1, z2), f102_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f101_out1(z0), z1, z2, z3, z4, z5) → f77_out1(z0)
U29(z0, f102_out2(z1), z2, z3, z4, z5) → f77_out3(z1)
f221_in(z0, z1) → U30(f2_in(s(z0), z1), f224_in(z0, z1), z0, z1)
U30(f2_out1(z0), z1, z2, z3) → f221_out1(z0)
U30(z0, f224_out1(z1), z2, z3) → f221_out2(z1)

Tuples:

F2_IN(z0, tree(z0, z1, z2)) → c2(U1'(f26_in(z0, z1, z2), z0, tree(z0, z1, z2)), F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(U2'(f31_in(z0, z2), s(z0), tree(s(z0), z1, z2)), F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(U3'(f74_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(U4'(f77_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(U5'(f221_in(z0, z2), s(z0), tree(0, z1, z2)), F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(U6'(f226_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(U7'(f205_in(z0, z1), s(z0), s(z1)), F205_IN(z0, z1))
F36_IN(s(z0)) → c22(U8'(f36_in(z0), s(z0)), F36_IN(z0))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c31(U9'(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))), F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c33(U10'(f87_in(z0, z2), z0, z1, z2), F87_IN(z0, z2))
F101_IN(s(z0), s(z1), z2) → c35(U11'(f105_in(z0, z1, z2), s(z0), s(z1), z2), F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(U12'(f214_in(z1, z0, z3), z0, z1, z2, z3), F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(U13'(f31_in(z0, z1), s(z0), z1), F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(U14'(f50_in(z0, z2), z0, z1, z2), F50_IN(z0, z2))
F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
U15'(f36_out1, z0, z1) → c44(U16'(f2_in(s(z0), z1), z0, z1), F2_IN(s(z0), z1))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
U17'(f36_out1, z0, z1) → c47(U18'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F87_IN(z0, z1) → c49(U19'(f91_in(z0), z0, z1))
U19'(f91_out1, z0, z1) → c50(U20'(f2_in(0, z1), z0, z1), F2_IN(0, z1))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
U21'(f107_out1, z0, z1, z2) → c53(U22'(f2_in(s(z0), z2), z0, z1, z2), F2_IN(s(z0), z2))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
U23'(f205_out1, z0, z1, z2) → c56(U24'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
U25'(f205_out1, z0, z1, z2) → c59(U26'(f2_in(s(z1), z2), z0, z1, z2), F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(U27'(f28_in(z0, z1), f30_in(z0, z1, z2), z0, z1, z2), F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(U28'(f2_in(0, z0), f79_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(U29'(f101_in(z0, z1, z2), f102_in(z0, z1, z2, z3), z0, z1, z2, z3), F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(U30'(f2_in(s(z0), z1), f224_in(z0, z1), z0, z1), F2_IN(s(z0), z1))

S tuples:

F2_IN(z0, tree(z0, z1, z2)) → c2(U1'(f26_in(z0, z1, z2), z0, tree(z0, z1, z2)), F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(U2'(f31_in(z0, z2), s(z0), tree(s(z0), z1, z2)), F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(U3'(f74_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(U4'(f77_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(U5'(f221_in(z0, z2), s(z0), tree(0, z1, z2)), F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(U6'(f226_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(U7'(f205_in(z0, z1), s(z0), s(z1)), F205_IN(z0, z1))
F36_IN(s(z0)) → c22(U8'(f36_in(z0), s(z0)), F36_IN(z0))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c31(U9'(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))), F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c33(U10'(f87_in(z0, z2), z0, z1, z2), F87_IN(z0, z2))
F101_IN(s(z0), s(z1), z2) → c35(U11'(f105_in(z0, z1, z2), s(z0), s(z1), z2), F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(U12'(f214_in(z1, z0, z3), z0, z1, z2, z3), F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(U13'(f31_in(z0, z1), s(z0), z1), F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(U14'(f50_in(z0, z2), z0, z1, z2), F50_IN(z0, z2))
F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
U15'(f36_out1, z0, z1) → c44(U16'(f2_in(s(z0), z1), z0, z1), F2_IN(s(z0), z1))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
U17'(f36_out1, z0, z1) → c47(U18'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F87_IN(z0, z1) → c49(U19'(f91_in(z0), z0, z1))
U19'(f91_out1, z0, z1) → c50(U20'(f2_in(0, z1), z0, z1), F2_IN(0, z1))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
U21'(f107_out1, z0, z1, z2) → c53(U22'(f2_in(s(z0), z2), z0, z1, z2), F2_IN(s(z0), z2))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
U23'(f205_out1, z0, z1, z2) → c56(U24'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
U25'(f205_out1, z0, z1, z2) → c59(U26'(f2_in(s(z1), z2), z0, z1, z2), F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(U27'(f28_in(z0, z1), f30_in(z0, z1, z2), z0, z1, z2), F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(U28'(f2_in(0, z0), f79_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(U29'(f101_in(z0, z1, z2), f102_in(z0, z1, z2, z3), z0, z1, z2, z3), F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(U30'(f2_in(s(z0), z1), f224_in(z0, z1), z0, z1), F2_IN(s(z0), z1))

K tuples:none
Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, f205_in, U7, f36_in, U8, f107_in, U9, f79_in, U10, f101_in, U11, f102_in, U12, f28_in, U13, f30_in, U14, f31_in, U15, U16, f50_in, U17, U18, f87_in, U19, U20, f105_in, U21, U22, f214_in, U23, U24, f226_in, U25, U26, f26_in, U27, f74_in, U28, f77_in, U29, f221_in, U30

Defined Pair Symbols:

F2_IN, F205_IN, F36_IN, F107_IN, F79_IN, F101_IN, F102_IN, F28_IN, F30_IN, F31_IN, U15', F50_IN, U17', F87_IN, U19', F105_IN, U21', F214_IN, U23', F226_IN, U25', F26_IN, F74_IN, F77_IN, F221_IN

Compound Symbols:

c2, c3, c4, c5, c6, c7, c20, c22, c31, c33, c35, c37, c39, c41, c43, c44, c46, c47, c49, c50, c52, c53, c55, c56, c58, c59, c61, c64, c68, c71

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

Split RHS of tuples not part of any SCC

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, void) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U1(f26_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(s(z0), tree(s(z0), z1, z2)) → U2(f31_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U3(f74_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f77_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f221_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f226_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f26_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(tree(z1, z0, z3))
U1(f26_out3(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U2(f31_out1(z0), s(z1), tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z2, z0))
U3(f74_out1(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out2(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out4(z0), 0, tree(s(z1), z2, z3)) → f2_out1(z0)
U4(f77_out1(z0), z1, tree(z2, z3, z4)) → f2_out1(tree(z2, z0, z4))
U4(f77_out3(z0), z1, tree(z2, z3, z4)) → f2_out1(z0)
U5(f221_out1(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U5(f221_out2(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U6(f226_out1(z0), s(z1), tree(s(z2), z3, z4)) → f2_out1(tree(s(z2), z3, z0))
f205_in(0, s(z0)) → f205_out1
f205_in(s(z0), s(z1)) → U7(f205_in(z0, z1), s(z0), s(z1))
U7(f205_out1, s(z0), s(z1)) → f205_out1
f36_in(s(z0)) → U8(f36_in(z0), s(z0))
U8(f36_out1, s(z0)) → f36_out1
f107_in(0, s(z0)) → f107_out1
f107_in(s(0), s(s(z0))) → f107_out1
f107_in(s(s(0)), s(s(s(z0)))) → f107_out1
f107_in(s(s(s(0))), s(s(s(s(z0))))) → f107_out1
f107_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f107_out1
f107_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f107_out1
f107_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f107_out1
f107_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U9(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U9(f205_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f107_out1
f79_in(z0, z1, z2) → U10(f87_in(z0, z2), z0, z1, z2)
U10(f87_out1(z0), z1, z2, z3) → f79_out3(tree(s(z1), z2, z0))
f101_in(s(z0), s(z1), z2) → U11(f105_in(z0, z1, z2), s(z0), s(z1), z2)
U11(f105_out1(z0), s(z1), s(z2), z3) → f101_out1(z0)
f102_in(z0, z1, z2, z3) → U12(f214_in(z1, z0, z3), z0, z1, z2, z3)
U12(f214_out1(z0), z1, z2, z3, z4) → f102_out2(tree(z2, z3, z0))
f28_in(s(z0), z1) → U13(f31_in(z0, z1), s(z0), z1)
U13(f31_out1(z0), s(z1), z2) → f28_out1(z0)
f30_in(z0, z1, z2) → U14(f50_in(z0, z2), z0, z1, z2)
U14(f50_out1(z0), z1, z2, z3) → f30_out2(tree(z1, z2, z0))
f31_in(z0, z1) → U15(f36_in(z0), z0, z1)
U15(f36_out1, z0, z1) → U16(f2_in(s(z0), z1), z0, z1)
U16(f2_out1(z0), z1, z2) → f31_out1(z0)
f50_in(z0, z1) → U17(f36_in(z0), z0, z1)
U17(f36_out1, z0, z1) → U18(f2_in(z0, z1), z0, z1)
U18(f2_out1(z0), z1, z2) → f50_out1(z0)
f87_in(z0, z1) → U19(f91_in(z0), z0, z1)
U19(f91_out1, z0, z1) → U20(f2_in(0, z1), z0, z1)
U20(f2_out1(z0), z1, z2) → f87_out1(z0)
f105_in(z0, z1, z2) → U21(f107_in(z0, z1), z0, z1, z2)
U21(f107_out1, z0, z1, z2) → U22(f2_in(s(z0), z2), z0, z1, z2)
U22(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f214_in(z0, z1, z2) → U23(f205_in(z0, z1), z0, z1, z2)
U23(f205_out1, z0, z1, z2) → U24(f2_in(z1, z2), z0, z1, z2)
U24(f2_out1(z0), z1, z2, z3) → f214_out1(z0)
f226_in(z0, z1, z2) → U25(f205_in(z0, z1), z0, z1, z2)
U25(f205_out1, z0, z1, z2) → U26(f2_in(s(z1), z2), z0, z1, z2)
U26(f2_out1(z0), z1, z2, z3) → f226_out1(z0)
f26_in(z0, z1, z2) → U27(f28_in(z0, z1), f30_in(z0, z1, z2), z0, z1, z2)
U27(f28_out1(z0), z1, z2, z3, z4) → f26_out1(z0)
U27(z0, f30_out2(z1), z2, z3, z4) → f26_out3(z1)
f74_in(z0, z1, z2) → U28(f2_in(0, z0), f79_in(z1, z0, z2), z0, z1, z2)
U28(f2_out1(z0), z1, z2, z3, z4) → f74_out1(z0)
U28(z0, f79_out1(z1), z2, z3, z4) → f74_out2(z1)
U28(z0, f79_out3(z1), z2, z3, z4) → f74_out4(z1)
f77_in(z0, z1, z2, z3) → U29(f101_in(z0, z1, z2), f102_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f101_out1(z0), z1, z2, z3, z4, z5) → f77_out1(z0)
U29(z0, f102_out2(z1), z2, z3, z4, z5) → f77_out3(z1)
f221_in(z0, z1) → U30(f2_in(s(z0), z1), f224_in(z0, z1), z0, z1)
U30(f2_out1(z0), z1, z2, z3) → f221_out1(z0)
U30(z0, f224_out1(z1), z2, z3) → f221_out2(z1)

Tuples:

F2_IN(z0, tree(z0, z1, z2)) → c2(U1'(f26_in(z0, z1, z2), z0, tree(z0, z1, z2)), F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(U2'(f31_in(z0, z2), s(z0), tree(s(z0), z1, z2)), F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(U3'(f74_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(U4'(f77_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(U5'(f221_in(z0, z2), s(z0), tree(0, z1, z2)), F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(U6'(f226_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(U7'(f205_in(z0, z1), s(z0), s(z1)), F205_IN(z0, z1))
F36_IN(s(z0)) → c22(U8'(f36_in(z0), s(z0)), F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(U11'(f105_in(z0, z1, z2), s(z0), s(z1), z2), F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(U12'(f214_in(z1, z0, z3), z0, z1, z2, z3), F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(U13'(f31_in(z0, z1), s(z0), z1), F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(U14'(f50_in(z0, z2), z0, z1, z2), F50_IN(z0, z2))
F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
U15'(f36_out1, z0, z1) → c44(U16'(f2_in(s(z0), z1), z0, z1), F2_IN(s(z0), z1))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
U17'(f36_out1, z0, z1) → c47(U18'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F87_IN(z0, z1) → c49(U19'(f91_in(z0), z0, z1))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
U21'(f107_out1, z0, z1, z2) → c53(U22'(f2_in(s(z0), z2), z0, z1, z2), F2_IN(s(z0), z2))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
U23'(f205_out1, z0, z1, z2) → c56(U24'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
U25'(f205_out1, z0, z1, z2) → c59(U26'(f2_in(s(z1), z2), z0, z1, z2), F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(U27'(f28_in(z0, z1), f30_in(z0, z1, z2), z0, z1, z2), F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(U28'(f2_in(0, z0), f79_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(U29'(f101_in(z0, z1, z2), f102_in(z0, z1, z2, z3), z0, z1, z2, z3), F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(U30'(f2_in(s(z0), z1), f224_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(U9'(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(U10'(f87_in(z0, z2), z0, z1, z2))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(U20'(f2_in(0, z1), z0, z1))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))

S tuples:

F2_IN(z0, tree(z0, z1, z2)) → c2(U1'(f26_in(z0, z1, z2), z0, tree(z0, z1, z2)), F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(U2'(f31_in(z0, z2), s(z0), tree(s(z0), z1, z2)), F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(U3'(f74_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(U4'(f77_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(U5'(f221_in(z0, z2), s(z0), tree(0, z1, z2)), F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(U6'(f226_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(U7'(f205_in(z0, z1), s(z0), s(z1)), F205_IN(z0, z1))
F36_IN(s(z0)) → c22(U8'(f36_in(z0), s(z0)), F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(U11'(f105_in(z0, z1, z2), s(z0), s(z1), z2), F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(U12'(f214_in(z1, z0, z3), z0, z1, z2, z3), F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(U13'(f31_in(z0, z1), s(z0), z1), F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(U14'(f50_in(z0, z2), z0, z1, z2), F50_IN(z0, z2))
F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
U15'(f36_out1, z0, z1) → c44(U16'(f2_in(s(z0), z1), z0, z1), F2_IN(s(z0), z1))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
U17'(f36_out1, z0, z1) → c47(U18'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F87_IN(z0, z1) → c49(U19'(f91_in(z0), z0, z1))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
U21'(f107_out1, z0, z1, z2) → c53(U22'(f2_in(s(z0), z2), z0, z1, z2), F2_IN(s(z0), z2))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
U23'(f205_out1, z0, z1, z2) → c56(U24'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
U25'(f205_out1, z0, z1, z2) → c59(U26'(f2_in(s(z1), z2), z0, z1, z2), F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(U27'(f28_in(z0, z1), f30_in(z0, z1, z2), z0, z1, z2), F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(U28'(f2_in(0, z0), f79_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(U29'(f101_in(z0, z1, z2), f102_in(z0, z1, z2, z3), z0, z1, z2, z3), F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(U30'(f2_in(s(z0), z1), f224_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(U9'(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(U10'(f87_in(z0, z2), z0, z1, z2))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(U20'(f2_in(0, z1), z0, z1))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))

K tuples:none
Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, f205_in, U7, f36_in, U8, f107_in, U9, f79_in, U10, f101_in, U11, f102_in, U12, f28_in, U13, f30_in, U14, f31_in, U15, U16, f50_in, U17, U18, f87_in, U19, U20, f105_in, U21, U22, f214_in, U23, U24, f226_in, U25, U26, f26_in, U27, f74_in, U28, f77_in, U29, f221_in, U30

Defined Pair Symbols:

F2_IN, F205_IN, F36_IN, F101_IN, F102_IN, F28_IN, F30_IN, F31_IN, U15', F50_IN, U17', F87_IN, F105_IN, U21', F214_IN, U23', F226_IN, U25', F26_IN, F74_IN, F77_IN, F221_IN, F107_IN, F79_IN, U19'

Compound Symbols:

c2, c3, c4, c5, c6, c7, c20, c22, c35, c37, c39, c41, c43, c44, c46, c47, c49, c52, c53, c55, c56, c58, c59, c61, c64, c68, c71, c

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

Removed 25 trailing tuple parts

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, void) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U1(f26_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(s(z0), tree(s(z0), z1, z2)) → U2(f31_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U3(f74_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f77_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f221_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f226_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f26_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(tree(z1, z0, z3))
U1(f26_out3(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U2(f31_out1(z0), s(z1), tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z2, z0))
U3(f74_out1(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out2(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out4(z0), 0, tree(s(z1), z2, z3)) → f2_out1(z0)
U4(f77_out1(z0), z1, tree(z2, z3, z4)) → f2_out1(tree(z2, z0, z4))
U4(f77_out3(z0), z1, tree(z2, z3, z4)) → f2_out1(z0)
U5(f221_out1(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U5(f221_out2(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U6(f226_out1(z0), s(z1), tree(s(z2), z3, z4)) → f2_out1(tree(s(z2), z3, z0))
f205_in(0, s(z0)) → f205_out1
f205_in(s(z0), s(z1)) → U7(f205_in(z0, z1), s(z0), s(z1))
U7(f205_out1, s(z0), s(z1)) → f205_out1
f36_in(s(z0)) → U8(f36_in(z0), s(z0))
U8(f36_out1, s(z0)) → f36_out1
f107_in(0, s(z0)) → f107_out1
f107_in(s(0), s(s(z0))) → f107_out1
f107_in(s(s(0)), s(s(s(z0)))) → f107_out1
f107_in(s(s(s(0))), s(s(s(s(z0))))) → f107_out1
f107_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f107_out1
f107_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f107_out1
f107_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f107_out1
f107_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U9(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U9(f205_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f107_out1
f79_in(z0, z1, z2) → U10(f87_in(z0, z2), z0, z1, z2)
U10(f87_out1(z0), z1, z2, z3) → f79_out3(tree(s(z1), z2, z0))
f101_in(s(z0), s(z1), z2) → U11(f105_in(z0, z1, z2), s(z0), s(z1), z2)
U11(f105_out1(z0), s(z1), s(z2), z3) → f101_out1(z0)
f102_in(z0, z1, z2, z3) → U12(f214_in(z1, z0, z3), z0, z1, z2, z3)
U12(f214_out1(z0), z1, z2, z3, z4) → f102_out2(tree(z2, z3, z0))
f28_in(s(z0), z1) → U13(f31_in(z0, z1), s(z0), z1)
U13(f31_out1(z0), s(z1), z2) → f28_out1(z0)
f30_in(z0, z1, z2) → U14(f50_in(z0, z2), z0, z1, z2)
U14(f50_out1(z0), z1, z2, z3) → f30_out2(tree(z1, z2, z0))
f31_in(z0, z1) → U15(f36_in(z0), z0, z1)
U15(f36_out1, z0, z1) → U16(f2_in(s(z0), z1), z0, z1)
U16(f2_out1(z0), z1, z2) → f31_out1(z0)
f50_in(z0, z1) → U17(f36_in(z0), z0, z1)
U17(f36_out1, z0, z1) → U18(f2_in(z0, z1), z0, z1)
U18(f2_out1(z0), z1, z2) → f50_out1(z0)
f87_in(z0, z1) → U19(f91_in(z0), z0, z1)
U19(f91_out1, z0, z1) → U20(f2_in(0, z1), z0, z1)
U20(f2_out1(z0), z1, z2) → f87_out1(z0)
f105_in(z0, z1, z2) → U21(f107_in(z0, z1), z0, z1, z2)
U21(f107_out1, z0, z1, z2) → U22(f2_in(s(z0), z2), z0, z1, z2)
U22(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f214_in(z0, z1, z2) → U23(f205_in(z0, z1), z0, z1, z2)
U23(f205_out1, z0, z1, z2) → U24(f2_in(z1, z2), z0, z1, z2)
U24(f2_out1(z0), z1, z2, z3) → f214_out1(z0)
f226_in(z0, z1, z2) → U25(f205_in(z0, z1), z0, z1, z2)
U25(f205_out1, z0, z1, z2) → U26(f2_in(s(z1), z2), z0, z1, z2)
U26(f2_out1(z0), z1, z2, z3) → f226_out1(z0)
f26_in(z0, z1, z2) → U27(f28_in(z0, z1), f30_in(z0, z1, z2), z0, z1, z2)
U27(f28_out1(z0), z1, z2, z3, z4) → f26_out1(z0)
U27(z0, f30_out2(z1), z2, z3, z4) → f26_out3(z1)
f74_in(z0, z1, z2) → U28(f2_in(0, z0), f79_in(z1, z0, z2), z0, z1, z2)
U28(f2_out1(z0), z1, z2, z3, z4) → f74_out1(z0)
U28(z0, f79_out1(z1), z2, z3, z4) → f74_out2(z1)
U28(z0, f79_out3(z1), z2, z3, z4) → f74_out4(z1)
f77_in(z0, z1, z2, z3) → U29(f101_in(z0, z1, z2), f102_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f101_out1(z0), z1, z2, z3, z4, z5) → f77_out1(z0)
U29(z0, f102_out2(z1), z2, z3, z4, z5) → f77_out3(z1)
f221_in(z0, z1) → U30(f2_in(s(z0), z1), f224_in(z0, z1), z0, z1)
U30(f2_out1(z0), z1, z2, z3) → f221_out1(z0)
U30(z0, f224_out1(z1), z2, z3) → f221_out2(z1)

Tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c
U19'(f91_out1, z0, z1) → c

S tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c
U19'(f91_out1, z0, z1) → c

K tuples:none
Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, f205_in, U7, f36_in, U8, f107_in, U9, f79_in, U10, f101_in, U11, f102_in, U12, f28_in, U13, f30_in, U14, f31_in, U15, U16, f50_in, U17, U18, f87_in, U19, U20, f105_in, U21, U22, f214_in, U23, U24, f226_in, U25, U26, f26_in, U27, f74_in, U28, f77_in, U29, f221_in, U30

Defined Pair Symbols:

F31_IN, F50_IN, F105_IN, F214_IN, F226_IN, F107_IN, F79_IN, U19', F2_IN, F205_IN, F36_IN, F101_IN, F102_IN, F28_IN, F30_IN, U15', U17', F87_IN, U21', U23', U25', F26_IN, F74_IN, F77_IN, F221_IN

Compound Symbols:

c43, c46, c52, c55, c58, c, c2, c3, c4, c5, c6, c7, c20, c22, c35, c37, c39, c41, c44, c47, c49, c53, c56, c59, c61, c64, c68, c71, c

(25) CdtKnowledgeProof (EQUIVALENT transformation)

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

U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
U19'(f91_out1, z0, z1) → c

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, void) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U1(f26_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(s(z0), tree(s(z0), z1, z2)) → U2(f31_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U3(f74_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f77_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f221_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f226_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f26_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(tree(z1, z0, z3))
U1(f26_out3(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U2(f31_out1(z0), s(z1), tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z2, z0))
U3(f74_out1(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out2(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out4(z0), 0, tree(s(z1), z2, z3)) → f2_out1(z0)
U4(f77_out1(z0), z1, tree(z2, z3, z4)) → f2_out1(tree(z2, z0, z4))
U4(f77_out3(z0), z1, tree(z2, z3, z4)) → f2_out1(z0)
U5(f221_out1(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U5(f221_out2(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U6(f226_out1(z0), s(z1), tree(s(z2), z3, z4)) → f2_out1(tree(s(z2), z3, z0))
f205_in(0, s(z0)) → f205_out1
f205_in(s(z0), s(z1)) → U7(f205_in(z0, z1), s(z0), s(z1))
U7(f205_out1, s(z0), s(z1)) → f205_out1
f36_in(s(z0)) → U8(f36_in(z0), s(z0))
U8(f36_out1, s(z0)) → f36_out1
f107_in(0, s(z0)) → f107_out1
f107_in(s(0), s(s(z0))) → f107_out1
f107_in(s(s(0)), s(s(s(z0)))) → f107_out1
f107_in(s(s(s(0))), s(s(s(s(z0))))) → f107_out1
f107_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f107_out1
f107_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f107_out1
f107_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f107_out1
f107_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U9(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U9(f205_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f107_out1
f79_in(z0, z1, z2) → U10(f87_in(z0, z2), z0, z1, z2)
U10(f87_out1(z0), z1, z2, z3) → f79_out3(tree(s(z1), z2, z0))
f101_in(s(z0), s(z1), z2) → U11(f105_in(z0, z1, z2), s(z0), s(z1), z2)
U11(f105_out1(z0), s(z1), s(z2), z3) → f101_out1(z0)
f102_in(z0, z1, z2, z3) → U12(f214_in(z1, z0, z3), z0, z1, z2, z3)
U12(f214_out1(z0), z1, z2, z3, z4) → f102_out2(tree(z2, z3, z0))
f28_in(s(z0), z1) → U13(f31_in(z0, z1), s(z0), z1)
U13(f31_out1(z0), s(z1), z2) → f28_out1(z0)
f30_in(z0, z1, z2) → U14(f50_in(z0, z2), z0, z1, z2)
U14(f50_out1(z0), z1, z2, z3) → f30_out2(tree(z1, z2, z0))
f31_in(z0, z1) → U15(f36_in(z0), z0, z1)
U15(f36_out1, z0, z1) → U16(f2_in(s(z0), z1), z0, z1)
U16(f2_out1(z0), z1, z2) → f31_out1(z0)
f50_in(z0, z1) → U17(f36_in(z0), z0, z1)
U17(f36_out1, z0, z1) → U18(f2_in(z0, z1), z0, z1)
U18(f2_out1(z0), z1, z2) → f50_out1(z0)
f87_in(z0, z1) → U19(f91_in(z0), z0, z1)
U19(f91_out1, z0, z1) → U20(f2_in(0, z1), z0, z1)
U20(f2_out1(z0), z1, z2) → f87_out1(z0)
f105_in(z0, z1, z2) → U21(f107_in(z0, z1), z0, z1, z2)
U21(f107_out1, z0, z1, z2) → U22(f2_in(s(z0), z2), z0, z1, z2)
U22(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f214_in(z0, z1, z2) → U23(f205_in(z0, z1), z0, z1, z2)
U23(f205_out1, z0, z1, z2) → U24(f2_in(z1, z2), z0, z1, z2)
U24(f2_out1(z0), z1, z2, z3) → f214_out1(z0)
f226_in(z0, z1, z2) → U25(f205_in(z0, z1), z0, z1, z2)
U25(f205_out1, z0, z1, z2) → U26(f2_in(s(z1), z2), z0, z1, z2)
U26(f2_out1(z0), z1, z2, z3) → f226_out1(z0)
f26_in(z0, z1, z2) → U27(f28_in(z0, z1), f30_in(z0, z1, z2), z0, z1, z2)
U27(f28_out1(z0), z1, z2, z3, z4) → f26_out1(z0)
U27(z0, f30_out2(z1), z2, z3, z4) → f26_out3(z1)
f74_in(z0, z1, z2) → U28(f2_in(0, z0), f79_in(z1, z0, z2), z0, z1, z2)
U28(f2_out1(z0), z1, z2, z3, z4) → f74_out1(z0)
U28(z0, f79_out1(z1), z2, z3, z4) → f74_out2(z1)
U28(z0, f79_out3(z1), z2, z3, z4) → f74_out4(z1)
f77_in(z0, z1, z2, z3) → U29(f101_in(z0, z1, z2), f102_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f101_out1(z0), z1, z2, z3, z4, z5) → f77_out1(z0)
U29(z0, f102_out2(z1), z2, z3, z4, z5) → f77_out3(z1)
f221_in(z0, z1) → U30(f2_in(s(z0), z1), f224_in(z0, z1), z0, z1)
U30(f2_out1(z0), z1, z2, z3) → f221_out1(z0)
U30(z0, f224_out1(z1), z2, z3) → f221_out2(z1)

Tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c
U19'(f91_out1, z0, z1) → c

S tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c

K tuples:

U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
U19'(f91_out1, z0, z1) → c

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, f205_in, U7, f36_in, U8, f107_in, U9, f79_in, U10, f101_in, U11, f102_in, U12, f28_in, U13, f30_in, U14, f31_in, U15, U16, f50_in, U17, U18, f87_in, U19, U20, f105_in, U21, U22, f214_in, U23, U24, f226_in, U25, U26, f26_in, U27, f74_in, U28, f77_in, U29, f221_in, U30

Defined Pair Symbols:

F31_IN, F50_IN, F105_IN, F214_IN, F226_IN, F107_IN, F79_IN, U19', F2_IN, F205_IN, F36_IN, F101_IN, F102_IN, F28_IN, F30_IN, U15', U17', F87_IN, U21', U23', U25', F26_IN, F74_IN, F77_IN, F221_IN

Compound Symbols:

c43, c46, c52, c55, c58, c, c2, c3, c4, c5, c6, c7, c20, c22, c35, c37, c39, c41, c44, c47, c49, c53, c56, c59, c61, c64, c68, c71, 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.

U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))

We considered the (Usable) Rules:

f205_in(0, s(z0)) → f205_out1
f205_in(s(z0), s(z1)) → U7(f205_in(z0, z1), s(z0), s(z1))
U7(f205_out1, s(z0), s(z1)) → f205_out1
f107_in(0, s(z0)) → f107_out1
f107_in(s(0), s(s(z0))) → f107_out1
f107_in(s(s(0)), s(s(s(z0)))) → f107_out1
f107_in(s(s(s(0))), s(s(s(s(z0))))) → f107_out1
f107_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f107_out1
f107_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f107_out1
f107_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f107_out1
f107_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U9(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U9(f205_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f107_out1
f36_in(s(z0)) → U8(f36_in(z0), s(z0))
U8(f36_out1, s(z0)) → f36_out1

And the Tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c
U19'(f91_out1, z0, z1) → c

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

POL(0) = 0   
POL(F101_IN(x₁, x₂, x₃)) = 0   
POL(F102_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F105_IN(x₁, x₂, x₃)) = 0   
POL(F107_IN(x₁, x₂)) = 0   
POL(F205_IN(x₁, x₂)) = 0   
POL(F214_IN(x₁, x₂, x₃)) = 0   
POL(F221_IN(x₁, x₂)) = 0   
POL(F226_IN(x₁, x₂, x₃)) = 0   
POL(F26_IN(x₁, x₂, x₃)) = 0   
POL(F28_IN(x₁, x₂)) = 0   
POL(F2_IN(x₁, x₂)) = 0   
POL(F30_IN(x₁, x₂, x₃)) = 0   
POL(F31_IN(x₁, x₂)) = 0   
POL(F36_IN(x₁)) = 0   
POL(F50_IN(x₁, x₂)) = 0   
POL(F74_IN(x₁, x₂, x₃)) = 0   
POL(F77_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F79_IN(x₁, x₂, x₃)) = 0   
POL(F87_IN(x₁, x₂)) = 0   
POL(U15'(x₁, x₂, x₃)) = [2]x₁   
POL(U17'(x₁, x₂, x₃)) = [2]x₁   
POL(U19'(x₁, x₂, x₃)) = [3]x₃   
POL(U21'(x₁, x₂, x₃, x₄)) = 0   
POL(U23'(x₁, x₂, x₃, x₄)) = 0   
POL(U25'(x₁, x₂, x₃, x₄)) = 0   
POL(U7(x₁, x₂, x₃)) = 0   
POL(U8(x₁, x₂)) = x₁   
POL(U9(x₁, x₂, x₃)) = 0   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c2(x₁)) = x₁   
POL(c20(x₁)) = x₁   
POL(c22(x₁)) = x₁   
POL(c3(x₁)) = x₁   
POL(c35(x₁)) = x₁   
POL(c37(x₁)) = x₁   
POL(c39(x₁)) = x₁   
POL(c4(x₁)) = x₁   
POL(c41(x₁)) = x₁   
POL(c43(x₁, x₂)) = x₁ + x₂   
POL(c44(x₁)) = x₁   
POL(c46(x₁, x₂)) = x₁ + x₂   
POL(c47(x₁)) = x₁   
POL(c49) = 0   
POL(c5(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(c68(x₁, x₂)) = x₁ + x₂   
POL(c7(x₁)) = x₁   
POL(c71(x₁)) = x₁   
POL(f107_in(x₁, x₂)) = 0   
POL(f107_out1) = 0   
POL(f205_in(x₁, x₂)) = 0   
POL(f205_out1) = 0   
POL(f36_in(x₁)) = 0   
POL(f36_out1) = [2]   
POL(f91_out1) = 0   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = 0   

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, void) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U1(f26_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(s(z0), tree(s(z0), z1, z2)) → U2(f31_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U3(f74_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f77_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f221_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f226_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f26_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(tree(z1, z0, z3))
U1(f26_out3(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U2(f31_out1(z0), s(z1), tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z2, z0))
U3(f74_out1(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out2(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out4(z0), 0, tree(s(z1), z2, z3)) → f2_out1(z0)
U4(f77_out1(z0), z1, tree(z2, z3, z4)) → f2_out1(tree(z2, z0, z4))
U4(f77_out3(z0), z1, tree(z2, z3, z4)) → f2_out1(z0)
U5(f221_out1(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U5(f221_out2(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U6(f226_out1(z0), s(z1), tree(s(z2), z3, z4)) → f2_out1(tree(s(z2), z3, z0))
f205_in(0, s(z0)) → f205_out1
f205_in(s(z0), s(z1)) → U7(f205_in(z0, z1), s(z0), s(z1))
U7(f205_out1, s(z0), s(z1)) → f205_out1
f36_in(s(z0)) → U8(f36_in(z0), s(z0))
U8(f36_out1, s(z0)) → f36_out1
f107_in(0, s(z0)) → f107_out1
f107_in(s(0), s(s(z0))) → f107_out1
f107_in(s(s(0)), s(s(s(z0)))) → f107_out1
f107_in(s(s(s(0))), s(s(s(s(z0))))) → f107_out1
f107_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f107_out1
f107_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f107_out1
f107_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f107_out1
f107_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U9(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U9(f205_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f107_out1
f79_in(z0, z1, z2) → U10(f87_in(z0, z2), z0, z1, z2)
U10(f87_out1(z0), z1, z2, z3) → f79_out3(tree(s(z1), z2, z0))
f101_in(s(z0), s(z1), z2) → U11(f105_in(z0, z1, z2), s(z0), s(z1), z2)
U11(f105_out1(z0), s(z1), s(z2), z3) → f101_out1(z0)
f102_in(z0, z1, z2, z3) → U12(f214_in(z1, z0, z3), z0, z1, z2, z3)
U12(f214_out1(z0), z1, z2, z3, z4) → f102_out2(tree(z2, z3, z0))
f28_in(s(z0), z1) → U13(f31_in(z0, z1), s(z0), z1)
U13(f31_out1(z0), s(z1), z2) → f28_out1(z0)
f30_in(z0, z1, z2) → U14(f50_in(z0, z2), z0, z1, z2)
U14(f50_out1(z0), z1, z2, z3) → f30_out2(tree(z1, z2, z0))
f31_in(z0, z1) → U15(f36_in(z0), z0, z1)
U15(f36_out1, z0, z1) → U16(f2_in(s(z0), z1), z0, z1)
U16(f2_out1(z0), z1, z2) → f31_out1(z0)
f50_in(z0, z1) → U17(f36_in(z0), z0, z1)
U17(f36_out1, z0, z1) → U18(f2_in(z0, z1), z0, z1)
U18(f2_out1(z0), z1, z2) → f50_out1(z0)
f87_in(z0, z1) → U19(f91_in(z0), z0, z1)
U19(f91_out1, z0, z1) → U20(f2_in(0, z1), z0, z1)
U20(f2_out1(z0), z1, z2) → f87_out1(z0)
f105_in(z0, z1, z2) → U21(f107_in(z0, z1), z0, z1, z2)
U21(f107_out1, z0, z1, z2) → U22(f2_in(s(z0), z2), z0, z1, z2)
U22(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f214_in(z0, z1, z2) → U23(f205_in(z0, z1), z0, z1, z2)
U23(f205_out1, z0, z1, z2) → U24(f2_in(z1, z2), z0, z1, z2)
U24(f2_out1(z0), z1, z2, z3) → f214_out1(z0)
f226_in(z0, z1, z2) → U25(f205_in(z0, z1), z0, z1, z2)
U25(f205_out1, z0, z1, z2) → U26(f2_in(s(z1), z2), z0, z1, z2)
U26(f2_out1(z0), z1, z2, z3) → f226_out1(z0)
f26_in(z0, z1, z2) → U27(f28_in(z0, z1), f30_in(z0, z1, z2), z0, z1, z2)
U27(f28_out1(z0), z1, z2, z3, z4) → f26_out1(z0)
U27(z0, f30_out2(z1), z2, z3, z4) → f26_out3(z1)
f74_in(z0, z1, z2) → U28(f2_in(0, z0), f79_in(z1, z0, z2), z0, z1, z2)
U28(f2_out1(z0), z1, z2, z3, z4) → f74_out1(z0)
U28(z0, f79_out1(z1), z2, z3, z4) → f74_out2(z1)
U28(z0, f79_out3(z1), z2, z3, z4) → f74_out4(z1)
f77_in(z0, z1, z2, z3) → U29(f101_in(z0, z1, z2), f102_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f101_out1(z0), z1, z2, z3, z4, z5) → f77_out1(z0)
U29(z0, f102_out2(z1), z2, z3, z4, z5) → f77_out3(z1)
f221_in(z0, z1) → U30(f2_in(s(z0), z1), f224_in(z0, z1), z0, z1)
U30(f2_out1(z0), z1, z2, z3) → f221_out1(z0)
U30(z0, f224_out1(z1), z2, z3) → f221_out2(z1)

Tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c
U19'(f91_out1, z0, z1) → c

S tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c

K tuples:

U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
U19'(f91_out1, z0, z1) → c
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, f205_in, U7, f36_in, U8, f107_in, U9, f79_in, U10, f101_in, U11, f102_in, U12, f28_in, U13, f30_in, U14, f31_in, U15, U16, f50_in, U17, U18, f87_in, U19, U20, f105_in, U21, U22, f214_in, U23, U24, f226_in, U25, U26, f26_in, U27, f74_in, U28, f77_in, U29, f221_in, U30

Defined Pair Symbols:

F31_IN, F50_IN, F105_IN, F214_IN, F226_IN, F107_IN, F79_IN, U19', F2_IN, F205_IN, F36_IN, F101_IN, F102_IN, F28_IN, F30_IN, U15', U17', F87_IN, U21', U23', U25', F26_IN, F74_IN, F77_IN, F221_IN

Compound Symbols:

c43, c46, c52, c55, c58, c, c2, c3, c4, c5, c6, c7, c20, c22, c35, c37, c39, c41, c44, c47, c49, c53, c56, c59, c61, c64, c68, c71, c

(29) 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.

F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F79_IN(z0, z1, z2) → c

We considered the (Usable) Rules:

f205_in(0, s(z0)) → f205_out1
f205_in(s(z0), s(z1)) → U7(f205_in(z0, z1), s(z0), s(z1))
U7(f205_out1, s(z0), s(z1)) → f205_out1
f107_in(0, s(z0)) → f107_out1
f107_in(s(0), s(s(z0))) → f107_out1
f107_in(s(s(0)), s(s(s(z0)))) → f107_out1
f107_in(s(s(s(0))), s(s(s(s(z0))))) → f107_out1
f107_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f107_out1
f107_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f107_out1
f107_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f107_out1
f107_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U9(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U9(f205_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f107_out1
f36_in(s(z0)) → U8(f36_in(z0), s(z0))
U8(f36_out1, s(z0)) → f36_out1

And the Tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c
U19'(f91_out1, z0, z1) → c

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

POL(0) = 0   
POL(F101_IN(x₁, x₂, x₃)) = x₃   
POL(F102_IN(x₁, x₂, x₃, x₄)) = x₄   
POL(F105_IN(x₁, x₂, x₃)) = x₃   
POL(F107_IN(x₁, x₂)) = 0   
POL(F205_IN(x₁, x₂)) = 0   
POL(F214_IN(x₁, x₂, x₃)) = x₃   
POL(F221_IN(x₁, x₂)) = [1] + x₂   
POL(F226_IN(x₁, x₂, x₃)) = x₃   
POL(F26_IN(x₁, x₂, x₃)) = x₂ + x₃   
POL(F28_IN(x₁, x₂)) = x₂   
POL(F2_IN(x₁, x₂)) = x₂   
POL(F30_IN(x₁, x₂, x₃)) = x₃   
POL(F31_IN(x₁, x₂)) = x₂   
POL(F36_IN(x₁)) = 0   
POL(F50_IN(x₁, x₂)) = x₂   
POL(F74_IN(x₁, x₂, x₃)) = [1] + x₁   
POL(F77_IN(x₁, x₂, x₃, x₄)) = x₃ + x₄   
POL(F79_IN(x₁, x₂, x₃)) = [1]   
POL(F87_IN(x₁, x₂)) = 0   
POL(U15'(x₁, x₂, x₃)) = x₃   
POL(U17'(x₁, x₂, x₃)) = x₃   
POL(U19'(x₁, x₂, x₃)) = [3]x₁ + x₃   
POL(U21'(x₁, x₂, x₃, x₄)) = x₄   
POL(U23'(x₁, x₂, x₃, x₄)) = x₄   
POL(U25'(x₁, x₂, x₃, x₄)) = x₄   
POL(U7(x₁, x₂, x₃)) = 0   
POL(U8(x₁, x₂)) = 0   
POL(U9(x₁, x₂, x₃)) = 0   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c2(x₁)) = x₁   
POL(c20(x₁)) = x₁   
POL(c22(x₁)) = x₁   
POL(c3(x₁)) = x₁   
POL(c35(x₁)) = x₁   
POL(c37(x₁)) = x₁   
POL(c39(x₁)) = x₁   
POL(c4(x₁)) = x₁   
POL(c41(x₁)) = x₁   
POL(c43(x₁, x₂)) = x₁ + x₂   
POL(c44(x₁)) = x₁   
POL(c46(x₁, x₂)) = x₁ + x₂   
POL(c47(x₁)) = x₁   
POL(c49) = 0   
POL(c5(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(c68(x₁, x₂)) = x₁ + x₂   
POL(c7(x₁)) = x₁   
POL(c71(x₁)) = x₁   
POL(f107_in(x₁, x₂)) = 0   
POL(f107_out1) = 0   
POL(f205_in(x₁, x₂)) = 0   
POL(f205_out1) = 0   
POL(f36_in(x₁)) = 0   
POL(f36_out1) = 0   
POL(f91_out1) = [3]   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = [1] + x₂ + x₃   

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, void) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U1(f26_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(s(z0), tree(s(z0), z1, z2)) → U2(f31_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U3(f74_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f77_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f221_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f226_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f26_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(tree(z1, z0, z3))
U1(f26_out3(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U2(f31_out1(z0), s(z1), tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z2, z0))
U3(f74_out1(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out2(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out4(z0), 0, tree(s(z1), z2, z3)) → f2_out1(z0)
U4(f77_out1(z0), z1, tree(z2, z3, z4)) → f2_out1(tree(z2, z0, z4))
U4(f77_out3(z0), z1, tree(z2, z3, z4)) → f2_out1(z0)
U5(f221_out1(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U5(f221_out2(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U6(f226_out1(z0), s(z1), tree(s(z2), z3, z4)) → f2_out1(tree(s(z2), z3, z0))
f205_in(0, s(z0)) → f205_out1
f205_in(s(z0), s(z1)) → U7(f205_in(z0, z1), s(z0), s(z1))
U7(f205_out1, s(z0), s(z1)) → f205_out1
f36_in(s(z0)) → U8(f36_in(z0), s(z0))
U8(f36_out1, s(z0)) → f36_out1
f107_in(0, s(z0)) → f107_out1
f107_in(s(0), s(s(z0))) → f107_out1
f107_in(s(s(0)), s(s(s(z0)))) → f107_out1
f107_in(s(s(s(0))), s(s(s(s(z0))))) → f107_out1
f107_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f107_out1
f107_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f107_out1
f107_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f107_out1
f107_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U9(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U9(f205_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f107_out1
f79_in(z0, z1, z2) → U10(f87_in(z0, z2), z0, z1, z2)
U10(f87_out1(z0), z1, z2, z3) → f79_out3(tree(s(z1), z2, z0))
f101_in(s(z0), s(z1), z2) → U11(f105_in(z0, z1, z2), s(z0), s(z1), z2)
U11(f105_out1(z0), s(z1), s(z2), z3) → f101_out1(z0)
f102_in(z0, z1, z2, z3) → U12(f214_in(z1, z0, z3), z0, z1, z2, z3)
U12(f214_out1(z0), z1, z2, z3, z4) → f102_out2(tree(z2, z3, z0))
f28_in(s(z0), z1) → U13(f31_in(z0, z1), s(z0), z1)
U13(f31_out1(z0), s(z1), z2) → f28_out1(z0)
f30_in(z0, z1, z2) → U14(f50_in(z0, z2), z0, z1, z2)
U14(f50_out1(z0), z1, z2, z3) → f30_out2(tree(z1, z2, z0))
f31_in(z0, z1) → U15(f36_in(z0), z0, z1)
U15(f36_out1, z0, z1) → U16(f2_in(s(z0), z1), z0, z1)
U16(f2_out1(z0), z1, z2) → f31_out1(z0)
f50_in(z0, z1) → U17(f36_in(z0), z0, z1)
U17(f36_out1, z0, z1) → U18(f2_in(z0, z1), z0, z1)
U18(f2_out1(z0), z1, z2) → f50_out1(z0)
f87_in(z0, z1) → U19(f91_in(z0), z0, z1)
U19(f91_out1, z0, z1) → U20(f2_in(0, z1), z0, z1)
U20(f2_out1(z0), z1, z2) → f87_out1(z0)
f105_in(z0, z1, z2) → U21(f107_in(z0, z1), z0, z1, z2)
U21(f107_out1, z0, z1, z2) → U22(f2_in(s(z0), z2), z0, z1, z2)
U22(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f214_in(z0, z1, z2) → U23(f205_in(z0, z1), z0, z1, z2)
U23(f205_out1, z0, z1, z2) → U24(f2_in(z1, z2), z0, z1, z2)
U24(f2_out1(z0), z1, z2, z3) → f214_out1(z0)
f226_in(z0, z1, z2) → U25(f205_in(z0, z1), z0, z1, z2)
U25(f205_out1, z0, z1, z2) → U26(f2_in(s(z1), z2), z0, z1, z2)
U26(f2_out1(z0), z1, z2, z3) → f226_out1(z0)
f26_in(z0, z1, z2) → U27(f28_in(z0, z1), f30_in(z0, z1, z2), z0, z1, z2)
U27(f28_out1(z0), z1, z2, z3, z4) → f26_out1(z0)
U27(z0, f30_out2(z1), z2, z3, z4) → f26_out3(z1)
f74_in(z0, z1, z2) → U28(f2_in(0, z0), f79_in(z1, z0, z2), z0, z1, z2)
U28(f2_out1(z0), z1, z2, z3, z4) → f74_out1(z0)
U28(z0, f79_out1(z1), z2, z3, z4) → f74_out2(z1)
U28(z0, f79_out3(z1), z2, z3, z4) → f74_out4(z1)
f77_in(z0, z1, z2, z3) → U29(f101_in(z0, z1, z2), f102_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f101_out1(z0), z1, z2, z3, z4, z5) → f77_out1(z0)
U29(z0, f102_out2(z1), z2, z3, z4, z5) → f77_out3(z1)
f221_in(z0, z1) → U30(f2_in(s(z0), z1), f224_in(z0, z1), z0, z1)
U30(f2_out1(z0), z1, z2, z3) → f221_out1(z0)
U30(z0, f224_out1(z1), z2, z3) → f221_out2(z1)

Tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c
U19'(f91_out1, z0, z1) → c

S tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c

K tuples:

U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
U19'(f91_out1, z0, z1) → c
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F79_IN(z0, z1, z2) → c

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, f205_in, U7, f36_in, U8, f107_in, U9, f79_in, U10, f101_in, U11, f102_in, U12, f28_in, U13, f30_in, U14, f31_in, U15, U16, f50_in, U17, U18, f87_in, U19, U20, f105_in, U21, U22, f214_in, U23, U24, f226_in, U25, U26, f26_in, U27, f74_in, U28, f77_in, U29, f221_in, U30

Defined Pair Symbols:

F31_IN, F50_IN, F105_IN, F214_IN, F226_IN, F107_IN, F79_IN, U19', F2_IN, F205_IN, F36_IN, F101_IN, F102_IN, F28_IN, F30_IN, U15', U17', F87_IN, U21', U23', U25', F26_IN, F74_IN, F77_IN, F221_IN

Compound Symbols:

c43, c46, c52, c55, c58, c, c2, c3, c4, c5, c6, c7, c20, c22, c35, c37, c39, c41, c44, c47, c49, c53, c56, c59, c61, c64, c68, c71, c

(31) CdtKnowledgeProof (EQUIVALENT transformation)

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

F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F87_IN(z0, z1) → c49
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, void) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U1(f26_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(s(z0), tree(s(z0), z1, z2)) → U2(f31_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U3(f74_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f77_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f221_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f226_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f26_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(tree(z1, z0, z3))
U1(f26_out3(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U2(f31_out1(z0), s(z1), tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z2, z0))
U3(f74_out1(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out2(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out4(z0), 0, tree(s(z1), z2, z3)) → f2_out1(z0)
U4(f77_out1(z0), z1, tree(z2, z3, z4)) → f2_out1(tree(z2, z0, z4))
U4(f77_out3(z0), z1, tree(z2, z3, z4)) → f2_out1(z0)
U5(f221_out1(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U5(f221_out2(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U6(f226_out1(z0), s(z1), tree(s(z2), z3, z4)) → f2_out1(tree(s(z2), z3, z0))
f205_in(0, s(z0)) → f205_out1
f205_in(s(z0), s(z1)) → U7(f205_in(z0, z1), s(z0), s(z1))
U7(f205_out1, s(z0), s(z1)) → f205_out1
f36_in(s(z0)) → U8(f36_in(z0), s(z0))
U8(f36_out1, s(z0)) → f36_out1
f107_in(0, s(z0)) → f107_out1
f107_in(s(0), s(s(z0))) → f107_out1
f107_in(s(s(0)), s(s(s(z0)))) → f107_out1
f107_in(s(s(s(0))), s(s(s(s(z0))))) → f107_out1
f107_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f107_out1
f107_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f107_out1
f107_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f107_out1
f107_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U9(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U9(f205_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f107_out1
f79_in(z0, z1, z2) → U10(f87_in(z0, z2), z0, z1, z2)
U10(f87_out1(z0), z1, z2, z3) → f79_out3(tree(s(z1), z2, z0))
f101_in(s(z0), s(z1), z2) → U11(f105_in(z0, z1, z2), s(z0), s(z1), z2)
U11(f105_out1(z0), s(z1), s(z2), z3) → f101_out1(z0)
f102_in(z0, z1, z2, z3) → U12(f214_in(z1, z0, z3), z0, z1, z2, z3)
U12(f214_out1(z0), z1, z2, z3, z4) → f102_out2(tree(z2, z3, z0))
f28_in(s(z0), z1) → U13(f31_in(z0, z1), s(z0), z1)
U13(f31_out1(z0), s(z1), z2) → f28_out1(z0)
f30_in(z0, z1, z2) → U14(f50_in(z0, z2), z0, z1, z2)
U14(f50_out1(z0), z1, z2, z3) → f30_out2(tree(z1, z2, z0))
f31_in(z0, z1) → U15(f36_in(z0), z0, z1)
U15(f36_out1, z0, z1) → U16(f2_in(s(z0), z1), z0, z1)
U16(f2_out1(z0), z1, z2) → f31_out1(z0)
f50_in(z0, z1) → U17(f36_in(z0), z0, z1)
U17(f36_out1, z0, z1) → U18(f2_in(z0, z1), z0, z1)
U18(f2_out1(z0), z1, z2) → f50_out1(z0)
f87_in(z0, z1) → U19(f91_in(z0), z0, z1)
U19(f91_out1, z0, z1) → U20(f2_in(0, z1), z0, z1)
U20(f2_out1(z0), z1, z2) → f87_out1(z0)
f105_in(z0, z1, z2) → U21(f107_in(z0, z1), z0, z1, z2)
U21(f107_out1, z0, z1, z2) → U22(f2_in(s(z0), z2), z0, z1, z2)
U22(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f214_in(z0, z1, z2) → U23(f205_in(z0, z1), z0, z1, z2)
U23(f205_out1, z0, z1, z2) → U24(f2_in(z1, z2), z0, z1, z2)
U24(f2_out1(z0), z1, z2, z3) → f214_out1(z0)
f226_in(z0, z1, z2) → U25(f205_in(z0, z1), z0, z1, z2)
U25(f205_out1, z0, z1, z2) → U26(f2_in(s(z1), z2), z0, z1, z2)
U26(f2_out1(z0), z1, z2, z3) → f226_out1(z0)
f26_in(z0, z1, z2) → U27(f28_in(z0, z1), f30_in(z0, z1, z2), z0, z1, z2)
U27(f28_out1(z0), z1, z2, z3, z4) → f26_out1(z0)
U27(z0, f30_out2(z1), z2, z3, z4) → f26_out3(z1)
f74_in(z0, z1, z2) → U28(f2_in(0, z0), f79_in(z1, z0, z2), z0, z1, z2)
U28(f2_out1(z0), z1, z2, z3, z4) → f74_out1(z0)
U28(z0, f79_out1(z1), z2, z3, z4) → f74_out2(z1)
U28(z0, f79_out3(z1), z2, z3, z4) → f74_out4(z1)
f77_in(z0, z1, z2, z3) → U29(f101_in(z0, z1, z2), f102_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f101_out1(z0), z1, z2, z3, z4, z5) → f77_out1(z0)
U29(z0, f102_out2(z1), z2, z3, z4, z5) → f77_out3(z1)
f221_in(z0, z1) → U30(f2_in(s(z0), z1), f224_in(z0, z1), z0, z1)
U30(f2_out1(z0), z1, z2, z3) → f221_out1(z0)
U30(z0, f224_out1(z1), z2, z3) → f221_out2(z1)

Tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c
U19'(f91_out1, z0, z1) → c

S tuples:

F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))

K tuples:

U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
U19'(f91_out1, z0, z1) → c
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F79_IN(z0, z1, z2) → c
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F87_IN(z0, z1) → c49
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, f205_in, U7, f36_in, U8, f107_in, U9, f79_in, U10, f101_in, U11, f102_in, U12, f28_in, U13, f30_in, U14, f31_in, U15, U16, f50_in, U17, U18, f87_in, U19, U20, f105_in, U21, U22, f214_in, U23, U24, f226_in, U25, U26, f26_in, U27, f74_in, U28, f77_in, U29, f221_in, U30

Defined Pair Symbols:

F31_IN, F50_IN, F105_IN, F214_IN, F226_IN, F107_IN, F79_IN, U19', F2_IN, F205_IN, F36_IN, F101_IN, F102_IN, F28_IN, F30_IN, U15', U17', F87_IN, U21', U23', U25', F26_IN, F74_IN, F77_IN, F221_IN

Compound Symbols:

c43, c46, c52, c55, c58, c, c2, c3, c4, c5, c6, c7, c20, c22, c35, c37, c39, c41, c44, c47, c49, c53, c56, c59, c61, c64, c68, c71, 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.

F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))

We considered the (Usable) Rules:

f205_in(0, s(z0)) → f205_out1
f205_in(s(z0), s(z1)) → U7(f205_in(z0, z1), s(z0), s(z1))
U7(f205_out1, s(z0), s(z1)) → f205_out1
f107_in(0, s(z0)) → f107_out1
f107_in(s(0), s(s(z0))) → f107_out1
f107_in(s(s(0)), s(s(s(z0)))) → f107_out1
f107_in(s(s(s(0))), s(s(s(s(z0))))) → f107_out1
f107_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f107_out1
f107_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f107_out1
f107_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f107_out1
f107_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U9(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U9(f205_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f107_out1
f36_in(s(z0)) → U8(f36_in(z0), s(z0))
U8(f36_out1, s(z0)) → f36_out1

And the Tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c
U19'(f91_out1, z0, z1) → c

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

POL(0) = 0   
POL(F101_IN(x₁, x₂, x₃)) = [1] + x₃   
POL(F102_IN(x₁, x₂, x₃, x₄)) = x₄   
POL(F105_IN(x₁, x₂, x₃)) = x₃   
POL(F107_IN(x₁, x₂)) = 0   
POL(F205_IN(x₁, x₂)) = 0   
POL(F214_IN(x₁, x₂, x₃)) = x₃   
POL(F221_IN(x₁, x₂)) = [1] + x₂   
POL(F226_IN(x₁, x₂, x₃)) = [2] + x₃   
POL(F26_IN(x₁, x₂, x₃)) = [1] + x₁ + x₂ + x₃   
POL(F28_IN(x₁, x₂)) = x₂   
POL(F2_IN(x₁, x₂)) = x₂   
POL(F30_IN(x₁, x₂, x₃)) = x₃   
POL(F31_IN(x₁, x₂)) = x₂   
POL(F36_IN(x₁)) = 0   
POL(F50_IN(x₁, x₂)) = x₂   
POL(F74_IN(x₁, x₂, x₃)) = [3] + x₁ + x₃   
POL(F77_IN(x₁, x₂, x₃, x₄)) = [2] + x₃ + x₄   
POL(F79_IN(x₁, x₂, x₃)) = 0   
POL(F87_IN(x₁, x₂)) = 0   
POL(U15'(x₁, x₂, x₃)) = x₃   
POL(U17'(x₁, x₂, x₃)) = x₃   
POL(U19'(x₁, x₂, x₃)) = [3] + [2]x₃   
POL(U21'(x₁, x₂, x₃, x₄)) = x₄   
POL(U23'(x₁, x₂, x₃, x₄)) = x₄   
POL(U25'(x₁, x₂, x₃, x₄)) = x₄   
POL(U7(x₁, x₂, x₃)) = 0   
POL(U8(x₁, x₂)) = 0   
POL(U9(x₁, x₂, x₃)) = 0   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c2(x₁)) = x₁   
POL(c20(x₁)) = x₁   
POL(c22(x₁)) = x₁   
POL(c3(x₁)) = x₁   
POL(c35(x₁)) = x₁   
POL(c37(x₁)) = x₁   
POL(c39(x₁)) = x₁   
POL(c4(x₁)) = x₁   
POL(c41(x₁)) = x₁   
POL(c43(x₁, x₂)) = x₁ + x₂   
POL(c44(x₁)) = x₁   
POL(c46(x₁, x₂)) = x₁ + x₂   
POL(c47(x₁)) = x₁   
POL(c49) = 0   
POL(c5(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(c68(x₁, x₂)) = x₁ + x₂   
POL(c7(x₁)) = x₁   
POL(c71(x₁)) = x₁   
POL(f107_in(x₁, x₂)) = x₂   
POL(f107_out1) = 0   
POL(f205_in(x₁, x₂)) = 0   
POL(f205_out1) = 0   
POL(f36_in(x₁)) = 0   
POL(f36_out1) = 0   
POL(f91_out1) = 0   
POL(s(x₁)) = [2]   
POL(tree(x₁, x₂, x₃)) = [2] + x₁ + x₂ + x₃   

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, void) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U1(f26_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(s(z0), tree(s(z0), z1, z2)) → U2(f31_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U3(f74_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f77_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f221_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f226_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f26_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(tree(z1, z0, z3))
U1(f26_out3(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U2(f31_out1(z0), s(z1), tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z2, z0))
U3(f74_out1(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out2(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out4(z0), 0, tree(s(z1), z2, z3)) → f2_out1(z0)
U4(f77_out1(z0), z1, tree(z2, z3, z4)) → f2_out1(tree(z2, z0, z4))
U4(f77_out3(z0), z1, tree(z2, z3, z4)) → f2_out1(z0)
U5(f221_out1(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U5(f221_out2(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U6(f226_out1(z0), s(z1), tree(s(z2), z3, z4)) → f2_out1(tree(s(z2), z3, z0))
f205_in(0, s(z0)) → f205_out1
f205_in(s(z0), s(z1)) → U7(f205_in(z0, z1), s(z0), s(z1))
U7(f205_out1, s(z0), s(z1)) → f205_out1
f36_in(s(z0)) → U8(f36_in(z0), s(z0))
U8(f36_out1, s(z0)) → f36_out1
f107_in(0, s(z0)) → f107_out1
f107_in(s(0), s(s(z0))) → f107_out1
f107_in(s(s(0)), s(s(s(z0)))) → f107_out1
f107_in(s(s(s(0))), s(s(s(s(z0))))) → f107_out1
f107_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f107_out1
f107_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f107_out1
f107_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f107_out1
f107_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U9(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U9(f205_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f107_out1
f79_in(z0, z1, z2) → U10(f87_in(z0, z2), z0, z1, z2)
U10(f87_out1(z0), z1, z2, z3) → f79_out3(tree(s(z1), z2, z0))
f101_in(s(z0), s(z1), z2) → U11(f105_in(z0, z1, z2), s(z0), s(z1), z2)
U11(f105_out1(z0), s(z1), s(z2), z3) → f101_out1(z0)
f102_in(z0, z1, z2, z3) → U12(f214_in(z1, z0, z3), z0, z1, z2, z3)
U12(f214_out1(z0), z1, z2, z3, z4) → f102_out2(tree(z2, z3, z0))
f28_in(s(z0), z1) → U13(f31_in(z0, z1), s(z0), z1)
U13(f31_out1(z0), s(z1), z2) → f28_out1(z0)
f30_in(z0, z1, z2) → U14(f50_in(z0, z2), z0, z1, z2)
U14(f50_out1(z0), z1, z2, z3) → f30_out2(tree(z1, z2, z0))
f31_in(z0, z1) → U15(f36_in(z0), z0, z1)
U15(f36_out1, z0, z1) → U16(f2_in(s(z0), z1), z0, z1)
U16(f2_out1(z0), z1, z2) → f31_out1(z0)
f50_in(z0, z1) → U17(f36_in(z0), z0, z1)
U17(f36_out1, z0, z1) → U18(f2_in(z0, z1), z0, z1)
U18(f2_out1(z0), z1, z2) → f50_out1(z0)
f87_in(z0, z1) → U19(f91_in(z0), z0, z1)
U19(f91_out1, z0, z1) → U20(f2_in(0, z1), z0, z1)
U20(f2_out1(z0), z1, z2) → f87_out1(z0)
f105_in(z0, z1, z2) → U21(f107_in(z0, z1), z0, z1, z2)
U21(f107_out1, z0, z1, z2) → U22(f2_in(s(z0), z2), z0, z1, z2)
U22(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f214_in(z0, z1, z2) → U23(f205_in(z0, z1), z0, z1, z2)
U23(f205_out1, z0, z1, z2) → U24(f2_in(z1, z2), z0, z1, z2)
U24(f2_out1(z0), z1, z2, z3) → f214_out1(z0)
f226_in(z0, z1, z2) → U25(f205_in(z0, z1), z0, z1, z2)
U25(f205_out1, z0, z1, z2) → U26(f2_in(s(z1), z2), z0, z1, z2)
U26(f2_out1(z0), z1, z2, z3) → f226_out1(z0)
f26_in(z0, z1, z2) → U27(f28_in(z0, z1), f30_in(z0, z1, z2), z0, z1, z2)
U27(f28_out1(z0), z1, z2, z3, z4) → f26_out1(z0)
U27(z0, f30_out2(z1), z2, z3, z4) → f26_out3(z1)
f74_in(z0, z1, z2) → U28(f2_in(0, z0), f79_in(z1, z0, z2), z0, z1, z2)
U28(f2_out1(z0), z1, z2, z3, z4) → f74_out1(z0)
U28(z0, f79_out1(z1), z2, z3, z4) → f74_out2(z1)
U28(z0, f79_out3(z1), z2, z3, z4) → f74_out4(z1)
f77_in(z0, z1, z2, z3) → U29(f101_in(z0, z1, z2), f102_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f101_out1(z0), z1, z2, z3, z4, z5) → f77_out1(z0)
U29(z0, f102_out2(z1), z2, z3, z4, z5) → f77_out3(z1)
f221_in(z0, z1) → U30(f2_in(s(z0), z1), f224_in(z0, z1), z0, z1)
U30(f2_out1(z0), z1, z2, z3) → f221_out1(z0)
U30(z0, f224_out1(z1), z2, z3) → f221_out2(z1)

Tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c
U19'(f91_out1, z0, z1) → c

S tuples:

F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))

K tuples:

U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
U19'(f91_out1, z0, z1) → c
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F79_IN(z0, z1, z2) → c
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F87_IN(z0, z1) → c49
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, f205_in, U7, f36_in, U8, f107_in, U9, f79_in, U10, f101_in, U11, f102_in, U12, f28_in, U13, f30_in, U14, f31_in, U15, U16, f50_in, U17, U18, f87_in, U19, U20, f105_in, U21, U22, f214_in, U23, U24, f226_in, U25, U26, f26_in, U27, f74_in, U28, f77_in, U29, f221_in, U30

Defined Pair Symbols:

F31_IN, F50_IN, F105_IN, F214_IN, F226_IN, F107_IN, F79_IN, U19', F2_IN, F205_IN, F36_IN, F101_IN, F102_IN, F28_IN, F30_IN, U15', U17', F87_IN, U21', U23', U25', F26_IN, F74_IN, F77_IN, F221_IN

Compound Symbols:

c43, c46, c52, c55, c58, c, c2, c3, c4, c5, c6, c7, c20, c22, c35, c37, c39, c41, c44, c47, c49, c53, c56, c59, c61, c64, c68, c71, c

(35) 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.

F36_IN(s(z0)) → c22(F36_IN(z0))

We considered the (Usable) Rules:

f205_in(0, s(z0)) → f205_out1
f205_in(s(z0), s(z1)) → U7(f205_in(z0, z1), s(z0), s(z1))
U7(f205_out1, s(z0), s(z1)) → f205_out1
f107_in(0, s(z0)) → f107_out1
f107_in(s(0), s(s(z0))) → f107_out1
f107_in(s(s(0)), s(s(s(z0)))) → f107_out1
f107_in(s(s(s(0))), s(s(s(s(z0))))) → f107_out1
f107_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f107_out1
f107_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f107_out1
f107_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f107_out1
f107_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U9(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U9(f205_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f107_out1
f36_in(s(z0)) → U8(f36_in(z0), s(z0))
U8(f36_out1, s(z0)) → f36_out1

And the Tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c
U19'(f91_out1, z0, z1) → c

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

POL(0) = 0   
POL(F101_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F102_IN(x₁, x₂, x₃, x₄)) = [2]x₂ + [2]x₄   
POL(F105_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F107_IN(x₁, x₂)) = 0   
POL(F205_IN(x₁, x₂)) = 0   
POL(F214_IN(x₁, x₂, x₃)) = x₁ + [2]x₃   
POL(F221_IN(x₁, x₂)) = [2]x₂   
POL(F226_IN(x₁, x₂, x₃)) = [2]x₁ + [2]x₃   
POL(F26_IN(x₁, x₂, x₃)) = [2]x₁ + [2]x₂ + [2]x₃   
POL(F28_IN(x₁, x₂)) = x₁ + [2]x₂   
POL(F2_IN(x₁, x₂)) = [2]x₂   
POL(F30_IN(x₁, x₂, x₃)) = x₁ + [2]x₃   
POL(F31_IN(x₁, x₂)) = [1] + x₁ + [2]x₂   
POL(F36_IN(x₁)) = x₁   
POL(F50_IN(x₁, x₂)) = x₁ + [2]x₂   
POL(F74_IN(x₁, x₂, x₃)) = [1] + [2]x₁ + x₂ + [2]x₃   
POL(F77_IN(x₁, x₂, x₃, x₄)) = [2]x₂ + [2]x₃ + [2]x₄   
POL(F79_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F87_IN(x₁, x₂)) = [2]x₂   
POL(U15'(x₁, x₂, x₃)) = [2]x₃   
POL(U17'(x₁, x₂, x₃)) = [2]x₃   
POL(U19'(x₁, x₂, x₃)) = [3] + [2]x₃   
POL(U21'(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(U23'(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(U25'(x₁, x₂, x₃, x₄)) = [2]x₂ + [2]x₄   
POL(U7(x₁, x₂, x₃)) = 0   
POL(U8(x₁, x₂)) = 0   
POL(U9(x₁, x₂, x₃)) = 0   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c2(x₁)) = x₁   
POL(c20(x₁)) = x₁   
POL(c22(x₁)) = x₁   
POL(c3(x₁)) = x₁   
POL(c35(x₁)) = x₁   
POL(c37(x₁)) = x₁   
POL(c39(x₁)) = x₁   
POL(c4(x₁)) = x₁   
POL(c41(x₁)) = x₁   
POL(c43(x₁, x₂)) = x₁ + x₂   
POL(c44(x₁)) = x₁   
POL(c46(x₁, x₂)) = x₁ + x₂   
POL(c47(x₁)) = x₁   
POL(c49) = 0   
POL(c5(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(c68(x₁, x₂)) = x₁ + x₂   
POL(c7(x₁)) = x₁   
POL(c71(x₁)) = x₁   
POL(f107_in(x₁, x₂)) = 0   
POL(f107_out1) = 0   
POL(f205_in(x₁, x₂)) = 0   
POL(f205_out1) = 0   
POL(f36_in(x₁)) = 0   
POL(f36_out1) = 0   
POL(f91_out1) = 0   
POL(s(x₁)) = [1] + x₁   
POL(tree(x₁, x₂, x₃)) = x₁ + x₂ + x₃   

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, void) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U1(f26_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(s(z0), tree(s(z0), z1, z2)) → U2(f31_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U3(f74_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f77_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f221_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f226_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f26_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(tree(z1, z0, z3))
U1(f26_out3(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U2(f31_out1(z0), s(z1), tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z2, z0))
U3(f74_out1(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out2(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out4(z0), 0, tree(s(z1), z2, z3)) → f2_out1(z0)
U4(f77_out1(z0), z1, tree(z2, z3, z4)) → f2_out1(tree(z2, z0, z4))
U4(f77_out3(z0), z1, tree(z2, z3, z4)) → f2_out1(z0)
U5(f221_out1(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U5(f221_out2(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U6(f226_out1(z0), s(z1), tree(s(z2), z3, z4)) → f2_out1(tree(s(z2), z3, z0))
f205_in(0, s(z0)) → f205_out1
f205_in(s(z0), s(z1)) → U7(f205_in(z0, z1), s(z0), s(z1))
U7(f205_out1, s(z0), s(z1)) → f205_out1
f36_in(s(z0)) → U8(f36_in(z0), s(z0))
U8(f36_out1, s(z0)) → f36_out1
f107_in(0, s(z0)) → f107_out1
f107_in(s(0), s(s(z0))) → f107_out1
f107_in(s(s(0)), s(s(s(z0)))) → f107_out1
f107_in(s(s(s(0))), s(s(s(s(z0))))) → f107_out1
f107_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f107_out1
f107_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f107_out1
f107_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f107_out1
f107_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U9(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U9(f205_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f107_out1
f79_in(z0, z1, z2) → U10(f87_in(z0, z2), z0, z1, z2)
U10(f87_out1(z0), z1, z2, z3) → f79_out3(tree(s(z1), z2, z0))
f101_in(s(z0), s(z1), z2) → U11(f105_in(z0, z1, z2), s(z0), s(z1), z2)
U11(f105_out1(z0), s(z1), s(z2), z3) → f101_out1(z0)
f102_in(z0, z1, z2, z3) → U12(f214_in(z1, z0, z3), z0, z1, z2, z3)
U12(f214_out1(z0), z1, z2, z3, z4) → f102_out2(tree(z2, z3, z0))
f28_in(s(z0), z1) → U13(f31_in(z0, z1), s(z0), z1)
U13(f31_out1(z0), s(z1), z2) → f28_out1(z0)
f30_in(z0, z1, z2) → U14(f50_in(z0, z2), z0, z1, z2)
U14(f50_out1(z0), z1, z2, z3) → f30_out2(tree(z1, z2, z0))
f31_in(z0, z1) → U15(f36_in(z0), z0, z1)
U15(f36_out1, z0, z1) → U16(f2_in(s(z0), z1), z0, z1)
U16(f2_out1(z0), z1, z2) → f31_out1(z0)
f50_in(z0, z1) → U17(f36_in(z0), z0, z1)
U17(f36_out1, z0, z1) → U18(f2_in(z0, z1), z0, z1)
U18(f2_out1(z0), z1, z2) → f50_out1(z0)
f87_in(z0, z1) → U19(f91_in(z0), z0, z1)
U19(f91_out1, z0, z1) → U20(f2_in(0, z1), z0, z1)
U20(f2_out1(z0), z1, z2) → f87_out1(z0)
f105_in(z0, z1, z2) → U21(f107_in(z0, z1), z0, z1, z2)
U21(f107_out1, z0, z1, z2) → U22(f2_in(s(z0), z2), z0, z1, z2)
U22(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f214_in(z0, z1, z2) → U23(f205_in(z0, z1), z0, z1, z2)
U23(f205_out1, z0, z1, z2) → U24(f2_in(z1, z2), z0, z1, z2)
U24(f2_out1(z0), z1, z2, z3) → f214_out1(z0)
f226_in(z0, z1, z2) → U25(f205_in(z0, z1), z0, z1, z2)
U25(f205_out1, z0, z1, z2) → U26(f2_in(s(z1), z2), z0, z1, z2)
U26(f2_out1(z0), z1, z2, z3) → f226_out1(z0)
f26_in(z0, z1, z2) → U27(f28_in(z0, z1), f30_in(z0, z1, z2), z0, z1, z2)
U27(f28_out1(z0), z1, z2, z3, z4) → f26_out1(z0)
U27(z0, f30_out2(z1), z2, z3, z4) → f26_out3(z1)
f74_in(z0, z1, z2) → U28(f2_in(0, z0), f79_in(z1, z0, z2), z0, z1, z2)
U28(f2_out1(z0), z1, z2, z3, z4) → f74_out1(z0)
U28(z0, f79_out1(z1), z2, z3, z4) → f74_out2(z1)
U28(z0, f79_out3(z1), z2, z3, z4) → f74_out4(z1)
f77_in(z0, z1, z2, z3) → U29(f101_in(z0, z1, z2), f102_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f101_out1(z0), z1, z2, z3, z4, z5) → f77_out1(z0)
U29(z0, f102_out2(z1), z2, z3, z4, z5) → f77_out3(z1)
f221_in(z0, z1) → U30(f2_in(s(z0), z1), f224_in(z0, z1), z0, z1)
U30(f2_out1(z0), z1, z2, z3) → f221_out1(z0)
U30(z0, f224_out1(z1), z2, z3) → f221_out2(z1)

Tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c
U19'(f91_out1, z0, z1) → c

S tuples:

F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))

K tuples:

U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
U19'(f91_out1, z0, z1) → c
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F79_IN(z0, z1, z2) → c
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F87_IN(z0, z1) → c49
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F36_IN(s(z0)) → c22(F36_IN(z0))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, f205_in, U7, f36_in, U8, f107_in, U9, f79_in, U10, f101_in, U11, f102_in, U12, f28_in, U13, f30_in, U14, f31_in, U15, U16, f50_in, U17, U18, f87_in, U19, U20, f105_in, U21, U22, f214_in, U23, U24, f226_in, U25, U26, f26_in, U27, f74_in, U28, f77_in, U29, f221_in, U30

Defined Pair Symbols:

F31_IN, F50_IN, F105_IN, F214_IN, F226_IN, F107_IN, F79_IN, U19', F2_IN, F205_IN, F36_IN, F101_IN, F102_IN, F28_IN, F30_IN, U15', U17', F87_IN, U21', U23', U25', F26_IN, F74_IN, F77_IN, F221_IN

Compound Symbols:

c43, c46, c52, c55, c58, c, c2, c3, c4, c5, c6, c7, c20, c22, c35, c37, c39, c41, c44, c47, c49, c53, c56, c59, c61, c64, c68, c71, c

(37) 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.

F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))

We considered the (Usable) Rules:

f205_in(0, s(z0)) → f205_out1
f205_in(s(z0), s(z1)) → U7(f205_in(z0, z1), s(z0), s(z1))
U7(f205_out1, s(z0), s(z1)) → f205_out1
f107_in(0, s(z0)) → f107_out1
f107_in(s(0), s(s(z0))) → f107_out1
f107_in(s(s(0)), s(s(s(z0)))) → f107_out1
f107_in(s(s(s(0))), s(s(s(s(z0))))) → f107_out1
f107_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f107_out1
f107_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f107_out1
f107_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f107_out1
f107_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U9(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U9(f205_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f107_out1
f36_in(s(z0)) → U8(f36_in(z0), s(z0))
U8(f36_out1, s(z0)) → f36_out1

And the Tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c
U19'(f91_out1, z0, z1) → c

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

POL(0) = 0   
POL(F101_IN(x₁, x₂, x₃)) = x₃² + x₂·x₃ + x₁·x₃ + x₂²   
POL(F102_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₄ + x₄² + x₁·x₄ + x₁·x₂   
POL(F105_IN(x₁, x₂, x₃)) = x₂ + x₃ + x₃² + x₁·x₃ + x₂²   
POL(F107_IN(x₁, x₂)) = x₂²   
POL(F205_IN(x₁, x₂)) = x₂   
POL(F214_IN(x₁, x₂, x₃)) = x₁ + x₂ + x₃ + x₃² + x₂·x₃ + x₁·x₂   
POL(F221_IN(x₁, x₂)) = [1] + x₂ + x₂² + x₁·x₂   
POL(F226_IN(x₁, x₂, x₃)) = [1] + x₁ + x₂ + x₃ + x₃² + x₂·x₃ + x₁·x₃   
POL(F26_IN(x₁, x₂, x₃)) = [1] + x₁ + x₃ + x₃² + x₁·x₃ + x₁² + x₁·x₂ + x₂²   
POL(F28_IN(x₁, x₂)) = x₂² + x₁·x₂   
POL(F2_IN(x₁, x₂)) = x₂² + x₁·x₂   
POL(F30_IN(x₁, x₂, x₃)) = [1] + x₃ + x₃² + x₁·x₃ + x₁²   
POL(F31_IN(x₁, x₂)) = x₂ + x₂² + x₁·x₂   
POL(F36_IN(x₁)) = 0   
POL(F50_IN(x₁, x₂)) = x₂ + x₂² + x₁·x₂ + x₁²   
POL(F74_IN(x₁, x₂, x₃)) = x₁ + x₂ + x₁²   
POL(F77_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂·x₃ + x₂²   
POL(F79_IN(x₁, x₂, x₃)) = 0   
POL(F87_IN(x₁, x₂)) = 0   
POL(U15'(x₁, x₂, x₃)) = x₃ + x₃² + x₂·x₃   
POL(U17'(x₁, x₂, x₃)) = x₃² + x₂·x₃ + x₂²   
POL(U19'(x₁, x₂, x₃)) = [1] + x₁ + x₃ + x₃² + x₁·x₃ + x₁²   
POL(U21'(x₁, x₂, x₃, x₄)) = x₄ + x₄² + x₂·x₄   
POL(U23'(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₃·x₄ + x₁·x₃   
POL(U25'(x₁, x₂, x₃, x₄)) = x₄ + x₄² + x₃·x₄   
POL(U7(x₁, x₂, x₃)) = 0   
POL(U8(x₁, x₂)) = 0   
POL(U9(x₁, x₂, x₃)) = x₂ + x₃ + x₂²   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c2(x₁)) = x₁   
POL(c20(x₁)) = x₁   
POL(c22(x₁)) = x₁   
POL(c3(x₁)) = x₁   
POL(c35(x₁)) = x₁   
POL(c37(x₁)) = x₁   
POL(c39(x₁)) = x₁   
POL(c4(x₁)) = x₁   
POL(c41(x₁)) = x₁   
POL(c43(x₁, x₂)) = x₁ + x₂   
POL(c44(x₁)) = x₁   
POL(c46(x₁, x₂)) = x₁ + x₂   
POL(c47(x₁)) = x₁   
POL(c49) = 0   
POL(c5(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(c68(x₁, x₂)) = x₁ + x₂   
POL(c7(x₁)) = x₁   
POL(c71(x₁)) = x₁   
POL(f107_in(x₁, x₂)) = [1] + x₁ + x₂ + x₁²   
POL(f107_out1) = 0   
POL(f205_in(x₁, x₂)) = x₁   
POL(f205_out1) = 0   
POL(f36_in(x₁)) = 0   
POL(f36_out1) = 0   
POL(f91_out1) = [1]   
POL(s(x₁)) = [1] + x₁   
POL(tree(x₁, x₂, x₃)) = [1] + x₁ + x₂ + x₃   

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, void) → f2_out1(tree(z0, void, void))
f2_in(z0, tree(z0, z1, z2)) → f2_out1(tree(z0, z1, z2))
f2_in(z0, tree(z0, z1, z2)) → U1(f26_in(z0, z1, z2), z0, tree(z0, z1, z2))
f2_in(s(z0), tree(s(z0), z1, z2)) → U2(f31_in(z0, z2), s(z0), tree(s(z0), z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U3(f74_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f77_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f221_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f226_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f26_out1(z0), z1, tree(z1, z2, z3)) → f2_out1(tree(z1, z0, z3))
U1(f26_out3(z0), z1, tree(z1, z2, z3)) → f2_out1(z0)
U2(f31_out1(z0), s(z1), tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z2, z0))
U3(f74_out1(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out2(z0), 0, tree(s(z1), z2, z3)) → f2_out1(tree(s(z1), z0, z3))
U3(f74_out4(z0), 0, tree(s(z1), z2, z3)) → f2_out1(z0)
U4(f77_out1(z0), z1, tree(z2, z3, z4)) → f2_out1(tree(z2, z0, z4))
U4(f77_out3(z0), z1, tree(z2, z3, z4)) → f2_out1(z0)
U5(f221_out1(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U5(f221_out2(z0), s(z1), tree(0, z2, z3)) → f2_out1(tree(0, z2, z0))
U6(f226_out1(z0), s(z1), tree(s(z2), z3, z4)) → f2_out1(tree(s(z2), z3, z0))
f205_in(0, s(z0)) → f205_out1
f205_in(s(z0), s(z1)) → U7(f205_in(z0, z1), s(z0), s(z1))
U7(f205_out1, s(z0), s(z1)) → f205_out1
f36_in(s(z0)) → U8(f36_in(z0), s(z0))
U8(f36_out1, s(z0)) → f36_out1
f107_in(0, s(z0)) → f107_out1
f107_in(s(0), s(s(z0))) → f107_out1
f107_in(s(s(0)), s(s(s(z0)))) → f107_out1
f107_in(s(s(s(0))), s(s(s(s(z0))))) → f107_out1
f107_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f107_out1
f107_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f107_out1
f107_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f107_out1
f107_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U9(f205_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U9(f205_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f107_out1
f79_in(z0, z1, z2) → U10(f87_in(z0, z2), z0, z1, z2)
U10(f87_out1(z0), z1, z2, z3) → f79_out3(tree(s(z1), z2, z0))
f101_in(s(z0), s(z1), z2) → U11(f105_in(z0, z1, z2), s(z0), s(z1), z2)
U11(f105_out1(z0), s(z1), s(z2), z3) → f101_out1(z0)
f102_in(z0, z1, z2, z3) → U12(f214_in(z1, z0, z3), z0, z1, z2, z3)
U12(f214_out1(z0), z1, z2, z3, z4) → f102_out2(tree(z2, z3, z0))
f28_in(s(z0), z1) → U13(f31_in(z0, z1), s(z0), z1)
U13(f31_out1(z0), s(z1), z2) → f28_out1(z0)
f30_in(z0, z1, z2) → U14(f50_in(z0, z2), z0, z1, z2)
U14(f50_out1(z0), z1, z2, z3) → f30_out2(tree(z1, z2, z0))
f31_in(z0, z1) → U15(f36_in(z0), z0, z1)
U15(f36_out1, z0, z1) → U16(f2_in(s(z0), z1), z0, z1)
U16(f2_out1(z0), z1, z2) → f31_out1(z0)
f50_in(z0, z1) → U17(f36_in(z0), z0, z1)
U17(f36_out1, z0, z1) → U18(f2_in(z0, z1), z0, z1)
U18(f2_out1(z0), z1, z2) → f50_out1(z0)
f87_in(z0, z1) → U19(f91_in(z0), z0, z1)
U19(f91_out1, z0, z1) → U20(f2_in(0, z1), z0, z1)
U20(f2_out1(z0), z1, z2) → f87_out1(z0)
f105_in(z0, z1, z2) → U21(f107_in(z0, z1), z0, z1, z2)
U21(f107_out1, z0, z1, z2) → U22(f2_in(s(z0), z2), z0, z1, z2)
U22(f2_out1(z0), z1, z2, z3) → f105_out1(z0)
f214_in(z0, z1, z2) → U23(f205_in(z0, z1), z0, z1, z2)
U23(f205_out1, z0, z1, z2) → U24(f2_in(z1, z2), z0, z1, z2)
U24(f2_out1(z0), z1, z2, z3) → f214_out1(z0)
f226_in(z0, z1, z2) → U25(f205_in(z0, z1), z0, z1, z2)
U25(f205_out1, z0, z1, z2) → U26(f2_in(s(z1), z2), z0, z1, z2)
U26(f2_out1(z0), z1, z2, z3) → f226_out1(z0)
f26_in(z0, z1, z2) → U27(f28_in(z0, z1), f30_in(z0, z1, z2), z0, z1, z2)
U27(f28_out1(z0), z1, z2, z3, z4) → f26_out1(z0)
U27(z0, f30_out2(z1), z2, z3, z4) → f26_out3(z1)
f74_in(z0, z1, z2) → U28(f2_in(0, z0), f79_in(z1, z0, z2), z0, z1, z2)
U28(f2_out1(z0), z1, z2, z3, z4) → f74_out1(z0)
U28(z0, f79_out1(z1), z2, z3, z4) → f74_out2(z1)
U28(z0, f79_out3(z1), z2, z3, z4) → f74_out4(z1)
f77_in(z0, z1, z2, z3) → U29(f101_in(z0, z1, z2), f102_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f101_out1(z0), z1, z2, z3, z4, z5) → f77_out1(z0)
U29(z0, f102_out2(z1), z2, z3, z4, z5) → f77_out3(z1)
f221_in(z0, z1) → U30(f2_in(s(z0), z1), f224_in(z0, z1), z0, z1)
U30(f2_out1(z0), z1, z2, z3) → f221_out1(z0)
U30(z0, f224_out1(z1), z2, z3) → f221_out2(z1)

Tuples:

F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))
F36_IN(s(z0)) → c22(F36_IN(z0))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F87_IN(z0, z1) → c49
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F79_IN(z0, z1, z2) → c
U19'(f91_out1, z0, z1) → c

S tuples:none
K tuples:

U19'(f91_out1, z0, z1) → c(F2_IN(0, z1))
U19'(f91_out1, z0, z1) → c
U15'(f36_out1, z0, z1) → c44(F2_IN(s(z0), z1))
U17'(f36_out1, z0, z1) → c47(F2_IN(z0, z1))
F79_IN(z0, z1, z2) → c(F87_IN(z0, z2))
F2_IN(z0, tree(z0, z1, z2)) → c2(F26_IN(z0, z1, z2))
F2_IN(s(z0), tree(s(z0), z1, z2)) → c3(F31_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F77_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F226_IN(z1, z0, z3))
F221_IN(z0, z1) → c71(F2_IN(s(z0), z1))
F79_IN(z0, z1, z2) → c
F226_IN(z0, z1, z2) → c58(U25'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F87_IN(z0, z1) → c49
U25'(f205_out1, z0, z1, z2) → c59(F2_IN(s(z1), z2))
F26_IN(z0, z1, z2) → c61(F28_IN(z0, z1), F30_IN(z0, z1, z2))
F77_IN(z0, z1, z2, z3) → c68(F101_IN(z0, z1, z2), F102_IN(z0, z1, z2, z3))
F28_IN(s(z0), z1) → c39(F31_IN(z0, z1))
F30_IN(z0, z1, z2) → c41(F50_IN(z0, z2))
F101_IN(s(z0), s(z1), z2) → c35(F105_IN(z0, z1, z2))
F102_IN(z0, z1, z2, z3) → c37(F214_IN(z1, z0, z3))
F31_IN(z0, z1) → c43(U15'(f36_in(z0), z0, z1), F36_IN(z0))
F50_IN(z0, z1) → c46(U17'(f36_in(z0), z0, z1), F36_IN(z0))
F105_IN(z0, z1, z2) → c52(U21'(f107_in(z0, z1), z0, z1, z2), F107_IN(z0, z1))
F214_IN(z0, z1, z2) → c55(U23'(f205_in(z0, z1), z0, z1, z2), F205_IN(z0, z1))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F205_IN(z0, z1))
U21'(f107_out1, z0, z1, z2) → c53(F2_IN(s(z0), z2))
F107_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
U23'(f205_out1, z0, z1, z2) → c56(F2_IN(z1, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F221_IN(z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F74_IN(z1, z0, z2))
F74_IN(z0, z1, z2) → c64(F2_IN(0, z0), F79_IN(z1, z0, z2))
F36_IN(s(z0)) → c22(F36_IN(z0))
F205_IN(s(z0), s(z1)) → c20(F205_IN(z0, z1))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, f205_in, U7, f36_in, U8, f107_in, U9, f79_in, U10, f101_in, U11, f102_in, U12, f28_in, U13, f30_in, U14, f31_in, U15, U16, f50_in, U17, U18, f87_in, U19, U20, f105_in, U21, U22, f214_in, U23, U24, f226_in, U25, U26, f26_in, U27, f74_in, U28, f77_in, U29, f221_in, U30

Defined Pair Symbols:

F31_IN, F50_IN, F105_IN, F214_IN, F226_IN, F107_IN, F79_IN, U19', F2_IN, F205_IN, F36_IN, F101_IN, F102_IN, F28_IN, F30_IN, U15', U17', F87_IN, U21', U23', U25', F26_IN, F74_IN, F77_IN, F221_IN

Compound Symbols:

c43, c46, c52, c55, c58, c, c2, c3, c4, c5, c6, c7, c20, c22, c35, c37, c39, c41, c44, c47, c49, c53, c56, c59, c61, c64, c68, c71, c

(39) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

(40) BOUNDS(O(1), O(1))