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

(0) Obligation:

Clauses:

delete(X, tree(X, void, Right), Right).
delete(X, tree(X, Left, void), Left).
delete(X, tree(X, Left, Right), tree(Y, Left, Right1)) :- delmin(Right, Y, Right1).
delete(X, tree(Y, Left, Right), tree(Y, Left1, Right)) :- ','(less(X, Y), delete(X, Left, Left1)).
delete(X, tree(Y, Left, Right), tree(Y, Left, Right1)) :- ','(less(Y, X), delete(X, Right, Right1)).
delmin(tree(Y, void, Right), Y, Right).
delmin(tree(X, Left, X1), Y, tree(X, Left1, X2)) :- delmin(Left, Y, Left1).
less(0, s(X3)).
less(s(X), s(Y)) :- less(X, Y).

Query: delete(g,g,a)

(1) LPReorderTransformerProof (EQUIVALENT transformation)

Reordered facts before rules in definite LP [PROLOG].

(2) Obligation:

Clauses:

delete(X, tree(X, void, Right), Right).
delete(X, tree(X, Left, void), Left).
delmin(tree(Y, void, Right), Y, Right).
less(0, s(X3)).
delete(X, tree(X, Left, Right), tree(Y, Left, Right1)) :- delmin(Right, Y, Right1).
delete(X, tree(Y, Left, Right), tree(Y, Left1, Right)) :- ','(less(X, Y), delete(X, Left, Left1)).
delete(X, tree(Y, Left, Right), tree(Y, Left, Right1)) :- ','(less(Y, X), delete(X, Right, Right1)).
delmin(tree(X, Left, X1), Y, tree(X, Left1, X2)) :- delmin(Left, Y, Left1).
less(s(X), s(Y)) :- less(X, Y).

Query: delete(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: delete(T1, T2, T3)\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
3 [label="3: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 0 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 5 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 6\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: true | delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 1 | delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 4 | delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 5 | delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 6\n\nT8 is ground\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 5 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 6\n\nT1 is ground\nT2 is ground\nX8 is free\nX9 is free\ndelete(T1, T2, T3) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 1 | delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 4 | delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 5 | delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 6\n\nT8 is ground\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: true | delete(T12, tree(T12, void, void), T3), SCOPE: 1, CLAUSE: 4 | delete(T12, tree(T12, void, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T12, tree(T12, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT12 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 4 | delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 5 | delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 6\n\nT8 is ground\nT9 is ground\nX14 is free\nX15 is free\ndelete(T8, tree(T8, void, T9), T3) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: delete(T12, tree(T12, void, void), T3), SCOPE: 1, CLAUSE: 4 | delete(T12, tree(T12, void, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T12, tree(T12, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT12 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: delete(T12, tree(T12, void, void), T3), SCOPE: 1, CLAUSE: 4\n\nT12 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: delete(T12, tree(T12, void, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T12, tree(T12, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT12 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: delmin(void, T28, T29)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: delmin(void, T28, T29), SCOPE: 2, CLAUSE: 2 | delmin(void, T28, T29), SCOPE: 2, CLAUSE: 7\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: delmin(void, T28, T29), SCOPE: 2, CLAUSE: 7\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: delete(T12, tree(T12, void, void), T3), SCOPE: 1, CLAUSE: 5\n\nT12 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: delete(T12, tree(T12, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT12 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: ','(less(T38, T38), delete(T38, void, T40))\n\nT38 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: less(T38, T38)\n\nT38 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: delete(T38, void, T40)\n\nT38 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: less(T38, T38), SCOPE: 3, CLAUSE: 3 | less(T38, T38), SCOPE: 3, CLAUSE: 8\n\nT38 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: less(T38, T38), SCOPE: 3, CLAUSE: 8\n\nT38 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: less(T43, T43)\n\nT43 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: ','(less(T50, T50), delete(T50, void, T52))\n\nT50 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 4\n\nT8 is ground\nT9 is ground\nX14 is free\nX15 is free\ndelete(T8, tree(T8, void, T9), T3) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 5 | delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 6\n\nT8 is ground\nT9 is ground\nX14 is free\nX15 is free\ndelete(T8, tree(T8, void, T9), T3) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: delmin(T70, T73, T74)\n\nT69 is ground\nT70 is ground\nX14 is free\nX15 is free\ndelete(T69, tree(T69, void, T70), T3) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: delmin(T70, T73, T74), SCOPE: 4, CLAUSE: 2 | delmin(T70, T73, T74), SCOPE: 4, CLAUSE: 7\n\nT69 is ground\nT70 is ground\nX14 is free\nX15 is free\ndelete(T69, tree(T69, void, T70), T3) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: true | delmin(tree(T83, void, T84), T73, T74), SCOPE: 4, CLAUSE: 7\n\nT83 is ground\nT84 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: delmin(T70, T73, T74), SCOPE: 4, CLAUSE: 7\n\nT69 is ground\nT70 is ground\nX14 is free\nX15 is free\nX145 is free\nX146 is free\ndelete(T69, tree(T69, void, T70), T3) !=? delete(X14, tree(X14, X15, void), X15)\ndelmin(T70, T73, T74) !=? delmin(tree(X145, void, X146), X145, X146)", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: delmin(tree(T83, void, T84), T73, T74), SCOPE: 4, CLAUSE: 7\n\nT83 is ground\nT84 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: delmin(void, T100, T101)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: delmin(T115, T120, T121)\n\nT114 is ground\nT115 is ground\nT116 is ground\nX145 is free\nX146 is free\ndelmin(tree(T114, T115, T116), T73, T74) !=? delmin(tree(X145, void, X146), X145, X146)", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: delmin(T115, T120, T121), SCOPE: 5, CLAUSE: 2 | delmin(T115, T120, T121), SCOPE: 5, CLAUSE: 7\n\nT114 is ground\nT115 is ground\nT116 is ground\nX145 is free\nX146 is free\ndelmin(tree(T114, T115, T116), T73, T74) !=? delmin(tree(X145, void, X146), X145, X146)", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: true | delmin(tree(T130, void, T131), T120, T121), SCOPE: 5, CLAUSE: 7\n\nT130 is ground\nT131 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: delmin(T115, T120, T121), SCOPE: 5, CLAUSE: 7\n\nT114 is ground\nT115 is ground\nT116 is ground\nX145 is free\nX146 is free\nX195 is free\nX196 is free\ndelmin(tree(T114, T115, T116), T73, T74) !=? delmin(tree(X145, void, X146), X145, X146)\ndelmin(T115, T120, T121) !=? delmin(tree(X195, void, X196), X195, X196)", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: delmin(tree(T130, void, T131), T120, T121), SCOPE: 5, CLAUSE: 7\n\nT130 is ground\nT131 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: delmin(void, T147, T148)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: delmin(T162, T167, T168)\n\nT161 is ground\nT162 is ground\nT163 is ground\nX195 is free\nX196 is free\ndelmin(tree(T161, T162, T163), T120, T121) !=? delmin(tree(X195, void, X196), X195, X196)", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: delmin(T162, T167, T168), SCOPE: 6, CLAUSE: 2 | delmin(T162, T167, T168), SCOPE: 6, CLAUSE: 7\n\nT161 is ground\nT162 is ground\nT163 is ground\nX195 is free\nX196 is free\ndelmin(tree(T161, T162, T163), T120, T121) !=? delmin(tree(X195, void, X196), X195, X196)", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: true | delmin(tree(T177, void, T178), T167, T168), SCOPE: 6, CLAUSE: 7\n\nT177 is ground\nT178 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: delmin(T162, T167, T168), SCOPE: 6, CLAUSE: 7\n\nT161 is ground\nT162 is ground\nT163 is ground\nX195 is free\nX196 is free\nX245 is free\nX246 is free\ndelmin(tree(T161, T162, T163), T120, T121) !=? delmin(tree(X195, void, X196), X195, X196)\ndelmin(T162, T167, T168) !=? delmin(tree(X245, void, X246), X245, X246)", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: delmin(tree(T177, void, T178), T167, T168), SCOPE: 6, CLAUSE: 7\n\nT177 is ground\nT178 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: delmin(void, T194, T195)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: delmin(T209, T214, T215)\n\nT208 is ground\nT209 is ground\nT210 is ground\nX245 is free\nX246 is free\ndelmin(tree(T208, T209, T210), T167, T168) !=? delmin(tree(X245, void, X246), X245, X246)", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 5\n\nT8 is ground\nT9 is ground\nX14 is free\nX15 is free\ndelete(T8, tree(T8, void, T9), T3) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: delete(T8, tree(T8, void, T9), T3), SCOPE: 1, CLAUSE: 6\n\nT8 is ground\nT9 is ground\nX14 is free\nX15 is free\ndelete(T8, tree(T8, void, T9), T3) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: ','(less(T232, T232), delete(T232, void, T235))\n\nT232 is ground\nT233 is ground\nX14 is free\nX15 is free\ndelete(T232, tree(T232, void, T233), T3) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ','(less(T242, T242), delete(T242, T243, T245))\n\nT242 is ground\nT243 is ground\nX14 is free\nX15 is free\ndelete(T242, tree(T242, void, T243), T3) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: less(T242, T242)\n\nT242 is ground\nT243 is ground\nX14 is free\nX15 is free\ndelete(T242, tree(T242, void, T243), T3) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: delete(T242, T243, T245)\n\nT242 is ground\nT243 is ground\nX14 is free\nX15 is free\ndelete(T242, tree(T242, void, T243), T3) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: true | delete(T254, tree(T254, T255, void), T3), SCOPE: 1, CLAUSE: 4 | delete(T254, tree(T254, T255, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T254, tree(T254, T255, void), T3), SCOPE: 1, CLAUSE: 6\n\nT254 is ground\nT255 is ground\nX8 is free\nX9 is free\ndelete(T254, tree(T254, T255, void), T3) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 5 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 6\n\nT1 is ground\nT2 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(T1, T2, T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T1, T2, T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: delete(T254, tree(T254, T255, void), T3), SCOPE: 1, CLAUSE: 4 | delete(T254, tree(T254, T255, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T254, tree(T254, T255, void), T3), SCOPE: 1, CLAUSE: 6\n\nT254 is ground\nT255 is ground\nX8 is free\nX9 is free\ndelete(T254, tree(T254, T255, void), T3) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: delete(T254, tree(T254, T255, void), T3), SCOPE: 1, CLAUSE: 4\n\nT254 is ground\nT255 is ground\nX8 is free\nX9 is free\ndelete(T254, tree(T254, T255, void), T3) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: delete(T254, tree(T254, T255, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T254, tree(T254, T255, void), T3), SCOPE: 1, CLAUSE: 6\n\nT254 is ground\nT255 is ground\nX8 is free\nX9 is free\ndelete(T254, tree(T254, T255, void), T3) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: delmin(void, T276, T277)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: delete(T254, tree(T254, T255, void), T3), SCOPE: 1, CLAUSE: 5\n\nT254 is ground\nT255 is ground\nX8 is free\nX9 is free\ndelete(T254, tree(T254, T255, void), T3) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: delete(T254, tree(T254, T255, void), T3), SCOPE: 1, CLAUSE: 6\n\nT254 is ground\nT255 is ground\nX8 is free\nX9 is free\ndelete(T254, tree(T254, T255, void), T3) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: ','(less(T290, T290), delete(T290, T291, T293))\n\nT290 is ground\nT291 is ground\nX8 is free\nX9 is free\ndelete(T290, tree(T290, T291, void), T3) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: less(T290, T290)\n\nT290 is ground\nT291 is ground\nX8 is free\nX9 is free\ndelete(T290, tree(T290, T291, void), T3) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: delete(T290, T291, T293)\n\nT290 is ground\nT291 is ground\nX8 is free\nX9 is free\ndelete(T290, tree(T290, T291, void), T3) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: ','(less(T304, T304), delete(T304, void, T307))\n\nT304 is ground\nT305 is ground\nX8 is free\nX9 is free\ndelete(T304, tree(T304, T305, void), T3) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT2 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(T1, T2, T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T1, T2, T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 5 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 6\n\nT1 is ground\nT2 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(T1, T2, T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T1, T2, T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: delmin(T330, T333, T334)\n\nT328 is ground\nT329 is ground\nT330 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(T328, tree(T328, T329, T330), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T328, tree(T328, T329, T330), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: delmin(T330, T333, T334), SCOPE: 7, CLAUSE: 2 | delmin(T330, T333, T334), SCOPE: 7, CLAUSE: 7\n\nT328 is ground\nT329 is ground\nT330 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(T328, tree(T328, T329, T330), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T328, tree(T328, T329, T330), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: true | delmin(tree(T343, void, T344), T333, T334), SCOPE: 7, CLAUSE: 7\n\nT328 is ground\nT329 is ground\nT343 is ground\nT344 is ground\nX8 is free\nX9 is free\ndelete(T328, tree(T328, T329, tree(T343, void, T344)), T3) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: delmin(T330, T333, T334), SCOPE: 7, CLAUSE: 7\n\nT328 is ground\nT329 is ground\nT330 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\nX459 is free\nX460 is free\ndelete(T328, tree(T328, T329, T330), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T328, tree(T328, T329, T330), T3) !=? delete(X345, tree(X345, X346, void), X346)\ndelmin(T330, T333, T334) !=? delmin(tree(X459, void, X460), X459, X460)", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: delmin(tree(T343, void, T344), T333, T334), SCOPE: 7, CLAUSE: 7\n\nT328 is ground\nT329 is ground\nT343 is ground\nT344 is ground\nX8 is free\nX9 is free\ndelete(T328, tree(T328, T329, tree(T343, void, T344)), T3) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: delmin(void, T360, T361)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: delmin(T375, T380, T381)\n\nT328 is ground\nT329 is ground\nT374 is ground\nT375 is ground\nT376 is ground\nX8 is free\nX9 is free\nX459 is free\nX460 is free\ndelete(T328, tree(T328, T329, tree(T374, T375, T376)), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelmin(tree(T374, T375, T376), T333, T334) !=? delmin(tree(X459, void, X460), X459, X460)", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 5\n\nT1 is ground\nT2 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(T1, T2, T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T1, T2, T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 6\n\nT1 is ground\nT2 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(T1, T2, T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T1, T2, T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: ','(less(T406, T407), delete(T406, T408, T411))\n\nT406 is ground\nT407 is ground\nT408 is ground\nT409 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(T406, tree(T407, T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T406, tree(T407, T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: less(T406, T407)\n\nT406 is ground\nT407 is ground\nT408 is ground\nT409 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(T406, tree(T407, T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T406, tree(T407, T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: delete(T406, T408, T411)\n\nT406 is ground\nT407 is ground\nT408 is ground\nT409 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(T406, tree(T407, T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T406, tree(T407, T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: less(T406, T407), SCOPE: 8, CLAUSE: 3 | less(T406, T407), SCOPE: 8, CLAUSE: 8\n\nT406 is ground\nT407 is ground\nT408 is ground\nT409 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(T406, tree(T407, T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T406, tree(T407, T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: true | less(0, s(T418)), SCOPE: 8, CLAUSE: 8\n\nT418 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: less(T406, T407), SCOPE: 8, CLAUSE: 8\n\nT406 is ground\nT407 is ground\nT408 is ground\nT409 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\nX536 is free\ndelete(T406, tree(T407, T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T406, tree(T407, T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)\nless(T406, T407) !=? less(0, s(X536))", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: less(0, s(T418)), SCOPE: 8, CLAUSE: 8\n\nT418 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: less(T423, T424)\n\nT408 is ground\nT409 is ground\nT423 is ground\nT424 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(s(T423), tree(s(T424), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(T423), tree(s(T424), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: less(T423, T424), SCOPE: 9, CLAUSE: 3 | less(T423, T424), SCOPE: 9, CLAUSE: 8\n\nT408 is ground\nT409 is ground\nT423 is ground\nT424 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(s(T423), tree(s(T424), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(T423), tree(s(T424), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: true | less(0, s(T429)), SCOPE: 9, CLAUSE: 8\n\nT429 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: less(T423, T424), SCOPE: 9, CLAUSE: 8\n\nT408 is ground\nT409 is ground\nT423 is ground\nT424 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\nX549 is free\ndelete(s(T423), tree(s(T424), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(T423), tree(s(T424), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)\nless(T423, T424) !=? less(0, s(X549))", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: less(0, s(T429)), SCOPE: 9, CLAUSE: 8\n\nT429 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: less(T434, T435)\n\nT408 is ground\nT409 is ground\nT434 is ground\nT435 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(s(s(T434)), tree(s(s(T435)), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(T434)), tree(s(s(T435)), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: less(T434, T435), SCOPE: 10, CLAUSE: 3 | less(T434, T435), SCOPE: 10, CLAUSE: 8\n\nT408 is ground\nT409 is ground\nT434 is ground\nT435 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(s(s(T434)), tree(s(s(T435)), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(T434)), tree(s(s(T435)), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: true | less(0, s(T440)), SCOPE: 10, CLAUSE: 8\n\nT440 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: less(T434, T435), SCOPE: 10, CLAUSE: 8\n\nT408 is ground\nT409 is ground\nT434 is ground\nT435 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\nX562 is free\ndelete(s(s(T434)), tree(s(s(T435)), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(T434)), tree(s(s(T435)), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)\nless(T434, T435) !=? less(0, s(X562))", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: less(0, s(T440)), SCOPE: 10, CLAUSE: 8\n\nT440 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
227 [label="227: less(T445, T446)\n\nT408 is ground\nT409 is ground\nT445 is ground\nT446 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(s(s(s(T445))), tree(s(s(s(T446))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(T445))), tree(s(s(s(T446))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
228 [label="228: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
229 [label="229: less(T445, T446), SCOPE: 11, CLAUSE: 3 | less(T445, T446), SCOPE: 11, CLAUSE: 8\n\nT408 is ground\nT409 is ground\nT445 is ground\nT446 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(s(s(s(T445))), tree(s(s(s(T446))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(T445))), tree(s(s(s(T446))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="230: true | less(0, s(T451)), SCOPE: 11, CLAUSE: 8\n\nT451 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
231 [label="231: less(T445, T446), SCOPE: 11, CLAUSE: 8\n\nT408 is ground\nT409 is ground\nT445 is ground\nT446 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\nX575 is free\ndelete(s(s(s(T445))), tree(s(s(s(T446))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(T445))), tree(s(s(s(T446))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)\nless(T445, T446) !=? less(0, s(X575))", fontsize=16, style=filled, fillcolor=lightyellow];
232 [label="232: less(0, s(T451)), SCOPE: 11, CLAUSE: 8\n\nT451 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
233 [label="233: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
238 [label="238: less(T456, T457)\n\nT408 is ground\nT409 is ground\nT456 is ground\nT457 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(s(s(s(s(T456)))), tree(s(s(s(s(T457)))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(s(T456)))), tree(s(s(s(s(T457)))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
239 [label="239: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
242 [label="242: less(T456, T457), SCOPE: 12, CLAUSE: 3 | less(T456, T457), SCOPE: 12, CLAUSE: 8\n\nT408 is ground\nT409 is ground\nT456 is ground\nT457 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(s(s(s(s(T456)))), tree(s(s(s(s(T457)))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(s(T456)))), tree(s(s(s(s(T457)))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
244 [label="244: true | less(0, s(T462)), SCOPE: 12, CLAUSE: 8\n\nT462 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
246 [label="246: less(T456, T457), SCOPE: 12, CLAUSE: 8\n\nT408 is ground\nT409 is ground\nT456 is ground\nT457 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\nX588 is free\ndelete(s(s(s(s(T456)))), tree(s(s(s(s(T457)))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(s(T456)))), tree(s(s(s(s(T457)))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)\nless(T456, T457) !=? less(0, s(X588))", fontsize=16, style=filled, fillcolor=lightyellow];
247 [label="247: less(0, s(T462)), SCOPE: 12, CLAUSE: 8\n\nT462 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
248 [label="248: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
249 [label="249: less(T467, T468)\n\nT408 is ground\nT409 is ground\nT467 is ground\nT468 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(s(s(s(s(s(T467))))), tree(s(s(s(s(s(T468))))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(s(s(T467))))), tree(s(s(s(s(s(T468))))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
250 [label="250: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
254 [label="254: less(T467, T468), SCOPE: 13, CLAUSE: 3 | less(T467, T468), SCOPE: 13, CLAUSE: 8\n\nT408 is ground\nT409 is ground\nT467 is ground\nT468 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(s(s(s(s(s(T467))))), tree(s(s(s(s(s(T468))))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(s(s(T467))))), tree(s(s(s(s(s(T468))))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
255 [label="255: true | less(0, s(T473)), SCOPE: 13, CLAUSE: 8\n\nT473 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
258 [label="258: less(T467, T468), SCOPE: 13, CLAUSE: 8\n\nT408 is ground\nT409 is ground\nT467 is ground\nT468 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\nX601 is free\ndelete(s(s(s(s(s(T467))))), tree(s(s(s(s(s(T468))))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(s(s(T467))))), tree(s(s(s(s(s(T468))))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)\nless(T467, T468) !=? less(0, s(X601))", fontsize=16, style=filled, fillcolor=lightyellow];
259 [label="259: less(0, s(T473)), SCOPE: 13, CLAUSE: 8\n\nT473 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
261 [label="261: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
265 [label="265: less(T478, T479)\n\nT408 is ground\nT409 is ground\nT478 is ground\nT479 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(s(s(s(s(s(s(T478)))))), tree(s(s(s(s(s(s(T479)))))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(s(s(s(T478)))))), tree(s(s(s(s(s(s(T479)))))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
266 [label="266: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
269 [label="269: less(T478, T479), SCOPE: 14, CLAUSE: 3 | less(T478, T479), SCOPE: 14, CLAUSE: 8\n\nT408 is ground\nT409 is ground\nT478 is ground\nT479 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(s(s(s(s(s(s(T478)))))), tree(s(s(s(s(s(s(T479)))))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(s(s(s(T478)))))), tree(s(s(s(s(s(s(T479)))))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
272 [label="272: true | less(0, s(T484)), SCOPE: 14, CLAUSE: 8\n\nT484 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
273 [label="273: less(T478, T479), SCOPE: 14, CLAUSE: 8\n\nT408 is ground\nT409 is ground\nT478 is ground\nT479 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\nX614 is free\ndelete(s(s(s(s(s(s(T478)))))), tree(s(s(s(s(s(s(T479)))))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(s(s(s(T478)))))), tree(s(s(s(s(s(s(T479)))))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)\nless(T478, T479) !=? less(0, s(X614))", fontsize=16, style=filled, fillcolor=lightyellow];
274 [label="274: less(0, s(T484)), SCOPE: 14, CLAUSE: 8\n\nT484 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
275 [label="275: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
278 [label="278: less(T489, T490)\n\nT408 is ground\nT409 is ground\nT489 is ground\nT490 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(s(s(s(s(s(s(s(T489))))))), tree(s(s(s(s(s(s(s(T490))))))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(s(s(s(s(T489))))))), tree(s(s(s(s(s(s(s(T490))))))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
279 [label="279: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
280 [label="280: less(T489, T490), SCOPE: 15, CLAUSE: 3 | less(T489, T490), SCOPE: 15, CLAUSE: 8\n\nT408 is ground\nT409 is ground\nT489 is ground\nT490 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(s(s(s(s(s(s(s(T489))))))), tree(s(s(s(s(s(s(s(T490))))))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(s(s(s(s(T489))))))), tree(s(s(s(s(s(s(s(T490))))))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
283 [label="283: true | less(0, s(T495)), SCOPE: 15, CLAUSE: 8\n\nT495 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
284 [label="284: less(T489, T490), SCOPE: 15, CLAUSE: 8\n\nT408 is ground\nT409 is ground\nT489 is ground\nT490 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\nX627 is free\ndelete(s(s(s(s(s(s(s(T489))))))), tree(s(s(s(s(s(s(s(T490))))))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(s(s(s(s(T489))))))), tree(s(s(s(s(s(s(s(T490))))))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)\nless(T489, T490) !=? less(0, s(X627))", fontsize=16, style=filled, fillcolor=lightyellow];
285 [label="285: less(0, s(T495)), SCOPE: 15, CLAUSE: 8\n\nT495 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
286 [label="286: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
287 [label="287: less(T500, T501)\n\nT408 is ground\nT409 is ground\nT500 is ground\nT501 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(s(s(s(s(s(s(s(s(T500)))))))), tree(s(s(s(s(s(s(s(s(T501)))))))), T408, T409), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(s(s(s(s(s(s(s(s(T500)))))))), tree(s(s(s(s(s(s(s(s(T501)))))))), T408, T409), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
288 [label="288: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
295 [label="295: less(T500, T501)\n\nT500 is ground\nT501 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
298 [label="298: less(T500, T501), SCOPE: 16, CLAUSE: 3 | less(T500, T501), SCOPE: 16, CLAUSE: 8\n\nT500 is ground\nT501 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
299 [label="299: true | less(0, s(T510)), SCOPE: 16, CLAUSE: 8\n\nT510 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
300 [label="300: less(T500, T501), SCOPE: 16, CLAUSE: 8\n\nT500 is ground\nT501 is ground\nX642 is free\nless(T500, T501) !=? less(0, s(X642))", fontsize=16, style=filled, fillcolor=lightyellow];
301 [label="301: less(0, s(T510)), SCOPE: 16, CLAUSE: 8\n\nT510 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
303 [label="303: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
305 [label="305: less(T515, T516)\n\nT515 is ground\nT516 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
306 [label="306: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
310 [label="310: ','(less(T534, T533), delete(T533, T536, T538))\n\nT533 is ground\nT534 is ground\nT535 is ground\nT536 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(T533, tree(T534, T535, T536), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T533, tree(T534, T535, T536), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
311 [label="311: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
313 [label="313: less(T534, T533)\n\nT533 is ground\nT534 is ground\nT535 is ground\nT536 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(T533, tree(T534, T535, T536), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T533, tree(T534, T535, T536), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
314 [label="314: delete(T533, T536, T538)\n\nT533 is ground\nT534 is ground\nT535 is ground\nT536 is ground\nX8 is free\nX9 is free\nX345 is free\nX346 is free\ndelete(T533, tree(T534, T535, T536), T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T533, tree(T534, T535, T536), T3) !=? delete(X345, tree(X345, X346, void), X346)", fontsize=16, style=filled, fillcolor=lightyellow];
315 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 315 [arrowhead = none ];
315 -> 3;

316 [label="EVAL with clause\ndelete(X8, tree(X8, void, X9), X9).\nand substitutionT1 -> T8,\nX8 -> T8,\nX9 -> T9,\nT2 -> tree(T8, void, T9),\nT3 -> T9", fontsize=14, style = filled, fillcolor = lightblue];
3 -> 316 [arrowhead = none ];
316 -> 5;

317 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 317 [arrowhead = none ];
317 -> 7;

318 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 318 [arrowhead = none ];
318 -> 10;

319 [label="EVAL with clause\ndelete(X345, tree(X345, X346, void), X346).\nand substitutionT1 -> T254,\nX345 -> T254,\nX346 -> T255,\nT2 -> tree(T254, T255, void),\nT3 -> T255", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 319 [arrowhead = none ];
319 -> 123;

320 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 320 [arrowhead = none ];
320 -> 126;

321 [label="EVAL with clause\ndelete(X14, tree(X14, X15, void), X15).\nand substitutionT8 -> T12,\nX14 -> T12,\nX15 -> void,\nT9 -> void,\nT3 -> void", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 321 [arrowhead = none ];
321 -> 12;

322 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
10 -> 322 [arrowhead = none ];
322 -> 15;

323 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 323 [arrowhead = none ];
323 -> 16;

324 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
15 -> 324 [arrowhead = none ];
324 -> 54;

325 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
15 -> 325 [arrowhead = none ];
325 -> 55;

326 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
16 -> 326 [arrowhead = none ];
326 -> 18;

327 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
16 -> 327 [arrowhead = none ];
327 -> 19;

328 [label="EVAL with clause\ndelete(X36, tree(X36, X37, X38), tree(X39, X37, X40)) :- delmin(X38, X39, X40).\nand substitutionT12 -> T25,\nX36 -> T25,\nX37 -> void,\nX38 -> void,\nX39 -> T28,\nX40 -> T29,\nT3 -> tree(T28, void, T29),\nT26 -> T28,\nT27 -> T29", fontsize=14, style = filled, fillcolor = lightblue];
18 -> 328 [arrowhead = none ];
328 -> 25;

329 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
18 -> 329 [arrowhead = none ];
329 -> 26;

330 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
19 -> 330 [arrowhead = none ];
330 -> 36;

331 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
19 -> 331 [arrowhead = none ];
331 -> 38;

332 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
25 -> 332 [arrowhead = none ];
332 -> 30;

333 [label="BACKTRACK\nfor clause: delmin(tree(Y, void, Right), Y, Right)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 333 [arrowhead = none ];
333 -> 32;

334 [label="BACKTRACK\nfor clause: delmin(tree(X, Left, X1), Y, tree(X, Left1, X2)) :- delmin(Left, Y, Left1)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
32 -> 334 [arrowhead = none ];
334 -> 33;

335 [label="EVAL with clause\ndelete(X73, tree(X74, X75, X76), tree(X74, X77, X76)) :- ','(less(X73, X74), delete(X73, X75, X77)).\nand substitutionT12 -> T38,\nX73 -> T38,\nX74 -> T38,\nX75 -> void,\nX76 -> void,\nX77 -> T40,\nT3 -> tree(T38, T40, void),\nT39 -> T40", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 335 [arrowhead = none ];
335 -> 42;

336 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
36 -> 336 [arrowhead = none ];
336 -> 43;

337 [label="EVAL with clause\ndelete(X105, tree(X106, X107, X108), tree(X106, X107, X109)) :- ','(less(X106, X105), delete(X105, X108, X109)).\nand substitutionT12 -> T50,\nX105 -> T50,\nX106 -> T50,\nX107 -> void,\nX108 -> void,\nX109 -> T52,\nT3 -> tree(T50, void, T52),\nT51 -> T52", fontsize=14, style = filled, fillcolor = lightblue];
38 -> 337 [arrowhead = none ];
337 -> 52;

338 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
38 -> 338 [arrowhead = none ];
338 -> 53;

339 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
42 -> 339 [arrowhead = none ];
339 -> 44;

340 [label="SPLIT 2\nnew knowledge:\nT38 is ground", fontsize=14, style = filled, fillcolor = violet];
42 -> 340 [arrowhead = none ];
340 -> 45;

341 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
44 -> 341 [arrowhead = none ];
341 -> 46;

342 [label="INSTANCE with matching:\nT1 -> T38\nT2 -> void\nT3 -> T40", fontsize=14, style = filled, fillcolor = lightgrey];
45 -> 342 [arrowhead = none , style=dashed];
342 -> 1[style=dashed];

343 [label="BACKTRACK\nfor clause: less(0, s(X3))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
46 -> 343 [arrowhead = none ];
343 -> 47;

344 [label="EVAL with clause\nless(s(X87), s(X88)) :- less(X87, X88).\nand substitutionX87 -> T43,\nT38 -> s(T43),\nX88 -> T43", fontsize=14, style = filled, fillcolor = lightblue];
47 -> 344 [arrowhead = none ];
344 -> 48;

345 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
47 -> 345 [arrowhead = none ];
345 -> 49;

346 [label="INSTANCE with matching:\nT38 -> T43", fontsize=14, style = filled, fillcolor = lightgrey];
48 -> 346 [arrowhead = none , style=dashed];
346 -> 44[style=dashed];

347 [label="INSTANCE with matching:\nT38 -> T50\nT40 -> T52", fontsize=14, style = filled, fillcolor = lightgrey];
52 -> 347 [arrowhead = none , style=dashed];
347 -> 42[style=dashed];

348 [label="EVAL with clause\ndelete(X132, tree(X132, X133, X134), tree(X135, X133, X136)) :- delmin(X134, X135, X136).\nand substitutionT8 -> T69,\nX132 -> T69,\nX133 -> void,\nT9 -> T70,\nX134 -> T70,\nX135 -> T73,\nX136 -> T74,\nT3 -> tree(T73, void, T74),\nT71 -> T73,\nT72 -> T74", fontsize=14, style = filled, fillcolor = lightblue];
54 -> 348 [arrowhead = none ];
348 -> 56;

349 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
54 -> 349 [arrowhead = none ];
349 -> 57;

350 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
55 -> 350 [arrowhead = none ];
350 -> 101;

351 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
55 -> 351 [arrowhead = none ];
351 -> 102;

352 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
56 -> 352 [arrowhead = none ];
352 -> 59;

353 [label="EVAL with clause\ndelmin(tree(X145, void, X146), X145, X146).\nand substitutionX145 -> T83,\nX146 -> T84,\nT70 -> tree(T83, void, T84),\nT73 -> T83,\nT74 -> T84", fontsize=14, style = filled, fillcolor = lightblue];
59 -> 353 [arrowhead = none ];
353 -> 62;

354 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
59 -> 354 [arrowhead = none ];
354 -> 64;

355 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
62 -> 355 [arrowhead = none ];
355 -> 65;

356 [label="EVAL with clause\ndelmin(tree(X181, X182, X183), X184, tree(X181, X185, X186)) :- delmin(X182, X184, X185).\nand substitutionX181 -> T114,\nX182 -> T115,\nX183 -> T116,\nT70 -> tree(T114, T115, T116),\nT73 -> T120,\nX184 -> T120,\nX185 -> T121,\nX186 -> T119,\nT74 -> tree(T114, T121, T119),\nT117 -> T120,\nT118 -> T121", fontsize=14, style = filled, fillcolor = lightblue];
64 -> 356 [arrowhead = none ];
356 -> 70;

357 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
64 -> 357 [arrowhead = none ];
357 -> 71;

358 [label="EVAL with clause\ndelmin(tree(X159, X160, X161), X162, tree(X159, X163, X164)) :- delmin(X160, X162, X163).\nand substitutionT83 -> T95,\nX159 -> T95,\nX160 -> void,\nT84 -> T96,\nX161 -> T96,\nT73 -> T100,\nX162 -> T100,\nX163 -> T101,\nX164 -> T99,\nT74 -> tree(T95, T101, T99),\nT97 -> T100,\nT98 -> T101", fontsize=14, style = filled, fillcolor = lightblue];
65 -> 358 [arrowhead = none ];
358 -> 66;

359 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
65 -> 359 [arrowhead = none ];
359 -> 67;

360 [label="INSTANCE with matching:\nT28 -> T100\nT29 -> T101", fontsize=14, style = filled, fillcolor = lightgrey];
66 -> 360 [arrowhead = none , style=dashed];
360 -> 25[style=dashed];

361 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
70 -> 361 [arrowhead = none ];
361 -> 74;

362 [label="EVAL with clause\ndelmin(tree(X195, void, X196), X195, X196).\nand substitutionX195 -> T130,\nX196 -> T131,\nT115 -> tree(T130, void, T131),\nT120 -> T130,\nT121 -> T131", fontsize=14, style = filled, fillcolor = lightblue];
74 -> 362 [arrowhead = none ];
362 -> 76;

363 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
74 -> 363 [arrowhead = none ];
363 -> 78;

364 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
76 -> 364 [arrowhead = none ];
364 -> 79;

365 [label="EVAL with clause\ndelmin(tree(X231, X232, X233), X234, tree(X231, X235, X236)) :- delmin(X232, X234, X235).\nand substitutionX231 -> T161,\nX232 -> T162,\nX233 -> T163,\nT115 -> tree(T161, T162, T163),\nT120 -> T167,\nX234 -> T167,\nX235 -> T168,\nX236 -> T166,\nT121 -> tree(T161, T168, T166),\nT164 -> T167,\nT165 -> T168", fontsize=14, style = filled, fillcolor = lightblue];
78 -> 365 [arrowhead = none ];
365 -> 83;

366 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
78 -> 366 [arrowhead = none ];
366 -> 84;

367 [label="EVAL with clause\ndelmin(tree(X209, X210, X211), X212, tree(X209, X213, X214)) :- delmin(X210, X212, X213).\nand substitutionT130 -> T142,\nX209 -> T142,\nX210 -> void,\nT131 -> T143,\nX211 -> T143,\nT120 -> T147,\nX212 -> T147,\nX213 -> T148,\nX214 -> T146,\nT121 -> tree(T142, T148, T146),\nT144 -> T147,\nT145 -> T148", fontsize=14, style = filled, fillcolor = lightblue];
79 -> 367 [arrowhead = none ];
367 -> 81;

368 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
79 -> 368 [arrowhead = none ];
368 -> 82;

369 [label="INSTANCE with matching:\nT28 -> T147\nT29 -> T148", fontsize=14, style = filled, fillcolor = lightgrey];
81 -> 369 [arrowhead = none , style=dashed];
369 -> 25[style=dashed];

370 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
83 -> 370 [arrowhead = none ];
370 -> 87;

371 [label="EVAL with clause\ndelmin(tree(X245, void, X246), X245, X246).\nand substitutionX245 -> T177,\nX246 -> T178,\nT162 -> tree(T177, void, T178),\nT167 -> T177,\nT168 -> T178", fontsize=14, style = filled, fillcolor = lightblue];
87 -> 371 [arrowhead = none ];
371 -> 88;

372 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
87 -> 372 [arrowhead = none ];
372 -> 89;

373 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
88 -> 373 [arrowhead = none ];
373 -> 90;

374 [label="EVAL with clause\ndelmin(tree(X281, X282, X283), X284, tree(X281, X285, X286)) :- delmin(X282, X284, X285).\nand substitutionX281 -> T208,\nX282 -> T209,\nX283 -> T210,\nT162 -> tree(T208, T209, T210),\nT167 -> T214,\nX284 -> T214,\nX285 -> T215,\nX286 -> T213,\nT168 -> tree(T208, T215, T213),\nT211 -> T214,\nT212 -> T215", fontsize=14, style = filled, fillcolor = lightblue];
89 -> 374 [arrowhead = none ];
374 -> 97;

375 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
89 -> 375 [arrowhead = none ];
375 -> 99;

376 [label="EVAL with clause\ndelmin(tree(X259, X260, X261), X262, tree(X259, X263, X264)) :- delmin(X260, X262, X263).\nand substitutionT177 -> T189,\nX259 -> T189,\nX260 -> void,\nT178 -> T190,\nX261 -> T190,\nT167 -> T194,\nX262 -> T194,\nX263 -> T195,\nX264 -> T193,\nT168 -> tree(T189, T195, T193),\nT191 -> T194,\nT192 -> T195", fontsize=14, style = filled, fillcolor = lightblue];
90 -> 376 [arrowhead = none ];
376 -> 91;

377 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
90 -> 377 [arrowhead = none ];
377 -> 92;

378 [label="INSTANCE with matching:\nT28 -> T194\nT29 -> T195", fontsize=14, style = filled, fillcolor = lightgrey];
91 -> 378 [arrowhead = none , style=dashed];
378 -> 25[style=dashed];

379 [label="INSTANCE with matching:\nT115 -> T209\nT120 -> T214\nT121 -> T215\nT114 -> T208\nT116 -> T210\nT73 -> T167\nT74 -> T168\nX145 -> X245\nX146 -> X246", fontsize=14, style = filled, fillcolor = lightgrey];
97 -> 379 [arrowhead = none , style=dashed];
379 -> 70[style=dashed];

380 [label="EVAL with clause\ndelete(X311, tree(X312, X313, X314), tree(X312, X315, X314)) :- ','(less(X311, X312), delete(X311, X313, X315)).\nand substitutionT8 -> T232,\nX311 -> T232,\nX312 -> T232,\nX313 -> void,\nT9 -> T233,\nX314 -> T233,\nX315 -> T235,\nT3 -> tree(T232, T235, T233),\nT234 -> T235", fontsize=14, style = filled, fillcolor = lightblue];
101 -> 380 [arrowhead = none ];
380 -> 103;

381 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
101 -> 381 [arrowhead = none ];
381 -> 104;

382 [label="EVAL with clause\ndelete(X328, tree(X329, X330, X331), tree(X329, X330, X332)) :- ','(less(X329, X328), delete(X328, X331, X332)).\nand substitutionT8 -> T242,\nX328 -> T242,\nX329 -> T242,\nX330 -> void,\nT9 -> T243,\nX331 -> T243,\nX332 -> T245,\nT3 -> tree(T242, void, T245),\nT244 -> T245", fontsize=14, style = filled, fillcolor = lightblue];
102 -> 382 [arrowhead = none ];
382 -> 111;

383 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
102 -> 383 [arrowhead = none ];
383 -> 114;

384 [label="INSTANCE with matching:\nT38 -> T232\nT40 -> T235", fontsize=14, style = filled, fillcolor = lightgrey];
103 -> 384 [arrowhead = none , style=dashed];
384 -> 42[style=dashed];

385 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
111 -> 385 [arrowhead = none ];
385 -> 115;

386 [label="SPLIT 2\nnew knowledge:\nT242 is ground", fontsize=14, style = filled, fillcolor = violet];
111 -> 386 [arrowhead = none ];
386 -> 116;

387 [label="INSTANCE with matching:\nT38 -> T242", fontsize=14, style = filled, fillcolor = lightgrey];
115 -> 387 [arrowhead = none , style=dashed];
387 -> 44[style=dashed];

388 [label="INSTANCE with matching:\nT1 -> T242\nT2 -> T243\nT3 -> T245", fontsize=14, style = filled, fillcolor = lightgrey];
116 -> 388 [arrowhead = none , style=dashed];
388 -> 1[style=dashed];

389 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
123 -> 389 [arrowhead = none ];
389 -> 127;

390 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
126 -> 390 [arrowhead = none ];
390 -> 156;

391 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
126 -> 391 [arrowhead = none ];
391 -> 157;

392 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
127 -> 392 [arrowhead = none ];
392 -> 129;

393 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
127 -> 393 [arrowhead = none ];
393 -> 131;

394 [label="EVAL with clause\ndelete(X367, tree(X367, X368, X369), tree(X370, X368, X371)) :- delmin(X369, X370, X371).\nand substitutionT254 -> T272,\nX367 -> T272,\nT255 -> T273,\nX368 -> T273,\nX369 -> void,\nX370 -> T276,\nX371 -> T277,\nT3 -> tree(T276, T273, T277),\nT274 -> T276,\nT275 -> T277", fontsize=14, style = filled, fillcolor = lightblue];
129 -> 394 [arrowhead = none ];
394 -> 133;

395 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 395 [arrowhead = none ];
395 -> 135;

396 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
131 -> 396 [arrowhead = none ];
396 -> 138;

397 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
131 -> 397 [arrowhead = none ];
397 -> 139;

398 [label="INSTANCE with matching:\nT28 -> T276\nT29 -> T277", fontsize=14, style = filled, fillcolor = lightgrey];
133 -> 398 [arrowhead = none , style=dashed];
398 -> 25[style=dashed];

399 [label="EVAL with clause\ndelete(X396, tree(X397, X398, X399), tree(X397, X400, X399)) :- ','(less(X396, X397), delete(X396, X398, X400)).\nand substitutionT254 -> T290,\nX396 -> T290,\nX397 -> T290,\nT255 -> T291,\nX398 -> T291,\nX399 -> void,\nX400 -> T293,\nT3 -> tree(T290, T293, void),\nT292 -> T293", fontsize=14, style = filled, fillcolor = lightblue];
138 -> 399 [arrowhead = none ];
399 -> 142;

400 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
138 -> 400 [arrowhead = none ];
400 -> 143;

401 [label="EVAL with clause\ndelete(X419, tree(X420, X421, X422), tree(X420, X421, X423)) :- ','(less(X420, X419), delete(X419, X422, X423)).\nand substitutionT254 -> T304,\nX419 -> T304,\nX420 -> T304,\nT255 -> T305,\nX421 -> T305,\nX422 -> void,\nX423 -> T307,\nT3 -> tree(T304, T305, T307),\nT306 -> T307", fontsize=14, style = filled, fillcolor = lightblue];
139 -> 401 [arrowhead = none ];
401 -> 152;

402 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
139 -> 402 [arrowhead = none ];
402 -> 153;

403 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
142 -> 403 [arrowhead = none ];
403 -> 144;

404 [label="SPLIT 2\nnew knowledge:\nT290 is ground", fontsize=14, style = filled, fillcolor = violet];
142 -> 404 [arrowhead = none ];
404 -> 145;

405 [label="INSTANCE with matching:\nT38 -> T290", fontsize=14, style = filled, fillcolor = lightgrey];
144 -> 405 [arrowhead = none , style=dashed];
405 -> 44[style=dashed];

406 [label="INSTANCE with matching:\nT1 -> T290\nT2 -> T291\nT3 -> T293", fontsize=14, style = filled, fillcolor = lightgrey];
145 -> 406 [arrowhead = none , style=dashed];
406 -> 1[style=dashed];

407 [label="INSTANCE with matching:\nT38 -> T304\nT40 -> T307", fontsize=14, style = filled, fillcolor = lightgrey];
152 -> 407 [arrowhead = none , style=dashed];
407 -> 42[style=dashed];

408 [label="EVAL with clause\ndelete(X446, tree(X446, X447, X448), tree(X449, X447, X450)) :- delmin(X448, X449, X450).\nand substitutionT1 -> T328,\nX446 -> T328,\nX447 -> T329,\nX448 -> T330,\nT2 -> tree(T328, T329, T330),\nX449 -> T333,\nX450 -> T334,\nT3 -> tree(T333, T329, T334),\nT331 -> T333,\nT332 -> T334", fontsize=14, style = filled, fillcolor = lightblue];
156 -> 408 [arrowhead = none ];
408 -> 160;

409 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
156 -> 409 [arrowhead = none ];
409 -> 161;

410 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
157 -> 410 [arrowhead = none ];
410 -> 183;

411 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
157 -> 411 [arrowhead = none ];
411 -> 184;

412 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
160 -> 412 [arrowhead = none ];
412 -> 164;

413 [label="EVAL with clause\ndelmin(tree(X459, void, X460), X459, X460).\nand substitutionX459 -> T343,\nX460 -> T344,\nT330 -> tree(T343, void, T344),\nT333 -> T343,\nT334 -> T344", fontsize=14, style = filled, fillcolor = lightblue];
164 -> 413 [arrowhead = none ];
413 -> 167;

414 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
164 -> 414 [arrowhead = none ];
414 -> 168;

415 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
167 -> 415 [arrowhead = none ];
415 -> 169;

416 [label="EVAL with clause\ndelmin(tree(X495, X496, X497), X498, tree(X495, X499, X500)) :- delmin(X496, X498, X499).\nand substitutionX495 -> T374,\nX496 -> T375,\nX497 -> T376,\nT330 -> tree(T374, T375, T376),\nT333 -> T380,\nX498 -> T380,\nX499 -> T381,\nX500 -> T379,\nT334 -> tree(T374, T381, T379),\nT377 -> T380,\nT378 -> T381", fontsize=14, style = filled, fillcolor = lightblue];
168 -> 416 [arrowhead = none ];
416 -> 179;

417 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
168 -> 417 [arrowhead = none ];
417 -> 180;

418 [label="EVAL with clause\ndelmin(tree(X473, X474, X475), X476, tree(X473, X477, X478)) :- delmin(X474, X476, X477).\nand substitutionT343 -> T355,\nX473 -> T355,\nX474 -> void,\nT344 -> T356,\nX475 -> T356,\nT333 -> T360,\nX476 -> T360,\nX477 -> T361,\nX478 -> T359,\nT334 -> tree(T355, T361, T359),\nT357 -> T360,\nT358 -> T361", fontsize=14, style = filled, fillcolor = lightblue];
169 -> 418 [arrowhead = none ];
418 -> 172;

419 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
169 -> 419 [arrowhead = none ];
419 -> 173;

420 [label="INSTANCE with matching:\nT28 -> T360\nT29 -> T361", fontsize=14, style = filled, fillcolor = lightgrey];
172 -> 420 [arrowhead = none , style=dashed];
420 -> 25[style=dashed];

421 [label="INSTANCE with matching:\nT115 -> T375\nT120 -> T380\nT121 -> T381\nT114 -> T374\nT116 -> T376\nT73 -> T333\nT74 -> T334\nX145 -> X459\nX146 -> X460", fontsize=14, style = filled, fillcolor = lightgrey];
179 -> 421 [arrowhead = none , style=dashed];
421 -> 70[style=dashed];

422 [label="EVAL with clause\ndelete(X525, tree(X526, X527, X528), tree(X526, X529, X528)) :- ','(less(X525, X526), delete(X525, X527, X529)).\nand substitutionT1 -> T406,\nX525 -> T406,\nX526 -> T407,\nX527 -> T408,\nX528 -> T409,\nT2 -> tree(T407, T408, T409),\nX529 -> T411,\nT3 -> tree(T407, T411, T409),\nT410 -> T411", fontsize=14, style = filled, fillcolor = lightblue];
183 -> 422 [arrowhead = none ];
422 -> 189;

423 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
183 -> 423 [arrowhead = none ];
423 -> 190;

424 [label="EVAL with clause\ndelete(X667, tree(X668, X669, X670), tree(X668, X669, X671)) :- ','(less(X668, X667), delete(X667, X670, X671)).\nand substitutionT1 -> T533,\nX667 -> T533,\nX668 -> T534,\nX669 -> T535,\nX670 -> T536,\nT2 -> tree(T534, T535, T536),\nX671 -> T538,\nT3 -> tree(T534, T535, T538),\nT537 -> T538", fontsize=14, style = filled, fillcolor = lightblue];
184 -> 424 [arrowhead = none ];
424 -> 310;

425 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
184 -> 425 [arrowhead = none ];
425 -> 311;

426 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
189 -> 426 [arrowhead = none ];
426 -> 191;

427 [label="SPLIT 2\nnew knowledge:\nT406 is ground\nT407 is ground", fontsize=14, style = filled, fillcolor = violet];
189 -> 427 [arrowhead = none ];
427 -> 192;

428 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
191 -> 428 [arrowhead = none ];
428 -> 193;

429 [label="INSTANCE with matching:\nT1 -> T406\nT2 -> T408\nT3 -> T411", fontsize=14, style = filled, fillcolor = lightgrey];
192 -> 429 [arrowhead = none , style=dashed];
429 -> 1[style=dashed];

430 [label="EVAL with clause\nless(0, s(X536)).\nand substitutionT406 -> 0,\nX536 -> T418,\nT407 -> s(T418)", fontsize=14, style = filled, fillcolor = lightblue];
193 -> 430 [arrowhead = none ];
430 -> 195;

431 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
193 -> 431 [arrowhead = none ];
431 -> 197;

432 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
195 -> 432 [arrowhead = none ];
432 -> 199;

433 [label="EVAL with clause\nless(s(X543), s(X544)) :- less(X543, X544).\nand substitutionX543 -> T423,\nT406 -> s(T423),\nX544 -> T424,\nT407 -> s(T424)", fontsize=14, style = filled, fillcolor = lightblue];
197 -> 433 [arrowhead = none ];
433 -> 204;

434 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
197 -> 434 [arrowhead = none ];
434 -> 205;

435 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
199 -> 435 [arrowhead = none ];
435 -> 200;

436 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
204 -> 436 [arrowhead = none ];
436 -> 208;

437 [label="EVAL with clause\nless(0, s(X549)).\nand substitutionT423 -> 0,\nX549 -> T429,\nT424 -> s(T429)", fontsize=14, style = filled, fillcolor = lightblue];
208 -> 437 [arrowhead = none ];
437 -> 209;

438 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
208 -> 438 [arrowhead = none ];
438 -> 212;

439 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
209 -> 439 [arrowhead = none ];
439 -> 213;

440 [label="EVAL with clause\nless(s(X556), s(X557)) :- less(X556, X557).\nand substitutionX556 -> T434,\nT423 -> s(T434),\nX557 -> T435,\nT424 -> s(T435)", fontsize=14, style = filled, fillcolor = lightblue];
212 -> 440 [arrowhead = none ];
440 -> 215;

441 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
212 -> 441 [arrowhead = none ];
441 -> 217;

442 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
213 -> 442 [arrowhead = none ];
442 -> 214;

443 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
215 -> 443 [arrowhead = none ];
443 -> 218;

444 [label="EVAL with clause\nless(0, s(X562)).\nand substitutionT434 -> 0,\nX562 -> T440,\nT435 -> s(T440)", fontsize=14, style = filled, fillcolor = lightblue];
218 -> 444 [arrowhead = none ];
444 -> 220;

445 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
218 -> 445 [arrowhead = none ];
445 -> 222;

446 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
220 -> 446 [arrowhead = none ];
446 -> 223;

447 [label="EVAL with clause\nless(s(X569), s(X570)) :- less(X569, X570).\nand substitutionX569 -> T445,\nT434 -> s(T445),\nX570 -> T446,\nT435 -> s(T446)", fontsize=14, style = filled, fillcolor = lightblue];
222 -> 447 [arrowhead = none ];
447 -> 227;

448 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
222 -> 448 [arrowhead = none ];
448 -> 228;

449 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
223 -> 449 [arrowhead = none ];
449 -> 224;

450 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
227 -> 450 [arrowhead = none ];
450 -> 229;

451 [label="EVAL with clause\nless(0, s(X575)).\nand substitutionT445 -> 0,\nX575 -> T451,\nT446 -> s(T451)", fontsize=14, style = filled, fillcolor = lightblue];
229 -> 451 [arrowhead = none ];
451 -> 230;

452 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
229 -> 452 [arrowhead = none ];
452 -> 231;

453 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
230 -> 453 [arrowhead = none ];
453 -> 232;

454 [label="EVAL with clause\nless(s(X582), s(X583)) :- less(X582, X583).\nand substitutionX582 -> T456,\nT445 -> s(T456),\nX583 -> T457,\nT446 -> s(T457)", fontsize=14, style = filled, fillcolor = lightblue];
231 -> 454 [arrowhead = none ];
454 -> 238;

455 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
231 -> 455 [arrowhead = none ];
455 -> 239;

456 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
232 -> 456 [arrowhead = none ];
456 -> 233;

457 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
238 -> 457 [arrowhead = none ];
457 -> 242;

458 [label="EVAL with clause\nless(0, s(X588)).\nand substitutionT456 -> 0,\nX588 -> T462,\nT457 -> s(T462)", fontsize=14, style = filled, fillcolor = lightblue];
242 -> 458 [arrowhead = none ];
458 -> 244;

459 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
242 -> 459 [arrowhead = none ];
459 -> 246;

460 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
244 -> 460 [arrowhead = none ];
460 -> 247;

461 [label="EVAL with clause\nless(s(X595), s(X596)) :- less(X595, X596).\nand substitutionX595 -> T467,\nT456 -> s(T467),\nX596 -> T468,\nT457 -> s(T468)", fontsize=14, style = filled, fillcolor = lightblue];
246 -> 461 [arrowhead = none ];
461 -> 249;

462 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
246 -> 462 [arrowhead = none ];
462 -> 250;

463 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
247 -> 463 [arrowhead = none ];
463 -> 248;

464 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
249 -> 464 [arrowhead = none ];
464 -> 254;

465 [label="EVAL with clause\nless(0, s(X601)).\nand substitutionT467 -> 0,\nX601 -> T473,\nT468 -> s(T473)", fontsize=14, style = filled, fillcolor = lightblue];
254 -> 465 [arrowhead = none ];
465 -> 255;

466 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
254 -> 466 [arrowhead = none ];
466 -> 258;

467 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
255 -> 467 [arrowhead = none ];
467 -> 259;

468 [label="EVAL with clause\nless(s(X608), s(X609)) :- less(X608, X609).\nand substitutionX608 -> T478,\nT467 -> s(T478),\nX609 -> T479,\nT468 -> s(T479)", fontsize=14, style = filled, fillcolor = lightblue];
258 -> 468 [arrowhead = none ];
468 -> 265;

469 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
258 -> 469 [arrowhead = none ];
469 -> 266;

470 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
259 -> 470 [arrowhead = none ];
470 -> 261;

471 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
265 -> 471 [arrowhead = none ];
471 -> 269;

472 [label="EVAL with clause\nless(0, s(X614)).\nand substitutionT478 -> 0,\nX614 -> T484,\nT479 -> s(T484)", fontsize=14, style = filled, fillcolor = lightblue];
269 -> 472 [arrowhead = none ];
472 -> 272;

473 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
269 -> 473 [arrowhead = none ];
473 -> 273;

474 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
272 -> 474 [arrowhead = none ];
474 -> 274;

475 [label="EVAL with clause\nless(s(X621), s(X622)) :- less(X621, X622).\nand substitutionX621 -> T489,\nT478 -> s(T489),\nX622 -> T490,\nT479 -> s(T490)", fontsize=14, style = filled, fillcolor = lightblue];
273 -> 475 [arrowhead = none ];
475 -> 278;

476 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
273 -> 476 [arrowhead = none ];
476 -> 279;

477 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
274 -> 477 [arrowhead = none ];
477 -> 275;

478 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
278 -> 478 [arrowhead = none ];
478 -> 280;

479 [label="EVAL with clause\nless(0, s(X627)).\nand substitutionT489 -> 0,\nX627 -> T495,\nT490 -> s(T495)", fontsize=14, style = filled, fillcolor = lightblue];
280 -> 479 [arrowhead = none ];
479 -> 283;

480 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
280 -> 480 [arrowhead = none ];
480 -> 284;

481 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
283 -> 481 [arrowhead = none ];
481 -> 285;

482 [label="EVAL with clause\nless(s(X634), s(X635)) :- less(X634, X635).\nand substitutionX634 -> T500,\nT489 -> s(T500),\nX635 -> T501,\nT490 -> s(T501)", fontsize=14, style = filled, fillcolor = lightblue];
284 -> 482 [arrowhead = none ];
482 -> 287;

483 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
284 -> 483 [arrowhead = none ];
483 -> 288;

484 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
285 -> 484 [arrowhead = none ];
484 -> 286;

485 [label="GENERALIZATION\nT504 <-- s(s(s(s(s(s(s(T500)))))))\nT505 <-- s(s(s(s(s(s(s(T501)))))))\n\nNew Knowledge:\nT504 is ground\nT505 is ground", fontsize=14, style = filled, fillcolor = violet];
287 -> 485 [arrowhead = none ];
485 -> 295;

486 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
295 -> 486 [arrowhead = none ];
486 -> 298;

487 [label="EVAL with clause\nless(0, s(X642)).\nand substitutionT500 -> 0,\nX642 -> T510,\nT501 -> s(T510)", fontsize=14, style = filled, fillcolor = lightblue];
298 -> 487 [arrowhead = none ];
487 -> 299;

488 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
298 -> 488 [arrowhead = none ];
488 -> 300;

489 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
299 -> 489 [arrowhead = none ];
489 -> 301;

490 [label="EVAL with clause\nless(s(X649), s(X650)) :- less(X649, X650).\nand substitutionX649 -> T515,\nT500 -> s(T515),\nX650 -> T516,\nT501 -> s(T516)", fontsize=14, style = filled, fillcolor = lightblue];
300 -> 490 [arrowhead = none ];
490 -> 305;

491 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
300 -> 491 [arrowhead = none ];
491 -> 306;

492 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
301 -> 492 [arrowhead = none ];
492 -> 303;

493 [label="INSTANCE with matching:\nT500 -> T515\nT501 -> T516", fontsize=14, style = filled, fillcolor = lightgrey];
305 -> 493 [arrowhead = none , style=dashed];
493 -> 295[style=dashed];

494 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
310 -> 494 [arrowhead = none ];
494 -> 313;

495 [label="SPLIT 2\nnew knowledge:\nT534 is ground\nT533 is ground", fontsize=14, style = filled, fillcolor = violet];
310 -> 495 [arrowhead = none ];
495 -> 314;

496 [label="INSTANCE with matching:\nT500 -> T534\nT501 -> T533", fontsize=14, style = filled, fillcolor = lightgrey];
313 -> 496 [arrowhead = none , style=dashed];
496 -> 295[style=dashed];

497 [label="INSTANCE with matching:\nT1 -> T533\nT2 -> T536\nT3 -> T538", fontsize=14, style = filled, fillcolor = lightgrey];
314 -> 497 [arrowhead = none , style=dashed];
497 -> 1[style=dashed];

}

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, z1)) → f1_out1
f1_in(z0, tree(z0, void, void)) → f1_out1
f1_in(z0, tree(z0, void, void)) → U1(f16_in(z0), z0, tree(z0, void, void))
f1_in(z0, tree(z0, void, z1)) → U2(f15_in(z0, z1), z0, tree(z0, void, z1))
f1_in(z0, tree(z0, z1, void)) → f1_out1
f1_in(z0, tree(z0, z1, void)) → U3(f127_in(z0, z1), z0, tree(z0, z1, void))
f1_in(z0, z1) → U4(f126_in(z0, z1), z0, z1)
U1(f16_out1, z0, tree(z0, void, void)) → f1_out1
U1(f16_out2, z0, tree(z0, void, void)) → f1_out1
U1(f16_out3, z0, tree(z0, void, void)) → f1_out1
U2(f15_out1, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out2, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out3, z0, tree(z0, void, z1)) → f1_out1
U3(f127_out1, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out2, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out3, z0, tree(z0, z1, void)) → f1_out1
U4(f126_out1, z0, z1) → f1_out1
U4(f126_out2, z0, z1) → f1_out1
U4(f126_out3, z0, z1) → f1_out1
f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1
f70_in(tree(z0, void, z1)) → f70_out1(z0)
f70_in(tree(z0, void, z1)) → U7(f25_in, tree(z0, void, z1))
f70_in(tree(z0, tree(z1, void, z2), z3)) → f70_out1(z1)
f70_in(tree(z0, tree(z1, void, z2), z3)) → U8(f25_in, tree(z0, tree(z1, void, z2), z3))
f70_in(tree(z0, tree(z1, z2, z3), z4)) → U9(f70_in(z2), tree(z0, tree(z1, z2, z3), z4))
U7(f25_out1(z0), tree(z1, void, z2)) → f70_out1(z0)
U8(f25_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f70_out1(z0)
U9(f70_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f70_out1(z0)
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → f156_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f25_in, z0, tree(z0, z1, tree(z2, void, z3)))
f156_in(z0, tree(z0, z1, tree(z2, z3, z4))) → U12(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4)))
U11(f25_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f156_out1
U12(f70_out1(z0), z1, tree(z1, z2, tree(z3, z4, z5))) → f156_out1
f54_in(z0, tree(z1, void, z2)) → f54_out1
f54_in(z0, tree(z1, void, z2)) → U13(f25_in, z0, tree(z1, void, z2))
f54_in(z0, tree(z1, z2, z3)) → U14(f70_in(z2), z0, tree(z1, z2, z3))
U13(f25_out1(z0), z1, tree(z2, void, z3)) → f54_out1
U14(f70_out1(z0), z1, tree(z2, z3, z4)) → f54_out1
f129_in(z0, z1) → U15(f25_in, z0, z1)
U15(f25_out1(z0), z1, z2) → f129_out1
f183_in(z0, tree(z1, z2, z3)) → U16(f189_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f189_out1, z0, tree(z1, z2, z3)) → f183_out1
f184_in(z0, tree(z1, z2, z3)) → U17(f310_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f310_out1, z0, tree(z1, z2, z3)) → f184_out1
f18_in(z0) → U18(f25_in, z0)
U18(f25_out1(z0), z1) → f18_out1
f101_in(z0, z1) → U19(f42_in(z0), z0, z1)
U19(f42_out1, z0, z1) → f101_out1
f102_in(z0, z1) → U20(f111_in(z0, z1), z0, z1)
U20(f111_out1, z0, z1) → f102_out1
f138_in(z0, z1) → U21(f142_in(z0, z1), z0, z1)
U21(f142_out1, z0, z1) → f138_out1
f139_in(z0, z1) → U22(f42_in(z0), z0, z1)
U22(f42_out1, z0, z1) → f139_out1
f36_in(z0) → U23(f42_in(z0), z0)
U23(f42_out1, z0) → f36_out1
f38_in(z0) → U24(f42_in(z0), z0)
U24(f42_out1, z0) → f38_out1
f42_in(z0) → U25(f44_in(z0), z0)
U25(f44_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1, z0) → f42_out1
f111_in(z0, z1) → U27(f44_in(z0), z0, z1)
U27(f44_out1, z0, z1) → U28(f1_in(z0, z1), z0, z1)
U28(f1_out1, z0, z1) → f111_out1
f142_in(z0, z1) → U29(f44_in(z0), z0, z1)
U29(f44_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1, z0, z1) → f142_out1
f189_in(z0, z1, z2) → U31(f191_in(z0, z1), z0, z1, z2)
U31(f191_out1, z0, z1, z2) → U32(f1_in(z0, z2), z0, z1, z2)
U32(f1_out1, z0, z1, z2) → f189_out1
f310_in(z0, z1, z2) → U33(f295_in(z0, z1), z0, z1, z2)
U33(f295_out1, z0, z1, z2) → U34(f1_in(z1, z2), z0, z1, z2)
U34(f1_out1, z0, z1, z2) → f310_out1
f15_in(z0, z1) → U35(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U35(f54_out1, z0, z1, z2) → f15_out1
U35(z0, f55_out1, z1, z2) → f15_out2
U35(z0, f55_out2, z1, z2) → f15_out3
f16_in(z0) → U36(f18_in(z0), f19_in(z0), z0)
U36(f18_out1, z0, z1) → f16_out1
U36(z0, f19_out1, z1) → f16_out2
U36(z0, f19_out2, z1) → f16_out3
f19_in(z0) → U37(f36_in(z0), f38_in(z0), z0)
U37(f36_out1, z0, z1) → f19_out1
U37(z0, f38_out1, z1) → f19_out2
f55_in(z0, z1) → U38(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U38(f101_out1, z0, z1, z2) → f55_out1
U38(z0, f102_out1, z1, z2) → f55_out2
f126_in(z0, z1) → U39(f156_in(z0, z1), f157_in(z0, z1), z0, z1)
U39(f156_out1, z0, z1, z2) → f126_out1
U39(z0, f157_out1, z1, z2) → f126_out2
U39(z0, f157_out2, z1, z2) → f126_out3
f127_in(z0, z1) → U40(f129_in(z0, z1), f131_in(z0, z1), z0, z1)
U40(f129_out1, z0, z1, z2) → f127_out1
U40(z0, f131_out1, z1, z2) → f127_out2
U40(z0, f131_out2, z1, z2) → f127_out3
f131_in(z0, z1) → U41(f138_in(z0, z1), f139_in(z0, z1), z0, z1)
U41(f138_out1, z0, z1, z2) → f131_out1
U41(z0, f139_out1, z1, z2) → f131_out2
f157_in(z0, z1) → U42(f183_in(z0, z1), f184_in(z0, z1), z0, z1)
U42(f183_out1, z0, z1, z2) → f157_out1
U42(z0, f184_out1, z1, z2) → f157_out2

Tuples:

F1_IN(z0, tree(z0, void, void)) → c2(U1'(f16_in(z0), z0, tree(z0, void, void)), F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(U2'(f15_in(z0, z1), z0, tree(z0, void, z1)), F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(U3'(f127_in(z0, z1), z0, tree(z0, z1, void)), F127_IN(z0, z1))
F1_IN(z0, z1) → c6(U4'(f126_in(z0, z1), z0, z1), F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(U5'(f295_in(z0, z1), s(z0), s(z1)), F295_IN(z0, z1))
F44_IN(s(z0)) → c22(U6'(f44_in(z0), s(z0)), F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25(U7'(f25_in, tree(z0, void, z1)))
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27(U8'(f25_in, tree(z0, tree(z1, void, z2), z3)))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(U9'(f70_in(z2), tree(z0, tree(z1, z2, z3), z4)), F70_IN(z2))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c40(U10'(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))), F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43(U11'(f25_in, z0, tree(z0, z1, tree(z2, void, z3))))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c44(U12'(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4))), F70_IN(z3))
F54_IN(z0, tree(z1, void, z2)) → c48(U13'(f25_in, z0, tree(z1, void, z2)))
F54_IN(z0, tree(z1, z2, z3)) → c49(U14'(f70_in(z2), z0, tree(z1, z2, z3)), F70_IN(z2))
F129_IN(z0, z1) → c52(U15'(f25_in, z0, z1))
F183_IN(z0, tree(z1, z2, z3)) → c54(U16'(f189_in(z0, z1, z2), z0, tree(z1, z2, z3)), F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(U17'(f310_in(z1, z0, z3), z0, tree(z1, z2, z3)), F310_IN(z1, z0, z3))
F18_IN(z0) → c58(U18'(f25_in, z0))
F101_IN(z0, z1) → c60(U19'(f42_in(z0), z0, z1), F42_IN(z0))
F102_IN(z0, z1) → c62(U20'(f111_in(z0, z1), z0, z1), F111_IN(z0, z1))
F138_IN(z0, z1) → c64(U21'(f142_in(z0, z1), z0, z1), F142_IN(z0, z1))
F139_IN(z0, z1) → c66(U22'(f42_in(z0), z0, z1), F42_IN(z0))
F36_IN(z0) → c68(U23'(f42_in(z0), z0), F42_IN(z0))
F38_IN(z0) → c70(U24'(f42_in(z0), z0), F42_IN(z0))
F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0))
U25'(f44_out1, z0) → c73(U26'(f1_in(z0, void), z0), F1_IN(z0, void))
F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
U27'(f44_out1, z0, z1) → c76(U28'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
U29'(f44_out1, z0, z1) → c79(U30'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(U32'(f1_in(z0, z2), z0, z1, z2), F1_IN(z0, z2))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
U33'(f295_out1, z0, z1, z2) → c85(U34'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F15_IN(z0, z1) → c87(U35'(f54_in(z0, z1), f55_in(z0, z1), z0, z1), F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(U36'(f18_in(z0), f19_in(z0), z0), F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(U37'(f36_in(z0), f38_in(z0), z0), F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(U38'(f101_in(z0, z1), f102_in(z0, z1), z0, z1), F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(U39'(f156_in(z0, z1), f157_in(z0, z1), z0, z1), F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(U40'(f129_in(z0, z1), f131_in(z0, z1), z0, z1), F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(U41'(f138_in(z0, z1), f139_in(z0, z1), z0, z1), F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(U42'(f183_in(z0, z1), f184_in(z0, z1), z0, z1), F183_IN(z0, z1), F184_IN(z0, z1))

S tuples:

F1_IN(z0, tree(z0, void, void)) → c2(U1'(f16_in(z0), z0, tree(z0, void, void)), F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(U2'(f15_in(z0, z1), z0, tree(z0, void, z1)), F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(U3'(f127_in(z0, z1), z0, tree(z0, z1, void)), F127_IN(z0, z1))
F1_IN(z0, z1) → c6(U4'(f126_in(z0, z1), z0, z1), F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(U5'(f295_in(z0, z1), s(z0), s(z1)), F295_IN(z0, z1))
F44_IN(s(z0)) → c22(U6'(f44_in(z0), s(z0)), F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25(U7'(f25_in, tree(z0, void, z1)))
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27(U8'(f25_in, tree(z0, tree(z1, void, z2), z3)))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(U9'(f70_in(z2), tree(z0, tree(z1, z2, z3), z4)), F70_IN(z2))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c40(U10'(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))), F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43(U11'(f25_in, z0, tree(z0, z1, tree(z2, void, z3))))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c44(U12'(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4))), F70_IN(z3))
F54_IN(z0, tree(z1, void, z2)) → c48(U13'(f25_in, z0, tree(z1, void, z2)))
F54_IN(z0, tree(z1, z2, z3)) → c49(U14'(f70_in(z2), z0, tree(z1, z2, z3)), F70_IN(z2))
F129_IN(z0, z1) → c52(U15'(f25_in, z0, z1))
F183_IN(z0, tree(z1, z2, z3)) → c54(U16'(f189_in(z0, z1, z2), z0, tree(z1, z2, z3)), F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(U17'(f310_in(z1, z0, z3), z0, tree(z1, z2, z3)), F310_IN(z1, z0, z3))
F18_IN(z0) → c58(U18'(f25_in, z0))
F101_IN(z0, z1) → c60(U19'(f42_in(z0), z0, z1), F42_IN(z0))
F102_IN(z0, z1) → c62(U20'(f111_in(z0, z1), z0, z1), F111_IN(z0, z1))
F138_IN(z0, z1) → c64(U21'(f142_in(z0, z1), z0, z1), F142_IN(z0, z1))
F139_IN(z0, z1) → c66(U22'(f42_in(z0), z0, z1), F42_IN(z0))
F36_IN(z0) → c68(U23'(f42_in(z0), z0), F42_IN(z0))
F38_IN(z0) → c70(U24'(f42_in(z0), z0), F42_IN(z0))
F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0))
U25'(f44_out1, z0) → c73(U26'(f1_in(z0, void), z0), F1_IN(z0, void))
F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
U27'(f44_out1, z0, z1) → c76(U28'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
U29'(f44_out1, z0, z1) → c79(U30'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(U32'(f1_in(z0, z2), z0, z1, z2), F1_IN(z0, z2))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
U33'(f295_out1, z0, z1, z2) → c85(U34'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F15_IN(z0, z1) → c87(U35'(f54_in(z0, z1), f55_in(z0, z1), z0, z1), F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(U36'(f18_in(z0), f19_in(z0), z0), F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(U37'(f36_in(z0), f38_in(z0), z0), F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(U38'(f101_in(z0, z1), f102_in(z0, z1), z0, z1), F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(U39'(f156_in(z0, z1), f157_in(z0, z1), z0, z1), F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(U40'(f129_in(z0, z1), f131_in(z0, z1), z0, z1), F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(U41'(f138_in(z0, z1), f139_in(z0, z1), z0, z1), F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(U42'(f183_in(z0, z1), f184_in(z0, z1), z0, z1), F183_IN(z0, z1), F184_IN(z0, z1))

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f295_in, U5, f44_in, U6, f70_in, U7, U8, U9, f191_in, U10, f156_in, U11, U12, f54_in, U13, U14, f129_in, U15, f183_in, U16, f184_in, U17, f18_in, U18, f101_in, U19, f102_in, U20, f138_in, U21, f139_in, U22, f36_in, U23, f38_in, U24, f42_in, U25, U26, f111_in, U27, U28, f142_in, U29, U30, f189_in, U31, U32, f310_in, U33, U34, f15_in, U35, f16_in, U36, f19_in, U37, f55_in, U38, f126_in, U39, f127_in, U40, f131_in, U41, f157_in, U42

Defined Pair Symbols:

F1_IN, F295_IN, F44_IN, F70_IN, F191_IN, F156_IN, F54_IN, F129_IN, F183_IN, F184_IN, F18_IN, F101_IN, F102_IN, F138_IN, F139_IN, F36_IN, F38_IN, F42_IN, U25', F111_IN, U27', F142_IN, U29', F189_IN, U31', F310_IN, U33', F15_IN, F16_IN, F19_IN, F55_IN, F126_IN, F127_IN, F131_IN, F157_IN

Compound Symbols:

c2, c3, c5, c6, c20, c22, c25, c27, c28, c40, c43, c44, c48, c49, c52, c54, c56, c58, c60, c62, c64, c66, c68, c70, c72, c73, c75, c76, c78, c79, c81, c82, c84, c85, c87, c91, c95, c98, c101, c105, c109, c112

(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, tree(z0, void, z1)) → f1_out1
f1_in(z0, tree(z0, void, void)) → f1_out1
f1_in(z0, tree(z0, void, void)) → U1(f16_in(z0), z0, tree(z0, void, void))
f1_in(z0, tree(z0, void, z1)) → U2(f15_in(z0, z1), z0, tree(z0, void, z1))
f1_in(z0, tree(z0, z1, void)) → f1_out1
f1_in(z0, tree(z0, z1, void)) → U3(f127_in(z0, z1), z0, tree(z0, z1, void))
f1_in(z0, z1) → U4(f126_in(z0, z1), z0, z1)
U1(f16_out1, z0, tree(z0, void, void)) → f1_out1
U1(f16_out2, z0, tree(z0, void, void)) → f1_out1
U1(f16_out3, z0, tree(z0, void, void)) → f1_out1
U2(f15_out1, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out2, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out3, z0, tree(z0, void, z1)) → f1_out1
U3(f127_out1, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out2, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out3, z0, tree(z0, z1, void)) → f1_out1
U4(f126_out1, z0, z1) → f1_out1
U4(f126_out2, z0, z1) → f1_out1
U4(f126_out3, z0, z1) → f1_out1
f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1
f70_in(tree(z0, void, z1)) → f70_out1(z0)
f70_in(tree(z0, void, z1)) → U7(f25_in, tree(z0, void, z1))
f70_in(tree(z0, tree(z1, void, z2), z3)) → f70_out1(z1)
f70_in(tree(z0, tree(z1, void, z2), z3)) → U8(f25_in, tree(z0, tree(z1, void, z2), z3))
f70_in(tree(z0, tree(z1, z2, z3), z4)) → U9(f70_in(z2), tree(z0, tree(z1, z2, z3), z4))
U7(f25_out1(z0), tree(z1, void, z2)) → f70_out1(z0)
U8(f25_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f70_out1(z0)
U9(f70_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f70_out1(z0)
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → f156_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f25_in, z0, tree(z0, z1, tree(z2, void, z3)))
f156_in(z0, tree(z0, z1, tree(z2, z3, z4))) → U12(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4)))
U11(f25_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f156_out1
U12(f70_out1(z0), z1, tree(z1, z2, tree(z3, z4, z5))) → f156_out1
f54_in(z0, tree(z1, void, z2)) → f54_out1
f54_in(z0, tree(z1, void, z2)) → U13(f25_in, z0, tree(z1, void, z2))
f54_in(z0, tree(z1, z2, z3)) → U14(f70_in(z2), z0, tree(z1, z2, z3))
U13(f25_out1(z0), z1, tree(z2, void, z3)) → f54_out1
U14(f70_out1(z0), z1, tree(z2, z3, z4)) → f54_out1
f129_in(z0, z1) → U15(f25_in, z0, z1)
U15(f25_out1(z0), z1, z2) → f129_out1
f183_in(z0, tree(z1, z2, z3)) → U16(f189_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f189_out1, z0, tree(z1, z2, z3)) → f183_out1
f184_in(z0, tree(z1, z2, z3)) → U17(f310_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f310_out1, z0, tree(z1, z2, z3)) → f184_out1
f18_in(z0) → U18(f25_in, z0)
U18(f25_out1(z0), z1) → f18_out1
f101_in(z0, z1) → U19(f42_in(z0), z0, z1)
U19(f42_out1, z0, z1) → f101_out1
f102_in(z0, z1) → U20(f111_in(z0, z1), z0, z1)
U20(f111_out1, z0, z1) → f102_out1
f138_in(z0, z1) → U21(f142_in(z0, z1), z0, z1)
U21(f142_out1, z0, z1) → f138_out1
f139_in(z0, z1) → U22(f42_in(z0), z0, z1)
U22(f42_out1, z0, z1) → f139_out1
f36_in(z0) → U23(f42_in(z0), z0)
U23(f42_out1, z0) → f36_out1
f38_in(z0) → U24(f42_in(z0), z0)
U24(f42_out1, z0) → f38_out1
f42_in(z0) → U25(f44_in(z0), z0)
U25(f44_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1, z0) → f42_out1
f111_in(z0, z1) → U27(f44_in(z0), z0, z1)
U27(f44_out1, z0, z1) → U28(f1_in(z0, z1), z0, z1)
U28(f1_out1, z0, z1) → f111_out1
f142_in(z0, z1) → U29(f44_in(z0), z0, z1)
U29(f44_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1, z0, z1) → f142_out1
f189_in(z0, z1, z2) → U31(f191_in(z0, z1), z0, z1, z2)
U31(f191_out1, z0, z1, z2) → U32(f1_in(z0, z2), z0, z1, z2)
U32(f1_out1, z0, z1, z2) → f189_out1
f310_in(z0, z1, z2) → U33(f295_in(z0, z1), z0, z1, z2)
U33(f295_out1, z0, z1, z2) → U34(f1_in(z1, z2), z0, z1, z2)
U34(f1_out1, z0, z1, z2) → f310_out1
f15_in(z0, z1) → U35(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U35(f54_out1, z0, z1, z2) → f15_out1
U35(z0, f55_out1, z1, z2) → f15_out2
U35(z0, f55_out2, z1, z2) → f15_out3
f16_in(z0) → U36(f18_in(z0), f19_in(z0), z0)
U36(f18_out1, z0, z1) → f16_out1
U36(z0, f19_out1, z1) → f16_out2
U36(z0, f19_out2, z1) → f16_out3
f19_in(z0) → U37(f36_in(z0), f38_in(z0), z0)
U37(f36_out1, z0, z1) → f19_out1
U37(z0, f38_out1, z1) → f19_out2
f55_in(z0, z1) → U38(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U38(f101_out1, z0, z1, z2) → f55_out1
U38(z0, f102_out1, z1, z2) → f55_out2
f126_in(z0, z1) → U39(f156_in(z0, z1), f157_in(z0, z1), z0, z1)
U39(f156_out1, z0, z1, z2) → f126_out1
U39(z0, f157_out1, z1, z2) → f126_out2
U39(z0, f157_out2, z1, z2) → f126_out3
f127_in(z0, z1) → U40(f129_in(z0, z1), f131_in(z0, z1), z0, z1)
U40(f129_out1, z0, z1, z2) → f127_out1
U40(z0, f131_out1, z1, z2) → f127_out2
U40(z0, f131_out2, z1, z2) → f127_out3
f131_in(z0, z1) → U41(f138_in(z0, z1), f139_in(z0, z1), z0, z1)
U41(f138_out1, z0, z1, z2) → f131_out1
U41(z0, f139_out1, z1, z2) → f131_out2
f157_in(z0, z1) → U42(f183_in(z0, z1), f184_in(z0, z1), z0, z1)
U42(f183_out1, z0, z1, z2) → f157_out1
U42(z0, f184_out1, z1, z2) → f157_out2

Tuples:

F1_IN(z0, tree(z0, void, void)) → c2(U1'(f16_in(z0), z0, tree(z0, void, void)), F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(U2'(f15_in(z0, z1), z0, tree(z0, void, z1)), F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(U3'(f127_in(z0, z1), z0, tree(z0, z1, void)), F127_IN(z0, z1))
F1_IN(z0, z1) → c6(U4'(f126_in(z0, z1), z0, z1), F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(U5'(f295_in(z0, z1), s(z0), s(z1)), F295_IN(z0, z1))
F44_IN(s(z0)) → c22(U6'(f44_in(z0), s(z0)), F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25(U7'(f25_in, tree(z0, void, z1)))
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27(U8'(f25_in, tree(z0, tree(z1, void, z2), z3)))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(U9'(f70_in(z2), tree(z0, tree(z1, z2, z3), z4)), F70_IN(z2))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43(U11'(f25_in, z0, tree(z0, z1, tree(z2, void, z3))))
F54_IN(z0, tree(z1, void, z2)) → c48(U13'(f25_in, z0, tree(z1, void, z2)))
F129_IN(z0, z1) → c52(U15'(f25_in, z0, z1))
F183_IN(z0, tree(z1, z2, z3)) → c54(U16'(f189_in(z0, z1, z2), z0, tree(z1, z2, z3)), F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(U17'(f310_in(z1, z0, z3), z0, tree(z1, z2, z3)), F310_IN(z1, z0, z3))
F18_IN(z0) → c58(U18'(f25_in, z0))
F101_IN(z0, z1) → c60(U19'(f42_in(z0), z0, z1), F42_IN(z0))
F102_IN(z0, z1) → c62(U20'(f111_in(z0, z1), z0, z1), F111_IN(z0, z1))
F138_IN(z0, z1) → c64(U21'(f142_in(z0, z1), z0, z1), F142_IN(z0, z1))
F139_IN(z0, z1) → c66(U22'(f42_in(z0), z0, z1), F42_IN(z0))
F36_IN(z0) → c68(U23'(f42_in(z0), z0), F42_IN(z0))
F38_IN(z0) → c70(U24'(f42_in(z0), z0), F42_IN(z0))
F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0))
U25'(f44_out1, z0) → c73(U26'(f1_in(z0, void), z0), F1_IN(z0, void))
F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
U27'(f44_out1, z0, z1) → c76(U28'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
U29'(f44_out1, z0, z1) → c79(U30'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(U32'(f1_in(z0, z2), z0, z1, z2), F1_IN(z0, z2))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
U33'(f295_out1, z0, z1, z2) → c85(U34'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F15_IN(z0, z1) → c87(U35'(f54_in(z0, z1), f55_in(z0, z1), z0, z1), F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(U36'(f18_in(z0), f19_in(z0), z0), F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(U37'(f36_in(z0), f38_in(z0), z0), F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(U38'(f101_in(z0, z1), f102_in(z0, z1), z0, z1), F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(U39'(f156_in(z0, z1), f157_in(z0, z1), z0, z1), F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(U40'(f129_in(z0, z1), f131_in(z0, z1), z0, z1), F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(U41'(f138_in(z0, z1), f139_in(z0, z1), z0, z1), F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(U42'(f183_in(z0, z1), f184_in(z0, z1), z0, z1), F183_IN(z0, z1), F184_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(U10'(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(U12'(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4))))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(U14'(f70_in(z2), z0, tree(z1, z2, z3)))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))

S tuples:

F1_IN(z0, tree(z0, void, void)) → c2(U1'(f16_in(z0), z0, tree(z0, void, void)), F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(U2'(f15_in(z0, z1), z0, tree(z0, void, z1)), F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(U3'(f127_in(z0, z1), z0, tree(z0, z1, void)), F127_IN(z0, z1))
F1_IN(z0, z1) → c6(U4'(f126_in(z0, z1), z0, z1), F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(U5'(f295_in(z0, z1), s(z0), s(z1)), F295_IN(z0, z1))
F44_IN(s(z0)) → c22(U6'(f44_in(z0), s(z0)), F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25(U7'(f25_in, tree(z0, void, z1)))
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27(U8'(f25_in, tree(z0, tree(z1, void, z2), z3)))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(U9'(f70_in(z2), tree(z0, tree(z1, z2, z3), z4)), F70_IN(z2))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43(U11'(f25_in, z0, tree(z0, z1, tree(z2, void, z3))))
F54_IN(z0, tree(z1, void, z2)) → c48(U13'(f25_in, z0, tree(z1, void, z2)))
F129_IN(z0, z1) → c52(U15'(f25_in, z0, z1))
F183_IN(z0, tree(z1, z2, z3)) → c54(U16'(f189_in(z0, z1, z2), z0, tree(z1, z2, z3)), F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(U17'(f310_in(z1, z0, z3), z0, tree(z1, z2, z3)), F310_IN(z1, z0, z3))
F18_IN(z0) → c58(U18'(f25_in, z0))
F101_IN(z0, z1) → c60(U19'(f42_in(z0), z0, z1), F42_IN(z0))
F102_IN(z0, z1) → c62(U20'(f111_in(z0, z1), z0, z1), F111_IN(z0, z1))
F138_IN(z0, z1) → c64(U21'(f142_in(z0, z1), z0, z1), F142_IN(z0, z1))
F139_IN(z0, z1) → c66(U22'(f42_in(z0), z0, z1), F42_IN(z0))
F36_IN(z0) → c68(U23'(f42_in(z0), z0), F42_IN(z0))
F38_IN(z0) → c70(U24'(f42_in(z0), z0), F42_IN(z0))
F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0))
U25'(f44_out1, z0) → c73(U26'(f1_in(z0, void), z0), F1_IN(z0, void))
F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
U27'(f44_out1, z0, z1) → c76(U28'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
U29'(f44_out1, z0, z1) → c79(U30'(f1_in(z0, z1), z0, z1), F1_IN(z0, z1))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(U32'(f1_in(z0, z2), z0, z1, z2), F1_IN(z0, z2))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
U33'(f295_out1, z0, z1, z2) → c85(U34'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F15_IN(z0, z1) → c87(U35'(f54_in(z0, z1), f55_in(z0, z1), z0, z1), F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(U36'(f18_in(z0), f19_in(z0), z0), F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(U37'(f36_in(z0), f38_in(z0), z0), F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(U38'(f101_in(z0, z1), f102_in(z0, z1), z0, z1), F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(U39'(f156_in(z0, z1), f157_in(z0, z1), z0, z1), F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(U40'(f129_in(z0, z1), f131_in(z0, z1), z0, z1), F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(U41'(f138_in(z0, z1), f139_in(z0, z1), z0, z1), F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(U42'(f183_in(z0, z1), f184_in(z0, z1), z0, z1), F183_IN(z0, z1), F184_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(U10'(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(U12'(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4))))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(U14'(f70_in(z2), z0, tree(z1, z2, z3)))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f295_in, U5, f44_in, U6, f70_in, U7, U8, U9, f191_in, U10, f156_in, U11, U12, f54_in, U13, U14, f129_in, U15, f183_in, U16, f184_in, U17, f18_in, U18, f101_in, U19, f102_in, U20, f138_in, U21, f139_in, U22, f36_in, U23, f38_in, U24, f42_in, U25, U26, f111_in, U27, U28, f142_in, U29, U30, f189_in, U31, U32, f310_in, U33, U34, f15_in, U35, f16_in, U36, f19_in, U37, f55_in, U38, f126_in, U39, f127_in, U40, f131_in, U41, f157_in, U42

Defined Pair Symbols:

F1_IN, F295_IN, F44_IN, F70_IN, F156_IN, F54_IN, F129_IN, F183_IN, F184_IN, F18_IN, F101_IN, F102_IN, F138_IN, F139_IN, F36_IN, F38_IN, F42_IN, U25', F111_IN, U27', F142_IN, U29', F189_IN, U31', F310_IN, U33', F15_IN, F16_IN, F19_IN, F55_IN, F126_IN, F127_IN, F131_IN, F157_IN, F191_IN

Compound Symbols:

c2, c3, c5, c6, c20, c22, c25, c27, c28, c43, c48, c52, c54, c56, c58, c60, c62, c64, c66, c68, c70, c72, c73, c75, c76, c78, c79, c81, c82, c84, c85, c87, c91, c95, c98, c101, c105, c109, c112, c

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

Removed 37 trailing tuple parts

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, z1)) → f1_out1
f1_in(z0, tree(z0, void, void)) → f1_out1
f1_in(z0, tree(z0, void, void)) → U1(f16_in(z0), z0, tree(z0, void, void))
f1_in(z0, tree(z0, void, z1)) → U2(f15_in(z0, z1), z0, tree(z0, void, z1))
f1_in(z0, tree(z0, z1, void)) → f1_out1
f1_in(z0, tree(z0, z1, void)) → U3(f127_in(z0, z1), z0, tree(z0, z1, void))
f1_in(z0, z1) → U4(f126_in(z0, z1), z0, z1)
U1(f16_out1, z0, tree(z0, void, void)) → f1_out1
U1(f16_out2, z0, tree(z0, void, void)) → f1_out1
U1(f16_out3, z0, tree(z0, void, void)) → f1_out1
U2(f15_out1, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out2, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out3, z0, tree(z0, void, z1)) → f1_out1
U3(f127_out1, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out2, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out3, z0, tree(z0, z1, void)) → f1_out1
U4(f126_out1, z0, z1) → f1_out1
U4(f126_out2, z0, z1) → f1_out1
U4(f126_out3, z0, z1) → f1_out1
f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1
f70_in(tree(z0, void, z1)) → f70_out1(z0)
f70_in(tree(z0, void, z1)) → U7(f25_in, tree(z0, void, z1))
f70_in(tree(z0, tree(z1, void, z2), z3)) → f70_out1(z1)
f70_in(tree(z0, tree(z1, void, z2), z3)) → U8(f25_in, tree(z0, tree(z1, void, z2), z3))
f70_in(tree(z0, tree(z1, z2, z3), z4)) → U9(f70_in(z2), tree(z0, tree(z1, z2, z3), z4))
U7(f25_out1(z0), tree(z1, void, z2)) → f70_out1(z0)
U8(f25_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f70_out1(z0)
U9(f70_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f70_out1(z0)
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → f156_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f25_in, z0, tree(z0, z1, tree(z2, void, z3)))
f156_in(z0, tree(z0, z1, tree(z2, z3, z4))) → U12(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4)))
U11(f25_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f156_out1
U12(f70_out1(z0), z1, tree(z1, z2, tree(z3, z4, z5))) → f156_out1
f54_in(z0, tree(z1, void, z2)) → f54_out1
f54_in(z0, tree(z1, void, z2)) → U13(f25_in, z0, tree(z1, void, z2))
f54_in(z0, tree(z1, z2, z3)) → U14(f70_in(z2), z0, tree(z1, z2, z3))
U13(f25_out1(z0), z1, tree(z2, void, z3)) → f54_out1
U14(f70_out1(z0), z1, tree(z2, z3, z4)) → f54_out1
f129_in(z0, z1) → U15(f25_in, z0, z1)
U15(f25_out1(z0), z1, z2) → f129_out1
f183_in(z0, tree(z1, z2, z3)) → U16(f189_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f189_out1, z0, tree(z1, z2, z3)) → f183_out1
f184_in(z0, tree(z1, z2, z3)) → U17(f310_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f310_out1, z0, tree(z1, z2, z3)) → f184_out1
f18_in(z0) → U18(f25_in, z0)
U18(f25_out1(z0), z1) → f18_out1
f101_in(z0, z1) → U19(f42_in(z0), z0, z1)
U19(f42_out1, z0, z1) → f101_out1
f102_in(z0, z1) → U20(f111_in(z0, z1), z0, z1)
U20(f111_out1, z0, z1) → f102_out1
f138_in(z0, z1) → U21(f142_in(z0, z1), z0, z1)
U21(f142_out1, z0, z1) → f138_out1
f139_in(z0, z1) → U22(f42_in(z0), z0, z1)
U22(f42_out1, z0, z1) → f139_out1
f36_in(z0) → U23(f42_in(z0), z0)
U23(f42_out1, z0) → f36_out1
f38_in(z0) → U24(f42_in(z0), z0)
U24(f42_out1, z0) → f38_out1
f42_in(z0) → U25(f44_in(z0), z0)
U25(f44_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1, z0) → f42_out1
f111_in(z0, z1) → U27(f44_in(z0), z0, z1)
U27(f44_out1, z0, z1) → U28(f1_in(z0, z1), z0, z1)
U28(f1_out1, z0, z1) → f111_out1
f142_in(z0, z1) → U29(f44_in(z0), z0, z1)
U29(f44_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1, z0, z1) → f142_out1
f189_in(z0, z1, z2) → U31(f191_in(z0, z1), z0, z1, z2)
U31(f191_out1, z0, z1, z2) → U32(f1_in(z0, z2), z0, z1, z2)
U32(f1_out1, z0, z1, z2) → f189_out1
f310_in(z0, z1, z2) → U33(f295_in(z0, z1), z0, z1, z2)
U33(f295_out1, z0, z1, z2) → U34(f1_in(z1, z2), z0, z1, z2)
U34(f1_out1, z0, z1, z2) → f310_out1
f15_in(z0, z1) → U35(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U35(f54_out1, z0, z1, z2) → f15_out1
U35(z0, f55_out1, z1, z2) → f15_out2
U35(z0, f55_out2, z1, z2) → f15_out3
f16_in(z0) → U36(f18_in(z0), f19_in(z0), z0)
U36(f18_out1, z0, z1) → f16_out1
U36(z0, f19_out1, z1) → f16_out2
U36(z0, f19_out2, z1) → f16_out3
f19_in(z0) → U37(f36_in(z0), f38_in(z0), z0)
U37(f36_out1, z0, z1) → f19_out1
U37(z0, f38_out1, z1) → f19_out2
f55_in(z0, z1) → U38(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U38(f101_out1, z0, z1, z2) → f55_out1
U38(z0, f102_out1, z1, z2) → f55_out2
f126_in(z0, z1) → U39(f156_in(z0, z1), f157_in(z0, z1), z0, z1)
U39(f156_out1, z0, z1, z2) → f126_out1
U39(z0, f157_out1, z1, z2) → f126_out2
U39(z0, f157_out2, z1, z2) → f126_out3
f127_in(z0, z1) → U40(f129_in(z0, z1), f131_in(z0, z1), z0, z1)
U40(f129_out1, z0, z1, z2) → f127_out1
U40(z0, f131_out1, z1, z2) → f127_out2
U40(z0, f131_out2, z1, z2) → f127_out3
f131_in(z0, z1) → U41(f138_in(z0, z1), f139_in(z0, z1), z0, z1)
U41(f138_out1, z0, z1, z2) → f131_out1
U41(z0, f139_out1, z1, z2) → f131_out2
f157_in(z0, z1) → U42(f183_in(z0, z1), f184_in(z0, z1), z0, z1)
U42(f183_out1, z0, z1, z2) → f157_out1
U42(z0, f184_out1, z1, z2) → f157_out2

Tuples:

F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0))
F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43
F54_IN(z0, tree(z1, void, z2)) → c48
F129_IN(z0, z1) → c52
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F18_IN(z0) → c58
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c
F54_IN(z0, tree(z1, z2, z3)) → c

S tuples:

F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0))
F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43
F54_IN(z0, tree(z1, void, z2)) → c48
F129_IN(z0, z1) → c52
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F18_IN(z0) → c58
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c
F54_IN(z0, tree(z1, z2, z3)) → c

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f295_in, U5, f44_in, U6, f70_in, U7, U8, U9, f191_in, U10, f156_in, U11, U12, f54_in, U13, U14, f129_in, U15, f183_in, U16, f184_in, U17, f18_in, U18, f101_in, U19, f102_in, U20, f138_in, U21, f139_in, U22, f36_in, U23, f38_in, U24, f42_in, U25, U26, f111_in, U27, U28, f142_in, U29, U30, f189_in, U31, U32, f310_in, U33, U34, f15_in, U35, f16_in, U36, f19_in, U37, f55_in, U38, f126_in, U39, f127_in, U40, f131_in, U41, f157_in, U42

Defined Pair Symbols:

F42_IN, F111_IN, F142_IN, F189_IN, F310_IN, F191_IN, F156_IN, F54_IN, F1_IN, F295_IN, F44_IN, F70_IN, F129_IN, F183_IN, F184_IN, F18_IN, F101_IN, F102_IN, F138_IN, F139_IN, F36_IN, F38_IN, U25', U27', U29', U31', U33', F15_IN, F16_IN, F19_IN, F55_IN, F126_IN, F127_IN, F131_IN, F157_IN

Compound Symbols:

c72, c75, c78, c81, c84, c, c2, c3, c5, c6, c20, c22, c25, c27, c28, c43, c48, c52, c54, c56, c58, c60, c62, c64, c66, c68, c70, c73, c76, c79, c82, c85, c87, c91, c95, c98, c101, c105, c109, c112, 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.

U25'(f44_out1, z0) → c73(F1_IN(z0, void))

We considered the (Usable) Rules:

f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1

And the Tuples:

F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0))
F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43
F54_IN(z0, tree(z1, void, z2)) → c48
F129_IN(z0, z1) → c52
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F18_IN(z0) → c58
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c
F54_IN(z0, tree(z1, z2, z3)) → c

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

POL(0) = 0   
POL(F101_IN(x₁, x₂)) = 0   
POL(F102_IN(x₁, x₂)) = 0   
POL(F111_IN(x₁, x₂)) = 0   
POL(F126_IN(x₁, x₂)) = 0   
POL(F127_IN(x₁, x₂)) = 0   
POL(F129_IN(x₁, x₂)) = 0   
POL(F131_IN(x₁, x₂)) = 0   
POL(F138_IN(x₁, x₂)) = 0   
POL(F139_IN(x₁, x₂)) = 0   
POL(F142_IN(x₁, x₂)) = 0   
POL(F156_IN(x₁, x₂)) = 0   
POL(F157_IN(x₁, x₂)) = 0   
POL(F15_IN(x₁, x₂)) = 0   
POL(F16_IN(x₁)) = 0   
POL(F183_IN(x₁, x₂)) = 0   
POL(F184_IN(x₁, x₂)) = 0   
POL(F189_IN(x₁, x₂, x₃)) = 0   
POL(F18_IN(x₁)) = 0   
POL(F191_IN(x₁, x₂)) = 0   
POL(F19_IN(x₁)) = 0   
POL(F1_IN(x₁, x₂)) = 0   
POL(F295_IN(x₁, x₂)) = 0   
POL(F310_IN(x₁, x₂, x₃)) = 0   
POL(F36_IN(x₁)) = 0   
POL(F38_IN(x₁)) = 0   
POL(F42_IN(x₁)) = 0   
POL(F44_IN(x₁)) = 0   
POL(F54_IN(x₁, x₂)) = 0   
POL(F55_IN(x₁, x₂)) = 0   
POL(F70_IN(x₁)) = 0   
POL(U10(x₁, x₂, x₃)) = 0   
POL(U25'(x₁, x₂)) = [2]x₁   
POL(U27'(x₁, x₂, x₃)) = 0   
POL(U29'(x₁, x₂, x₃)) = 0   
POL(U31'(x₁, x₂, x₃, x₄)) = 0   
POL(U33'(x₁, x₂, x₃, x₄)) = 0   
POL(U5(x₁, x₂, x₃)) = 0   
POL(U6(x₁, x₂)) = x₁   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c101(x₁, x₂)) = x₁ + x₂   
POL(c105(x₁, x₂)) = x₁ + x₂   
POL(c109(x₁, x₂)) = x₁ + x₂   
POL(c112(x₁, x₂)) = x₁ + x₂   
POL(c2(x₁)) = x₁   
POL(c20(x₁)) = x₁   
POL(c22(x₁)) = x₁   
POL(c25) = 0   
POL(c27) = 0   
POL(c28(x₁)) = x₁   
POL(c3(x₁)) = x₁   
POL(c43) = 0   
POL(c48) = 0   
POL(c5(x₁)) = x₁   
POL(c52) = 0   
POL(c54(x₁)) = x₁   
POL(c56(x₁)) = x₁   
POL(c58) = 0   
POL(c6(x₁)) = x₁   
POL(c60(x₁)) = x₁   
POL(c62(x₁)) = x₁   
POL(c64(x₁)) = x₁   
POL(c66(x₁)) = x₁   
POL(c68(x₁)) = x₁   
POL(c70(x₁)) = x₁   
POL(c72(x₁, x₂)) = x₁ + x₂   
POL(c73(x₁)) = x₁   
POL(c75(x₁, x₂)) = x₁ + x₂   
POL(c76(x₁)) = x₁   
POL(c78(x₁, x₂)) = x₁ + x₂   
POL(c79(x₁)) = x₁   
POL(c81(x₁, x₂)) = x₁ + x₂   
POL(c82(x₁)) = x₁   
POL(c84(x₁, x₂)) = x₁ + x₂   
POL(c85(x₁)) = x₁   
POL(c87(x₁, x₂)) = x₁ + x₂   
POL(c91(x₁, x₂)) = x₁ + x₂   
POL(c95(x₁, x₂)) = x₁ + x₂   
POL(c98(x₁, x₂)) = x₁ + x₂   
POL(f191_in(x₁, x₂)) = 0   
POL(f191_out1) = 0   
POL(f295_in(x₁, x₂)) = 0   
POL(f295_out1) = 0   
POL(f44_in(x₁)) = 0   
POL(f44_out1) = [2]   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = 0   
POL(void) = 0   

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, z1)) → f1_out1
f1_in(z0, tree(z0, void, void)) → f1_out1
f1_in(z0, tree(z0, void, void)) → U1(f16_in(z0), z0, tree(z0, void, void))
f1_in(z0, tree(z0, void, z1)) → U2(f15_in(z0, z1), z0, tree(z0, void, z1))
f1_in(z0, tree(z0, z1, void)) → f1_out1
f1_in(z0, tree(z0, z1, void)) → U3(f127_in(z0, z1), z0, tree(z0, z1, void))
f1_in(z0, z1) → U4(f126_in(z0, z1), z0, z1)
U1(f16_out1, z0, tree(z0, void, void)) → f1_out1
U1(f16_out2, z0, tree(z0, void, void)) → f1_out1
U1(f16_out3, z0, tree(z0, void, void)) → f1_out1
U2(f15_out1, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out2, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out3, z0, tree(z0, void, z1)) → f1_out1
U3(f127_out1, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out2, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out3, z0, tree(z0, z1, void)) → f1_out1
U4(f126_out1, z0, z1) → f1_out1
U4(f126_out2, z0, z1) → f1_out1
U4(f126_out3, z0, z1) → f1_out1
f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1
f70_in(tree(z0, void, z1)) → f70_out1(z0)
f70_in(tree(z0, void, z1)) → U7(f25_in, tree(z0, void, z1))
f70_in(tree(z0, tree(z1, void, z2), z3)) → f70_out1(z1)
f70_in(tree(z0, tree(z1, void, z2), z3)) → U8(f25_in, tree(z0, tree(z1, void, z2), z3))
f70_in(tree(z0, tree(z1, z2, z3), z4)) → U9(f70_in(z2), tree(z0, tree(z1, z2, z3), z4))
U7(f25_out1(z0), tree(z1, void, z2)) → f70_out1(z0)
U8(f25_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f70_out1(z0)
U9(f70_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f70_out1(z0)
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → f156_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f25_in, z0, tree(z0, z1, tree(z2, void, z3)))
f156_in(z0, tree(z0, z1, tree(z2, z3, z4))) → U12(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4)))
U11(f25_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f156_out1
U12(f70_out1(z0), z1, tree(z1, z2, tree(z3, z4, z5))) → f156_out1
f54_in(z0, tree(z1, void, z2)) → f54_out1
f54_in(z0, tree(z1, void, z2)) → U13(f25_in, z0, tree(z1, void, z2))
f54_in(z0, tree(z1, z2, z3)) → U14(f70_in(z2), z0, tree(z1, z2, z3))
U13(f25_out1(z0), z1, tree(z2, void, z3)) → f54_out1
U14(f70_out1(z0), z1, tree(z2, z3, z4)) → f54_out1
f129_in(z0, z1) → U15(f25_in, z0, z1)
U15(f25_out1(z0), z1, z2) → f129_out1
f183_in(z0, tree(z1, z2, z3)) → U16(f189_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f189_out1, z0, tree(z1, z2, z3)) → f183_out1
f184_in(z0, tree(z1, z2, z3)) → U17(f310_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f310_out1, z0, tree(z1, z2, z3)) → f184_out1
f18_in(z0) → U18(f25_in, z0)
U18(f25_out1(z0), z1) → f18_out1
f101_in(z0, z1) → U19(f42_in(z0), z0, z1)
U19(f42_out1, z0, z1) → f101_out1
f102_in(z0, z1) → U20(f111_in(z0, z1), z0, z1)
U20(f111_out1, z0, z1) → f102_out1
f138_in(z0, z1) → U21(f142_in(z0, z1), z0, z1)
U21(f142_out1, z0, z1) → f138_out1
f139_in(z0, z1) → U22(f42_in(z0), z0, z1)
U22(f42_out1, z0, z1) → f139_out1
f36_in(z0) → U23(f42_in(z0), z0)
U23(f42_out1, z0) → f36_out1
f38_in(z0) → U24(f42_in(z0), z0)
U24(f42_out1, z0) → f38_out1
f42_in(z0) → U25(f44_in(z0), z0)
U25(f44_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1, z0) → f42_out1
f111_in(z0, z1) → U27(f44_in(z0), z0, z1)
U27(f44_out1, z0, z1) → U28(f1_in(z0, z1), z0, z1)
U28(f1_out1, z0, z1) → f111_out1
f142_in(z0, z1) → U29(f44_in(z0), z0, z1)
U29(f44_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1, z0, z1) → f142_out1
f189_in(z0, z1, z2) → U31(f191_in(z0, z1), z0, z1, z2)
U31(f191_out1, z0, z1, z2) → U32(f1_in(z0, z2), z0, z1, z2)
U32(f1_out1, z0, z1, z2) → f189_out1
f310_in(z0, z1, z2) → U33(f295_in(z0, z1), z0, z1, z2)
U33(f295_out1, z0, z1, z2) → U34(f1_in(z1, z2), z0, z1, z2)
U34(f1_out1, z0, z1, z2) → f310_out1
f15_in(z0, z1) → U35(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U35(f54_out1, z0, z1, z2) → f15_out1
U35(z0, f55_out1, z1, z2) → f15_out2
U35(z0, f55_out2, z1, z2) → f15_out3
f16_in(z0) → U36(f18_in(z0), f19_in(z0), z0)
U36(f18_out1, z0, z1) → f16_out1
U36(z0, f19_out1, z1) → f16_out2
U36(z0, f19_out2, z1) → f16_out3
f19_in(z0) → U37(f36_in(z0), f38_in(z0), z0)
U37(f36_out1, z0, z1) → f19_out1
U37(z0, f38_out1, z1) → f19_out2
f55_in(z0, z1) → U38(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U38(f101_out1, z0, z1, z2) → f55_out1
U38(z0, f102_out1, z1, z2) → f55_out2
f126_in(z0, z1) → U39(f156_in(z0, z1), f157_in(z0, z1), z0, z1)
U39(f156_out1, z0, z1, z2) → f126_out1
U39(z0, f157_out1, z1, z2) → f126_out2
U39(z0, f157_out2, z1, z2) → f126_out3
f127_in(z0, z1) → U40(f129_in(z0, z1), f131_in(z0, z1), z0, z1)
U40(f129_out1, z0, z1, z2) → f127_out1
U40(z0, f131_out1, z1, z2) → f127_out2
U40(z0, f131_out2, z1, z2) → f127_out3
f131_in(z0, z1) → U41(f138_in(z0, z1), f139_in(z0, z1), z0, z1)
U41(f138_out1, z0, z1, z2) → f131_out1
U41(z0, f139_out1, z1, z2) → f131_out2
f157_in(z0, z1) → U42(f183_in(z0, z1), f184_in(z0, z1), z0, z1)
U42(f183_out1, z0, z1, z2) → f157_out1
U42(z0, f184_out1, z1, z2) → f157_out2

Tuples:

F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0))
F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43
F54_IN(z0, tree(z1, void, z2)) → c48
F129_IN(z0, z1) → c52
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F18_IN(z0) → c58
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c
F54_IN(z0, tree(z1, z2, z3)) → c

S tuples:

F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0))
F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43
F54_IN(z0, tree(z1, void, z2)) → c48
F129_IN(z0, z1) → c52
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F18_IN(z0) → c58
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c
F54_IN(z0, tree(z1, z2, z3)) → c

K tuples:

U25'(f44_out1, z0) → c73(F1_IN(z0, void))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f295_in, U5, f44_in, U6, f70_in, U7, U8, U9, f191_in, U10, f156_in, U11, U12, f54_in, U13, U14, f129_in, U15, f183_in, U16, f184_in, U17, f18_in, U18, f101_in, U19, f102_in, U20, f138_in, U21, f139_in, U22, f36_in, U23, f38_in, U24, f42_in, U25, U26, f111_in, U27, U28, f142_in, U29, U30, f189_in, U31, U32, f310_in, U33, U34, f15_in, U35, f16_in, U36, f19_in, U37, f55_in, U38, f126_in, U39, f127_in, U40, f131_in, U41, f157_in, U42

Defined Pair Symbols:

F42_IN, F111_IN, F142_IN, F189_IN, F310_IN, F191_IN, F156_IN, F54_IN, F1_IN, F295_IN, F44_IN, F70_IN, F129_IN, F183_IN, F184_IN, F18_IN, F101_IN, F102_IN, F138_IN, F139_IN, F36_IN, F38_IN, U25', U27', U29', U31', U33', F15_IN, F16_IN, F19_IN, F55_IN, F126_IN, F127_IN, F131_IN, F157_IN

Compound Symbols:

c72, c75, c78, c81, c84, c, c2, c3, c5, c6, c20, c22, c25, c27, c28, c43, c48, c52, c54, c56, c58, c60, c62, c64, c66, c68, c70, c73, c76, c79, c82, c85, c87, c91, c95, c98, c101, c105, c109, c112, c

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

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

U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))

We considered the (Usable) Rules:

f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1

And the Tuples:

F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0))
F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43
F54_IN(z0, tree(z1, void, z2)) → c48
F129_IN(z0, z1) → c52
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F18_IN(z0) → c58
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c
F54_IN(z0, tree(z1, z2, z3)) → c

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

POL(0) = 0   
POL(F101_IN(x₁, x₂)) = 0   
POL(F102_IN(x₁, x₂)) = 0   
POL(F111_IN(x₁, x₂)) = 0   
POL(F126_IN(x₁, x₂)) = 0   
POL(F127_IN(x₁, x₂)) = 0   
POL(F129_IN(x₁, x₂)) = 0   
POL(F131_IN(x₁, x₂)) = 0   
POL(F138_IN(x₁, x₂)) = 0   
POL(F139_IN(x₁, x₂)) = 0   
POL(F142_IN(x₁, x₂)) = 0   
POL(F156_IN(x₁, x₂)) = 0   
POL(F157_IN(x₁, x₂)) = 0   
POL(F15_IN(x₁, x₂)) = 0   
POL(F16_IN(x₁)) = 0   
POL(F183_IN(x₁, x₂)) = 0   
POL(F184_IN(x₁, x₂)) = 0   
POL(F189_IN(x₁, x₂, x₃)) = 0   
POL(F18_IN(x₁)) = 0   
POL(F191_IN(x₁, x₂)) = 0   
POL(F19_IN(x₁)) = 0   
POL(F1_IN(x₁, x₂)) = 0   
POL(F295_IN(x₁, x₂)) = 0   
POL(F310_IN(x₁, x₂, x₃)) = 0   
POL(F36_IN(x₁)) = 0   
POL(F38_IN(x₁)) = 0   
POL(F42_IN(x₁)) = 0   
POL(F44_IN(x₁)) = 0   
POL(F54_IN(x₁, x₂)) = 0   
POL(F55_IN(x₁, x₂)) = 0   
POL(F70_IN(x₁)) = 0   
POL(U10(x₁, x₂, x₃)) = 0   
POL(U25'(x₁, x₂)) = 0   
POL(U27'(x₁, x₂, x₃)) = [2]x₁   
POL(U29'(x₁, x₂, x₃)) = 0   
POL(U31'(x₁, x₂, x₃, x₄)) = 0   
POL(U33'(x₁, x₂, x₃, x₄)) = 0   
POL(U5(x₁, x₂, x₃)) = 0   
POL(U6(x₁, x₂)) = x₁   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c101(x₁, x₂)) = x₁ + x₂   
POL(c105(x₁, x₂)) = x₁ + x₂   
POL(c109(x₁, x₂)) = x₁ + x₂   
POL(c112(x₁, x₂)) = x₁ + x₂   
POL(c2(x₁)) = x₁   
POL(c20(x₁)) = x₁   
POL(c22(x₁)) = x₁   
POL(c25) = 0   
POL(c27) = 0   
POL(c28(x₁)) = x₁   
POL(c3(x₁)) = x₁   
POL(c43) = 0   
POL(c48) = 0   
POL(c5(x₁)) = x₁   
POL(c52) = 0   
POL(c54(x₁)) = x₁   
POL(c56(x₁)) = x₁   
POL(c58) = 0   
POL(c6(x₁)) = x₁   
POL(c60(x₁)) = x₁   
POL(c62(x₁)) = x₁   
POL(c64(x₁)) = x₁   
POL(c66(x₁)) = x₁   
POL(c68(x₁)) = x₁   
POL(c70(x₁)) = x₁   
POL(c72(x₁, x₂)) = x₁ + x₂   
POL(c73(x₁)) = x₁   
POL(c75(x₁, x₂)) = x₁ + x₂   
POL(c76(x₁)) = x₁   
POL(c78(x₁, x₂)) = x₁ + x₂   
POL(c79(x₁)) = x₁   
POL(c81(x₁, x₂)) = x₁ + x₂   
POL(c82(x₁)) = x₁   
POL(c84(x₁, x₂)) = x₁ + x₂   
POL(c85(x₁)) = x₁   
POL(c87(x₁, x₂)) = x₁ + x₂   
POL(c91(x₁, x₂)) = x₁ + x₂   
POL(c95(x₁, x₂)) = x₁ + x₂   
POL(c98(x₁, x₂)) = x₁ + x₂   
POL(f191_in(x₁, x₂)) = 0   
POL(f191_out1) = 0   
POL(f295_in(x₁, x₂)) = 0   
POL(f295_out1) = 0   
POL(f44_in(x₁)) = 0   
POL(f44_out1) = [1]   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = 0   
POL(void) = 0   

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, z1)) → f1_out1
f1_in(z0, tree(z0, void, void)) → f1_out1
f1_in(z0, tree(z0, void, void)) → U1(f16_in(z0), z0, tree(z0, void, void))
f1_in(z0, tree(z0, void, z1)) → U2(f15_in(z0, z1), z0, tree(z0, void, z1))
f1_in(z0, tree(z0, z1, void)) → f1_out1
f1_in(z0, tree(z0, z1, void)) → U3(f127_in(z0, z1), z0, tree(z0, z1, void))
f1_in(z0, z1) → U4(f126_in(z0, z1), z0, z1)
U1(f16_out1, z0, tree(z0, void, void)) → f1_out1
U1(f16_out2, z0, tree(z0, void, void)) → f1_out1
U1(f16_out3, z0, tree(z0, void, void)) → f1_out1
U2(f15_out1, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out2, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out3, z0, tree(z0, void, z1)) → f1_out1
U3(f127_out1, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out2, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out3, z0, tree(z0, z1, void)) → f1_out1
U4(f126_out1, z0, z1) → f1_out1
U4(f126_out2, z0, z1) → f1_out1
U4(f126_out3, z0, z1) → f1_out1
f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1
f70_in(tree(z0, void, z1)) → f70_out1(z0)
f70_in(tree(z0, void, z1)) → U7(f25_in, tree(z0, void, z1))
f70_in(tree(z0, tree(z1, void, z2), z3)) → f70_out1(z1)
f70_in(tree(z0, tree(z1, void, z2), z3)) → U8(f25_in, tree(z0, tree(z1, void, z2), z3))
f70_in(tree(z0, tree(z1, z2, z3), z4)) → U9(f70_in(z2), tree(z0, tree(z1, z2, z3), z4))
U7(f25_out1(z0), tree(z1, void, z2)) → f70_out1(z0)
U8(f25_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f70_out1(z0)
U9(f70_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f70_out1(z0)
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → f156_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f25_in, z0, tree(z0, z1, tree(z2, void, z3)))
f156_in(z0, tree(z0, z1, tree(z2, z3, z4))) → U12(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4)))
U11(f25_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f156_out1
U12(f70_out1(z0), z1, tree(z1, z2, tree(z3, z4, z5))) → f156_out1
f54_in(z0, tree(z1, void, z2)) → f54_out1
f54_in(z0, tree(z1, void, z2)) → U13(f25_in, z0, tree(z1, void, z2))
f54_in(z0, tree(z1, z2, z3)) → U14(f70_in(z2), z0, tree(z1, z2, z3))
U13(f25_out1(z0), z1, tree(z2, void, z3)) → f54_out1
U14(f70_out1(z0), z1, tree(z2, z3, z4)) → f54_out1
f129_in(z0, z1) → U15(f25_in, z0, z1)
U15(f25_out1(z0), z1, z2) → f129_out1
f183_in(z0, tree(z1, z2, z3)) → U16(f189_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f189_out1, z0, tree(z1, z2, z3)) → f183_out1
f184_in(z0, tree(z1, z2, z3)) → U17(f310_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f310_out1, z0, tree(z1, z2, z3)) → f184_out1
f18_in(z0) → U18(f25_in, z0)
U18(f25_out1(z0), z1) → f18_out1
f101_in(z0, z1) → U19(f42_in(z0), z0, z1)
U19(f42_out1, z0, z1) → f101_out1
f102_in(z0, z1) → U20(f111_in(z0, z1), z0, z1)
U20(f111_out1, z0, z1) → f102_out1
f138_in(z0, z1) → U21(f142_in(z0, z1), z0, z1)
U21(f142_out1, z0, z1) → f138_out1
f139_in(z0, z1) → U22(f42_in(z0), z0, z1)
U22(f42_out1, z0, z1) → f139_out1
f36_in(z0) → U23(f42_in(z0), z0)
U23(f42_out1, z0) → f36_out1
f38_in(z0) → U24(f42_in(z0), z0)
U24(f42_out1, z0) → f38_out1
f42_in(z0) → U25(f44_in(z0), z0)
U25(f44_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1, z0) → f42_out1
f111_in(z0, z1) → U27(f44_in(z0), z0, z1)
U27(f44_out1, z0, z1) → U28(f1_in(z0, z1), z0, z1)
U28(f1_out1, z0, z1) → f111_out1
f142_in(z0, z1) → U29(f44_in(z0), z0, z1)
U29(f44_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1, z0, z1) → f142_out1
f189_in(z0, z1, z2) → U31(f191_in(z0, z1), z0, z1, z2)
U31(f191_out1, z0, z1, z2) → U32(f1_in(z0, z2), z0, z1, z2)
U32(f1_out1, z0, z1, z2) → f189_out1
f310_in(z0, z1, z2) → U33(f295_in(z0, z1), z0, z1, z2)
U33(f295_out1, z0, z1, z2) → U34(f1_in(z1, z2), z0, z1, z2)
U34(f1_out1, z0, z1, z2) → f310_out1
f15_in(z0, z1) → U35(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U35(f54_out1, z0, z1, z2) → f15_out1
U35(z0, f55_out1, z1, z2) → f15_out2
U35(z0, f55_out2, z1, z2) → f15_out3
f16_in(z0) → U36(f18_in(z0), f19_in(z0), z0)
U36(f18_out1, z0, z1) → f16_out1
U36(z0, f19_out1, z1) → f16_out2
U36(z0, f19_out2, z1) → f16_out3
f19_in(z0) → U37(f36_in(z0), f38_in(z0), z0)
U37(f36_out1, z0, z1) → f19_out1
U37(z0, f38_out1, z1) → f19_out2
f55_in(z0, z1) → U38(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U38(f101_out1, z0, z1, z2) → f55_out1
U38(z0, f102_out1, z1, z2) → f55_out2
f126_in(z0, z1) → U39(f156_in(z0, z1), f157_in(z0, z1), z0, z1)
U39(f156_out1, z0, z1, z2) → f126_out1
U39(z0, f157_out1, z1, z2) → f126_out2
U39(z0, f157_out2, z1, z2) → f126_out3
f127_in(z0, z1) → U40(f129_in(z0, z1), f131_in(z0, z1), z0, z1)
U40(f129_out1, z0, z1, z2) → f127_out1
U40(z0, f131_out1, z1, z2) → f127_out2
U40(z0, f131_out2, z1, z2) → f127_out3
f131_in(z0, z1) → U41(f138_in(z0, z1), f139_in(z0, z1), z0, z1)
U41(f138_out1, z0, z1, z2) → f131_out1
U41(z0, f139_out1, z1, z2) → f131_out2
f157_in(z0, z1) → U42(f183_in(z0, z1), f184_in(z0, z1), z0, z1)
U42(f183_out1, z0, z1, z2) → f157_out1
U42(z0, f184_out1, z1, z2) → f157_out2

Tuples:

F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0))
F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43
F54_IN(z0, tree(z1, void, z2)) → c48
F129_IN(z0, z1) → c52
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F18_IN(z0) → c58
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c
F54_IN(z0, tree(z1, z2, z3)) → c

S tuples:

F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0))
F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43
F54_IN(z0, tree(z1, void, z2)) → c48
F129_IN(z0, z1) → c52
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F18_IN(z0) → c58
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c
F54_IN(z0, tree(z1, z2, z3)) → c

K tuples:

U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f295_in, U5, f44_in, U6, f70_in, U7, U8, U9, f191_in, U10, f156_in, U11, U12, f54_in, U13, U14, f129_in, U15, f183_in, U16, f184_in, U17, f18_in, U18, f101_in, U19, f102_in, U20, f138_in, U21, f139_in, U22, f36_in, U23, f38_in, U24, f42_in, U25, U26, f111_in, U27, U28, f142_in, U29, U30, f189_in, U31, U32, f310_in, U33, U34, f15_in, U35, f16_in, U36, f19_in, U37, f55_in, U38, f126_in, U39, f127_in, U40, f131_in, U41, f157_in, U42

Defined Pair Symbols:

F42_IN, F111_IN, F142_IN, F189_IN, F310_IN, F191_IN, F156_IN, F54_IN, F1_IN, F295_IN, F44_IN, F70_IN, F129_IN, F183_IN, F184_IN, F18_IN, F101_IN, F102_IN, F138_IN, F139_IN, F36_IN, F38_IN, U25', U27', U29', U31', U33', F15_IN, F16_IN, F19_IN, F55_IN, F126_IN, F127_IN, F131_IN, F157_IN

Compound Symbols:

c72, c75, c78, c81, c84, c, c2, c3, c5, c6, c20, c22, c25, c27, c28, c43, c48, c52, c54, c56, c58, c60, c62, c64, c66, c68, c70, c73, c76, c79, c82, c85, c87, c91, c95, c98, c101, c105, c109, c112, c

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

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

U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))

We considered the (Usable) Rules:

f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1

And the Tuples:

F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0))
F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43
F54_IN(z0, tree(z1, void, z2)) → c48
F129_IN(z0, z1) → c52
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F18_IN(z0) → c58
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c
F54_IN(z0, tree(z1, z2, z3)) → c

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

POL(0) = 0   
POL(F101_IN(x₁, x₂)) = 0   
POL(F102_IN(x₁, x₂)) = 0   
POL(F111_IN(x₁, x₂)) = 0   
POL(F126_IN(x₁, x₂)) = 0   
POL(F127_IN(x₁, x₂)) = 0   
POL(F129_IN(x₁, x₂)) = 0   
POL(F131_IN(x₁, x₂)) = 0   
POL(F138_IN(x₁, x₂)) = 0   
POL(F139_IN(x₁, x₂)) = 0   
POL(F142_IN(x₁, x₂)) = 0   
POL(F156_IN(x₁, x₂)) = 0   
POL(F157_IN(x₁, x₂)) = 0   
POL(F15_IN(x₁, x₂)) = 0   
POL(F16_IN(x₁)) = 0   
POL(F183_IN(x₁, x₂)) = 0   
POL(F184_IN(x₁, x₂)) = 0   
POL(F189_IN(x₁, x₂, x₃)) = 0   
POL(F18_IN(x₁)) = 0   
POL(F191_IN(x₁, x₂)) = 0   
POL(F19_IN(x₁)) = 0   
POL(F1_IN(x₁, x₂)) = 0   
POL(F295_IN(x₁, x₂)) = 0   
POL(F310_IN(x₁, x₂, x₃)) = 0   
POL(F36_IN(x₁)) = 0   
POL(F38_IN(x₁)) = 0   
POL(F42_IN(x₁)) = 0   
POL(F44_IN(x₁)) = 0   
POL(F54_IN(x₁, x₂)) = 0   
POL(F55_IN(x₁, x₂)) = 0   
POL(F70_IN(x₁)) = 0   
POL(U10(x₁, x₂, x₃)) = 0   
POL(U25'(x₁, x₂)) = 0   
POL(U27'(x₁, x₂, x₃)) = 0   
POL(U29'(x₁, x₂, x₃)) = x₁   
POL(U31'(x₁, x₂, x₃, x₄)) = 0   
POL(U33'(x₁, x₂, x₃, x₄)) = 0   
POL(U5(x₁, x₂, x₃)) = 0   
POL(U6(x₁, x₂)) = x₁   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c101(x₁, x₂)) = x₁ + x₂   
POL(c105(x₁, x₂)) = x₁ + x₂   
POL(c109(x₁, x₂)) = x₁ + x₂   
POL(c112(x₁, x₂)) = x₁ + x₂   
POL(c2(x₁)) = x₁   
POL(c20(x₁)) = x₁   
POL(c22(x₁)) = x₁   
POL(c25) = 0   
POL(c27) = 0   
POL(c28(x₁)) = x₁   
POL(c3(x₁)) = x₁   
POL(c43) = 0   
POL(c48) = 0   
POL(c5(x₁)) = x₁   
POL(c52) = 0   
POL(c54(x₁)) = x₁   
POL(c56(x₁)) = x₁   
POL(c58) = 0   
POL(c6(x₁)) = x₁   
POL(c60(x₁)) = x₁   
POL(c62(x₁)) = x₁   
POL(c64(x₁)) = x₁   
POL(c66(x₁)) = x₁   
POL(c68(x₁)) = x₁   
POL(c70(x₁)) = x₁   
POL(c72(x₁, x₂)) = x₁ + x₂   
POL(c73(x₁)) = x₁   
POL(c75(x₁, x₂)) = x₁ + x₂   
POL(c76(x₁)) = x₁   
POL(c78(x₁, x₂)) = x₁ + x₂   
POL(c79(x₁)) = x₁   
POL(c81(x₁, x₂)) = x₁ + x₂   
POL(c82(x₁)) = x₁   
POL(c84(x₁, x₂)) = x₁ + x₂   
POL(c85(x₁)) = x₁   
POL(c87(x₁, x₂)) = x₁ + x₂   
POL(c91(x₁, x₂)) = x₁ + x₂   
POL(c95(x₁, x₂)) = x₁ + x₂   
POL(c98(x₁, x₂)) = x₁ + x₂   
POL(f191_in(x₁, x₂)) = 0   
POL(f191_out1) = 0   
POL(f295_in(x₁, x₂)) = 0   
POL(f295_out1) = 0   
POL(f44_in(x₁)) = 0   
POL(f44_out1) = [1]   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = 0   
POL(void) = 0   

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, z1)) → f1_out1
f1_in(z0, tree(z0, void, void)) → f1_out1
f1_in(z0, tree(z0, void, void)) → U1(f16_in(z0), z0, tree(z0, void, void))
f1_in(z0, tree(z0, void, z1)) → U2(f15_in(z0, z1), z0, tree(z0, void, z1))
f1_in(z0, tree(z0, z1, void)) → f1_out1
f1_in(z0, tree(z0, z1, void)) → U3(f127_in(z0, z1), z0, tree(z0, z1, void))
f1_in(z0, z1) → U4(f126_in(z0, z1), z0, z1)
U1(f16_out1, z0, tree(z0, void, void)) → f1_out1
U1(f16_out2, z0, tree(z0, void, void)) → f1_out1
U1(f16_out3, z0, tree(z0, void, void)) → f1_out1
U2(f15_out1, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out2, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out3, z0, tree(z0, void, z1)) → f1_out1
U3(f127_out1, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out2, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out3, z0, tree(z0, z1, void)) → f1_out1
U4(f126_out1, z0, z1) → f1_out1
U4(f126_out2, z0, z1) → f1_out1
U4(f126_out3, z0, z1) → f1_out1
f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1
f70_in(tree(z0, void, z1)) → f70_out1(z0)
f70_in(tree(z0, void, z1)) → U7(f25_in, tree(z0, void, z1))
f70_in(tree(z0, tree(z1, void, z2), z3)) → f70_out1(z1)
f70_in(tree(z0, tree(z1, void, z2), z3)) → U8(f25_in, tree(z0, tree(z1, void, z2), z3))
f70_in(tree(z0, tree(z1, z2, z3), z4)) → U9(f70_in(z2), tree(z0, tree(z1, z2, z3), z4))
U7(f25_out1(z0), tree(z1, void, z2)) → f70_out1(z0)
U8(f25_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f70_out1(z0)
U9(f70_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f70_out1(z0)
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → f156_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f25_in, z0, tree(z0, z1, tree(z2, void, z3)))
f156_in(z0, tree(z0, z1, tree(z2, z3, z4))) → U12(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4)))
U11(f25_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f156_out1
U12(f70_out1(z0), z1, tree(z1, z2, tree(z3, z4, z5))) → f156_out1
f54_in(z0, tree(z1, void, z2)) → f54_out1
f54_in(z0, tree(z1, void, z2)) → U13(f25_in, z0, tree(z1, void, z2))
f54_in(z0, tree(z1, z2, z3)) → U14(f70_in(z2), z0, tree(z1, z2, z3))
U13(f25_out1(z0), z1, tree(z2, void, z3)) → f54_out1
U14(f70_out1(z0), z1, tree(z2, z3, z4)) → f54_out1
f129_in(z0, z1) → U15(f25_in, z0, z1)
U15(f25_out1(z0), z1, z2) → f129_out1
f183_in(z0, tree(z1, z2, z3)) → U16(f189_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f189_out1, z0, tree(z1, z2, z3)) → f183_out1
f184_in(z0, tree(z1, z2, z3)) → U17(f310_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f310_out1, z0, tree(z1, z2, z3)) → f184_out1
f18_in(z0) → U18(f25_in, z0)
U18(f25_out1(z0), z1) → f18_out1
f101_in(z0, z1) → U19(f42_in(z0), z0, z1)
U19(f42_out1, z0, z1) → f101_out1
f102_in(z0, z1) → U20(f111_in(z0, z1), z0, z1)
U20(f111_out1, z0, z1) → f102_out1
f138_in(z0, z1) → U21(f142_in(z0, z1), z0, z1)
U21(f142_out1, z0, z1) → f138_out1
f139_in(z0, z1) → U22(f42_in(z0), z0, z1)
U22(f42_out1, z0, z1) → f139_out1
f36_in(z0) → U23(f42_in(z0), z0)
U23(f42_out1, z0) → f36_out1
f38_in(z0) → U24(f42_in(z0), z0)
U24(f42_out1, z0) → f38_out1
f42_in(z0) → U25(f44_in(z0), z0)
U25(f44_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1, z0) → f42_out1
f111_in(z0, z1) → U27(f44_in(z0), z0, z1)
U27(f44_out1, z0, z1) → U28(f1_in(z0, z1), z0, z1)
U28(f1_out1, z0, z1) → f111_out1
f142_in(z0, z1) → U29(f44_in(z0), z0, z1)
U29(f44_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1, z0, z1) → f142_out1
f189_in(z0, z1, z2) → U31(f191_in(z0, z1), z0, z1, z2)
U31(f191_out1, z0, z1, z2) → U32(f1_in(z0, z2), z0, z1, z2)
U32(f1_out1, z0, z1, z2) → f189_out1
f310_in(z0, z1, z2) → U33(f295_in(z0, z1), z0, z1, z2)
U33(f295_out1, z0, z1, z2) → U34(f1_in(z1, z2), z0, z1, z2)
U34(f1_out1, z0, z1, z2) → f310_out1
f15_in(z0, z1) → U35(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U35(f54_out1, z0, z1, z2) → f15_out1
U35(z0, f55_out1, z1, z2) → f15_out2
U35(z0, f55_out2, z1, z2) → f15_out3
f16_in(z0) → U36(f18_in(z0), f19_in(z0), z0)
U36(f18_out1, z0, z1) → f16_out1
U36(z0, f19_out1, z1) → f16_out2
U36(z0, f19_out2, z1) → f16_out3
f19_in(z0) → U37(f36_in(z0), f38_in(z0), z0)
U37(f36_out1, z0, z1) → f19_out1
U37(z0, f38_out1, z1) → f19_out2
f55_in(z0, z1) → U38(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U38(f101_out1, z0, z1, z2) → f55_out1
U38(z0, f102_out1, z1, z2) → f55_out2
f126_in(z0, z1) → U39(f156_in(z0, z1), f157_in(z0, z1), z0, z1)
U39(f156_out1, z0, z1, z2) → f126_out1
U39(z0, f157_out1, z1, z2) → f126_out2
U39(z0, f157_out2, z1, z2) → f126_out3
f127_in(z0, z1) → U40(f129_in(z0, z1), f131_in(z0, z1), z0, z1)
U40(f129_out1, z0, z1, z2) → f127_out1
U40(z0, f131_out1, z1, z2) → f127_out2
U40(z0, f131_out2, z1, z2) → f127_out3
f131_in(z0, z1) → U41(f138_in(z0, z1), f139_in(z0, z1), z0, z1)
U41(f138_out1, z0, z1, z2) → f131_out1
U41(z0, f139_out1, z1, z2) → f131_out2
f157_in(z0, z1) → U42(f183_in(z0, z1), f184_in(z0, z1), z0, z1)
U42(f183_out1, z0, z1, z2) → f157_out1
U42(z0, f184_out1, z1, z2) → f157_out2

Tuples:

F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0))
F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43
F54_IN(z0, tree(z1, void, z2)) → c48
F129_IN(z0, z1) → c52
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F18_IN(z0) → c58
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c
F54_IN(z0, tree(z1, z2, z3)) → c

S tuples:

F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0))
F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43
F54_IN(z0, tree(z1, void, z2)) → c48
F129_IN(z0, z1) → c52
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F18_IN(z0) → c58
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c
F54_IN(z0, tree(z1, z2, z3)) → c

K tuples:

U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f295_in, U5, f44_in, U6, f70_in, U7, U8, U9, f191_in, U10, f156_in, U11, U12, f54_in, U13, U14, f129_in, U15, f183_in, U16, f184_in, U17, f18_in, U18, f101_in, U19, f102_in, U20, f138_in, U21, f139_in, U22, f36_in, U23, f38_in, U24, f42_in, U25, U26, f111_in, U27, U28, f142_in, U29, U30, f189_in, U31, U32, f310_in, U33, U34, f15_in, U35, f16_in, U36, f19_in, U37, f55_in, U38, f126_in, U39, f127_in, U40, f131_in, U41, f157_in, U42

Defined Pair Symbols:

F42_IN, F111_IN, F142_IN, F189_IN, F310_IN, F191_IN, F156_IN, F54_IN, F1_IN, F295_IN, F44_IN, F70_IN, F129_IN, F183_IN, F184_IN, F18_IN, F101_IN, F102_IN, F138_IN, F139_IN, F36_IN, F38_IN, U25', U27', U29', U31', U33', F15_IN, F16_IN, F19_IN, F55_IN, F126_IN, F127_IN, F131_IN, F157_IN

Compound Symbols:

c72, c75, c78, c81, c84, c, c2, c3, c5, c6, c20, c22, c25, c27, c28, c43, c48, c52, c54, c56, c58, c60, c62, c64, c66, c68, c70, c73, c76, c79, c82, c85, c87, c91, c95, c98, c101, c105, c109, c112, c

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

Use narrowing to replace F42_IN(z0) → c72(U25'(f44_in(z0), z0), F44_IN(z0)) by

F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, z1)) → f1_out1
f1_in(z0, tree(z0, void, void)) → f1_out1
f1_in(z0, tree(z0, void, void)) → U1(f16_in(z0), z0, tree(z0, void, void))
f1_in(z0, tree(z0, void, z1)) → U2(f15_in(z0, z1), z0, tree(z0, void, z1))
f1_in(z0, tree(z0, z1, void)) → f1_out1
f1_in(z0, tree(z0, z1, void)) → U3(f127_in(z0, z1), z0, tree(z0, z1, void))
f1_in(z0, z1) → U4(f126_in(z0, z1), z0, z1)
U1(f16_out1, z0, tree(z0, void, void)) → f1_out1
U1(f16_out2, z0, tree(z0, void, void)) → f1_out1
U1(f16_out3, z0, tree(z0, void, void)) → f1_out1
U2(f15_out1, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out2, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out3, z0, tree(z0, void, z1)) → f1_out1
U3(f127_out1, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out2, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out3, z0, tree(z0, z1, void)) → f1_out1
U4(f126_out1, z0, z1) → f1_out1
U4(f126_out2, z0, z1) → f1_out1
U4(f126_out3, z0, z1) → f1_out1
f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1
f70_in(tree(z0, void, z1)) → f70_out1(z0)
f70_in(tree(z0, void, z1)) → U7(f25_in, tree(z0, void, z1))
f70_in(tree(z0, tree(z1, void, z2), z3)) → f70_out1(z1)
f70_in(tree(z0, tree(z1, void, z2), z3)) → U8(f25_in, tree(z0, tree(z1, void, z2), z3))
f70_in(tree(z0, tree(z1, z2, z3), z4)) → U9(f70_in(z2), tree(z0, tree(z1, z2, z3), z4))
U7(f25_out1(z0), tree(z1, void, z2)) → f70_out1(z0)
U8(f25_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f70_out1(z0)
U9(f70_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f70_out1(z0)
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → f156_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f25_in, z0, tree(z0, z1, tree(z2, void, z3)))
f156_in(z0, tree(z0, z1, tree(z2, z3, z4))) → U12(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4)))
U11(f25_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f156_out1
U12(f70_out1(z0), z1, tree(z1, z2, tree(z3, z4, z5))) → f156_out1
f54_in(z0, tree(z1, void, z2)) → f54_out1
f54_in(z0, tree(z1, void, z2)) → U13(f25_in, z0, tree(z1, void, z2))
f54_in(z0, tree(z1, z2, z3)) → U14(f70_in(z2), z0, tree(z1, z2, z3))
U13(f25_out1(z0), z1, tree(z2, void, z3)) → f54_out1
U14(f70_out1(z0), z1, tree(z2, z3, z4)) → f54_out1
f129_in(z0, z1) → U15(f25_in, z0, z1)
U15(f25_out1(z0), z1, z2) → f129_out1
f183_in(z0, tree(z1, z2, z3)) → U16(f189_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f189_out1, z0, tree(z1, z2, z3)) → f183_out1
f184_in(z0, tree(z1, z2, z3)) → U17(f310_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f310_out1, z0, tree(z1, z2, z3)) → f184_out1
f18_in(z0) → U18(f25_in, z0)
U18(f25_out1(z0), z1) → f18_out1
f101_in(z0, z1) → U19(f42_in(z0), z0, z1)
U19(f42_out1, z0, z1) → f101_out1
f102_in(z0, z1) → U20(f111_in(z0, z1), z0, z1)
U20(f111_out1, z0, z1) → f102_out1
f138_in(z0, z1) → U21(f142_in(z0, z1), z0, z1)
U21(f142_out1, z0, z1) → f138_out1
f139_in(z0, z1) → U22(f42_in(z0), z0, z1)
U22(f42_out1, z0, z1) → f139_out1
f36_in(z0) → U23(f42_in(z0), z0)
U23(f42_out1, z0) → f36_out1
f38_in(z0) → U24(f42_in(z0), z0)
U24(f42_out1, z0) → f38_out1
f42_in(z0) → U25(f44_in(z0), z0)
U25(f44_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1, z0) → f42_out1
f111_in(z0, z1) → U27(f44_in(z0), z0, z1)
U27(f44_out1, z0, z1) → U28(f1_in(z0, z1), z0, z1)
U28(f1_out1, z0, z1) → f111_out1
f142_in(z0, z1) → U29(f44_in(z0), z0, z1)
U29(f44_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1, z0, z1) → f142_out1
f189_in(z0, z1, z2) → U31(f191_in(z0, z1), z0, z1, z2)
U31(f191_out1, z0, z1, z2) → U32(f1_in(z0, z2), z0, z1, z2)
U32(f1_out1, z0, z1, z2) → f189_out1
f310_in(z0, z1, z2) → U33(f295_in(z0, z1), z0, z1, z2)
U33(f295_out1, z0, z1, z2) → U34(f1_in(z1, z2), z0, z1, z2)
U34(f1_out1, z0, z1, z2) → f310_out1
f15_in(z0, z1) → U35(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U35(f54_out1, z0, z1, z2) → f15_out1
U35(z0, f55_out1, z1, z2) → f15_out2
U35(z0, f55_out2, z1, z2) → f15_out3
f16_in(z0) → U36(f18_in(z0), f19_in(z0), z0)
U36(f18_out1, z0, z1) → f16_out1
U36(z0, f19_out1, z1) → f16_out2
U36(z0, f19_out2, z1) → f16_out3
f19_in(z0) → U37(f36_in(z0), f38_in(z0), z0)
U37(f36_out1, z0, z1) → f19_out1
U37(z0, f38_out1, z1) → f19_out2
f55_in(z0, z1) → U38(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U38(f101_out1, z0, z1, z2) → f55_out1
U38(z0, f102_out1, z1, z2) → f55_out2
f126_in(z0, z1) → U39(f156_in(z0, z1), f157_in(z0, z1), z0, z1)
U39(f156_out1, z0, z1, z2) → f126_out1
U39(z0, f157_out1, z1, z2) → f126_out2
U39(z0, f157_out2, z1, z2) → f126_out3
f127_in(z0, z1) → U40(f129_in(z0, z1), f131_in(z0, z1), z0, z1)
U40(f129_out1, z0, z1, z2) → f127_out1
U40(z0, f131_out1, z1, z2) → f127_out2
U40(z0, f131_out2, z1, z2) → f127_out3
f131_in(z0, z1) → U41(f138_in(z0, z1), f139_in(z0, z1), z0, z1)
U41(f138_out1, z0, z1, z2) → f131_out1
U41(z0, f139_out1, z1, z2) → f131_out2
f157_in(z0, z1) → U42(f183_in(z0, z1), f184_in(z0, z1), z0, z1)
U42(f183_out1, z0, z1, z2) → f157_out1
U42(z0, f184_out1, z1, z2) → f157_out2

Tuples:

F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43
F54_IN(z0, tree(z1, void, z2)) → c48
F129_IN(z0, z1) → c52
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F18_IN(z0) → c58
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c
F54_IN(z0, tree(z1, z2, z3)) → c
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))

S tuples:

F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, void, z1)) → c25
F70_IN(tree(z0, tree(z1, void, z2), z3)) → c27
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F156_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c43
F54_IN(z0, tree(z1, void, z2)) → c48
F129_IN(z0, z1) → c52
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F18_IN(z0) → c58
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c
F54_IN(z0, tree(z1, z2, z3)) → c
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))

K tuples:

U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f295_in, U5, f44_in, U6, f70_in, U7, U8, U9, f191_in, U10, f156_in, U11, U12, f54_in, U13, U14, f129_in, U15, f183_in, U16, f184_in, U17, f18_in, U18, f101_in, U19, f102_in, U20, f138_in, U21, f139_in, U22, f36_in, U23, f38_in, U24, f42_in, U25, U26, f111_in, U27, U28, f142_in, U29, U30, f189_in, U31, U32, f310_in, U33, U34, f15_in, U35, f16_in, U36, f19_in, U37, f55_in, U38, f126_in, U39, f127_in, U40, f131_in, U41, f157_in, U42

Defined Pair Symbols:

F111_IN, F142_IN, F189_IN, F310_IN, F191_IN, F156_IN, F54_IN, F1_IN, F295_IN, F44_IN, F70_IN, F129_IN, F183_IN, F184_IN, F18_IN, F101_IN, F102_IN, F138_IN, F139_IN, F36_IN, F38_IN, U25', U27', U29', U31', U33', F15_IN, F16_IN, F19_IN, F55_IN, F126_IN, F127_IN, F131_IN, F157_IN, F42_IN

Compound Symbols:

c75, c78, c81, c84, c, c2, c3, c5, c6, c20, c22, c25, c27, c28, c43, c48, c52, c54, c56, c58, c60, c62, c64, c66, c68, c70, c73, c76, c79, c82, c85, c87, c91, c95, c98, c101, c105, c109, c112, c, c72

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

Split RHS of tuples not part of any SCC

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, z1)) → f1_out1
f1_in(z0, tree(z0, void, void)) → f1_out1
f1_in(z0, tree(z0, void, void)) → U1(f16_in(z0), z0, tree(z0, void, void))
f1_in(z0, tree(z0, void, z1)) → U2(f15_in(z0, z1), z0, tree(z0, void, z1))
f1_in(z0, tree(z0, z1, void)) → f1_out1
f1_in(z0, tree(z0, z1, void)) → U3(f127_in(z0, z1), z0, tree(z0, z1, void))
f1_in(z0, z1) → U4(f126_in(z0, z1), z0, z1)
U1(f16_out1, z0, tree(z0, void, void)) → f1_out1
U1(f16_out2, z0, tree(z0, void, void)) → f1_out1
U1(f16_out3, z0, tree(z0, void, void)) → f1_out1
U2(f15_out1, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out2, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out3, z0, tree(z0, void, z1)) → f1_out1
U3(f127_out1, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out2, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out3, z0, tree(z0, z1, void)) → f1_out1
U4(f126_out1, z0, z1) → f1_out1
U4(f126_out2, z0, z1) → f1_out1
U4(f126_out3, z0, z1) → f1_out1
f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1
f70_in(tree(z0, void, z1)) → f70_out1(z0)
f70_in(tree(z0, void, z1)) → U7(f25_in, tree(z0, void, z1))
f70_in(tree(z0, tree(z1, void, z2), z3)) → f70_out1(z1)
f70_in(tree(z0, tree(z1, void, z2), z3)) → U8(f25_in, tree(z0, tree(z1, void, z2), z3))
f70_in(tree(z0, tree(z1, z2, z3), z4)) → U9(f70_in(z2), tree(z0, tree(z1, z2, z3), z4))
U7(f25_out1(z0), tree(z1, void, z2)) → f70_out1(z0)
U8(f25_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f70_out1(z0)
U9(f70_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f70_out1(z0)
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → f156_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f25_in, z0, tree(z0, z1, tree(z2, void, z3)))
f156_in(z0, tree(z0, z1, tree(z2, z3, z4))) → U12(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4)))
U11(f25_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f156_out1
U12(f70_out1(z0), z1, tree(z1, z2, tree(z3, z4, z5))) → f156_out1
f54_in(z0, tree(z1, void, z2)) → f54_out1
f54_in(z0, tree(z1, void, z2)) → U13(f25_in, z0, tree(z1, void, z2))
f54_in(z0, tree(z1, z2, z3)) → U14(f70_in(z2), z0, tree(z1, z2, z3))
U13(f25_out1(z0), z1, tree(z2, void, z3)) → f54_out1
U14(f70_out1(z0), z1, tree(z2, z3, z4)) → f54_out1
f129_in(z0, z1) → U15(f25_in, z0, z1)
U15(f25_out1(z0), z1, z2) → f129_out1
f183_in(z0, tree(z1, z2, z3)) → U16(f189_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f189_out1, z0, tree(z1, z2, z3)) → f183_out1
f184_in(z0, tree(z1, z2, z3)) → U17(f310_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f310_out1, z0, tree(z1, z2, z3)) → f184_out1
f18_in(z0) → U18(f25_in, z0)
U18(f25_out1(z0), z1) → f18_out1
f101_in(z0, z1) → U19(f42_in(z0), z0, z1)
U19(f42_out1, z0, z1) → f101_out1
f102_in(z0, z1) → U20(f111_in(z0, z1), z0, z1)
U20(f111_out1, z0, z1) → f102_out1
f138_in(z0, z1) → U21(f142_in(z0, z1), z0, z1)
U21(f142_out1, z0, z1) → f138_out1
f139_in(z0, z1) → U22(f42_in(z0), z0, z1)
U22(f42_out1, z0, z1) → f139_out1
f36_in(z0) → U23(f42_in(z0), z0)
U23(f42_out1, z0) → f36_out1
f38_in(z0) → U24(f42_in(z0), z0)
U24(f42_out1, z0) → f38_out1
f42_in(z0) → U25(f44_in(z0), z0)
U25(f44_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1, z0) → f42_out1
f111_in(z0, z1) → U27(f44_in(z0), z0, z1)
U27(f44_out1, z0, z1) → U28(f1_in(z0, z1), z0, z1)
U28(f1_out1, z0, z1) → f111_out1
f142_in(z0, z1) → U29(f44_in(z0), z0, z1)
U29(f44_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1, z0, z1) → f142_out1
f189_in(z0, z1, z2) → U31(f191_in(z0, z1), z0, z1, z2)
U31(f191_out1, z0, z1, z2) → U32(f1_in(z0, z2), z0, z1, z2)
U32(f1_out1, z0, z1, z2) → f189_out1
f310_in(z0, z1, z2) → U33(f295_in(z0, z1), z0, z1, z2)
U33(f295_out1, z0, z1, z2) → U34(f1_in(z1, z2), z0, z1, z2)
U34(f1_out1, z0, z1, z2) → f310_out1
f15_in(z0, z1) → U35(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U35(f54_out1, z0, z1, z2) → f15_out1
U35(z0, f55_out1, z1, z2) → f15_out2
U35(z0, f55_out2, z1, z2) → f15_out3
f16_in(z0) → U36(f18_in(z0), f19_in(z0), z0)
U36(f18_out1, z0, z1) → f16_out1
U36(z0, f19_out1, z1) → f16_out2
U36(z0, f19_out2, z1) → f16_out3
f19_in(z0) → U37(f36_in(z0), f38_in(z0), z0)
U37(f36_out1, z0, z1) → f19_out1
U37(z0, f38_out1, z1) → f19_out2
f55_in(z0, z1) → U38(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U38(f101_out1, z0, z1, z2) → f55_out1
U38(z0, f102_out1, z1, z2) → f55_out2
f126_in(z0, z1) → U39(f156_in(z0, z1), f157_in(z0, z1), z0, z1)
U39(f156_out1, z0, z1, z2) → f126_out1
U39(z0, f157_out1, z1, z2) → f126_out2
U39(z0, f157_out2, z1, z2) → f126_out3
f127_in(z0, z1) → U40(f129_in(z0, z1), f131_in(z0, z1), z0, z1)
U40(f129_out1, z0, z1, z2) → f127_out1
U40(z0, f131_out1, z1, z2) → f127_out2
U40(z0, f131_out2, z1, z2) → f127_out3
f131_in(z0, z1) → U41(f138_in(z0, z1), f139_in(z0, z1), z0, z1)
U41(f138_out1, z0, z1, z2) → f131_out1
U41(z0, f139_out1, z1, z2) → f131_out2
f157_in(z0, z1) → U42(f183_in(z0, z1), f184_in(z0, z1), z0, z1)
U42(f183_out1, z0, z1, z2) → f157_out1
U42(z0, f184_out1, z1, z2) → f157_out2

Tuples:

F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))

S tuples:

F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F16_IN(z0) → c91(F18_IN(z0), F19_IN(z0))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F127_IN(z0, z1) → c105(F129_IN(z0, z1), F131_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))

K tuples:

U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f295_in, U5, f44_in, U6, f70_in, U7, U8, U9, f191_in, U10, f156_in, U11, U12, f54_in, U13, U14, f129_in, U15, f183_in, U16, f184_in, U17, f18_in, U18, f101_in, U19, f102_in, U20, f138_in, U21, f139_in, U22, f36_in, U23, f38_in, U24, f42_in, U25, U26, f111_in, U27, U28, f142_in, U29, U30, f189_in, U31, U32, f310_in, U33, U34, f15_in, U35, f16_in, U36, f19_in, U37, f55_in, U38, f126_in, U39, f127_in, U40, f131_in, U41, f157_in, U42

Defined Pair Symbols:

F111_IN, F142_IN, F189_IN, F310_IN, F191_IN, F156_IN, F54_IN, F1_IN, F295_IN, F44_IN, F70_IN, F183_IN, F184_IN, F101_IN, F102_IN, F138_IN, F139_IN, F36_IN, F38_IN, U25', U27', U29', U31', U33', F15_IN, F16_IN, F19_IN, F55_IN, F126_IN, F127_IN, F131_IN, F157_IN, F42_IN

Compound Symbols:

c75, c78, c81, c84, c, c2, c3, c5, c6, c20, c22, c28, c54, c56, c60, c62, c64, c66, c68, c70, c73, c76, c79, c82, c85, c87, c91, c95, c98, c101, c105, c109, c112, c72

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

Removed 2 trailing tuple parts

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, z1)) → f1_out1
f1_in(z0, tree(z0, void, void)) → f1_out1
f1_in(z0, tree(z0, void, void)) → U1(f16_in(z0), z0, tree(z0, void, void))
f1_in(z0, tree(z0, void, z1)) → U2(f15_in(z0, z1), z0, tree(z0, void, z1))
f1_in(z0, tree(z0, z1, void)) → f1_out1
f1_in(z0, tree(z0, z1, void)) → U3(f127_in(z0, z1), z0, tree(z0, z1, void))
f1_in(z0, z1) → U4(f126_in(z0, z1), z0, z1)
U1(f16_out1, z0, tree(z0, void, void)) → f1_out1
U1(f16_out2, z0, tree(z0, void, void)) → f1_out1
U1(f16_out3, z0, tree(z0, void, void)) → f1_out1
U2(f15_out1, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out2, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out3, z0, tree(z0, void, z1)) → f1_out1
U3(f127_out1, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out2, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out3, z0, tree(z0, z1, void)) → f1_out1
U4(f126_out1, z0, z1) → f1_out1
U4(f126_out2, z0, z1) → f1_out1
U4(f126_out3, z0, z1) → f1_out1
f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1
f70_in(tree(z0, void, z1)) → f70_out1(z0)
f70_in(tree(z0, void, z1)) → U7(f25_in, tree(z0, void, z1))
f70_in(tree(z0, tree(z1, void, z2), z3)) → f70_out1(z1)
f70_in(tree(z0, tree(z1, void, z2), z3)) → U8(f25_in, tree(z0, tree(z1, void, z2), z3))
f70_in(tree(z0, tree(z1, z2, z3), z4)) → U9(f70_in(z2), tree(z0, tree(z1, z2, z3), z4))
U7(f25_out1(z0), tree(z1, void, z2)) → f70_out1(z0)
U8(f25_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f70_out1(z0)
U9(f70_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f70_out1(z0)
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → f156_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f25_in, z0, tree(z0, z1, tree(z2, void, z3)))
f156_in(z0, tree(z0, z1, tree(z2, z3, z4))) → U12(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4)))
U11(f25_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f156_out1
U12(f70_out1(z0), z1, tree(z1, z2, tree(z3, z4, z5))) → f156_out1
f54_in(z0, tree(z1, void, z2)) → f54_out1
f54_in(z0, tree(z1, void, z2)) → U13(f25_in, z0, tree(z1, void, z2))
f54_in(z0, tree(z1, z2, z3)) → U14(f70_in(z2), z0, tree(z1, z2, z3))
U13(f25_out1(z0), z1, tree(z2, void, z3)) → f54_out1
U14(f70_out1(z0), z1, tree(z2, z3, z4)) → f54_out1
f129_in(z0, z1) → U15(f25_in, z0, z1)
U15(f25_out1(z0), z1, z2) → f129_out1
f183_in(z0, tree(z1, z2, z3)) → U16(f189_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f189_out1, z0, tree(z1, z2, z3)) → f183_out1
f184_in(z0, tree(z1, z2, z3)) → U17(f310_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f310_out1, z0, tree(z1, z2, z3)) → f184_out1
f18_in(z0) → U18(f25_in, z0)
U18(f25_out1(z0), z1) → f18_out1
f101_in(z0, z1) → U19(f42_in(z0), z0, z1)
U19(f42_out1, z0, z1) → f101_out1
f102_in(z0, z1) → U20(f111_in(z0, z1), z0, z1)
U20(f111_out1, z0, z1) → f102_out1
f138_in(z0, z1) → U21(f142_in(z0, z1), z0, z1)
U21(f142_out1, z0, z1) → f138_out1
f139_in(z0, z1) → U22(f42_in(z0), z0, z1)
U22(f42_out1, z0, z1) → f139_out1
f36_in(z0) → U23(f42_in(z0), z0)
U23(f42_out1, z0) → f36_out1
f38_in(z0) → U24(f42_in(z0), z0)
U24(f42_out1, z0) → f38_out1
f42_in(z0) → U25(f44_in(z0), z0)
U25(f44_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1, z0) → f42_out1
f111_in(z0, z1) → U27(f44_in(z0), z0, z1)
U27(f44_out1, z0, z1) → U28(f1_in(z0, z1), z0, z1)
U28(f1_out1, z0, z1) → f111_out1
f142_in(z0, z1) → U29(f44_in(z0), z0, z1)
U29(f44_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1, z0, z1) → f142_out1
f189_in(z0, z1, z2) → U31(f191_in(z0, z1), z0, z1, z2)
U31(f191_out1, z0, z1, z2) → U32(f1_in(z0, z2), z0, z1, z2)
U32(f1_out1, z0, z1, z2) → f189_out1
f310_in(z0, z1, z2) → U33(f295_in(z0, z1), z0, z1, z2)
U33(f295_out1, z0, z1, z2) → U34(f1_in(z1, z2), z0, z1, z2)
U34(f1_out1, z0, z1, z2) → f310_out1
f15_in(z0, z1) → U35(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U35(f54_out1, z0, z1, z2) → f15_out1
U35(z0, f55_out1, z1, z2) → f15_out2
U35(z0, f55_out2, z1, z2) → f15_out3
f16_in(z0) → U36(f18_in(z0), f19_in(z0), z0)
U36(f18_out1, z0, z1) → f16_out1
U36(z0, f19_out1, z1) → f16_out2
U36(z0, f19_out2, z1) → f16_out3
f19_in(z0) → U37(f36_in(z0), f38_in(z0), z0)
U37(f36_out1, z0, z1) → f19_out1
U37(z0, f38_out1, z1) → f19_out2
f55_in(z0, z1) → U38(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U38(f101_out1, z0, z1, z2) → f55_out1
U38(z0, f102_out1, z1, z2) → f55_out2
f126_in(z0, z1) → U39(f156_in(z0, z1), f157_in(z0, z1), z0, z1)
U39(f156_out1, z0, z1, z2) → f126_out1
U39(z0, f157_out1, z1, z2) → f126_out2
U39(z0, f157_out2, z1, z2) → f126_out3
f127_in(z0, z1) → U40(f129_in(z0, z1), f131_in(z0, z1), z0, z1)
U40(f129_out1, z0, z1, z2) → f127_out1
U40(z0, f131_out1, z1, z2) → f127_out2
U40(z0, f131_out2, z1, z2) → f127_out3
f131_in(z0, z1) → U41(f138_in(z0, z1), f139_in(z0, z1), z0, z1)
U41(f138_out1, z0, z1, z2) → f131_out1
U41(z0, f139_out1, z1, z2) → f131_out2
f157_in(z0, z1) → U42(f183_in(z0, z1), f184_in(z0, z1), z0, z1)
U42(f183_out1, z0, z1, z2) → f157_out1
U42(z0, f184_out1, z1, z2) → f157_out2

Tuples:

F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))
F16_IN(z0) → c91(F19_IN(z0))
F127_IN(z0, z1) → c105(F131_IN(z0, z1))

S tuples:

F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0))
F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))
F16_IN(z0) → c91(F19_IN(z0))
F127_IN(z0, z1) → c105(F131_IN(z0, z1))

K tuples:

U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f295_in, U5, f44_in, U6, f70_in, U7, U8, U9, f191_in, U10, f156_in, U11, U12, f54_in, U13, U14, f129_in, U15, f183_in, U16, f184_in, U17, f18_in, U18, f101_in, U19, f102_in, U20, f138_in, U21, f139_in, U22, f36_in, U23, f38_in, U24, f42_in, U25, U26, f111_in, U27, U28, f142_in, U29, U30, f189_in, U31, U32, f310_in, U33, U34, f15_in, U35, f16_in, U36, f19_in, U37, f55_in, U38, f126_in, U39, f127_in, U40, f131_in, U41, f157_in, U42

Defined Pair Symbols:

F111_IN, F142_IN, F189_IN, F310_IN, F191_IN, F156_IN, F54_IN, F1_IN, F295_IN, F44_IN, F70_IN, F183_IN, F184_IN, F101_IN, F102_IN, F138_IN, F139_IN, F36_IN, F38_IN, U25', U27', U29', U31', U33', F15_IN, F19_IN, F55_IN, F126_IN, F131_IN, F157_IN, F42_IN, F16_IN, F127_IN

Compound Symbols:

c75, c78, c81, c84, c, c2, c3, c5, c6, c20, c22, c28, c54, c56, c60, c62, c64, c66, c68, c70, c73, c76, c79, c82, c85, c87, c95, c98, c101, c109, c112, c72, c91, c105

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

Use narrowing to replace F111_IN(z0, z1) → c75(U27'(f44_in(z0), z0, z1), F44_IN(z0)) by

F111_IN(s(z0), x1) → c75(U27'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, z1)) → f1_out1
f1_in(z0, tree(z0, void, void)) → f1_out1
f1_in(z0, tree(z0, void, void)) → U1(f16_in(z0), z0, tree(z0, void, void))
f1_in(z0, tree(z0, void, z1)) → U2(f15_in(z0, z1), z0, tree(z0, void, z1))
f1_in(z0, tree(z0, z1, void)) → f1_out1
f1_in(z0, tree(z0, z1, void)) → U3(f127_in(z0, z1), z0, tree(z0, z1, void))
f1_in(z0, z1) → U4(f126_in(z0, z1), z0, z1)
U1(f16_out1, z0, tree(z0, void, void)) → f1_out1
U1(f16_out2, z0, tree(z0, void, void)) → f1_out1
U1(f16_out3, z0, tree(z0, void, void)) → f1_out1
U2(f15_out1, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out2, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out3, z0, tree(z0, void, z1)) → f1_out1
U3(f127_out1, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out2, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out3, z0, tree(z0, z1, void)) → f1_out1
U4(f126_out1, z0, z1) → f1_out1
U4(f126_out2, z0, z1) → f1_out1
U4(f126_out3, z0, z1) → f1_out1
f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1
f70_in(tree(z0, void, z1)) → f70_out1(z0)
f70_in(tree(z0, void, z1)) → U7(f25_in, tree(z0, void, z1))
f70_in(tree(z0, tree(z1, void, z2), z3)) → f70_out1(z1)
f70_in(tree(z0, tree(z1, void, z2), z3)) → U8(f25_in, tree(z0, tree(z1, void, z2), z3))
f70_in(tree(z0, tree(z1, z2, z3), z4)) → U9(f70_in(z2), tree(z0, tree(z1, z2, z3), z4))
U7(f25_out1(z0), tree(z1, void, z2)) → f70_out1(z0)
U8(f25_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f70_out1(z0)
U9(f70_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f70_out1(z0)
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → f156_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f25_in, z0, tree(z0, z1, tree(z2, void, z3)))
f156_in(z0, tree(z0, z1, tree(z2, z3, z4))) → U12(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4)))
U11(f25_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f156_out1
U12(f70_out1(z0), z1, tree(z1, z2, tree(z3, z4, z5))) → f156_out1
f54_in(z0, tree(z1, void, z2)) → f54_out1
f54_in(z0, tree(z1, void, z2)) → U13(f25_in, z0, tree(z1, void, z2))
f54_in(z0, tree(z1, z2, z3)) → U14(f70_in(z2), z0, tree(z1, z2, z3))
U13(f25_out1(z0), z1, tree(z2, void, z3)) → f54_out1
U14(f70_out1(z0), z1, tree(z2, z3, z4)) → f54_out1
f129_in(z0, z1) → U15(f25_in, z0, z1)
U15(f25_out1(z0), z1, z2) → f129_out1
f183_in(z0, tree(z1, z2, z3)) → U16(f189_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f189_out1, z0, tree(z1, z2, z3)) → f183_out1
f184_in(z0, tree(z1, z2, z3)) → U17(f310_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f310_out1, z0, tree(z1, z2, z3)) → f184_out1
f18_in(z0) → U18(f25_in, z0)
U18(f25_out1(z0), z1) → f18_out1
f101_in(z0, z1) → U19(f42_in(z0), z0, z1)
U19(f42_out1, z0, z1) → f101_out1
f102_in(z0, z1) → U20(f111_in(z0, z1), z0, z1)
U20(f111_out1, z0, z1) → f102_out1
f138_in(z0, z1) → U21(f142_in(z0, z1), z0, z1)
U21(f142_out1, z0, z1) → f138_out1
f139_in(z0, z1) → U22(f42_in(z0), z0, z1)
U22(f42_out1, z0, z1) → f139_out1
f36_in(z0) → U23(f42_in(z0), z0)
U23(f42_out1, z0) → f36_out1
f38_in(z0) → U24(f42_in(z0), z0)
U24(f42_out1, z0) → f38_out1
f42_in(z0) → U25(f44_in(z0), z0)
U25(f44_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1, z0) → f42_out1
f111_in(z0, z1) → U27(f44_in(z0), z0, z1)
U27(f44_out1, z0, z1) → U28(f1_in(z0, z1), z0, z1)
U28(f1_out1, z0, z1) → f111_out1
f142_in(z0, z1) → U29(f44_in(z0), z0, z1)
U29(f44_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1, z0, z1) → f142_out1
f189_in(z0, z1, z2) → U31(f191_in(z0, z1), z0, z1, z2)
U31(f191_out1, z0, z1, z2) → U32(f1_in(z0, z2), z0, z1, z2)
U32(f1_out1, z0, z1, z2) → f189_out1
f310_in(z0, z1, z2) → U33(f295_in(z0, z1), z0, z1, z2)
U33(f295_out1, z0, z1, z2) → U34(f1_in(z1, z2), z0, z1, z2)
U34(f1_out1, z0, z1, z2) → f310_out1
f15_in(z0, z1) → U35(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U35(f54_out1, z0, z1, z2) → f15_out1
U35(z0, f55_out1, z1, z2) → f15_out2
U35(z0, f55_out2, z1, z2) → f15_out3
f16_in(z0) → U36(f18_in(z0), f19_in(z0), z0)
U36(f18_out1, z0, z1) → f16_out1
U36(z0, f19_out1, z1) → f16_out2
U36(z0, f19_out2, z1) → f16_out3
f19_in(z0) → U37(f36_in(z0), f38_in(z0), z0)
U37(f36_out1, z0, z1) → f19_out1
U37(z0, f38_out1, z1) → f19_out2
f55_in(z0, z1) → U38(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U38(f101_out1, z0, z1, z2) → f55_out1
U38(z0, f102_out1, z1, z2) → f55_out2
f126_in(z0, z1) → U39(f156_in(z0, z1), f157_in(z0, z1), z0, z1)
U39(f156_out1, z0, z1, z2) → f126_out1
U39(z0, f157_out1, z1, z2) → f126_out2
U39(z0, f157_out2, z1, z2) → f126_out3
f127_in(z0, z1) → U40(f129_in(z0, z1), f131_in(z0, z1), z0, z1)
U40(f129_out1, z0, z1, z2) → f127_out1
U40(z0, f131_out1, z1, z2) → f127_out2
U40(z0, f131_out2, z1, z2) → f127_out3
f131_in(z0, z1) → U41(f138_in(z0, z1), f139_in(z0, z1), z0, z1)
U41(f138_out1, z0, z1, z2) → f131_out1
U41(z0, f139_out1, z1, z2) → f131_out2
f157_in(z0, z1) → U42(f183_in(z0, z1), f184_in(z0, z1), z0, z1)
U42(f183_out1, z0, z1, z2) → f157_out1
U42(z0, f184_out1, z1, z2) → f157_out2

Tuples:

F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))
F16_IN(z0) → c91(F19_IN(z0))
F127_IN(z0, z1) → c105(F131_IN(z0, z1))
F111_IN(s(z0), x1) → c75(U27'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))

S tuples:

F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0))
F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))
F16_IN(z0) → c91(F19_IN(z0))
F127_IN(z0, z1) → c105(F131_IN(z0, z1))
F111_IN(s(z0), x1) → c75(U27'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))

K tuples:

U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f295_in, U5, f44_in, U6, f70_in, U7, U8, U9, f191_in, U10, f156_in, U11, U12, f54_in, U13, U14, f129_in, U15, f183_in, U16, f184_in, U17, f18_in, U18, f101_in, U19, f102_in, U20, f138_in, U21, f139_in, U22, f36_in, U23, f38_in, U24, f42_in, U25, U26, f111_in, U27, U28, f142_in, U29, U30, f189_in, U31, U32, f310_in, U33, U34, f15_in, U35, f16_in, U36, f19_in, U37, f55_in, U38, f126_in, U39, f127_in, U40, f131_in, U41, f157_in, U42

Defined Pair Symbols:

F142_IN, F189_IN, F310_IN, F191_IN, F156_IN, F54_IN, F1_IN, F295_IN, F44_IN, F70_IN, F183_IN, F184_IN, F101_IN, F102_IN, F138_IN, F139_IN, F36_IN, F38_IN, U25', U27', U29', U31', U33', F15_IN, F19_IN, F55_IN, F126_IN, F131_IN, F157_IN, F42_IN, F16_IN, F127_IN, F111_IN

Compound Symbols:

c78, c81, c84, c, c2, c3, c5, c6, c20, c22, c28, c54, c56, c60, c62, c64, c66, c68, c70, c73, c76, c79, c82, c85, c87, c95, c98, c101, c109, c112, c72, c91, c105, c75

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

Use narrowing to replace F142_IN(z0, z1) → c78(U29'(f44_in(z0), z0, z1), F44_IN(z0)) by

F142_IN(s(z0), x1) → c78(U29'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, z1)) → f1_out1
f1_in(z0, tree(z0, void, void)) → f1_out1
f1_in(z0, tree(z0, void, void)) → U1(f16_in(z0), z0, tree(z0, void, void))
f1_in(z0, tree(z0, void, z1)) → U2(f15_in(z0, z1), z0, tree(z0, void, z1))
f1_in(z0, tree(z0, z1, void)) → f1_out1
f1_in(z0, tree(z0, z1, void)) → U3(f127_in(z0, z1), z0, tree(z0, z1, void))
f1_in(z0, z1) → U4(f126_in(z0, z1), z0, z1)
U1(f16_out1, z0, tree(z0, void, void)) → f1_out1
U1(f16_out2, z0, tree(z0, void, void)) → f1_out1
U1(f16_out3, z0, tree(z0, void, void)) → f1_out1
U2(f15_out1, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out2, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out3, z0, tree(z0, void, z1)) → f1_out1
U3(f127_out1, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out2, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out3, z0, tree(z0, z1, void)) → f1_out1
U4(f126_out1, z0, z1) → f1_out1
U4(f126_out2, z0, z1) → f1_out1
U4(f126_out3, z0, z1) → f1_out1
f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1
f70_in(tree(z0, void, z1)) → f70_out1(z0)
f70_in(tree(z0, void, z1)) → U7(f25_in, tree(z0, void, z1))
f70_in(tree(z0, tree(z1, void, z2), z3)) → f70_out1(z1)
f70_in(tree(z0, tree(z1, void, z2), z3)) → U8(f25_in, tree(z0, tree(z1, void, z2), z3))
f70_in(tree(z0, tree(z1, z2, z3), z4)) → U9(f70_in(z2), tree(z0, tree(z1, z2, z3), z4))
U7(f25_out1(z0), tree(z1, void, z2)) → f70_out1(z0)
U8(f25_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f70_out1(z0)
U9(f70_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f70_out1(z0)
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → f156_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f25_in, z0, tree(z0, z1, tree(z2, void, z3)))
f156_in(z0, tree(z0, z1, tree(z2, z3, z4))) → U12(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4)))
U11(f25_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f156_out1
U12(f70_out1(z0), z1, tree(z1, z2, tree(z3, z4, z5))) → f156_out1
f54_in(z0, tree(z1, void, z2)) → f54_out1
f54_in(z0, tree(z1, void, z2)) → U13(f25_in, z0, tree(z1, void, z2))
f54_in(z0, tree(z1, z2, z3)) → U14(f70_in(z2), z0, tree(z1, z2, z3))
U13(f25_out1(z0), z1, tree(z2, void, z3)) → f54_out1
U14(f70_out1(z0), z1, tree(z2, z3, z4)) → f54_out1
f129_in(z0, z1) → U15(f25_in, z0, z1)
U15(f25_out1(z0), z1, z2) → f129_out1
f183_in(z0, tree(z1, z2, z3)) → U16(f189_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f189_out1, z0, tree(z1, z2, z3)) → f183_out1
f184_in(z0, tree(z1, z2, z3)) → U17(f310_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f310_out1, z0, tree(z1, z2, z3)) → f184_out1
f18_in(z0) → U18(f25_in, z0)
U18(f25_out1(z0), z1) → f18_out1
f101_in(z0, z1) → U19(f42_in(z0), z0, z1)
U19(f42_out1, z0, z1) → f101_out1
f102_in(z0, z1) → U20(f111_in(z0, z1), z0, z1)
U20(f111_out1, z0, z1) → f102_out1
f138_in(z0, z1) → U21(f142_in(z0, z1), z0, z1)
U21(f142_out1, z0, z1) → f138_out1
f139_in(z0, z1) → U22(f42_in(z0), z0, z1)
U22(f42_out1, z0, z1) → f139_out1
f36_in(z0) → U23(f42_in(z0), z0)
U23(f42_out1, z0) → f36_out1
f38_in(z0) → U24(f42_in(z0), z0)
U24(f42_out1, z0) → f38_out1
f42_in(z0) → U25(f44_in(z0), z0)
U25(f44_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1, z0) → f42_out1
f111_in(z0, z1) → U27(f44_in(z0), z0, z1)
U27(f44_out1, z0, z1) → U28(f1_in(z0, z1), z0, z1)
U28(f1_out1, z0, z1) → f111_out1
f142_in(z0, z1) → U29(f44_in(z0), z0, z1)
U29(f44_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1, z0, z1) → f142_out1
f189_in(z0, z1, z2) → U31(f191_in(z0, z1), z0, z1, z2)
U31(f191_out1, z0, z1, z2) → U32(f1_in(z0, z2), z0, z1, z2)
U32(f1_out1, z0, z1, z2) → f189_out1
f310_in(z0, z1, z2) → U33(f295_in(z0, z1), z0, z1, z2)
U33(f295_out1, z0, z1, z2) → U34(f1_in(z1, z2), z0, z1, z2)
U34(f1_out1, z0, z1, z2) → f310_out1
f15_in(z0, z1) → U35(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U35(f54_out1, z0, z1, z2) → f15_out1
U35(z0, f55_out1, z1, z2) → f15_out2
U35(z0, f55_out2, z1, z2) → f15_out3
f16_in(z0) → U36(f18_in(z0), f19_in(z0), z0)
U36(f18_out1, z0, z1) → f16_out1
U36(z0, f19_out1, z1) → f16_out2
U36(z0, f19_out2, z1) → f16_out3
f19_in(z0) → U37(f36_in(z0), f38_in(z0), z0)
U37(f36_out1, z0, z1) → f19_out1
U37(z0, f38_out1, z1) → f19_out2
f55_in(z0, z1) → U38(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U38(f101_out1, z0, z1, z2) → f55_out1
U38(z0, f102_out1, z1, z2) → f55_out2
f126_in(z0, z1) → U39(f156_in(z0, z1), f157_in(z0, z1), z0, z1)
U39(f156_out1, z0, z1, z2) → f126_out1
U39(z0, f157_out1, z1, z2) → f126_out2
U39(z0, f157_out2, z1, z2) → f126_out3
f127_in(z0, z1) → U40(f129_in(z0, z1), f131_in(z0, z1), z0, z1)
U40(f129_out1, z0, z1, z2) → f127_out1
U40(z0, f131_out1, z1, z2) → f127_out2
U40(z0, f131_out2, z1, z2) → f127_out3
f131_in(z0, z1) → U41(f138_in(z0, z1), f139_in(z0, z1), z0, z1)
U41(f138_out1, z0, z1, z2) → f131_out1
U41(z0, f139_out1, z1, z2) → f131_out2
f157_in(z0, z1) → U42(f183_in(z0, z1), f184_in(z0, z1), z0, z1)
U42(f183_out1, z0, z1, z2) → f157_out1
U42(z0, f184_out1, z1, z2) → f157_out2

Tuples:

F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))
F16_IN(z0) → c91(F19_IN(z0))
F127_IN(z0, z1) → c105(F131_IN(z0, z1))
F111_IN(s(z0), x1) → c75(U27'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F142_IN(s(z0), x1) → c78(U29'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))

S tuples:

F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1))
F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))
F16_IN(z0) → c91(F19_IN(z0))
F127_IN(z0, z1) → c105(F131_IN(z0, z1))
F111_IN(s(z0), x1) → c75(U27'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F142_IN(s(z0), x1) → c78(U29'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))

K tuples:

U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f295_in, U5, f44_in, U6, f70_in, U7, U8, U9, f191_in, U10, f156_in, U11, U12, f54_in, U13, U14, f129_in, U15, f183_in, U16, f184_in, U17, f18_in, U18, f101_in, U19, f102_in, U20, f138_in, U21, f139_in, U22, f36_in, U23, f38_in, U24, f42_in, U25, U26, f111_in, U27, U28, f142_in, U29, U30, f189_in, U31, U32, f310_in, U33, U34, f15_in, U35, f16_in, U36, f19_in, U37, f55_in, U38, f126_in, U39, f127_in, U40, f131_in, U41, f157_in, U42

Defined Pair Symbols:

F189_IN, F310_IN, F191_IN, F156_IN, F54_IN, F1_IN, F295_IN, F44_IN, F70_IN, F183_IN, F184_IN, F101_IN, F102_IN, F138_IN, F139_IN, F36_IN, F38_IN, U25', U27', U29', U31', U33', F15_IN, F19_IN, F55_IN, F126_IN, F131_IN, F157_IN, F42_IN, F16_IN, F127_IN, F111_IN, F142_IN

Compound Symbols:

c81, c84, c, c2, c3, c5, c6, c20, c22, c28, c54, c56, c60, c62, c64, c66, c68, c70, c73, c76, c79, c82, c85, c87, c95, c98, c101, c109, c112, c72, c91, c105, c75, c78

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

Use narrowing to replace F189_IN(z0, z1, z2) → c81(U31'(f191_in(z0, z1), z0, z1, z2), F191_IN(z0, z1)) by

F189_IN(0, s(z0), x2) → c81(U31'(f191_out1, 0, s(z0), x2), F191_IN(0, s(z0)))
F189_IN(s(0), s(s(z0)), x2) → c81(U31'(f191_out1, s(0), s(s(z0)), x2), F191_IN(s(0), s(s(z0))))
F189_IN(s(s(0)), s(s(s(z0))), x2) → c81(U31'(f191_out1, s(s(0)), s(s(s(z0))), x2), F191_IN(s(s(0)), s(s(s(z0)))))
F189_IN(s(s(s(0))), s(s(s(s(z0)))), x2) → c81(U31'(f191_out1, s(s(s(0))), s(s(s(s(z0)))), x2), F191_IN(s(s(s(0))), s(s(s(s(z0))))))
F189_IN(s(s(s(s(0)))), s(s(s(s(s(z0))))), x2) → c81(U31'(f191_out1, s(s(s(s(0)))), s(s(s(s(s(z0))))), x2), F191_IN(s(s(s(s(0)))), s(s(s(s(s(z0)))))))
F189_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2), F191_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))))
F189_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2), F191_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))))
F189_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2), F191_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))))
F189_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2) → c81(U31'(U10(f295_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), F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, z1)) → f1_out1
f1_in(z0, tree(z0, void, void)) → f1_out1
f1_in(z0, tree(z0, void, void)) → U1(f16_in(z0), z0, tree(z0, void, void))
f1_in(z0, tree(z0, void, z1)) → U2(f15_in(z0, z1), z0, tree(z0, void, z1))
f1_in(z0, tree(z0, z1, void)) → f1_out1
f1_in(z0, tree(z0, z1, void)) → U3(f127_in(z0, z1), z0, tree(z0, z1, void))
f1_in(z0, z1) → U4(f126_in(z0, z1), z0, z1)
U1(f16_out1, z0, tree(z0, void, void)) → f1_out1
U1(f16_out2, z0, tree(z0, void, void)) → f1_out1
U1(f16_out3, z0, tree(z0, void, void)) → f1_out1
U2(f15_out1, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out2, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out3, z0, tree(z0, void, z1)) → f1_out1
U3(f127_out1, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out2, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out3, z0, tree(z0, z1, void)) → f1_out1
U4(f126_out1, z0, z1) → f1_out1
U4(f126_out2, z0, z1) → f1_out1
U4(f126_out3, z0, z1) → f1_out1
f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1
f70_in(tree(z0, void, z1)) → f70_out1(z0)
f70_in(tree(z0, void, z1)) → U7(f25_in, tree(z0, void, z1))
f70_in(tree(z0, tree(z1, void, z2), z3)) → f70_out1(z1)
f70_in(tree(z0, tree(z1, void, z2), z3)) → U8(f25_in, tree(z0, tree(z1, void, z2), z3))
f70_in(tree(z0, tree(z1, z2, z3), z4)) → U9(f70_in(z2), tree(z0, tree(z1, z2, z3), z4))
U7(f25_out1(z0), tree(z1, void, z2)) → f70_out1(z0)
U8(f25_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f70_out1(z0)
U9(f70_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f70_out1(z0)
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → f156_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f25_in, z0, tree(z0, z1, tree(z2, void, z3)))
f156_in(z0, tree(z0, z1, tree(z2, z3, z4))) → U12(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4)))
U11(f25_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f156_out1
U12(f70_out1(z0), z1, tree(z1, z2, tree(z3, z4, z5))) → f156_out1
f54_in(z0, tree(z1, void, z2)) → f54_out1
f54_in(z0, tree(z1, void, z2)) → U13(f25_in, z0, tree(z1, void, z2))
f54_in(z0, tree(z1, z2, z3)) → U14(f70_in(z2), z0, tree(z1, z2, z3))
U13(f25_out1(z0), z1, tree(z2, void, z3)) → f54_out1
U14(f70_out1(z0), z1, tree(z2, z3, z4)) → f54_out1
f129_in(z0, z1) → U15(f25_in, z0, z1)
U15(f25_out1(z0), z1, z2) → f129_out1
f183_in(z0, tree(z1, z2, z3)) → U16(f189_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f189_out1, z0, tree(z1, z2, z3)) → f183_out1
f184_in(z0, tree(z1, z2, z3)) → U17(f310_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f310_out1, z0, tree(z1, z2, z3)) → f184_out1
f18_in(z0) → U18(f25_in, z0)
U18(f25_out1(z0), z1) → f18_out1
f101_in(z0, z1) → U19(f42_in(z0), z0, z1)
U19(f42_out1, z0, z1) → f101_out1
f102_in(z0, z1) → U20(f111_in(z0, z1), z0, z1)
U20(f111_out1, z0, z1) → f102_out1
f138_in(z0, z1) → U21(f142_in(z0, z1), z0, z1)
U21(f142_out1, z0, z1) → f138_out1
f139_in(z0, z1) → U22(f42_in(z0), z0, z1)
U22(f42_out1, z0, z1) → f139_out1
f36_in(z0) → U23(f42_in(z0), z0)
U23(f42_out1, z0) → f36_out1
f38_in(z0) → U24(f42_in(z0), z0)
U24(f42_out1, z0) → f38_out1
f42_in(z0) → U25(f44_in(z0), z0)
U25(f44_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1, z0) → f42_out1
f111_in(z0, z1) → U27(f44_in(z0), z0, z1)
U27(f44_out1, z0, z1) → U28(f1_in(z0, z1), z0, z1)
U28(f1_out1, z0, z1) → f111_out1
f142_in(z0, z1) → U29(f44_in(z0), z0, z1)
U29(f44_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1, z0, z1) → f142_out1
f189_in(z0, z1, z2) → U31(f191_in(z0, z1), z0, z1, z2)
U31(f191_out1, z0, z1, z2) → U32(f1_in(z0, z2), z0, z1, z2)
U32(f1_out1, z0, z1, z2) → f189_out1
f310_in(z0, z1, z2) → U33(f295_in(z0, z1), z0, z1, z2)
U33(f295_out1, z0, z1, z2) → U34(f1_in(z1, z2), z0, z1, z2)
U34(f1_out1, z0, z1, z2) → f310_out1
f15_in(z0, z1) → U35(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U35(f54_out1, z0, z1, z2) → f15_out1
U35(z0, f55_out1, z1, z2) → f15_out2
U35(z0, f55_out2, z1, z2) → f15_out3
f16_in(z0) → U36(f18_in(z0), f19_in(z0), z0)
U36(f18_out1, z0, z1) → f16_out1
U36(z0, f19_out1, z1) → f16_out2
U36(z0, f19_out2, z1) → f16_out3
f19_in(z0) → U37(f36_in(z0), f38_in(z0), z0)
U37(f36_out1, z0, z1) → f19_out1
U37(z0, f38_out1, z1) → f19_out2
f55_in(z0, z1) → U38(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U38(f101_out1, z0, z1, z2) → f55_out1
U38(z0, f102_out1, z1, z2) → f55_out2
f126_in(z0, z1) → U39(f156_in(z0, z1), f157_in(z0, z1), z0, z1)
U39(f156_out1, z0, z1, z2) → f126_out1
U39(z0, f157_out1, z1, z2) → f126_out2
U39(z0, f157_out2, z1, z2) → f126_out3
f127_in(z0, z1) → U40(f129_in(z0, z1), f131_in(z0, z1), z0, z1)
U40(f129_out1, z0, z1, z2) → f127_out1
U40(z0, f131_out1, z1, z2) → f127_out2
U40(z0, f131_out2, z1, z2) → f127_out3
f131_in(z0, z1) → U41(f138_in(z0, z1), f139_in(z0, z1), z0, z1)
U41(f138_out1, z0, z1, z2) → f131_out1
U41(z0, f139_out1, z1, z2) → f131_out2
f157_in(z0, z1) → U42(f183_in(z0, z1), f184_in(z0, z1), z0, z1)
U42(f183_out1, z0, z1, z2) → f157_out1
U42(z0, f184_out1, z1, z2) → f157_out2

Tuples:

F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))
F16_IN(z0) → c91(F19_IN(z0))
F127_IN(z0, z1) → c105(F131_IN(z0, z1))
F111_IN(s(z0), x1) → c75(U27'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F142_IN(s(z0), x1) → c78(U29'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F189_IN(0, s(z0), x2) → c81(U31'(f191_out1, 0, s(z0), x2), F191_IN(0, s(z0)))
F189_IN(s(0), s(s(z0)), x2) → c81(U31'(f191_out1, s(0), s(s(z0)), x2), F191_IN(s(0), s(s(z0))))
F189_IN(s(s(0)), s(s(s(z0))), x2) → c81(U31'(f191_out1, s(s(0)), s(s(s(z0))), x2), F191_IN(s(s(0)), s(s(s(z0)))))
F189_IN(s(s(s(0))), s(s(s(s(z0)))), x2) → c81(U31'(f191_out1, s(s(s(0))), s(s(s(s(z0)))), x2), F191_IN(s(s(s(0))), s(s(s(s(z0))))))
F189_IN(s(s(s(s(0)))), s(s(s(s(s(z0))))), x2) → c81(U31'(f191_out1, s(s(s(s(0)))), s(s(s(s(s(z0))))), x2), F191_IN(s(s(s(s(0)))), s(s(s(s(s(z0)))))))
F189_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2), F191_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))))
F189_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2), F191_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))))
F189_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2), F191_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))))
F189_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2) → c81(U31'(U10(f295_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), F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))

S tuples:

F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))
F16_IN(z0) → c91(F19_IN(z0))
F127_IN(z0, z1) → c105(F131_IN(z0, z1))
F111_IN(s(z0), x1) → c75(U27'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F142_IN(s(z0), x1) → c78(U29'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F189_IN(0, s(z0), x2) → c81(U31'(f191_out1, 0, s(z0), x2), F191_IN(0, s(z0)))
F189_IN(s(0), s(s(z0)), x2) → c81(U31'(f191_out1, s(0), s(s(z0)), x2), F191_IN(s(0), s(s(z0))))
F189_IN(s(s(0)), s(s(s(z0))), x2) → c81(U31'(f191_out1, s(s(0)), s(s(s(z0))), x2), F191_IN(s(s(0)), s(s(s(z0)))))
F189_IN(s(s(s(0))), s(s(s(s(z0)))), x2) → c81(U31'(f191_out1, s(s(s(0))), s(s(s(s(z0)))), x2), F191_IN(s(s(s(0))), s(s(s(s(z0))))))
F189_IN(s(s(s(s(0)))), s(s(s(s(s(z0))))), x2) → c81(U31'(f191_out1, s(s(s(s(0)))), s(s(s(s(s(z0))))), x2), F191_IN(s(s(s(s(0)))), s(s(s(s(s(z0)))))))
F189_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2), F191_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))))
F189_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2), F191_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))))
F189_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2), F191_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))))
F189_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2) → c81(U31'(U10(f295_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), F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))

K tuples:

U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f295_in, U5, f44_in, U6, f70_in, U7, U8, U9, f191_in, U10, f156_in, U11, U12, f54_in, U13, U14, f129_in, U15, f183_in, U16, f184_in, U17, f18_in, U18, f101_in, U19, f102_in, U20, f138_in, U21, f139_in, U22, f36_in, U23, f38_in, U24, f42_in, U25, U26, f111_in, U27, U28, f142_in, U29, U30, f189_in, U31, U32, f310_in, U33, U34, f15_in, U35, f16_in, U36, f19_in, U37, f55_in, U38, f126_in, U39, f127_in, U40, f131_in, U41, f157_in, U42

Defined Pair Symbols:

F310_IN, F191_IN, F156_IN, F54_IN, F1_IN, F295_IN, F44_IN, F70_IN, F183_IN, F184_IN, F101_IN, F102_IN, F138_IN, F139_IN, F36_IN, F38_IN, U25', U27', U29', U31', U33', F15_IN, F19_IN, F55_IN, F126_IN, F131_IN, F157_IN, F42_IN, F16_IN, F127_IN, F111_IN, F142_IN, F189_IN

Compound Symbols:

c84, c, c2, c3, c5, c6, c20, c22, c28, c54, c56, c60, c62, c64, c66, c68, c70, c73, c76, c79, c82, c85, c87, c95, c98, c101, c109, c112, c72, c91, c105, c75, c78, c81

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

Removed 8 trailing tuple parts

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, z1)) → f1_out1
f1_in(z0, tree(z0, void, void)) → f1_out1
f1_in(z0, tree(z0, void, void)) → U1(f16_in(z0), z0, tree(z0, void, void))
f1_in(z0, tree(z0, void, z1)) → U2(f15_in(z0, z1), z0, tree(z0, void, z1))
f1_in(z0, tree(z0, z1, void)) → f1_out1
f1_in(z0, tree(z0, z1, void)) → U3(f127_in(z0, z1), z0, tree(z0, z1, void))
f1_in(z0, z1) → U4(f126_in(z0, z1), z0, z1)
U1(f16_out1, z0, tree(z0, void, void)) → f1_out1
U1(f16_out2, z0, tree(z0, void, void)) → f1_out1
U1(f16_out3, z0, tree(z0, void, void)) → f1_out1
U2(f15_out1, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out2, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out3, z0, tree(z0, void, z1)) → f1_out1
U3(f127_out1, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out2, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out3, z0, tree(z0, z1, void)) → f1_out1
U4(f126_out1, z0, z1) → f1_out1
U4(f126_out2, z0, z1) → f1_out1
U4(f126_out3, z0, z1) → f1_out1
f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1
f70_in(tree(z0, void, z1)) → f70_out1(z0)
f70_in(tree(z0, void, z1)) → U7(f25_in, tree(z0, void, z1))
f70_in(tree(z0, tree(z1, void, z2), z3)) → f70_out1(z1)
f70_in(tree(z0, tree(z1, void, z2), z3)) → U8(f25_in, tree(z0, tree(z1, void, z2), z3))
f70_in(tree(z0, tree(z1, z2, z3), z4)) → U9(f70_in(z2), tree(z0, tree(z1, z2, z3), z4))
U7(f25_out1(z0), tree(z1, void, z2)) → f70_out1(z0)
U8(f25_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f70_out1(z0)
U9(f70_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f70_out1(z0)
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → f156_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f25_in, z0, tree(z0, z1, tree(z2, void, z3)))
f156_in(z0, tree(z0, z1, tree(z2, z3, z4))) → U12(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4)))
U11(f25_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f156_out1
U12(f70_out1(z0), z1, tree(z1, z2, tree(z3, z4, z5))) → f156_out1
f54_in(z0, tree(z1, void, z2)) → f54_out1
f54_in(z0, tree(z1, void, z2)) → U13(f25_in, z0, tree(z1, void, z2))
f54_in(z0, tree(z1, z2, z3)) → U14(f70_in(z2), z0, tree(z1, z2, z3))
U13(f25_out1(z0), z1, tree(z2, void, z3)) → f54_out1
U14(f70_out1(z0), z1, tree(z2, z3, z4)) → f54_out1
f129_in(z0, z1) → U15(f25_in, z0, z1)
U15(f25_out1(z0), z1, z2) → f129_out1
f183_in(z0, tree(z1, z2, z3)) → U16(f189_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f189_out1, z0, tree(z1, z2, z3)) → f183_out1
f184_in(z0, tree(z1, z2, z3)) → U17(f310_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f310_out1, z0, tree(z1, z2, z3)) → f184_out1
f18_in(z0) → U18(f25_in, z0)
U18(f25_out1(z0), z1) → f18_out1
f101_in(z0, z1) → U19(f42_in(z0), z0, z1)
U19(f42_out1, z0, z1) → f101_out1
f102_in(z0, z1) → U20(f111_in(z0, z1), z0, z1)
U20(f111_out1, z0, z1) → f102_out1
f138_in(z0, z1) → U21(f142_in(z0, z1), z0, z1)
U21(f142_out1, z0, z1) → f138_out1
f139_in(z0, z1) → U22(f42_in(z0), z0, z1)
U22(f42_out1, z0, z1) → f139_out1
f36_in(z0) → U23(f42_in(z0), z0)
U23(f42_out1, z0) → f36_out1
f38_in(z0) → U24(f42_in(z0), z0)
U24(f42_out1, z0) → f38_out1
f42_in(z0) → U25(f44_in(z0), z0)
U25(f44_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1, z0) → f42_out1
f111_in(z0, z1) → U27(f44_in(z0), z0, z1)
U27(f44_out1, z0, z1) → U28(f1_in(z0, z1), z0, z1)
U28(f1_out1, z0, z1) → f111_out1
f142_in(z0, z1) → U29(f44_in(z0), z0, z1)
U29(f44_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1, z0, z1) → f142_out1
f189_in(z0, z1, z2) → U31(f191_in(z0, z1), z0, z1, z2)
U31(f191_out1, z0, z1, z2) → U32(f1_in(z0, z2), z0, z1, z2)
U32(f1_out1, z0, z1, z2) → f189_out1
f310_in(z0, z1, z2) → U33(f295_in(z0, z1), z0, z1, z2)
U33(f295_out1, z0, z1, z2) → U34(f1_in(z1, z2), z0, z1, z2)
U34(f1_out1, z0, z1, z2) → f310_out1
f15_in(z0, z1) → U35(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U35(f54_out1, z0, z1, z2) → f15_out1
U35(z0, f55_out1, z1, z2) → f15_out2
U35(z0, f55_out2, z1, z2) → f15_out3
f16_in(z0) → U36(f18_in(z0), f19_in(z0), z0)
U36(f18_out1, z0, z1) → f16_out1
U36(z0, f19_out1, z1) → f16_out2
U36(z0, f19_out2, z1) → f16_out3
f19_in(z0) → U37(f36_in(z0), f38_in(z0), z0)
U37(f36_out1, z0, z1) → f19_out1
U37(z0, f38_out1, z1) → f19_out2
f55_in(z0, z1) → U38(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U38(f101_out1, z0, z1, z2) → f55_out1
U38(z0, f102_out1, z1, z2) → f55_out2
f126_in(z0, z1) → U39(f156_in(z0, z1), f157_in(z0, z1), z0, z1)
U39(f156_out1, z0, z1, z2) → f126_out1
U39(z0, f157_out1, z1, z2) → f126_out2
U39(z0, f157_out2, z1, z2) → f126_out3
f127_in(z0, z1) → U40(f129_in(z0, z1), f131_in(z0, z1), z0, z1)
U40(f129_out1, z0, z1, z2) → f127_out1
U40(z0, f131_out1, z1, z2) → f127_out2
U40(z0, f131_out2, z1, z2) → f127_out3
f131_in(z0, z1) → U41(f138_in(z0, z1), f139_in(z0, z1), z0, z1)
U41(f138_out1, z0, z1, z2) → f131_out1
U41(z0, f139_out1, z1, z2) → f131_out2
f157_in(z0, z1) → U42(f183_in(z0, z1), f184_in(z0, z1), z0, z1)
U42(f183_out1, z0, z1, z2) → f157_out1
U42(z0, f184_out1, z1, z2) → f157_out2

Tuples:

F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))
F16_IN(z0) → c91(F19_IN(z0))
F127_IN(z0, z1) → c105(F131_IN(z0, z1))
F111_IN(s(z0), x1) → c75(U27'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F142_IN(s(z0), x1) → c78(U29'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F189_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2) → c81(U31'(U10(f295_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), F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))
F189_IN(0, s(z0), x2) → c81(U31'(f191_out1, 0, s(z0), x2))
F189_IN(s(0), s(s(z0)), x2) → c81(U31'(f191_out1, s(0), s(s(z0)), x2))
F189_IN(s(s(0)), s(s(s(z0))), x2) → c81(U31'(f191_out1, s(s(0)), s(s(s(z0))), x2))
F189_IN(s(s(s(0))), s(s(s(s(z0)))), x2) → c81(U31'(f191_out1, s(s(s(0))), s(s(s(s(z0)))), x2))
F189_IN(s(s(s(s(0)))), s(s(s(s(s(z0))))), x2) → c81(U31'(f191_out1, s(s(s(s(0)))), s(s(s(s(s(z0))))), x2))
F189_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2))
F189_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2))
F189_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2))

S tuples:

F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1))
F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))
F16_IN(z0) → c91(F19_IN(z0))
F127_IN(z0, z1) → c105(F131_IN(z0, z1))
F111_IN(s(z0), x1) → c75(U27'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F142_IN(s(z0), x1) → c78(U29'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F189_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2) → c81(U31'(U10(f295_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), F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))
F189_IN(0, s(z0), x2) → c81(U31'(f191_out1, 0, s(z0), x2))
F189_IN(s(0), s(s(z0)), x2) → c81(U31'(f191_out1, s(0), s(s(z0)), x2))
F189_IN(s(s(0)), s(s(s(z0))), x2) → c81(U31'(f191_out1, s(s(0)), s(s(s(z0))), x2))
F189_IN(s(s(s(0))), s(s(s(s(z0)))), x2) → c81(U31'(f191_out1, s(s(s(0))), s(s(s(s(z0)))), x2))
F189_IN(s(s(s(s(0)))), s(s(s(s(s(z0))))), x2) → c81(U31'(f191_out1, s(s(s(s(0)))), s(s(s(s(s(z0))))), x2))
F189_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2))
F189_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2))
F189_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2))

K tuples:

U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f295_in, U5, f44_in, U6, f70_in, U7, U8, U9, f191_in, U10, f156_in, U11, U12, f54_in, U13, U14, f129_in, U15, f183_in, U16, f184_in, U17, f18_in, U18, f101_in, U19, f102_in, U20, f138_in, U21, f139_in, U22, f36_in, U23, f38_in, U24, f42_in, U25, U26, f111_in, U27, U28, f142_in, U29, U30, f189_in, U31, U32, f310_in, U33, U34, f15_in, U35, f16_in, U36, f19_in, U37, f55_in, U38, f126_in, U39, f127_in, U40, f131_in, U41, f157_in, U42

Defined Pair Symbols:

F310_IN, F191_IN, F156_IN, F54_IN, F1_IN, F295_IN, F44_IN, F70_IN, F183_IN, F184_IN, F101_IN, F102_IN, F138_IN, F139_IN, F36_IN, F38_IN, U25', U27', U29', U31', U33', F15_IN, F19_IN, F55_IN, F126_IN, F131_IN, F157_IN, F42_IN, F16_IN, F127_IN, F111_IN, F142_IN, F189_IN

Compound Symbols:

c84, c, c2, c3, c5, c6, c20, c22, c28, c54, c56, c60, c62, c64, c66, c68, c70, c73, c76, c79, c82, c85, c87, c95, c98, c101, c109, c112, c72, c91, c105, c75, c78, c81, c81

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

Use narrowing to replace F310_IN(z0, z1, z2) → c84(U33'(f295_in(z0, z1), z0, z1, z2), F295_IN(z0, z1)) by

F310_IN(0, s(z0), x2) → c84(U33'(f295_out1, 0, s(z0), x2), F295_IN(0, s(z0)))
F310_IN(s(z0), s(z1), x2) → c84(U33'(U5(f295_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F295_IN(s(z0), s(z1)))

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, z1)) → f1_out1
f1_in(z0, tree(z0, void, void)) → f1_out1
f1_in(z0, tree(z0, void, void)) → U1(f16_in(z0), z0, tree(z0, void, void))
f1_in(z0, tree(z0, void, z1)) → U2(f15_in(z0, z1), z0, tree(z0, void, z1))
f1_in(z0, tree(z0, z1, void)) → f1_out1
f1_in(z0, tree(z0, z1, void)) → U3(f127_in(z0, z1), z0, tree(z0, z1, void))
f1_in(z0, z1) → U4(f126_in(z0, z1), z0, z1)
U1(f16_out1, z0, tree(z0, void, void)) → f1_out1
U1(f16_out2, z0, tree(z0, void, void)) → f1_out1
U1(f16_out3, z0, tree(z0, void, void)) → f1_out1
U2(f15_out1, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out2, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out3, z0, tree(z0, void, z1)) → f1_out1
U3(f127_out1, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out2, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out3, z0, tree(z0, z1, void)) → f1_out1
U4(f126_out1, z0, z1) → f1_out1
U4(f126_out2, z0, z1) → f1_out1
U4(f126_out3, z0, z1) → f1_out1
f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1
f70_in(tree(z0, void, z1)) → f70_out1(z0)
f70_in(tree(z0, void, z1)) → U7(f25_in, tree(z0, void, z1))
f70_in(tree(z0, tree(z1, void, z2), z3)) → f70_out1(z1)
f70_in(tree(z0, tree(z1, void, z2), z3)) → U8(f25_in, tree(z0, tree(z1, void, z2), z3))
f70_in(tree(z0, tree(z1, z2, z3), z4)) → U9(f70_in(z2), tree(z0, tree(z1, z2, z3), z4))
U7(f25_out1(z0), tree(z1, void, z2)) → f70_out1(z0)
U8(f25_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f70_out1(z0)
U9(f70_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f70_out1(z0)
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → f156_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f25_in, z0, tree(z0, z1, tree(z2, void, z3)))
f156_in(z0, tree(z0, z1, tree(z2, z3, z4))) → U12(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4)))
U11(f25_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f156_out1
U12(f70_out1(z0), z1, tree(z1, z2, tree(z3, z4, z5))) → f156_out1
f54_in(z0, tree(z1, void, z2)) → f54_out1
f54_in(z0, tree(z1, void, z2)) → U13(f25_in, z0, tree(z1, void, z2))
f54_in(z0, tree(z1, z2, z3)) → U14(f70_in(z2), z0, tree(z1, z2, z3))
U13(f25_out1(z0), z1, tree(z2, void, z3)) → f54_out1
U14(f70_out1(z0), z1, tree(z2, z3, z4)) → f54_out1
f129_in(z0, z1) → U15(f25_in, z0, z1)
U15(f25_out1(z0), z1, z2) → f129_out1
f183_in(z0, tree(z1, z2, z3)) → U16(f189_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f189_out1, z0, tree(z1, z2, z3)) → f183_out1
f184_in(z0, tree(z1, z2, z3)) → U17(f310_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f310_out1, z0, tree(z1, z2, z3)) → f184_out1
f18_in(z0) → U18(f25_in, z0)
U18(f25_out1(z0), z1) → f18_out1
f101_in(z0, z1) → U19(f42_in(z0), z0, z1)
U19(f42_out1, z0, z1) → f101_out1
f102_in(z0, z1) → U20(f111_in(z0, z1), z0, z1)
U20(f111_out1, z0, z1) → f102_out1
f138_in(z0, z1) → U21(f142_in(z0, z1), z0, z1)
U21(f142_out1, z0, z1) → f138_out1
f139_in(z0, z1) → U22(f42_in(z0), z0, z1)
U22(f42_out1, z0, z1) → f139_out1
f36_in(z0) → U23(f42_in(z0), z0)
U23(f42_out1, z0) → f36_out1
f38_in(z0) → U24(f42_in(z0), z0)
U24(f42_out1, z0) → f38_out1
f42_in(z0) → U25(f44_in(z0), z0)
U25(f44_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1, z0) → f42_out1
f111_in(z0, z1) → U27(f44_in(z0), z0, z1)
U27(f44_out1, z0, z1) → U28(f1_in(z0, z1), z0, z1)
U28(f1_out1, z0, z1) → f111_out1
f142_in(z0, z1) → U29(f44_in(z0), z0, z1)
U29(f44_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1, z0, z1) → f142_out1
f189_in(z0, z1, z2) → U31(f191_in(z0, z1), z0, z1, z2)
U31(f191_out1, z0, z1, z2) → U32(f1_in(z0, z2), z0, z1, z2)
U32(f1_out1, z0, z1, z2) → f189_out1
f310_in(z0, z1, z2) → U33(f295_in(z0, z1), z0, z1, z2)
U33(f295_out1, z0, z1, z2) → U34(f1_in(z1, z2), z0, z1, z2)
U34(f1_out1, z0, z1, z2) → f310_out1
f15_in(z0, z1) → U35(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U35(f54_out1, z0, z1, z2) → f15_out1
U35(z0, f55_out1, z1, z2) → f15_out2
U35(z0, f55_out2, z1, z2) → f15_out3
f16_in(z0) → U36(f18_in(z0), f19_in(z0), z0)
U36(f18_out1, z0, z1) → f16_out1
U36(z0, f19_out1, z1) → f16_out2
U36(z0, f19_out2, z1) → f16_out3
f19_in(z0) → U37(f36_in(z0), f38_in(z0), z0)
U37(f36_out1, z0, z1) → f19_out1
U37(z0, f38_out1, z1) → f19_out2
f55_in(z0, z1) → U38(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U38(f101_out1, z0, z1, z2) → f55_out1
U38(z0, f102_out1, z1, z2) → f55_out2
f126_in(z0, z1) → U39(f156_in(z0, z1), f157_in(z0, z1), z0, z1)
U39(f156_out1, z0, z1, z2) → f126_out1
U39(z0, f157_out1, z1, z2) → f126_out2
U39(z0, f157_out2, z1, z2) → f126_out3
f127_in(z0, z1) → U40(f129_in(z0, z1), f131_in(z0, z1), z0, z1)
U40(f129_out1, z0, z1, z2) → f127_out1
U40(z0, f131_out1, z1, z2) → f127_out2
U40(z0, f131_out2, z1, z2) → f127_out3
f131_in(z0, z1) → U41(f138_in(z0, z1), f139_in(z0, z1), z0, z1)
U41(f138_out1, z0, z1, z2) → f131_out1
U41(z0, f139_out1, z1, z2) → f131_out2
f157_in(z0, z1) → U42(f183_in(z0, z1), f184_in(z0, z1), z0, z1)
U42(f183_out1, z0, z1, z2) → f157_out1
U42(z0, f184_out1, z1, z2) → f157_out2

Tuples:

F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))
F16_IN(z0) → c91(F19_IN(z0))
F127_IN(z0, z1) → c105(F131_IN(z0, z1))
F111_IN(s(z0), x1) → c75(U27'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F142_IN(s(z0), x1) → c78(U29'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F189_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2) → c81(U31'(U10(f295_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), F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))
F189_IN(0, s(z0), x2) → c81(U31'(f191_out1, 0, s(z0), x2))
F189_IN(s(0), s(s(z0)), x2) → c81(U31'(f191_out1, s(0), s(s(z0)), x2))
F189_IN(s(s(0)), s(s(s(z0))), x2) → c81(U31'(f191_out1, s(s(0)), s(s(s(z0))), x2))
F189_IN(s(s(s(0))), s(s(s(s(z0)))), x2) → c81(U31'(f191_out1, s(s(s(0))), s(s(s(s(z0)))), x2))
F189_IN(s(s(s(s(0)))), s(s(s(s(s(z0))))), x2) → c81(U31'(f191_out1, s(s(s(s(0)))), s(s(s(s(s(z0))))), x2))
F189_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2))
F189_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2))
F189_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2))
F310_IN(0, s(z0), x2) → c84(U33'(f295_out1, 0, s(z0), x2), F295_IN(0, s(z0)))
F310_IN(s(z0), s(z1), x2) → c84(U33'(U5(f295_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F295_IN(s(z0), s(z1)))

S tuples:

F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))
F16_IN(z0) → c91(F19_IN(z0))
F127_IN(z0, z1) → c105(F131_IN(z0, z1))
F111_IN(s(z0), x1) → c75(U27'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F142_IN(s(z0), x1) → c78(U29'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F189_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2) → c81(U31'(U10(f295_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), F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))
F189_IN(0, s(z0), x2) → c81(U31'(f191_out1, 0, s(z0), x2))
F189_IN(s(0), s(s(z0)), x2) → c81(U31'(f191_out1, s(0), s(s(z0)), x2))
F189_IN(s(s(0)), s(s(s(z0))), x2) → c81(U31'(f191_out1, s(s(0)), s(s(s(z0))), x2))
F189_IN(s(s(s(0))), s(s(s(s(z0)))), x2) → c81(U31'(f191_out1, s(s(s(0))), s(s(s(s(z0)))), x2))
F189_IN(s(s(s(s(0)))), s(s(s(s(s(z0))))), x2) → c81(U31'(f191_out1, s(s(s(s(0)))), s(s(s(s(s(z0))))), x2))
F189_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2))
F189_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2))
F189_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2))
F310_IN(0, s(z0), x2) → c84(U33'(f295_out1, 0, s(z0), x2), F295_IN(0, s(z0)))
F310_IN(s(z0), s(z1), x2) → c84(U33'(U5(f295_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F295_IN(s(z0), s(z1)))

K tuples:

U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f295_in, U5, f44_in, U6, f70_in, U7, U8, U9, f191_in, U10, f156_in, U11, U12, f54_in, U13, U14, f129_in, U15, f183_in, U16, f184_in, U17, f18_in, U18, f101_in, U19, f102_in, U20, f138_in, U21, f139_in, U22, f36_in, U23, f38_in, U24, f42_in, U25, U26, f111_in, U27, U28, f142_in, U29, U30, f189_in, U31, U32, f310_in, U33, U34, f15_in, U35, f16_in, U36, f19_in, U37, f55_in, U38, f126_in, U39, f127_in, U40, f131_in, U41, f157_in, U42

Defined Pair Symbols:

F191_IN, F156_IN, F54_IN, F1_IN, F295_IN, F44_IN, F70_IN, F183_IN, F184_IN, F101_IN, F102_IN, F138_IN, F139_IN, F36_IN, F38_IN, U25', U27', U29', U31', U33', F15_IN, F19_IN, F55_IN, F126_IN, F131_IN, F157_IN, F42_IN, F16_IN, F127_IN, F111_IN, F142_IN, F189_IN, F310_IN

Compound Symbols:

c, c2, c3, c5, c6, c20, c22, c28, c54, c56, c60, c62, c64, c66, c68, c70, c73, c76, c79, c82, c85, c87, c95, c98, c101, c109, c112, c72, c91, c105, c75, c78, c81, c81, c84

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

Removed 1 trailing tuple parts

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, tree(z0, void, z1)) → f1_out1
f1_in(z0, tree(z0, void, void)) → f1_out1
f1_in(z0, tree(z0, void, void)) → U1(f16_in(z0), z0, tree(z0, void, void))
f1_in(z0, tree(z0, void, z1)) → U2(f15_in(z0, z1), z0, tree(z0, void, z1))
f1_in(z0, tree(z0, z1, void)) → f1_out1
f1_in(z0, tree(z0, z1, void)) → U3(f127_in(z0, z1), z0, tree(z0, z1, void))
f1_in(z0, z1) → U4(f126_in(z0, z1), z0, z1)
U1(f16_out1, z0, tree(z0, void, void)) → f1_out1
U1(f16_out2, z0, tree(z0, void, void)) → f1_out1
U1(f16_out3, z0, tree(z0, void, void)) → f1_out1
U2(f15_out1, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out2, z0, tree(z0, void, z1)) → f1_out1
U2(f15_out3, z0, tree(z0, void, z1)) → f1_out1
U3(f127_out1, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out2, z0, tree(z0, z1, void)) → f1_out1
U3(f127_out3, z0, tree(z0, z1, void)) → f1_out1
U4(f126_out1, z0, z1) → f1_out1
U4(f126_out2, z0, z1) → f1_out1
U4(f126_out3, z0, z1) → f1_out1
f295_in(0, s(z0)) → f295_out1
f295_in(s(z0), s(z1)) → U5(f295_in(z0, z1), s(z0), s(z1))
U5(f295_out1, s(z0), s(z1)) → f295_out1
f44_in(s(z0)) → U6(f44_in(z0), s(z0))
U6(f44_out1, s(z0)) → f44_out1
f70_in(tree(z0, void, z1)) → f70_out1(z0)
f70_in(tree(z0, void, z1)) → U7(f25_in, tree(z0, void, z1))
f70_in(tree(z0, tree(z1, void, z2), z3)) → f70_out1(z1)
f70_in(tree(z0, tree(z1, void, z2), z3)) → U8(f25_in, tree(z0, tree(z1, void, z2), z3))
f70_in(tree(z0, tree(z1, z2, z3), z4)) → U9(f70_in(z2), tree(z0, tree(z1, z2, z3), z4))
U7(f25_out1(z0), tree(z1, void, z2)) → f70_out1(z0)
U8(f25_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f70_out1(z0)
U9(f70_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f70_out1(z0)
f191_in(0, s(z0)) → f191_out1
f191_in(s(0), s(s(z0))) → f191_out1
f191_in(s(s(0)), s(s(s(z0)))) → f191_out1
f191_in(s(s(s(0))), s(s(s(s(z0))))) → f191_out1
f191_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f191_out1
f191_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f191_out1
f191_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0))))))))) → f191_out1
f191_in(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → U10(f295_in(z0, z1), s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))))
U10(f295_out1, s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → f191_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → f156_out1
f156_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f25_in, z0, tree(z0, z1, tree(z2, void, z3)))
f156_in(z0, tree(z0, z1, tree(z2, z3, z4))) → U12(f70_in(z3), z0, tree(z0, z1, tree(z2, z3, z4)))
U11(f25_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f156_out1
U12(f70_out1(z0), z1, tree(z1, z2, tree(z3, z4, z5))) → f156_out1
f54_in(z0, tree(z1, void, z2)) → f54_out1
f54_in(z0, tree(z1, void, z2)) → U13(f25_in, z0, tree(z1, void, z2))
f54_in(z0, tree(z1, z2, z3)) → U14(f70_in(z2), z0, tree(z1, z2, z3))
U13(f25_out1(z0), z1, tree(z2, void, z3)) → f54_out1
U14(f70_out1(z0), z1, tree(z2, z3, z4)) → f54_out1
f129_in(z0, z1) → U15(f25_in, z0, z1)
U15(f25_out1(z0), z1, z2) → f129_out1
f183_in(z0, tree(z1, z2, z3)) → U16(f189_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f189_out1, z0, tree(z1, z2, z3)) → f183_out1
f184_in(z0, tree(z1, z2, z3)) → U17(f310_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f310_out1, z0, tree(z1, z2, z3)) → f184_out1
f18_in(z0) → U18(f25_in, z0)
U18(f25_out1(z0), z1) → f18_out1
f101_in(z0, z1) → U19(f42_in(z0), z0, z1)
U19(f42_out1, z0, z1) → f101_out1
f102_in(z0, z1) → U20(f111_in(z0, z1), z0, z1)
U20(f111_out1, z0, z1) → f102_out1
f138_in(z0, z1) → U21(f142_in(z0, z1), z0, z1)
U21(f142_out1, z0, z1) → f138_out1
f139_in(z0, z1) → U22(f42_in(z0), z0, z1)
U22(f42_out1, z0, z1) → f139_out1
f36_in(z0) → U23(f42_in(z0), z0)
U23(f42_out1, z0) → f36_out1
f38_in(z0) → U24(f42_in(z0), z0)
U24(f42_out1, z0) → f38_out1
f42_in(z0) → U25(f44_in(z0), z0)
U25(f44_out1, z0) → U26(f1_in(z0, void), z0)
U26(f1_out1, z0) → f42_out1
f111_in(z0, z1) → U27(f44_in(z0), z0, z1)
U27(f44_out1, z0, z1) → U28(f1_in(z0, z1), z0, z1)
U28(f1_out1, z0, z1) → f111_out1
f142_in(z0, z1) → U29(f44_in(z0), z0, z1)
U29(f44_out1, z0, z1) → U30(f1_in(z0, z1), z0, z1)
U30(f1_out1, z0, z1) → f142_out1
f189_in(z0, z1, z2) → U31(f191_in(z0, z1), z0, z1, z2)
U31(f191_out1, z0, z1, z2) → U32(f1_in(z0, z2), z0, z1, z2)
U32(f1_out1, z0, z1, z2) → f189_out1
f310_in(z0, z1, z2) → U33(f295_in(z0, z1), z0, z1, z2)
U33(f295_out1, z0, z1, z2) → U34(f1_in(z1, z2), z0, z1, z2)
U34(f1_out1, z0, z1, z2) → f310_out1
f15_in(z0, z1) → U35(f54_in(z0, z1), f55_in(z0, z1), z0, z1)
U35(f54_out1, z0, z1, z2) → f15_out1
U35(z0, f55_out1, z1, z2) → f15_out2
U35(z0, f55_out2, z1, z2) → f15_out3
f16_in(z0) → U36(f18_in(z0), f19_in(z0), z0)
U36(f18_out1, z0, z1) → f16_out1
U36(z0, f19_out1, z1) → f16_out2
U36(z0, f19_out2, z1) → f16_out3
f19_in(z0) → U37(f36_in(z0), f38_in(z0), z0)
U37(f36_out1, z0, z1) → f19_out1
U37(z0, f38_out1, z1) → f19_out2
f55_in(z0, z1) → U38(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U38(f101_out1, z0, z1, z2) → f55_out1
U38(z0, f102_out1, z1, z2) → f55_out2
f126_in(z0, z1) → U39(f156_in(z0, z1), f157_in(z0, z1), z0, z1)
U39(f156_out1, z0, z1, z2) → f126_out1
U39(z0, f157_out1, z1, z2) → f126_out2
U39(z0, f157_out2, z1, z2) → f126_out3
f127_in(z0, z1) → U40(f129_in(z0, z1), f131_in(z0, z1), z0, z1)
U40(f129_out1, z0, z1, z2) → f127_out1
U40(z0, f131_out1, z1, z2) → f127_out2
U40(z0, f131_out2, z1, z2) → f127_out3
f131_in(z0, z1) → U41(f138_in(z0, z1), f139_in(z0, z1), z0, z1)
U41(f138_out1, z0, z1, z2) → f131_out1
U41(z0, f139_out1, z1, z2) → f131_out2
f157_in(z0, z1) → U42(f183_in(z0, z1), f184_in(z0, z1), z0, z1)
U42(f183_out1, z0, z1, z2) → f157_out1
U42(z0, f184_out1, z1, z2) → f157_out2

Tuples:

F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))
F16_IN(z0) → c91(F19_IN(z0))
F127_IN(z0, z1) → c105(F131_IN(z0, z1))
F111_IN(s(z0), x1) → c75(U27'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F142_IN(s(z0), x1) → c78(U29'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F189_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2) → c81(U31'(U10(f295_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), F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))
F189_IN(0, s(z0), x2) → c81(U31'(f191_out1, 0, s(z0), x2))
F189_IN(s(0), s(s(z0)), x2) → c81(U31'(f191_out1, s(0), s(s(z0)), x2))
F189_IN(s(s(0)), s(s(s(z0))), x2) → c81(U31'(f191_out1, s(s(0)), s(s(s(z0))), x2))
F189_IN(s(s(s(0))), s(s(s(s(z0)))), x2) → c81(U31'(f191_out1, s(s(s(0))), s(s(s(s(z0)))), x2))
F189_IN(s(s(s(s(0)))), s(s(s(s(s(z0))))), x2) → c81(U31'(f191_out1, s(s(s(s(0)))), s(s(s(s(s(z0))))), x2))
F189_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2))
F189_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2))
F189_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2))
F310_IN(s(z0), s(z1), x2) → c84(U33'(U5(f295_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F295_IN(s(z0), s(z1)))
F310_IN(0, s(z0), x2) → c84(U33'(f295_out1, 0, s(z0), x2))

S tuples:

F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))) → c(F295_IN(z0, z1))
F156_IN(z0, tree(z0, z1, tree(z2, z3, z4))) → c(F70_IN(z3))
F54_IN(z0, tree(z1, z2, z3)) → c(F70_IN(z2))
F1_IN(z0, tree(z0, void, void)) → c2(F16_IN(z0))
F1_IN(z0, tree(z0, void, z1)) → c3(F15_IN(z0, z1))
F1_IN(z0, tree(z0, z1, void)) → c5(F127_IN(z0, z1))
F1_IN(z0, z1) → c6(F126_IN(z0, z1))
F295_IN(s(z0), s(z1)) → c20(F295_IN(z0, z1))
F44_IN(s(z0)) → c22(F44_IN(z0))
F70_IN(tree(z0, tree(z1, z2, z3), z4)) → c28(F70_IN(z2))
F183_IN(z0, tree(z1, z2, z3)) → c54(F189_IN(z0, z1, z2))
F184_IN(z0, tree(z1, z2, z3)) → c56(F310_IN(z1, z0, z3))
F101_IN(z0, z1) → c60(F42_IN(z0))
F102_IN(z0, z1) → c62(F111_IN(z0, z1))
F138_IN(z0, z1) → c64(F142_IN(z0, z1))
F139_IN(z0, z1) → c66(F42_IN(z0))
F36_IN(z0) → c68(F42_IN(z0))
F38_IN(z0) → c70(F42_IN(z0))
U31'(f191_out1, z0, z1, z2) → c82(F1_IN(z0, z2))
U33'(f295_out1, z0, z1, z2) → c85(F1_IN(z1, z2))
F15_IN(z0, z1) → c87(F54_IN(z0, z1), F55_IN(z0, z1))
F19_IN(z0) → c95(F36_IN(z0), F38_IN(z0))
F55_IN(z0, z1) → c98(F101_IN(z0, z1), F102_IN(z0, z1))
F126_IN(z0, z1) → c101(F156_IN(z0, z1), F157_IN(z0, z1))
F131_IN(z0, z1) → c109(F138_IN(z0, z1), F139_IN(z0, z1))
F157_IN(z0, z1) → c112(F183_IN(z0, z1), F184_IN(z0, z1))
F42_IN(s(z0)) → c72(U25'(U6(f44_in(z0), s(z0)), s(z0)), F44_IN(s(z0)))
F16_IN(z0) → c91(F19_IN(z0))
F127_IN(z0, z1) → c105(F131_IN(z0, z1))
F111_IN(s(z0), x1) → c75(U27'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F142_IN(s(z0), x1) → c78(U29'(U6(f44_in(z0), s(z0)), s(z0), x1), F44_IN(s(z0)))
F189_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1)))))))), x2) → c81(U31'(U10(f295_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), F191_IN(s(s(s(s(s(s(s(s(z0)))))))), s(s(s(s(s(s(s(s(z1))))))))))
F189_IN(0, s(z0), x2) → c81(U31'(f191_out1, 0, s(z0), x2))
F189_IN(s(0), s(s(z0)), x2) → c81(U31'(f191_out1, s(0), s(s(z0)), x2))
F189_IN(s(s(0)), s(s(s(z0))), x2) → c81(U31'(f191_out1, s(s(0)), s(s(s(z0))), x2))
F189_IN(s(s(s(0))), s(s(s(s(z0)))), x2) → c81(U31'(f191_out1, s(s(s(0))), s(s(s(s(z0)))), x2))
F189_IN(s(s(s(s(0)))), s(s(s(s(s(z0))))), x2) → c81(U31'(f191_out1, s(s(s(s(0)))), s(s(s(s(s(z0))))), x2))
F189_IN(s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(0))))), s(s(s(s(s(s(z0)))))), x2))
F189_IN(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0))))))), x2))
F189_IN(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2) → c81(U31'(f191_out1, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(z0)))))))), x2))
F310_IN(s(z0), s(z1), x2) → c84(U33'(U5(f295_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F295_IN(s(z0), s(z1)))
F310_IN(0, s(z0), x2) → c84(U33'(f295_out1, 0, s(z0), x2))

K tuples:

U25'(f44_out1, z0) → c73(F1_IN(z0, void))
U27'(f44_out1, z0, z1) → c76(F1_IN(z0, z1))
U29'(f44_out1, z0, z1) → c79(F1_IN(z0, z1))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f295_in, U5, f44_in, U6, f70_in, U7, U8, U9, f191_in, U10, f156_in, U11, U12, f54_in, U13, U14, f129_in, U15, f183_in, U16, f184_in, U17, f18_in, U18, f101_in, U19, f102_in, U20, f138_in, U21, f139_in, U22, f36_in, U23, f38_in, U24, f42_in, U25, U26, f111_in, U27, U28, f142_in, U29, U30, f189_in, U31, U32, f310_in, U33, U34, f15_in, U35, f16_in, U36, f19_in, U37, f55_in, U38, f126_in, U39, f127_in, U40, f131_in, U41, f157_in, U42

Defined Pair Symbols:

F191_IN, F156_IN, F54_IN, F1_IN, F295_IN, F44_IN, F70_IN, F183_IN, F184_IN, F101_IN, F102_IN, F138_IN, F139_IN, F36_IN, F38_IN, U25', U27', U29', U31', U33', F15_IN, F19_IN, F55_IN, F126_IN, F131_IN, F157_IN, F42_IN, F16_IN, F127_IN, F111_IN, F142_IN, F189_IN, F310_IN

Compound Symbols:

c, c2, c3, c5, c6, c20, c22, c28, c54, c56, c60, c62, c64, c66, c68, c70, c73, c76, c79, c82, c85, c87, c95, c98, c101, c109, c112, c72, c91, c105, c75, c78, c81, c81, c84, c84

(33) 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: delete(T1, T2, T3)\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
4 [label="4: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 0 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 5 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 6\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: true | delete(T6, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 1 | delete(T6, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 4 | delete(T6, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 5 | delete(T6, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 6\n\nT6 is ground\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 5 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 6\n\nT1 is ground\nT2 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: delete(T6, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 1 | delete(T6, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 4 | delete(T6, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 5 | delete(T6, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 6\n\nT6 is ground\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: true | delete(T9, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 4 | delete(T9, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T9, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: delete(T6, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 4 | delete(T6, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 5 | delete(T6, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 6\n\nT6 is ground\nT7 is ground\nX10 is free\nX11 is free\ndelete(T6, tree(T6, void, T7), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: delete(T9, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 4 | delete(T9, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T9, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: delmin(void, T16, T17) | delete(T13, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T13, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: delete(T9, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T9, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT9 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T9, tree(T9, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: delmin(void, T16, T17), SCOPE: 2, CLAUSE: 2 | delmin(void, T16, T17), SCOPE: 2, CLAUSE: 7 | ?_2 | delete(T13, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T13, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: delmin(void, T16, T17), SCOPE: 2, CLAUSE: 7 | ?_2 | delete(T13, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T13, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: ?_2 | delete(T13, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T13, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: delete(T13, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T13, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: delete(T13, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 5\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: delete(T13, tree(T13, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT13 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: ','(less(T26, T26), delete(T26, void, T28))\n\nT26 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: less(T26, T26)\n\nT26 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: delete(T26, void, T28)\n\nT26 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: less(T26, T26), SCOPE: 3, CLAUSE: 3 | less(T26, T26), SCOPE: 3, CLAUSE: 8\n\nT26 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: less(T26, T26), SCOPE: 3, CLAUSE: 8\n\nT26 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: less(T31, T31)\n\nT31 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(less(T38, T38), delete(T38, void, T40))\n\nT38 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: ','(less(T43, T43), delete(T43, void, T45)) | delete(T43, tree(T43, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT43 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T43, tree(T43, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: delete(T9, tree(T9, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT9 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX94 is free\nX95 is free\nX96 is free\nX97 is free\nX98 is free\ndelete(T9, tree(T9, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T9, tree(T9, void, void), T3) !=? delete(X94, tree(X95, X96, X97), tree(X95, X98, X97))", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(less(T43, T43), delete(T43, void, T45)), SCOPE: 4, CLAUSE: 3 | ','(less(T43, T43), delete(T43, void, T45)), SCOPE: 4, CLAUSE: 8 | ?_4 | delete(T43, tree(T43, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT43 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T43, tree(T43, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: ','(less(T43, T43), delete(T43, void, T45)), SCOPE: 4, CLAUSE: 8 | ?_4 | delete(T43, tree(T43, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT43 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T43, tree(T43, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: ','(less(T43, T43), delete(T43, void, T45)), SCOPE: 4, CLAUSE: 8\n\nT43 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T43, tree(T43, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: ?_4 | delete(T43, tree(T43, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT43 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T43, tree(T43, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: ','(less(T50, T50), delete(s(T50), void, T45))\n\nT50 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(s(T50), tree(s(T50), void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: less(T50, T50)\n\nT50 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(s(T50), tree(s(T50), void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: delete(s(T50), void, T45)\n\nT50 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(s(T50), tree(s(T50), void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: delete(T43, tree(T43, void, void), T3), SCOPE: 1, CLAUSE: 6\n\nT43 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T43, tree(T43, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: ','(less(T57, T57), delete(T57, void, T59))\n\nT57 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T57, tree(T57, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: ','(less(T62, T62), delete(T62, void, T64))\n\nT62 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX94 is free\nX95 is free\nX96 is free\nX97 is free\nX98 is free\ndelete(T62, tree(T62, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T62, tree(T62, void, void), T3) !=? delete(X94, tree(X95, X96, X97), tree(X95, X98, X97))", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: ','(less(T62, T62), delete(T62, void, T64)), SCOPE: 5, CLAUSE: 3 | ','(less(T62, T62), delete(T62, void, T64)), SCOPE: 5, CLAUSE: 8\n\nT62 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX94 is free\nX95 is free\nX96 is free\nX97 is free\nX98 is free\ndelete(T62, tree(T62, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T62, tree(T62, void, void), T3) !=? delete(X94, tree(X95, X96, X97), tree(X95, X98, X97))", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: ','(less(T62, T62), delete(T62, void, T64)), SCOPE: 5, CLAUSE: 8\n\nT62 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX94 is free\nX95 is free\nX96 is free\nX97 is free\nX98 is free\ndelete(T62, tree(T62, void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T62, tree(T62, void, void), T3) !=? delete(X94, tree(X95, X96, X97), tree(X95, X98, X97))", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: ','(less(T67, T67), delete(s(T67), void, T64))\n\nT67 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX94 is free\nX95 is free\nX96 is free\nX97 is free\nX98 is free\ndelete(s(T67), tree(s(T67), void, void), T3) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(s(T67), tree(s(T67), void, void), T3) !=? delete(X94, tree(X95, X96, X97), tree(X95, X98, X97))", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: delmin(T73, T76, T77) | delete(T72, tree(T72, void, T73), T3), SCOPE: 1, CLAUSE: 5 | delete(T72, tree(T72, void, T73), T3), SCOPE: 1, CLAUSE: 6\n\nT72 is ground\nT73 is ground\nX10 is free\nX11 is free\ndelete(T72, tree(T72, void, T73), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: delete(T6, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 5 | delete(T6, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 6\n\nT6 is ground\nT7 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\ndelete(T6, tree(T6, void, T7), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T6, tree(T6, void, T7), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: delmin(T73, T76, T77), SCOPE: 6, CLAUSE: 2 | delmin(T73, T76, T77), SCOPE: 6, CLAUSE: 7 | ?_6 | delete(T72, tree(T72, void, T73), T3), SCOPE: 1, CLAUSE: 5 | delete(T72, tree(T72, void, T73), T3), SCOPE: 1, CLAUSE: 6\n\nT72 is ground\nT73 is ground\nX10 is free\nX11 is free\ndelete(T72, tree(T72, void, T73), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: true | delmin(tree(T82, void, T83), T76, T77), SCOPE: 6, CLAUSE: 7 | ?_6 | delete(T72, tree(T72, void, tree(T82, void, T83)), T3), SCOPE: 1, CLAUSE: 5 | delete(T72, tree(T72, void, tree(T82, void, T83)), T3), SCOPE: 1, CLAUSE: 6\n\nT72 is ground\nT82 is ground\nT83 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: delmin(T73, T76, T77), SCOPE: 6, CLAUSE: 7 | ?_6 | delete(T72, tree(T72, void, T73), T3), SCOPE: 1, CLAUSE: 5 | delete(T72, tree(T72, void, T73), T3), SCOPE: 1, CLAUSE: 6\n\nT72 is ground\nT73 is ground\nX10 is free\nX11 is free\nX168 is free\nX169 is free\ndelete(T72, tree(T72, void, T73), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T73, T76, T77) !=? delmin(tree(X168, void, X169), X168, X169)", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: delmin(tree(T82, void, T83), T76, T77), SCOPE: 6, CLAUSE: 7 | ?_6 | delete(T72, tree(T72, void, tree(T82, void, T83)), T3), SCOPE: 1, CLAUSE: 5 | delete(T72, tree(T72, void, tree(T82, void, T83)), T3), SCOPE: 1, CLAUSE: 6\n\nT72 is ground\nT82 is ground\nT83 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: delmin(tree(T82, void, T83), T76, T77), SCOPE: 6, CLAUSE: 7\n\nT82 is ground\nT83 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: ?_6 | delete(T72, tree(T72, void, tree(T82, void, T83)), T3), SCOPE: 1, CLAUSE: 5 | delete(T72, tree(T72, void, tree(T82, void, T83)), T3), SCOPE: 1, CLAUSE: 6\n\nT72 is ground\nT82 is ground\nT83 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: delmin(void, T109, T110)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: delmin(void, T109, T110), SCOPE: 7, CLAUSE: 2 | delmin(void, T109, T110), SCOPE: 7, CLAUSE: 7\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: delmin(void, T109, T110), SCOPE: 7, CLAUSE: 7\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: delete(T72, tree(T72, void, tree(T82, void, T83)), T3), SCOPE: 1, CLAUSE: 5 | delete(T72, tree(T72, void, tree(T82, void, T83)), T3), SCOPE: 1, CLAUSE: 6\n\nT72 is ground\nT82 is ground\nT83 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: delete(T72, tree(T72, void, tree(T82, void, T83)), T3), SCOPE: 1, CLAUSE: 5\n\nT72 is ground\nT82 is ground\nT83 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: delete(T72, tree(T72, void, tree(T82, void, T83)), T3), SCOPE: 1, CLAUSE: 6\n\nT72 is ground\nT82 is ground\nT83 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: ','(less(T127, T127), delete(T127, void, T131))\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: ','(less(T140, T140), delete(T140, tree(T141, void, T142), T144))\n\nT140 is ground\nT141 is ground\nT142 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: less(T140, T140)\n\nT140 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: delete(T140, tree(T141, void, T142), T144)\n\nT140 is ground\nT141 is ground\nT142 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: delmin(T73, T76, T77), SCOPE: 6, CLAUSE: 7\n\nT72 is ground\nT73 is ground\nX10 is free\nX11 is free\nX168 is free\nX169 is free\ndelete(T72, tree(T72, void, T73), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T73, T76, T77) !=? delmin(tree(X168, void, X169), X168, X169)", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: ?_6 | delete(T72, tree(T72, void, T73), T3), SCOPE: 1, CLAUSE: 5 | delete(T72, tree(T72, void, T73), T3), SCOPE: 1, CLAUSE: 6\n\nT72 is ground\nT73 is ground\nX10 is free\nX11 is free\nX168 is free\nX169 is free\ndelete(T72, tree(T72, void, T73), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T73, T76, T77) !=? delmin(tree(X168, void, X169), X168, X169)", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: delmin(T174, T179, T180)\n\nT173 is ground\nT174 is ground\nT175 is ground\nX168 is free\nX169 is free\ndelmin(tree(T173, T174, T175), T76, T77) !=? delmin(tree(X168, void, X169), X168, X169)", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: delmin(T174, T179, T180), SCOPE: 8, CLAUSE: 2 | delmin(T174, T179, T180), SCOPE: 8, CLAUSE: 7\n\nT173 is ground\nT174 is ground\nT175 is ground\nX168 is free\nX169 is free\ndelmin(tree(T173, T174, T175), T76, T77) !=? delmin(tree(X168, void, X169), X168, X169)", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: true | delmin(tree(T189, void, T190), T179, T180), SCOPE: 8, CLAUSE: 7\n\nT189 is ground\nT190 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: delmin(T174, T179, T180), SCOPE: 8, CLAUSE: 7\n\nT173 is ground\nT174 is ground\nT175 is ground\nX168 is free\nX169 is free\nX300 is free\nX301 is free\ndelmin(tree(T173, T174, T175), T76, T77) !=? delmin(tree(X168, void, X169), X168, X169)\ndelmin(T174, T179, T180) !=? delmin(tree(X300, void, X301), X300, X301)", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: delmin(tree(T189, void, T190), T179, T180), SCOPE: 8, CLAUSE: 7\n\nT189 is ground\nT190 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: delmin(void, T206, T207)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: delmin(T221, T226, T227)\n\nT220 is ground\nT221 is ground\nT222 is ground\nX300 is free\nX301 is free\ndelmin(tree(T220, T221, T222), T179, T180) !=? delmin(tree(X300, void, X301), X300, X301)", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: delmin(T221, T226, T227), SCOPE: 9, CLAUSE: 2 | delmin(T221, T226, T227), SCOPE: 9, CLAUSE: 7\n\nT220 is ground\nT221 is ground\nT222 is ground\nX300 is free\nX301 is free\ndelmin(tree(T220, T221, T222), T179, T180) !=? delmin(tree(X300, void, X301), X300, X301)", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: true | delmin(tree(T236, void, T237), T226, T227), SCOPE: 9, CLAUSE: 7\n\nT236 is ground\nT237 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: delmin(T221, T226, T227), SCOPE: 9, CLAUSE: 7\n\nT220 is ground\nT221 is ground\nT222 is ground\nX300 is free\nX301 is free\nX350 is free\nX351 is free\ndelmin(tree(T220, T221, T222), T179, T180) !=? delmin(tree(X300, void, X301), X300, X301)\ndelmin(T221, T226, T227) !=? delmin(tree(X350, void, X351), X350, X351)", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: delmin(tree(T236, void, T237), T226, T227), SCOPE: 9, CLAUSE: 7\n\nT236 is ground\nT237 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: delmin(void, T253, T254)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: delmin(T268, T273, T274)\n\nT267 is ground\nT268 is ground\nT269 is ground\nX350 is free\nX351 is free\ndelmin(tree(T267, T268, T269), T226, T227) !=? delmin(tree(X350, void, X351), X350, X351)", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: delete(T72, tree(T72, void, T73), T3), SCOPE: 1, CLAUSE: 5 | delete(T72, tree(T72, void, T73), T3), SCOPE: 1, CLAUSE: 6\n\nT72 is ground\nT73 is ground\nX10 is free\nX11 is free\nX168 is free\nX169 is free\ndelete(T72, tree(T72, void, T73), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T73, T76, T77) !=? delmin(tree(X168, void, X169), X168, X169)", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: delete(T72, tree(T72, void, T73), T3), SCOPE: 1, CLAUSE: 5\n\nT72 is ground\nT73 is ground\nX10 is free\nX11 is free\nX168 is free\nX169 is free\ndelete(T72, tree(T72, void, T73), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T73, T76, T77) !=? delmin(tree(X168, void, X169), X168, X169)", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: delete(T72, tree(T72, void, T73), T3), SCOPE: 1, CLAUSE: 6\n\nT72 is ground\nT73 is ground\nX10 is free\nX11 is free\nX168 is free\nX169 is free\ndelete(T72, tree(T72, void, T73), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T73, T76, T77) !=? delmin(tree(X168, void, X169), X168, X169)", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: ','(less(T291, T291), delete(T291, void, T294))\n\nT291 is ground\nT292 is ground\nX10 is free\nX11 is free\ndelete(T291, tree(T291, void, T292), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: ','(less(T301, T301), delete(T301, T302, T304))\n\nT301 is ground\nT302 is ground\nX10 is free\nX11 is free\nX168 is free\nX169 is free\ndelete(T301, tree(T301, void, T302), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T302, T76, T77) !=? delmin(tree(X168, void, X169), X168, X169)", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: less(T301, T301)\n\nT301 is ground\nT302 is ground\nX10 is free\nX11 is free\ndelete(T301, tree(T301, void, T302), T3) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: delete(T301, T302, T304)\n\nT301 is ground\nT302 is ground\nX10 is free\nX11 is free\nX168 is free\nX169 is free\ndelete(T301, tree(T301, void, T302), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T302, T76, T77) !=? delmin(tree(X168, void, X169), X168, X169)", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: ','(less(T312, T312), delete(T312, void, T315)) | delete(T312, tree(T312, void, T313), T3), SCOPE: 1, CLAUSE: 6\n\nT312 is ground\nT313 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\ndelete(T312, tree(T312, void, T313), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T312, tree(T312, void, T313), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: delete(T6, tree(T6, void, T7), T3), SCOPE: 1, CLAUSE: 6\n\nT6 is ground\nT7 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\nX455 is free\ndelete(T6, tree(T6, void, T7), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T6, tree(T6, void, T7), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))\ndelete(T6, tree(T6, void, T7), T3) !=? delete(X451, tree(X452, X453, X454), tree(X452, X455, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: ','(less(T312, T312), delete(T312, void, T315)), SCOPE: 10, CLAUSE: 3 | ','(less(T312, T312), delete(T312, void, T315)), SCOPE: 10, CLAUSE: 8 | ?_10 | delete(T312, tree(T312, void, T313), T3), SCOPE: 1, CLAUSE: 6\n\nT312 is ground\nT313 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\ndelete(T312, tree(T312, void, T313), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T312, tree(T312, void, T313), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: ','(less(T312, T312), delete(T312, void, T315)), SCOPE: 10, CLAUSE: 8 | ?_10 | delete(T312, tree(T312, void, T313), T3), SCOPE: 1, CLAUSE: 6\n\nT312 is ground\nT313 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\ndelete(T312, tree(T312, void, T313), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T312, tree(T312, void, T313), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: ','(less(T312, T312), delete(T312, void, T315)), SCOPE: 10, CLAUSE: 8\n\nT312 is ground\nT313 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\ndelete(T312, tree(T312, void, T313), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T312, tree(T312, void, T313), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: ?_10 | delete(T312, tree(T312, void, T313), T3), SCOPE: 1, CLAUSE: 6\n\nT312 is ground\nT313 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\ndelete(T312, tree(T312, void, T313), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T312, tree(T312, void, T313), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: ','(less(T320, T320), delete(s(T320), void, T315))\n\nT313 is ground\nT320 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\ndelete(s(T320), tree(s(T320), void, T313), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(s(T320), tree(s(T320), void, T313), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: less(T320, T320)\n\nT313 is ground\nT320 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\ndelete(s(T320), tree(s(T320), void, T313), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(s(T320), tree(s(T320), void, T313), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: delete(s(T320), void, T315)\n\nT313 is ground\nT320 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\ndelete(s(T320), tree(s(T320), void, T313), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(s(T320), tree(s(T320), void, T313), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: delete(T312, tree(T312, void, T313), T3), SCOPE: 1, CLAUSE: 6\n\nT312 is ground\nT313 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\ndelete(T312, tree(T312, void, T313), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T312, tree(T312, void, T313), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: ','(less(T329, T329), delete(T329, T330, T332))\n\nT329 is ground\nT330 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\ndelete(T329, tree(T329, void, T330), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T329, tree(T329, void, T330), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: less(T329, T329)\n\nT329 is ground\nT330 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\ndelete(T329, tree(T329, void, T330), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T329, tree(T329, void, T330), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: delete(T329, T330, T332)\n\nT329 is ground\nT330 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\ndelete(T329, tree(T329, void, T330), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T329, tree(T329, void, T330), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))", fontsize=16, style=filled, fillcolor=lightyellow];
234 [label="234: ','(less(T340, T340), delete(T340, T341, T343))\n\nT340 is ground\nT341 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\nX455 is free\ndelete(T340, tree(T340, void, T341), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T340, tree(T340, void, T341), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))\ndelete(T340, tree(T340, void, T341), T3) !=? delete(X451, tree(X452, X453, X454), tree(X452, X455, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
235 [label="235: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
236 [label="236: ','(less(T340, T340), delete(T340, T341, T343)), SCOPE: 11, CLAUSE: 3 | ','(less(T340, T340), delete(T340, T341, T343)), SCOPE: 11, CLAUSE: 8\n\nT340 is ground\nT341 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\nX455 is free\ndelete(T340, tree(T340, void, T341), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T340, tree(T340, void, T341), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))\ndelete(T340, tree(T340, void, T341), T3) !=? delete(X451, tree(X452, X453, X454), tree(X452, X455, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
237 [label="237: ','(less(T340, T340), delete(T340, T341, T343)), SCOPE: 11, CLAUSE: 8\n\nT340 is ground\nT341 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\nX455 is free\ndelete(T340, tree(T340, void, T341), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T340, tree(T340, void, T341), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))\ndelete(T340, tree(T340, void, T341), T3) !=? delete(X451, tree(X452, X453, X454), tree(X452, X455, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
240 [label="240: ','(less(T346, T346), delete(s(T346), T341, T343))\n\nT341 is ground\nT346 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\nX455 is free\ndelete(s(T346), tree(s(T346), void, T341), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(s(T346), tree(s(T346), void, T341), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))\ndelete(s(T346), tree(s(T346), void, T341), T3) !=? delete(X451, tree(X452, X453, X454), tree(X452, X455, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
241 [label="241: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
243 [label="243: less(T346, T346)\n\nT341 is ground\nT346 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\nX455 is free\ndelete(s(T346), tree(s(T346), void, T341), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(s(T346), tree(s(T346), void, T341), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))\ndelete(s(T346), tree(s(T346), void, T341), T3) !=? delete(X451, tree(X452, X453, X454), tree(X452, X455, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
245 [label="245: delete(s(T346), T341, T343)\n\nT341 is ground\nT346 is ground\nX10 is free\nX11 is free\nX159 is free\nX160 is free\nX161 is free\nX162 is free\nX163 is free\nX451 is free\nX452 is free\nX453 is free\nX454 is free\nX455 is free\ndelete(s(T346), tree(s(T346), void, T341), T3) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(s(T346), tree(s(T346), void, T341), T3) !=? delete(X159, tree(X159, X160, X161), tree(X162, X160, X163))\ndelete(s(T346), tree(s(T346), void, T341), T3) !=? delete(X451, tree(X452, X453, X454), tree(X452, X455, X454))", fontsize=16, style=filled, fillcolor=lightyellow];
251 [label="251: true | delete(T353, tree(T353, T354, void), T3), SCOPE: 1, CLAUSE: 4 | delete(T353, tree(T353, T354, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T353, tree(T353, T354, void), T3), SCOPE: 1, CLAUSE: 6\n\nT353 is ground\nT354 is ground\nX6 is free\nX7 is free\ndelete(T353, tree(T353, T354, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
252 [label="252: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 5 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 6\n\nT1 is ground\nT2 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X525, tree(X525, X526, void), X526)", fontsize=16, style=filled, fillcolor=lightyellow];
253 [label="253: delete(T353, tree(T353, T354, void), T3), SCOPE: 1, CLAUSE: 4 | delete(T353, tree(T353, T354, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T353, tree(T353, T354, void), T3), SCOPE: 1, CLAUSE: 6\n\nT353 is ground\nT354 is ground\nX6 is free\nX7 is free\ndelete(T353, tree(T353, T354, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
256 [label="256: delmin(void, T363, T364) | delete(T359, tree(T359, T360, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T359, tree(T359, T360, void), T3), SCOPE: 1, CLAUSE: 6\n\nT359 is ground\nT360 is ground\nX6 is free\nX7 is free\ndelete(T359, tree(T359, T360, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
257 [label="257: delete(T353, tree(T353, T354, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T353, tree(T353, T354, void), T3), SCOPE: 1, CLAUSE: 6\n\nT353 is ground\nT354 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\ndelete(T353, tree(T353, T354, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T353, tree(T353, T354, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))", fontsize=16, style=filled, fillcolor=lightyellow];
260 [label="260: delmin(void, T363, T364), SCOPE: 12, CLAUSE: 2 | delmin(void, T363, T364), SCOPE: 12, CLAUSE: 7 | ?_12 | delete(T359, tree(T359, T360, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T359, tree(T359, T360, void), T3), SCOPE: 1, CLAUSE: 6\n\nT359 is ground\nT360 is ground\nX6 is free\nX7 is free\ndelete(T359, tree(T359, T360, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
262 [label="262: delmin(void, T363, T364), SCOPE: 12, CLAUSE: 7 | ?_12 | delete(T359, tree(T359, T360, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T359, tree(T359, T360, void), T3), SCOPE: 1, CLAUSE: 6\n\nT359 is ground\nT360 is ground\nX6 is free\nX7 is free\ndelete(T359, tree(T359, T360, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
263 [label="263: ?_12 | delete(T359, tree(T359, T360, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T359, tree(T359, T360, void), T3), SCOPE: 1, CLAUSE: 6\n\nT359 is ground\nT360 is ground\nX6 is free\nX7 is free\ndelete(T359, tree(T359, T360, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
264 [label="264: delete(T359, tree(T359, T360, void), T3), SCOPE: 1, CLAUSE: 5 | delete(T359, tree(T359, T360, void), T3), SCOPE: 1, CLAUSE: 6\n\nT359 is ground\nT360 is ground\nX6 is free\nX7 is free\ndelete(T359, tree(T359, T360, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
267 [label="267: delete(T359, tree(T359, T360, void), T3), SCOPE: 1, CLAUSE: 5\n\nT359 is ground\nT360 is ground\nX6 is free\nX7 is free\ndelete(T359, tree(T359, T360, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
268 [label="268: delete(T359, tree(T359, T360, void), T3), SCOPE: 1, CLAUSE: 6\n\nT359 is ground\nT360 is ground\nX6 is free\nX7 is free\ndelete(T359, tree(T359, T360, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
270 [label="270: ','(less(T377, T377), delete(T377, T378, T380))\n\nT377 is ground\nT378 is ground\nX6 is free\nX7 is free\ndelete(T377, tree(T377, T378, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
271 [label="271: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
276 [label="276: less(T377, T377)\n\nT377 is ground\nT378 is ground\nX6 is free\nX7 is free\ndelete(T377, tree(T377, T378, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
277 [label="277: delete(T377, T378, T380)\n\nT377 is ground\nT378 is ground\nX6 is free\nX7 is free\ndelete(T377, tree(T377, T378, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
281 [label="281: ','(less(T391, T391), delete(T391, void, T394))\n\nT391 is ground\nT392 is ground\nX6 is free\nX7 is free\ndelete(T391, tree(T391, T392, void), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
282 [label="282: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
289 [label="289: ','(less(T398, T398), delete(T398, T399, T401)) | delete(T398, tree(T398, T399, void), T3), SCOPE: 1, CLAUSE: 6\n\nT398 is ground\nT399 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\ndelete(T398, tree(T398, T399, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T398, tree(T398, T399, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))", fontsize=16, style=filled, fillcolor=lightyellow];
290 [label="290: delete(T353, tree(T353, T354, void), T3), SCOPE: 1, CLAUSE: 6\n\nT353 is ground\nT354 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\nX600 is free\nX601 is free\nX602 is free\nX603 is free\nX604 is free\ndelete(T353, tree(T353, T354, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T353, tree(T353, T354, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))\ndelete(T353, tree(T353, T354, void), T3) !=? delete(X600, tree(X601, X602, X603), tree(X601, X604, X603))", fontsize=16, style=filled, fillcolor=lightyellow];
291 [label="291: ','(less(T398, T398), delete(T398, T399, T401)), SCOPE: 13, CLAUSE: 3 | ','(less(T398, T398), delete(T398, T399, T401)), SCOPE: 13, CLAUSE: 8 | ?_13 | delete(T398, tree(T398, T399, void), T3), SCOPE: 1, CLAUSE: 6\n\nT398 is ground\nT399 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\ndelete(T398, tree(T398, T399, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T398, tree(T398, T399, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))", fontsize=16, style=filled, fillcolor=lightyellow];
292 [label="292: ','(less(T398, T398), delete(T398, T399, T401)), SCOPE: 13, CLAUSE: 8 | ?_13 | delete(T398, tree(T398, T399, void), T3), SCOPE: 1, CLAUSE: 6\n\nT398 is ground\nT399 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\ndelete(T398, tree(T398, T399, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T398, tree(T398, T399, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))", fontsize=16, style=filled, fillcolor=lightyellow];
293 [label="293: ','(less(T398, T398), delete(T398, T399, T401)), SCOPE: 13, CLAUSE: 8\n\nT398 is ground\nT399 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\ndelete(T398, tree(T398, T399, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T398, tree(T398, T399, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))", fontsize=16, style=filled, fillcolor=lightyellow];
294 [label="294: ?_13 | delete(T398, tree(T398, T399, void), T3), SCOPE: 1, CLAUSE: 6\n\nT398 is ground\nT399 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\ndelete(T398, tree(T398, T399, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T398, tree(T398, T399, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))", fontsize=16, style=filled, fillcolor=lightyellow];
296 [label="296: ','(less(T406, T406), delete(s(T406), T399, T401))\n\nT399 is ground\nT406 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\ndelete(s(T406), tree(s(T406), T399, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T406), tree(s(T406), T399, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))", fontsize=16, style=filled, fillcolor=lightyellow];
297 [label="297: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
302 [label="302: less(T406, T406)\n\nT399 is ground\nT406 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\ndelete(s(T406), tree(s(T406), T399, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T406), tree(s(T406), T399, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))", fontsize=16, style=filled, fillcolor=lightyellow];
304 [label="304: delete(s(T406), T399, T401)\n\nT399 is ground\nT406 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\ndelete(s(T406), tree(s(T406), T399, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T406), tree(s(T406), T399, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))", fontsize=16, style=filled, fillcolor=lightyellow];
307 [label="307: delete(T398, tree(T398, T399, void), T3), SCOPE: 1, CLAUSE: 6\n\nT398 is ground\nT399 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\ndelete(T398, tree(T398, T399, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T398, tree(T398, T399, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))", fontsize=16, style=filled, fillcolor=lightyellow];
308 [label="308: ','(less(T417, T417), delete(T417, void, T420))\n\nT417 is ground\nT418 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\ndelete(T417, tree(T417, T418, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T417, tree(T417, T418, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))", fontsize=16, style=filled, fillcolor=lightyellow];
309 [label="309: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
312 [label="312: ','(less(T424, T424), delete(T424, void, T427))\n\nT424 is ground\nT425 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\nX600 is free\nX601 is free\nX602 is free\nX603 is free\nX604 is free\ndelete(T424, tree(T424, T425, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T424, tree(T424, T425, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))\ndelete(T424, tree(T424, T425, void), T3) !=? delete(X600, tree(X601, X602, X603), tree(X601, X604, X603))", fontsize=16, style=filled, fillcolor=lightyellow];
315 [label="315: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
316 [label="316: ','(less(T424, T424), delete(T424, void, T427)), SCOPE: 14, CLAUSE: 3 | ','(less(T424, T424), delete(T424, void, T427)), SCOPE: 14, CLAUSE: 8\n\nT424 is ground\nT425 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\nX600 is free\nX601 is free\nX602 is free\nX603 is free\nX604 is free\ndelete(T424, tree(T424, T425, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T424, tree(T424, T425, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))\ndelete(T424, tree(T424, T425, void), T3) !=? delete(X600, tree(X601, X602, X603), tree(X601, X604, X603))", fontsize=16, style=filled, fillcolor=lightyellow];
317 [label="317: ','(less(T424, T424), delete(T424, void, T427)), SCOPE: 14, CLAUSE: 8\n\nT424 is ground\nT425 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\nX600 is free\nX601 is free\nX602 is free\nX603 is free\nX604 is free\ndelete(T424, tree(T424, T425, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T424, tree(T424, T425, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))\ndelete(T424, tree(T424, T425, void), T3) !=? delete(X600, tree(X601, X602, X603), tree(X601, X604, X603))", fontsize=16, style=filled, fillcolor=lightyellow];
318 [label="318: ','(less(T430, T430), delete(s(T430), void, T427))\n\nT425 is ground\nT430 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\nX600 is free\nX601 is free\nX602 is free\nX603 is free\nX604 is free\ndelete(s(T430), tree(s(T430), T425, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T430), tree(s(T430), T425, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))\ndelete(s(T430), tree(s(T430), T425, void), T3) !=? delete(X600, tree(X601, X602, X603), tree(X601, X604, X603))", fontsize=16, style=filled, fillcolor=lightyellow];
319 [label="319: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
320 [label="320: less(T430, T430)\n\nT425 is ground\nT430 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\nX600 is free\nX601 is free\nX602 is free\nX603 is free\nX604 is free\ndelete(s(T430), tree(s(T430), T425, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T430), tree(s(T430), T425, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))\ndelete(s(T430), tree(s(T430), T425, void), T3) !=? delete(X600, tree(X601, X602, X603), tree(X601, X604, X603))", fontsize=16, style=filled, fillcolor=lightyellow];
321 [label="321: delete(s(T430), void, T427)\n\nT425 is ground\nT430 is ground\nX6 is free\nX7 is free\nX532 is free\nX533 is free\nX534 is free\nX535 is free\nX536 is free\nX600 is free\nX601 is free\nX602 is free\nX603 is free\nX604 is free\ndelete(s(T430), tree(s(T430), T425, void), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T430), tree(s(T430), T425, void), T3) !=? delete(X532, tree(X532, X533, X534), tree(X535, X533, X536))\ndelete(s(T430), tree(s(T430), T425, void), T3) !=? delete(X600, tree(X601, X602, X603), tree(X601, X604, X603))", fontsize=16, style=filled, fillcolor=lightyellow];
322 [label="322: delmin(T440, T443, T444) | delete(T438, tree(T438, T439, T440), T3), SCOPE: 1, CLAUSE: 5 | delete(T438, tree(T438, T439, T440), T3), SCOPE: 1, CLAUSE: 6\n\nT438 is ground\nT439 is ground\nT440 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X525, tree(X525, X526, void), X526)", fontsize=16, style=filled, fillcolor=lightyellow];
323 [label="323: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 5 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 6\n\nT1 is ground\nT2 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(T1, T2, T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
324 [label="324: delmin(T440, T443, T444), SCOPE: 15, CLAUSE: 2 | delmin(T440, T443, T444), SCOPE: 15, CLAUSE: 7 | ?_15 | delete(T438, tree(T438, T439, T440), T3), SCOPE: 1, CLAUSE: 5 | delete(T438, tree(T438, T439, T440), T3), SCOPE: 1, CLAUSE: 6\n\nT438 is ground\nT439 is ground\nT440 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X525, tree(X525, X526, void), X526)", fontsize=16, style=filled, fillcolor=lightyellow];
325 [label="325: true | delmin(tree(T449, void, T450), T443, T444), SCOPE: 15, CLAUSE: 7 | ?_15 | delete(T438, tree(T438, T439, tree(T449, void, T450)), T3), SCOPE: 1, CLAUSE: 5 | delete(T438, tree(T438, T439, tree(T449, void, T450)), T3), SCOPE: 1, CLAUSE: 6\n\nT438 is ground\nT439 is ground\nT449 is ground\nT450 is ground\nX6 is free\nX7 is free\ndelete(T438, tree(T438, T439, tree(T449, void, T450)), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
326 [label="326: delmin(T440, T443, T444), SCOPE: 15, CLAUSE: 7 | ?_15 | delete(T438, tree(T438, T439, T440), T3), SCOPE: 1, CLAUSE: 5 | delete(T438, tree(T438, T439, T440), T3), SCOPE: 1, CLAUSE: 6\n\nT438 is ground\nT439 is ground\nT440 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX680 is free\nX681 is free\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelmin(T440, T443, T444) !=? delmin(tree(X680, void, X681), X680, X681)", fontsize=16, style=filled, fillcolor=lightyellow];
327 [label="327: delmin(tree(T449, void, T450), T443, T444), SCOPE: 15, CLAUSE: 7 | ?_15 | delete(T438, tree(T438, T439, tree(T449, void, T450)), T3), SCOPE: 1, CLAUSE: 5 | delete(T438, tree(T438, T439, tree(T449, void, T450)), T3), SCOPE: 1, CLAUSE: 6\n\nT438 is ground\nT439 is ground\nT449 is ground\nT450 is ground\nX6 is free\nX7 is free\ndelete(T438, tree(T438, T439, tree(T449, void, T450)), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
328 [label="328: delmin(tree(T449, void, T450), T443, T444), SCOPE: 15, CLAUSE: 7\n\nT438 is ground\nT439 is ground\nT449 is ground\nT450 is ground\nX6 is free\nX7 is free\ndelete(T438, tree(T438, T439, tree(T449, void, T450)), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
329 [label="329: ?_15 | delete(T438, tree(T438, T439, tree(T449, void, T450)), T3), SCOPE: 1, CLAUSE: 5 | delete(T438, tree(T438, T439, tree(T449, void, T450)), T3), SCOPE: 1, CLAUSE: 6\n\nT438 is ground\nT439 is ground\nT449 is ground\nT450 is ground\nX6 is free\nX7 is free\ndelete(T438, tree(T438, T439, tree(T449, void, T450)), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
330 [label="330: delmin(void, T476, T477)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
331 [label="331: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
332 [label="332: delete(T438, tree(T438, T439, tree(T449, void, T450)), T3), SCOPE: 1, CLAUSE: 5 | delete(T438, tree(T438, T439, tree(T449, void, T450)), T3), SCOPE: 1, CLAUSE: 6\n\nT438 is ground\nT439 is ground\nT449 is ground\nT450 is ground\nX6 is free\nX7 is free\ndelete(T438, tree(T438, T439, tree(T449, void, T450)), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
333 [label="333: delete(T438, tree(T438, T439, tree(T449, void, T450)), T3), SCOPE: 1, CLAUSE: 5\n\nT438 is ground\nT439 is ground\nT449 is ground\nT450 is ground\nX6 is free\nX7 is free\ndelete(T438, tree(T438, T439, tree(T449, void, T450)), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
334 [label="334: delete(T438, tree(T438, T439, tree(T449, void, T450)), T3), SCOPE: 1, CLAUSE: 6\n\nT438 is ground\nT439 is ground\nT449 is ground\nT450 is ground\nX6 is free\nX7 is free\ndelete(T438, tree(T438, T439, tree(T449, void, T450)), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
335 [label="335: ','(less(T498, T498), delete(T498, T499, T503))\n\nT498 is ground\nT499 is ground\nT500 is ground\nT501 is ground\nX6 is free\nX7 is free\ndelete(T498, tree(T498, T499, tree(T500, void, T501)), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
336 [label="336: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
337 [label="337: less(T498, T498)\n\nT498 is ground\nT499 is ground\nT500 is ground\nT501 is ground\nX6 is free\nX7 is free\ndelete(T498, tree(T498, T499, tree(T500, void, T501)), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
338 [label="338: delete(T498, T499, T503)\n\nT498 is ground\nT499 is ground\nT500 is ground\nT501 is ground\nX6 is free\nX7 is free\ndelete(T498, tree(T498, T499, tree(T500, void, T501)), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
339 [label="339: ','(less(T518, T518), delete(T518, tree(T520, void, T521), T523))\n\nT518 is ground\nT519 is ground\nT520 is ground\nT521 is ground\nX6 is free\nX7 is free\ndelete(T518, tree(T518, T519, tree(T520, void, T521)), T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
340 [label="340: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
341 [label="341: delmin(T440, T443, T444), SCOPE: 15, CLAUSE: 7\n\nT438 is ground\nT439 is ground\nT440 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX680 is free\nX681 is free\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelmin(T440, T443, T444) !=? delmin(tree(X680, void, X681), X680, X681)", fontsize=16, style=filled, fillcolor=lightyellow];
342 [label="342: ?_15 | delete(T438, tree(T438, T439, T440), T3), SCOPE: 1, CLAUSE: 5 | delete(T438, tree(T438, T439, T440), T3), SCOPE: 1, CLAUSE: 6\n\nT438 is ground\nT439 is ground\nT440 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX680 is free\nX681 is free\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelmin(T440, T443, T444) !=? delmin(tree(X680, void, X681), X680, X681)", fontsize=16, style=filled, fillcolor=lightyellow];
343 [label="343: delmin(T549, T554, T555)\n\nT438 is ground\nT439 is ground\nT548 is ground\nT549 is ground\nT550 is ground\nX6 is free\nX7 is free\nX680 is free\nX681 is free\ndelete(T438, tree(T438, T439, tree(T548, T549, T550)), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelmin(tree(T548, T549, T550), T443, T444) !=? delmin(tree(X680, void, X681), X680, X681)", fontsize=16, style=filled, fillcolor=lightyellow];
344 [label="344: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
387 [label="387: delete(T438, tree(T438, T439, T440), T3), SCOPE: 1, CLAUSE: 5 | delete(T438, tree(T438, T439, T440), T3), SCOPE: 1, CLAUSE: 6\n\nT438 is ground\nT439 is ground\nT440 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX680 is free\nX681 is free\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelmin(T440, T443, T444) !=? delmin(tree(X680, void, X681), X680, X681)", fontsize=16, style=filled, fillcolor=lightyellow];
388 [label="388: delete(T438, tree(T438, T439, T440), T3), SCOPE: 1, CLAUSE: 5\n\nT438 is ground\nT439 is ground\nT440 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX680 is free\nX681 is free\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelmin(T440, T443, T444) !=? delmin(tree(X680, void, X681), X680, X681)", fontsize=16, style=filled, fillcolor=lightyellow];
389 [label="389: delete(T438, tree(T438, T439, T440), T3), SCOPE: 1, CLAUSE: 6\n\nT438 is ground\nT439 is ground\nT440 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX680 is free\nX681 is free\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T438, tree(T438, T439, T440), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelmin(T440, T443, T444) !=? delmin(tree(X680, void, X681), X680, X681)", fontsize=16, style=filled, fillcolor=lightyellow];
390 [label="390: ','(less(T576, T576), delete(T576, T577, T580))\n\nT576 is ground\nT577 is ground\nT578 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\ndelete(T576, tree(T576, T577, T578), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T576, tree(T576, T577, T578), T3) !=? delete(X525, tree(X525, X526, void), X526)", fontsize=16, style=filled, fillcolor=lightyellow];
391 [label="391: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
392 [label="392: less(T576, T576)\n\nT576 is ground\nT577 is ground\nT578 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\ndelete(T576, tree(T576, T577, T578), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T576, tree(T576, T577, T578), T3) !=? delete(X525, tree(X525, X526, void), X526)", fontsize=16, style=filled, fillcolor=lightyellow];
393 [label="393: delete(T576, T577, T580)\n\nT576 is ground\nT577 is ground\nT578 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\ndelete(T576, tree(T576, T577, T578), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T576, tree(T576, T577, T578), T3) !=? delete(X525, tree(X525, X526, void), X526)", fontsize=16, style=filled, fillcolor=lightyellow];
394 [label="394: ','(less(T593, T593), delete(T593, T595, T597))\n\nT593 is ground\nT594 is ground\nT595 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX680 is free\nX681 is free\ndelete(T593, tree(T593, T594, T595), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T593, tree(T593, T594, T595), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelmin(T595, T443, T444) !=? delmin(tree(X680, void, X681), X680, X681)", fontsize=16, style=filled, fillcolor=lightyellow];
395 [label="395: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
439 [label="439: less(T593, T593)\n\nT593 is ground\nT594 is ground\nT595 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\ndelete(T593, tree(T593, T594, T595), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T593, tree(T593, T594, T595), T3) !=? delete(X525, tree(X525, X526, void), X526)", fontsize=16, style=filled, fillcolor=lightyellow];
441 [label="441: delete(T593, T595, T597)\n\nT593 is ground\nT594 is ground\nT595 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX680 is free\nX681 is free\ndelete(T593, tree(T593, T594, T595), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T593, tree(T593, T594, T595), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelmin(T595, T443, T444) !=? delmin(tree(X680, void, X681), X680, X681)", fontsize=16, style=filled, fillcolor=lightyellow];
446 [label="446: ','(less(T607, T608), delete(T607, T609, T612)) | delete(T607, tree(T608, T609, T610), T3), SCOPE: 1, CLAUSE: 6\n\nT607 is ground\nT608 is ground\nT609 is ground\nT610 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
447 [label="447: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 6\n\nT1 is ground\nT2 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX861 is free\nX862 is free\nX863 is free\nX864 is free\nX865 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(T1, T2, T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\ndelete(T1, T2, T3) !=? delete(X861, tree(X862, X863, X864), tree(X862, X865, X864))", fontsize=16, style=filled, fillcolor=lightyellow];
448 [label="448: ','(less(T607, T608), delete(T607, T609, T612)), SCOPE: 16, CLAUSE: 3 | ','(less(T607, T608), delete(T607, T609, T612)), SCOPE: 16, CLAUSE: 8 | ?_16 | delete(T607, tree(T608, T609, T610), T3), SCOPE: 1, CLAUSE: 6\n\nT607 is ground\nT608 is ground\nT609 is ground\nT610 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
449 [label="449: delete(0, T609, T612) | ','(less(0, s(T615)), delete(0, T609, T612)), SCOPE: 16, CLAUSE: 8 | ?_16 | delete(0, tree(s(T615), T609, T610), T3), SCOPE: 1, CLAUSE: 6\n\nT609 is ground\nT610 is ground\nT615 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
450 [label="450: ','(less(T607, T608), delete(T607, T609, T612)), SCOPE: 16, CLAUSE: 8 | ?_16 | delete(T607, tree(T608, T609, T610), T3), SCOPE: 1, CLAUSE: 6\n\nT607 is ground\nT608 is ground\nT609 is ground\nT610 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX868 is free\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\nless(T607, T608) !=? less(0, s(X868))", fontsize=16, style=filled, fillcolor=lightyellow];
459 [label="459: delete(0, T609, T612)\n\nT609 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
460 [label="460: ','(less(0, s(T615)), delete(0, T609, T612)), SCOPE: 16, CLAUSE: 8 | ?_16 | delete(0, tree(s(T615), T609, T610), T3), SCOPE: 1, CLAUSE: 6\n\nT609 is ground\nT610 is ground\nT615 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
461 [label="461: ?_16 | delete(0, tree(s(T615), T609, T610), T3), SCOPE: 1, CLAUSE: 6\n\nT609 is ground\nT610 is ground\nT615 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
462 [label="462: delete(0, tree(s(T615), T609, T610), T3), SCOPE: 1, CLAUSE: 6\n\nT609 is ground\nT610 is ground\nT615 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
487 [label="487: ','(less(s(T628), 0), delete(0, T630, T632))\n\nT628 is ground\nT630 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
489 [label="489: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
494 [label="494: less(s(T628), 0)\n\nT628 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
495 [label="495: delete(0, T630, T632)\n\nT630 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
496 [label="496: less(s(T628), 0), SCOPE: 17, CLAUSE: 3 | less(s(T628), 0), SCOPE: 17, CLAUSE: 8\n\nT628 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
497 [label="497: less(s(T628), 0), SCOPE: 17, CLAUSE: 8\n\nT628 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
498 [label="498: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
499 [label="499: ','(less(T607, T608), delete(T607, T609, T612)), SCOPE: 16, CLAUSE: 8\n\nT607 is ground\nT608 is ground\nT609 is ground\nT610 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX868 is free\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\nless(T607, T608) !=? less(0, s(X868))", fontsize=16, style=filled, fillcolor=lightyellow];
500 [label="500: ?_16 | delete(T607, tree(T608, T609, T610), T3), SCOPE: 1, CLAUSE: 6\n\nT607 is ground\nT608 is ground\nT609 is ground\nT610 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX868 is free\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\nless(T607, T608) !=? less(0, s(X868))", fontsize=16, style=filled, fillcolor=lightyellow];
501 [label="501: ','(less(T644, T645), delete(s(T644), T609, T612))\n\nT609 is ground\nT610 is ground\nT644 is ground\nT645 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(T644), tree(s(T645), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T644), tree(s(T645), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(T644), tree(s(T645), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
502 [label="502: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
503 [label="503: less(T644, T645)\n\nT609 is ground\nT610 is ground\nT644 is ground\nT645 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(T644), tree(s(T645), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T644), tree(s(T645), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(T644), tree(s(T645), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
504 [label="504: delete(s(T644), T609, T612)\n\nT609 is ground\nT610 is ground\nT644 is ground\nT645 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(T644), tree(s(T645), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T644), tree(s(T645), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(T644), tree(s(T645), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
505 [label="505: less(T644, T645), SCOPE: 18, CLAUSE: 3 | less(T644, T645), SCOPE: 18, CLAUSE: 8\n\nT609 is ground\nT610 is ground\nT644 is ground\nT645 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(T644), tree(s(T645), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T644), tree(s(T645), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(T644), tree(s(T645), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
506 [label="506: true | less(0, s(T652)), SCOPE: 18, CLAUSE: 8\n\nT652 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
507 [label="507: less(T644, T645), SCOPE: 18, CLAUSE: 8\n\nT609 is ground\nT610 is ground\nT644 is ground\nT645 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX921 is free\ndelete(s(T644), tree(s(T645), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T644), tree(s(T645), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(T644), tree(s(T645), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\nless(T644, T645) !=? less(0, s(X921))", fontsize=16, style=filled, fillcolor=lightyellow];
508 [label="508: less(0, s(T652)), SCOPE: 18, CLAUSE: 8\n\nT652 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
509 [label="509: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
510 [label="510: less(T657, T658)\n\nT609 is ground\nT610 is ground\nT657 is ground\nT658 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(s(T657)), tree(s(s(T658)), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(T657)), tree(s(s(T658)), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(T657)), tree(s(s(T658)), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
511 [label="511: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
512 [label="512: less(T657, T658), SCOPE: 19, CLAUSE: 3 | less(T657, T658), SCOPE: 19, CLAUSE: 8\n\nT609 is ground\nT610 is ground\nT657 is ground\nT658 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(s(T657)), tree(s(s(T658)), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(T657)), tree(s(s(T658)), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(T657)), tree(s(s(T658)), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
513 [label="513: true | less(0, s(T663)), SCOPE: 19, CLAUSE: 8\n\nT663 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
514 [label="514: less(T657, T658), SCOPE: 19, CLAUSE: 8\n\nT609 is ground\nT610 is ground\nT657 is ground\nT658 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX934 is free\ndelete(s(s(T657)), tree(s(s(T658)), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(T657)), tree(s(s(T658)), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(T657)), tree(s(s(T658)), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\nless(T657, T658) !=? less(0, s(X934))", fontsize=16, style=filled, fillcolor=lightyellow];
515 [label="515: less(0, s(T663)), SCOPE: 19, CLAUSE: 8\n\nT663 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
516 [label="516: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
517 [label="517: less(T668, T669)\n\nT609 is ground\nT610 is ground\nT668 is ground\nT669 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(s(s(T668))), tree(s(s(s(T669))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(T668))), tree(s(s(s(T669))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(T668))), tree(s(s(s(T669))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
518 [label="518: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
519 [label="519: less(T668, T669), SCOPE: 20, CLAUSE: 3 | less(T668, T669), SCOPE: 20, CLAUSE: 8\n\nT609 is ground\nT610 is ground\nT668 is ground\nT669 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(s(s(T668))), tree(s(s(s(T669))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(T668))), tree(s(s(s(T669))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(T668))), tree(s(s(s(T669))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
520 [label="520: true | less(0, s(T674)), SCOPE: 20, CLAUSE: 8\n\nT674 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
521 [label="521: less(T668, T669), SCOPE: 20, CLAUSE: 8\n\nT609 is ground\nT610 is ground\nT668 is ground\nT669 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX947 is free\ndelete(s(s(s(T668))), tree(s(s(s(T669))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(T668))), tree(s(s(s(T669))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(T668))), tree(s(s(s(T669))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\nless(T668, T669) !=? less(0, s(X947))", fontsize=16, style=filled, fillcolor=lightyellow];
522 [label="522: less(0, s(T674)), SCOPE: 20, CLAUSE: 8\n\nT674 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
523 [label="523: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
524 [label="524: less(T679, T680)\n\nT609 is ground\nT610 is ground\nT679 is ground\nT680 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(s(s(s(T679)))), tree(s(s(s(s(T680)))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(s(T679)))), tree(s(s(s(s(T680)))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(s(T679)))), tree(s(s(s(s(T680)))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
525 [label="525: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
526 [label="526: less(T679, T680), SCOPE: 21, CLAUSE: 3 | less(T679, T680), SCOPE: 21, CLAUSE: 8\n\nT609 is ground\nT610 is ground\nT679 is ground\nT680 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(s(s(s(T679)))), tree(s(s(s(s(T680)))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(s(T679)))), tree(s(s(s(s(T680)))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(s(T679)))), tree(s(s(s(s(T680)))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
527 [label="527: true | less(0, s(T685)), SCOPE: 21, CLAUSE: 8\n\nT685 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
528 [label="528: less(T679, T680), SCOPE: 21, CLAUSE: 8\n\nT609 is ground\nT610 is ground\nT679 is ground\nT680 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX960 is free\ndelete(s(s(s(s(T679)))), tree(s(s(s(s(T680)))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(s(T679)))), tree(s(s(s(s(T680)))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(s(T679)))), tree(s(s(s(s(T680)))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\nless(T679, T680) !=? less(0, s(X960))", fontsize=16, style=filled, fillcolor=lightyellow];
529 [label="529: less(0, s(T685)), SCOPE: 21, CLAUSE: 8\n\nT685 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
530 [label="530: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
531 [label="531: less(T690, T691)\n\nT609 is ground\nT610 is ground\nT690 is ground\nT691 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(s(s(s(s(T690))))), tree(s(s(s(s(s(T691))))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(s(s(T690))))), tree(s(s(s(s(s(T691))))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(s(s(T690))))), tree(s(s(s(s(s(T691))))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
532 [label="532: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
533 [label="533: less(T690, T691), SCOPE: 22, CLAUSE: 3 | less(T690, T691), SCOPE: 22, CLAUSE: 8\n\nT609 is ground\nT610 is ground\nT690 is ground\nT691 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(s(s(s(s(T690))))), tree(s(s(s(s(s(T691))))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(s(s(T690))))), tree(s(s(s(s(s(T691))))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(s(s(T690))))), tree(s(s(s(s(s(T691))))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
534 [label="534: true | less(0, s(T696)), SCOPE: 22, CLAUSE: 8\n\nT696 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
535 [label="535: less(T690, T691), SCOPE: 22, CLAUSE: 8\n\nT609 is ground\nT610 is ground\nT690 is ground\nT691 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX973 is free\ndelete(s(s(s(s(s(T690))))), tree(s(s(s(s(s(T691))))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(s(s(T690))))), tree(s(s(s(s(s(T691))))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(s(s(T690))))), tree(s(s(s(s(s(T691))))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\nless(T690, T691) !=? less(0, s(X973))", fontsize=16, style=filled, fillcolor=lightyellow];
536 [label="536: less(0, s(T696)), SCOPE: 22, CLAUSE: 8\n\nT696 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
537 [label="537: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
538 [label="538: less(T701, T702)\n\nT609 is ground\nT610 is ground\nT701 is ground\nT702 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(s(s(s(s(s(T701)))))), tree(s(s(s(s(s(s(T702)))))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(s(s(s(T701)))))), tree(s(s(s(s(s(s(T702)))))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(s(s(s(T701)))))), tree(s(s(s(s(s(s(T702)))))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
539 [label="539: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
540 [label="540: less(T701, T702), SCOPE: 23, CLAUSE: 3 | less(T701, T702), SCOPE: 23, CLAUSE: 8\n\nT609 is ground\nT610 is ground\nT701 is ground\nT702 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(s(s(s(s(s(T701)))))), tree(s(s(s(s(s(s(T702)))))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(s(s(s(T701)))))), tree(s(s(s(s(s(s(T702)))))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(s(s(s(T701)))))), tree(s(s(s(s(s(s(T702)))))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
541 [label="541: true | less(0, s(T707)), SCOPE: 23, CLAUSE: 8\n\nT707 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
542 [label="542: less(T701, T702), SCOPE: 23, CLAUSE: 8\n\nT609 is ground\nT610 is ground\nT701 is ground\nT702 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX986 is free\ndelete(s(s(s(s(s(s(T701)))))), tree(s(s(s(s(s(s(T702)))))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(s(s(s(T701)))))), tree(s(s(s(s(s(s(T702)))))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(s(s(s(T701)))))), tree(s(s(s(s(s(s(T702)))))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\nless(T701, T702) !=? less(0, s(X986))", fontsize=16, style=filled, fillcolor=lightyellow];
543 [label="543: less(0, s(T707)), SCOPE: 23, CLAUSE: 8\n\nT707 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
544 [label="544: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
545 [label="545: less(T712, T713)\n\nT609 is ground\nT610 is ground\nT712 is ground\nT713 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(s(s(s(s(s(s(T712))))))), tree(s(s(s(s(s(s(s(T713))))))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(s(s(s(s(T712))))))), tree(s(s(s(s(s(s(s(T713))))))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(s(s(s(s(T712))))))), tree(s(s(s(s(s(s(s(T713))))))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
546 [label="546: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
547 [label="547: less(T712, T713), SCOPE: 24, CLAUSE: 3 | less(T712, T713), SCOPE: 24, CLAUSE: 8\n\nT609 is ground\nT610 is ground\nT712 is ground\nT713 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(s(s(s(s(s(s(T712))))))), tree(s(s(s(s(s(s(s(T713))))))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(s(s(s(s(T712))))))), tree(s(s(s(s(s(s(s(T713))))))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(s(s(s(s(T712))))))), tree(s(s(s(s(s(s(s(T713))))))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
548 [label="548: true | less(0, s(T718)), SCOPE: 24, CLAUSE: 8\n\nT718 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
549 [label="549: less(T712, T713), SCOPE: 24, CLAUSE: 8\n\nT609 is ground\nT610 is ground\nT712 is ground\nT713 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX999 is free\ndelete(s(s(s(s(s(s(s(T712))))))), tree(s(s(s(s(s(s(s(T713))))))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(s(s(s(s(T712))))))), tree(s(s(s(s(s(s(s(T713))))))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(s(s(s(s(T712))))))), tree(s(s(s(s(s(s(s(T713))))))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\nless(T712, T713) !=? less(0, s(X999))", fontsize=16, style=filled, fillcolor=lightyellow];
550 [label="550: less(0, s(T718)), SCOPE: 24, CLAUSE: 8\n\nT718 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
551 [label="551: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
552 [label="552: less(T723, T724)\n\nT609 is ground\nT610 is ground\nT723 is ground\nT724 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\ndelete(s(s(s(s(s(s(s(s(T723)))))))), tree(s(s(s(s(s(s(s(s(T724)))))))), T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(s(s(s(s(s(s(s(T723)))))))), tree(s(s(s(s(s(s(s(s(T724)))))))), T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(s(s(s(s(s(s(s(T723)))))))), tree(s(s(s(s(s(s(s(s(T724)))))))), T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))", fontsize=16, style=filled, fillcolor=lightyellow];
553 [label="553: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
554 [label="554: less(T723, T724)\n\nT723 is ground\nT724 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
555 [label="555: less(T723, T724), SCOPE: 25, CLAUSE: 3 | less(T723, T724), SCOPE: 25, CLAUSE: 8\n\nT723 is ground\nT724 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
556 [label="556: true | less(0, s(T733)), SCOPE: 25, CLAUSE: 8\n\nT733 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
557 [label="557: less(T723, T724), SCOPE: 25, CLAUSE: 8\n\nT723 is ground\nT724 is ground\nX1014 is free\nless(T723, T724) !=? less(0, s(X1014))", fontsize=16, style=filled, fillcolor=lightyellow];
558 [label="558: less(0, s(T733)), SCOPE: 25, CLAUSE: 8\n\nT733 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
559 [label="559: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
560 [label="560: less(T738, T739)\n\nT738 is ground\nT739 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
561 [label="561: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
677 [label="677: delete(T607, tree(T608, T609, T610), T3), SCOPE: 1, CLAUSE: 6\n\nT607 is ground\nT608 is ground\nT609 is ground\nT610 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX868 is free\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(T607, tree(T608, T609, T610), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\nless(T607, T608) !=? less(0, s(X868))", fontsize=16, style=filled, fillcolor=lightyellow];
678 [label="678: ','(less(T757, T756), delete(T756, T759, T761))\n\nT756 is ground\nT757 is ground\nT758 is ground\nT759 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX868 is free\ndelete(T756, tree(T757, T758, T759), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T756, tree(T757, T758, T759), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(T756, tree(T757, T758, T759), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\nless(T756, T757) !=? less(0, s(X868))", fontsize=16, style=filled, fillcolor=lightyellow];
679 [label="679: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
680 [label="680: less(T757, T756)\n\nT756 is ground\nT757 is ground\nT758 is ground\nT759 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX868 is free\ndelete(T756, tree(T757, T758, T759), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T756, tree(T757, T758, T759), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(T756, tree(T757, T758, T759), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\nless(T756, T757) !=? less(0, s(X868))", fontsize=16, style=filled, fillcolor=lightyellow];
681 [label="681: delete(T756, T759, T761)\n\nT756 is ground\nT757 is ground\nT758 is ground\nT759 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX868 is free\ndelete(T756, tree(T757, T758, T759), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T756, tree(T757, T758, T759), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(T756, tree(T757, T758, T759), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\nless(T756, T757) !=? less(0, s(X868))", fontsize=16, style=filled, fillcolor=lightyellow];
682 [label="682: ','(less(T776, T775), delete(T775, T778, T780))\n\nT775 is ground\nT776 is ground\nT777 is ground\nT778 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX861 is free\nX862 is free\nX863 is free\nX864 is free\nX865 is free\ndelete(T775, tree(T776, T777, T778), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T775, tree(T776, T777, T778), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(T775, tree(T776, T777, T778), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\ndelete(T775, tree(T776, T777, T778), T3) !=? delete(X861, tree(X862, X863, X864), tree(X862, X865, X864))", fontsize=16, style=filled, fillcolor=lightyellow];
683 [label="683: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
684 [label="684: ','(less(T776, T775), delete(T775, T778, T780)), SCOPE: 26, CLAUSE: 3 | ','(less(T776, T775), delete(T775, T778, T780)), SCOPE: 26, CLAUSE: 8\n\nT775 is ground\nT776 is ground\nT777 is ground\nT778 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX861 is free\nX862 is free\nX863 is free\nX864 is free\nX865 is free\ndelete(T775, tree(T776, T777, T778), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T775, tree(T776, T777, T778), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(T775, tree(T776, T777, T778), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\ndelete(T775, tree(T776, T777, T778), T3) !=? delete(X861, tree(X862, X863, X864), tree(X862, X865, X864))", fontsize=16, style=filled, fillcolor=lightyellow];
685 [label="685: delete(s(T783), T778, T780) | ','(less(0, s(T783)), delete(s(T783), T778, T780)), SCOPE: 26, CLAUSE: 8\n\nT777 is ground\nT778 is ground\nT783 is ground\nX861 is free\nX862 is free\nX863 is free\nX864 is free\nX865 is free\ndelete(s(T783), tree(0, T777, T778), T3) !=? delete(X861, tree(X862, X863, X864), tree(X862, X865, X864))", fontsize=16, style=filled, fillcolor=lightyellow];
686 [label="686: ','(less(T776, T775), delete(T775, T778, T780)), SCOPE: 26, CLAUSE: 8\n\nT775 is ground\nT776 is ground\nT777 is ground\nT778 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX861 is free\nX862 is free\nX863 is free\nX864 is free\nX865 is free\nX1064 is free\ndelete(T775, tree(T776, T777, T778), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T775, tree(T776, T777, T778), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(T775, tree(T776, T777, T778), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\ndelete(T775, tree(T776, T777, T778), T3) !=? delete(X861, tree(X862, X863, X864), tree(X862, X865, X864))\nless(T776, T775) !=? less(0, s(X1064))", fontsize=16, style=filled, fillcolor=lightyellow];
687 [label="687: delete(s(T783), T778, T780)\n\nT777 is ground\nT778 is ground\nT783 is ground\nX861 is free\nX862 is free\nX863 is free\nX864 is free\nX865 is free\ndelete(s(T783), tree(0, T777, T778), T3) !=? delete(X861, tree(X862, X863, X864), tree(X862, X865, X864))", fontsize=16, style=filled, fillcolor=lightyellow];
688 [label="688: ','(less(0, s(T783)), delete(s(T783), T778, T780)), SCOPE: 26, CLAUSE: 8\n\nT777 is ground\nT778 is ground\nT783 is ground\nX861 is free\nX862 is free\nX863 is free\nX864 is free\nX865 is free\ndelete(s(T783), tree(0, T777, T778), T3) !=? delete(X861, tree(X862, X863, X864), tree(X862, X865, X864))", fontsize=16, style=filled, fillcolor=lightyellow];
689 [label="689: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
690 [label="690: ','(less(T796, T797), delete(s(T797), T778, T780))\n\nT777 is ground\nT778 is ground\nT796 is ground\nT797 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX861 is free\nX862 is free\nX863 is free\nX864 is free\nX865 is free\ndelete(s(T797), tree(s(T796), T777, T778), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T797), tree(s(T796), T777, T778), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(T797), tree(s(T796), T777, T778), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\ndelete(s(T797), tree(s(T796), T777, T778), T3) !=? delete(X861, tree(X862, X863, X864), tree(X862, X865, X864))", fontsize=16, style=filled, fillcolor=lightyellow];
691 [label="691: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
692 [label="692: less(T796, T797)\n\nT777 is ground\nT778 is ground\nT796 is ground\nT797 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX861 is free\nX862 is free\nX863 is free\nX864 is free\nX865 is free\ndelete(s(T797), tree(s(T796), T777, T778), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T797), tree(s(T796), T777, T778), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(T797), tree(s(T796), T777, T778), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\ndelete(s(T797), tree(s(T796), T777, T778), T3) !=? delete(X861, tree(X862, X863, X864), tree(X862, X865, X864))", fontsize=16, style=filled, fillcolor=lightyellow];
693 [label="693: delete(s(T797), T778, T780)\n\nT777 is ground\nT778 is ground\nT796 is ground\nT797 is ground\nX6 is free\nX7 is free\nX525 is free\nX526 is free\nX671 is free\nX672 is free\nX673 is free\nX674 is free\nX675 is free\nX861 is free\nX862 is free\nX863 is free\nX864 is free\nX865 is free\ndelete(s(T797), tree(s(T796), T777, T778), T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T797), tree(s(T796), T777, T778), T3) !=? delete(X525, tree(X525, X526, void), X526)\ndelete(s(T797), tree(s(T796), T777, T778), T3) !=? delete(X671, tree(X671, X672, X673), tree(X674, X672, X675))\ndelete(s(T797), tree(s(T796), T777, T778), T3) !=? delete(X861, tree(X862, X863, X864), tree(X862, X865, X864))", fontsize=16, style=filled, fillcolor=lightyellow];
694 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2 -> 694 [arrowhead = none ];
694 -> 4;

695 [label="EVAL with clause\ndelete(X6, tree(X6, void, X7), X7).\nand substitutionT1 -> T6,\nX6 -> T6,\nX7 -> T7,\nT2 -> tree(T6, void, T7),\nT3 -> T7", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 695 [arrowhead = none ];
695 -> 6;

696 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 696 [arrowhead = none ];
696 -> 8;

697 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 697 [arrowhead = none ];
697 -> 9;

698 [label="EVAL with clause\ndelete(X525, tree(X525, X526, void), X526).\nand substitutionT1 -> T353,\nX525 -> T353,\nX526 -> T354,\nT2 -> tree(T353, T354, void),\nT3 -> T354", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 698 [arrowhead = none ];
698 -> 251;

699 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 699 [arrowhead = none ];
699 -> 252;

700 [label="EVAL with clause\ndelete(X10, tree(X10, X11, void), X11).\nand substitutionT6 -> T9,\nX10 -> T9,\nX11 -> void,\nT7 -> void,\nT3 -> void", fontsize=14, style = filled, fillcolor = lightblue];
9 -> 700 [arrowhead = none ];
700 -> 11;

701 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
9 -> 701 [arrowhead = none ];
701 -> 13;

702 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 702 [arrowhead = none ];
702 -> 14;

703 [label="EVAL with clause\ndelete(X159, tree(X159, X160, X161), tree(X162, X160, X163)) :- delmin(X161, X162, X163).\nand substitutionT6 -> T72,\nX159 -> T72,\nX160 -> void,\nT7 -> T73,\nX161 -> T73,\nX162 -> T76,\nX163 -> T77,\nT3 -> tree(T76, void, T77),\nT74 -> T76,\nT75 -> T77", fontsize=14, style = filled, fillcolor = lightblue];
13 -> 703 [arrowhead = none ];
703 -> 105;

704 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
13 -> 704 [arrowhead = none ];
704 -> 106;

705 [label="EVAL with clause\ndelete(X17, tree(X17, X18, X19), tree(X20, X18, X21)) :- delmin(X19, X20, X21).\nand substitutionT9 -> T13,\nX17 -> T13,\nX18 -> void,\nX19 -> void,\nX20 -> T16,\nX21 -> T17,\nT3 -> tree(T16, void, T17),\nT14 -> T16,\nT15 -> T17", fontsize=14, style = filled, fillcolor = lightblue];
14 -> 705 [arrowhead = none ];
705 -> 17;

706 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
14 -> 706 [arrowhead = none ];
706 -> 20;

707 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
17 -> 707 [arrowhead = none ];
707 -> 21;

708 [label="EVAL with clause\ndelete(X94, tree(X95, X96, X97), tree(X95, X98, X97)) :- ','(less(X94, X95), delete(X94, X96, X98)).\nand substitutionT9 -> T43,\nX94 -> T43,\nX95 -> T43,\nX96 -> void,\nX97 -> void,\nX98 -> T45,\nT3 -> tree(T43, T45, void),\nT44 -> T45", fontsize=14, style = filled, fillcolor = lightblue];
20 -> 708 [arrowhead = none ];
708 -> 58;

709 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
20 -> 709 [arrowhead = none ];
709 -> 60;

710 [label="BACKTRACK\nfor clause: delmin(tree(Y, void, Right), Y, Right)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
21 -> 710 [arrowhead = none ];
710 -> 22;

711 [label="BACKTRACK\nfor clause: delmin(tree(X, Left, X1), Y, tree(X, Left1, X2)) :- delmin(Left, Y, Left1)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
22 -> 711 [arrowhead = none ];
711 -> 23;

712 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
23 -> 712 [arrowhead = none ];
712 -> 24;

713 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
24 -> 713 [arrowhead = none ];
713 -> 27;

714 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
24 -> 714 [arrowhead = none ];
714 -> 28;

715 [label="EVAL with clause\ndelete(X50, tree(X51, X52, X53), tree(X51, X54, X53)) :- ','(less(X50, X51), delete(X50, X52, X54)).\nand substitutionT13 -> T26,\nX50 -> T26,\nX51 -> T26,\nX52 -> void,\nX53 -> void,\nX54 -> T28,\nT3 -> tree(T26, T28, void),\nT27 -> T28", fontsize=14, style = filled, fillcolor = lightblue];
27 -> 715 [arrowhead = none ];
715 -> 29;

716 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
27 -> 716 [arrowhead = none ];
716 -> 31;

717 [label="EVAL with clause\ndelete(X82, tree(X83, X84, X85), tree(X83, X84, X86)) :- ','(less(X83, X82), delete(X82, X85, X86)).\nand substitutionT13 -> T38,\nX82 -> T38,\nX83 -> T38,\nX84 -> void,\nX85 -> void,\nX86 -> T40,\nT3 -> tree(T38, void, T40),\nT39 -> T40", fontsize=14, style = filled, fillcolor = lightblue];
28 -> 717 [arrowhead = none ];
717 -> 50;

718 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
28 -> 718 [arrowhead = none ];
718 -> 51;

719 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
29 -> 719 [arrowhead = none ];
719 -> 34;

720 [label="SPLIT 2\nnew knowledge:\nT26 is ground", fontsize=14, style = filled, fillcolor = violet];
29 -> 720 [arrowhead = none ];
720 -> 35;

721 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
34 -> 721 [arrowhead = none ];
721 -> 37;

722 [label="INSTANCE with matching:\nT1 -> T26\nT2 -> void\nT3 -> T28", fontsize=14, style = filled, fillcolor = lightgrey];
35 -> 722 [arrowhead = none , style=dashed];
722 -> 2[style=dashed];

723 [label="BACKTRACK\nfor clause: less(0, s(X3))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
37 -> 723 [arrowhead = none ];
723 -> 39;

724 [label="EVAL with clause\nless(s(X64), s(X65)) :- less(X64, X65).\nand substitutionX64 -> T31,\nT26 -> s(T31),\nX65 -> T31", fontsize=14, style = filled, fillcolor = lightblue];
39 -> 724 [arrowhead = none ];
724 -> 40;

725 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
39 -> 725 [arrowhead = none ];
725 -> 41;

726 [label="INSTANCE with matching:\nT26 -> T31", fontsize=14, style = filled, fillcolor = lightgrey];
40 -> 726 [arrowhead = none , style=dashed];
726 -> 34[style=dashed];

727 [label="INSTANCE with matching:\nT26 -> T38\nT28 -> T40", fontsize=14, style = filled, fillcolor = lightgrey];
50 -> 727 [arrowhead = none , style=dashed];
727 -> 29[style=dashed];

728 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
58 -> 728 [arrowhead = none ];
728 -> 61;

729 [label="EVAL with clause\ndelete(X140, tree(X141, X142, X143), tree(X141, X142, X144)) :- ','(less(X141, X140), delete(X140, X143, X144)).\nand substitutionT9 -> T62,\nX140 -> T62,\nX141 -> T62,\nX142 -> void,\nX143 -> void,\nX144 -> T64,\nT3 -> tree(T62, void, T64),\nT63 -> T64", fontsize=14, style = filled, fillcolor = lightblue];
60 -> 729 [arrowhead = none ];
729 -> 93;

730 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
60 -> 730 [arrowhead = none ];
730 -> 94;

731 [label="BACKTRACK\nfor clause: less(0, s(X3))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
61 -> 731 [arrowhead = none ];
731 -> 63;

732 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
63 -> 732 [arrowhead = none ];
732 -> 68;

733 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
63 -> 733 [arrowhead = none ];
733 -> 69;

734 [label="EVAL with clause\nless(s(X108), s(X109)) :- less(X108, X109).\nand substitutionX108 -> T50,\nT43 -> s(T50),\nX109 -> T50", fontsize=14, style = filled, fillcolor = lightblue];
68 -> 734 [arrowhead = none ];
734 -> 72;

735 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
68 -> 735 [arrowhead = none ];
735 -> 73;

736 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
69 -> 736 [arrowhead = none ];
736 -> 80;

737 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
72 -> 737 [arrowhead = none ];
737 -> 75;

738 [label="SPLIT 2\nnew knowledge:\nT50 is ground", fontsize=14, style = filled, fillcolor = violet];
72 -> 738 [arrowhead = none ];
738 -> 77;

739 [label="INSTANCE with matching:\nT26 -> T50", fontsize=14, style = filled, fillcolor = lightgrey];
75 -> 739 [arrowhead = none , style=dashed];
739 -> 34[style=dashed];

740 [label="INSTANCE with matching:\nT1 -> s(T50)\nT2 -> void\nT3 -> T45", fontsize=14, style = filled, fillcolor = lightgrey];
77 -> 740 [arrowhead = none , style=dashed];
740 -> 2[style=dashed];

741 [label="EVAL with clause\ndelete(X128, tree(X129, X130, X131), tree(X129, X130, X132)) :- ','(less(X129, X128), delete(X128, X131, X132)).\nand substitutionT43 -> T57,\nX128 -> T57,\nX129 -> T57,\nX130 -> void,\nX131 -> void,\nX132 -> T59,\nT3 -> tree(T57, void, T59),\nT58 -> T59", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 741 [arrowhead = none ];
741 -> 85;

742 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
80 -> 742 [arrowhead = none ];
742 -> 86;

743 [label="INSTANCE with matching:\nT26 -> T57\nT28 -> T59", fontsize=14, style = filled, fillcolor = lightgrey];
85 -> 743 [arrowhead = none , style=dashed];
743 -> 29[style=dashed];

744 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
93 -> 744 [arrowhead = none ];
744 -> 95;

745 [label="BACKTRACK\nfor clause: less(0, s(X3))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
95 -> 745 [arrowhead = none ];
745 -> 96;

746 [label="EVAL with clause\nless(s(X150), s(X151)) :- less(X150, X151).\nand substitutionX150 -> T67,\nT62 -> s(T67),\nX151 -> T67", fontsize=14, style = filled, fillcolor = lightblue];
96 -> 746 [arrowhead = none ];
746 -> 98;

747 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
96 -> 747 [arrowhead = none ];
747 -> 100;

748 [label="INSTANCE with matching:\nT50 -> T67\nT45 -> T64", fontsize=14, style = filled, fillcolor = lightgrey];
98 -> 748 [arrowhead = none , style=dashed];
748 -> 72[style=dashed];

749 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
105 -> 749 [arrowhead = none ];
749 -> 107;

750 [label="EVAL with clause\ndelete(X451, tree(X452, X453, X454), tree(X452, X455, X454)) :- ','(less(X451, X452), delete(X451, X453, X455)).\nand substitutionT6 -> T312,\nX451 -> T312,\nX452 -> T312,\nX453 -> void,\nT7 -> T313,\nX454 -> T313,\nX455 -> T315,\nT3 -> tree(T312, T315, T313),\nT314 -> T315", fontsize=14, style = filled, fillcolor = lightblue];
106 -> 750 [arrowhead = none ];
750 -> 194;

751 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
106 -> 751 [arrowhead = none ];
751 -> 196;

752 [label="EVAL with clause\ndelmin(tree(X168, void, X169), X168, X169).\nand substitutionX168 -> T82,\nX169 -> T83,\nT73 -> tree(T82, void, T83),\nT76 -> T82,\nT77 -> T83", fontsize=14, style = filled, fillcolor = lightblue];
107 -> 752 [arrowhead = none ];
752 -> 108;

753 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
107 -> 753 [arrowhead = none ];
753 -> 109;

754 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
108 -> 754 [arrowhead = none ];
754 -> 110;

755 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
109 -> 755 [arrowhead = none ];
755 -> 140;

756 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
109 -> 756 [arrowhead = none ];
756 -> 141;

757 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
110 -> 757 [arrowhead = none ];
757 -> 112;

758 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
110 -> 758 [arrowhead = none ];
758 -> 113;

759 [label="EVAL with clause\ndelmin(tree(X194, X195, X196), X197, tree(X194, X198, X199)) :- delmin(X195, X197, X198).\nand substitutionT82 -> T104,\nX194 -> T104,\nX195 -> void,\nT83 -> T105,\nX196 -> T105,\nT76 -> T109,\nX197 -> T109,\nX198 -> T110,\nX199 -> T108,\nT77 -> tree(T104, T110, T108),\nT106 -> T109,\nT107 -> T110", fontsize=14, style = filled, fillcolor = lightblue];
112 -> 759 [arrowhead = none ];
759 -> 117;

760 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
112 -> 760 [arrowhead = none ];
760 -> 118;

761 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
113 -> 761 [arrowhead = none ];
761 -> 122;

762 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
117 -> 762 [arrowhead = none ];
762 -> 119;

763 [label="BACKTRACK\nfor clause: delmin(tree(Y, void, Right), Y, Right)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
119 -> 763 [arrowhead = none ];
763 -> 120;

764 [label="BACKTRACK\nfor clause: delmin(tree(X, Left, X1), Y, tree(X, Left1, X2)) :- delmin(Left, Y, Left1)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
120 -> 764 [arrowhead = none ];
764 -> 121;

765 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
122 -> 765 [arrowhead = none ];
765 -> 124;

766 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
122 -> 766 [arrowhead = none ];
766 -> 125;

767 [label="EVAL with clause\ndelete(X232, tree(X233, X234, X235), tree(X233, X236, X235)) :- ','(less(X232, X233), delete(X232, X234, X236)).\nand substitutionT72 -> T127,\nX232 -> T127,\nX233 -> T127,\nX234 -> void,\nT82 -> T128,\nT83 -> T129,\nX235 -> tree(T128, void, T129),\nX236 -> T131,\nT3 -> tree(T127, T131, tree(T128, void, T129)),\nT130 -> T131", fontsize=14, style = filled, fillcolor = lightblue];
124 -> 767 [arrowhead = none ];
767 -> 128;

768 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
124 -> 768 [arrowhead = none ];
768 -> 130;

769 [label="EVAL with clause\ndelete(X249, tree(X250, X251, X252), tree(X250, X251, X253)) :- ','(less(X250, X249), delete(X249, X252, X253)).\nand substitutionT72 -> T140,\nX249 -> T140,\nX250 -> T140,\nX251 -> void,\nT82 -> T141,\nT83 -> T142,\nX252 -> tree(T141, void, T142),\nX253 -> T144,\nT3 -> tree(T140, void, T144),\nT143 -> T144", fontsize=14, style = filled, fillcolor = lightblue];
125 -> 769 [arrowhead = none ];
769 -> 132;

770 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
125 -> 770 [arrowhead = none ];
770 -> 134;

771 [label="INSTANCE with matching:\nT26 -> T127\nT28 -> T131", fontsize=14, style = filled, fillcolor = lightgrey];
128 -> 771 [arrowhead = none , style=dashed];
771 -> 29[style=dashed];

772 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
132 -> 772 [arrowhead = none ];
772 -> 136;

773 [label="SPLIT 2\nnew knowledge:\nT140 is ground", fontsize=14, style = filled, fillcolor = violet];
132 -> 773 [arrowhead = none ];
773 -> 137;

774 [label="INSTANCE with matching:\nT26 -> T140", fontsize=14, style = filled, fillcolor = lightgrey];
136 -> 774 [arrowhead = none , style=dashed];
774 -> 34[style=dashed];

775 [label="INSTANCE with matching:\nT1 -> T140\nT2 -> tree(T141, void, T142)\nT3 -> T144", fontsize=14, style = filled, fillcolor = lightgrey];
137 -> 775 [arrowhead = none , style=dashed];
775 -> 2[style=dashed];

776 [label="EVAL with clause\ndelmin(tree(X286, X287, X288), X289, tree(X286, X290, X291)) :- delmin(X287, X289, X290).\nand substitutionX286 -> T173,\nX287 -> T174,\nX288 -> T175,\nT73 -> tree(T173, T174, T175),\nT76 -> T179,\nX289 -> T179,\nX290 -> T180,\nX291 -> T178,\nT77 -> tree(T173, T180, T178),\nT176 -> T179,\nT177 -> T180", fontsize=14, style = filled, fillcolor = lightblue];
140 -> 776 [arrowhead = none ];
776 -> 146;

777 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
140 -> 777 [arrowhead = none ];
777 -> 147;

778 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
141 -> 778 [arrowhead = none ];
778 -> 176;

779 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
146 -> 779 [arrowhead = none ];
779 -> 148;

780 [label="EVAL with clause\ndelmin(tree(X300, void, X301), X300, X301).\nand substitutionX300 -> T189,\nX301 -> T190,\nT174 -> tree(T189, void, T190),\nT179 -> T189,\nT180 -> T190", fontsize=14, style = filled, fillcolor = lightblue];
148 -> 780 [arrowhead = none ];
780 -> 149;

781 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
148 -> 781 [arrowhead = none ];
781 -> 150;

782 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
149 -> 782 [arrowhead = none ];
782 -> 151;

783 [label="EVAL with clause\ndelmin(tree(X336, X337, X338), X339, tree(X336, X340, X341)) :- delmin(X337, X339, X340).\nand substitutionX336 -> T220,\nX337 -> T221,\nX338 -> T222,\nT174 -> tree(T220, T221, T222),\nT179 -> T226,\nX339 -> T226,\nX340 -> T227,\nX341 -> T225,\nT180 -> tree(T220, T227, T225),\nT223 -> T226,\nT224 -> T227", fontsize=14, style = filled, fillcolor = lightblue];
150 -> 783 [arrowhead = none ];
783 -> 158;

784 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
150 -> 784 [arrowhead = none ];
784 -> 159;

785 [label="EVAL with clause\ndelmin(tree(X314, X315, X316), X317, tree(X314, X318, X319)) :- delmin(X315, X317, X318).\nand substitutionT189 -> T201,\nX314 -> T201,\nX315 -> void,\nT190 -> T202,\nX316 -> T202,\nT179 -> T206,\nX317 -> T206,\nX318 -> T207,\nX319 -> T205,\nT180 -> tree(T201, T207, T205),\nT203 -> T206,\nT204 -> T207", fontsize=14, style = filled, fillcolor = lightblue];
151 -> 785 [arrowhead = none ];
785 -> 154;

786 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
151 -> 786 [arrowhead = none ];
786 -> 155;

787 [label="INSTANCE with matching:\nT109 -> T206\nT110 -> T207", fontsize=14, style = filled, fillcolor = lightgrey];
154 -> 787 [arrowhead = none , style=dashed];
787 -> 117[style=dashed];

788 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
158 -> 788 [arrowhead = none ];
788 -> 162;

789 [label="EVAL with clause\ndelmin(tree(X350, void, X351), X350, X351).\nand substitutionX350 -> T236,\nX351 -> T237,\nT221 -> tree(T236, void, T237),\nT226 -> T236,\nT227 -> T237", fontsize=14, style = filled, fillcolor = lightblue];
162 -> 789 [arrowhead = none ];
789 -> 163;

790 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
162 -> 790 [arrowhead = none ];
790 -> 165;

791 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
163 -> 791 [arrowhead = none ];
791 -> 166;

792 [label="EVAL with clause\ndelmin(tree(X386, X387, X388), X389, tree(X386, X390, X391)) :- delmin(X387, X389, X390).\nand substitutionX386 -> T267,\nX387 -> T268,\nX388 -> T269,\nT221 -> tree(T267, T268, T269),\nT226 -> T273,\nX389 -> T273,\nX390 -> T274,\nX391 -> T272,\nT227 -> tree(T267, T274, T272),\nT270 -> T273,\nT271 -> T274", fontsize=14, style = filled, fillcolor = lightblue];
165 -> 792 [arrowhead = none ];
792 -> 174;

793 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
165 -> 793 [arrowhead = none ];
793 -> 175;

794 [label="EVAL with clause\ndelmin(tree(X364, X365, X366), X367, tree(X364, X368, X369)) :- delmin(X365, X367, X368).\nand substitutionT236 -> T248,\nX364 -> T248,\nX365 -> void,\nT237 -> T249,\nX366 -> T249,\nT226 -> T253,\nX367 -> T253,\nX368 -> T254,\nX369 -> T252,\nT227 -> tree(T248, T254, T252),\nT250 -> T253,\nT251 -> T254", fontsize=14, style = filled, fillcolor = lightblue];
166 -> 794 [arrowhead = none ];
794 -> 170;

795 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
166 -> 795 [arrowhead = none ];
795 -> 171;

796 [label="INSTANCE with matching:\nT109 -> T253\nT110 -> T254", fontsize=14, style = filled, fillcolor = lightgrey];
170 -> 796 [arrowhead = none , style=dashed];
796 -> 117[style=dashed];

797 [label="INSTANCE with matching:\nT174 -> T268\nT179 -> T273\nT180 -> T274\nT173 -> T267\nT175 -> T269\nT76 -> T226\nT77 -> T227\nX168 -> X350\nX169 -> X351", fontsize=14, style = filled, fillcolor = lightgrey];
174 -> 797 [arrowhead = none , style=dashed];
797 -> 146[style=dashed];

798 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
176 -> 798 [arrowhead = none ];
798 -> 177;

799 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
176 -> 799 [arrowhead = none ];
799 -> 178;

800 [label="EVAL with clause\ndelete(X416, tree(X417, X418, X419), tree(X417, X420, X419)) :- ','(less(X416, X417), delete(X416, X418, X420)).\nand substitutionT72 -> T291,\nX416 -> T291,\nX417 -> T291,\nX418 -> void,\nT73 -> T292,\nX419 -> T292,\nX420 -> T294,\nT3 -> tree(T291, T294, T292),\nT293 -> T294", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 800 [arrowhead = none ];
800 -> 181;

801 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
177 -> 801 [arrowhead = none ];
801 -> 182;

802 [label="EVAL with clause\ndelete(X433, tree(X434, X435, X436), tree(X434, X435, X437)) :- ','(less(X434, X433), delete(X433, X436, X437)).\nand substitutionT72 -> T301,\nX433 -> T301,\nX434 -> T301,\nX435 -> void,\nT73 -> T302,\nX436 -> T302,\nX437 -> T304,\nT3 -> tree(T301, void, T304),\nT303 -> T304", fontsize=14, style = filled, fillcolor = lightblue];
178 -> 802 [arrowhead = none ];
802 -> 185;

803 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
178 -> 803 [arrowhead = none ];
803 -> 186;

804 [label="INSTANCE with matching:\nT26 -> T291\nT28 -> T294", fontsize=14, style = filled, fillcolor = lightgrey];
181 -> 804 [arrowhead = none , style=dashed];
804 -> 29[style=dashed];

805 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
185 -> 805 [arrowhead = none ];
805 -> 187;

806 [label="SPLIT 2\nnew knowledge:\nT301 is ground", fontsize=14, style = filled, fillcolor = violet];
185 -> 806 [arrowhead = none ];
806 -> 188;

807 [label="INSTANCE with matching:\nT26 -> T301", fontsize=14, style = filled, fillcolor = lightgrey];
187 -> 807 [arrowhead = none , style=dashed];
807 -> 34[style=dashed];

808 [label="INSTANCE with matching:\nT1 -> T301\nT2 -> T302\nT3 -> T304", fontsize=14, style = filled, fillcolor = lightgrey];
188 -> 808 [arrowhead = none , style=dashed];
808 -> 2[style=dashed];

809 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
194 -> 809 [arrowhead = none ];
809 -> 198;

810 [label="EVAL with clause\ndelete(X503, tree(X504, X505, X506), tree(X504, X505, X507)) :- ','(less(X504, X503), delete(X503, X506, X507)).\nand substitutionT6 -> T340,\nX503 -> T340,\nX504 -> T340,\nX505 -> void,\nT7 -> T341,\nX506 -> T341,\nX507 -> T343,\nT3 -> tree(T340, void, T343),\nT342 -> T343", fontsize=14, style = filled, fillcolor = lightblue];
196 -> 810 [arrowhead = none ];
810 -> 234;

811 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
196 -> 811 [arrowhead = none ];
811 -> 235;

812 [label="BACKTRACK\nfor clause: less(0, s(X3))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
198 -> 812 [arrowhead = none ];
812 -> 201;

813 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
201 -> 813 [arrowhead = none ];
813 -> 202;

814 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
201 -> 814 [arrowhead = none ];
814 -> 203;

815 [label="EVAL with clause\nless(s(X465), s(X466)) :- less(X465, X466).\nand substitutionX465 -> T320,\nT312 -> s(T320),\nX466 -> T320", fontsize=14, style = filled, fillcolor = lightblue];
202 -> 815 [arrowhead = none ];
815 -> 206;

816 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
202 -> 816 [arrowhead = none ];
816 -> 207;

817 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
203 -> 817 [arrowhead = none ];
817 -> 216;

818 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
206 -> 818 [arrowhead = none ];
818 -> 210;

819 [label="SPLIT 2\nnew knowledge:\nT320 is ground", fontsize=14, style = filled, fillcolor = violet];
206 -> 819 [arrowhead = none ];
819 -> 211;

820 [label="INSTANCE with matching:\nT26 -> T320", fontsize=14, style = filled, fillcolor = lightgrey];
210 -> 820 [arrowhead = none , style=dashed];
820 -> 34[style=dashed];

821 [label="INSTANCE with matching:\nT1 -> s(T320)\nT2 -> void\nT3 -> T315", fontsize=14, style = filled, fillcolor = lightgrey];
211 -> 821 [arrowhead = none , style=dashed];
821 -> 2[style=dashed];

822 [label="EVAL with clause\ndelete(X485, tree(X486, X487, X488), tree(X486, X487, X489)) :- ','(less(X486, X485), delete(X485, X488, X489)).\nand substitutionT312 -> T329,\nX485 -> T329,\nX486 -> T329,\nX487 -> void,\nT313 -> T330,\nX488 -> T330,\nX489 -> T332,\nT3 -> tree(T329, void, T332),\nT331 -> T332", fontsize=14, style = filled, fillcolor = lightblue];
216 -> 822 [arrowhead = none ];
822 -> 219;

823 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
216 -> 823 [arrowhead = none ];
823 -> 221;

824 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
219 -> 824 [arrowhead = none ];
824 -> 225;

825 [label="SPLIT 2\nnew knowledge:\nT329 is ground", fontsize=14, style = filled, fillcolor = violet];
219 -> 825 [arrowhead = none ];
825 -> 226;

826 [label="INSTANCE with matching:\nT26 -> T329", fontsize=14, style = filled, fillcolor = lightgrey];
225 -> 826 [arrowhead = none , style=dashed];
826 -> 34[style=dashed];

827 [label="INSTANCE with matching:\nT1 -> T329\nT2 -> T330\nT3 -> T332", fontsize=14, style = filled, fillcolor = lightgrey];
226 -> 827 [arrowhead = none , style=dashed];
827 -> 2[style=dashed];

828 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
234 -> 828 [arrowhead = none ];
828 -> 236;

829 [label="BACKTRACK\nfor clause: less(0, s(X3))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
236 -> 829 [arrowhead = none ];
829 -> 237;

830 [label="EVAL with clause\nless(s(X513), s(X514)) :- less(X513, X514).\nand substitutionX513 -> T346,\nT340 -> s(T346),\nX514 -> T346", fontsize=14, style = filled, fillcolor = lightblue];
237 -> 830 [arrowhead = none ];
830 -> 240;

831 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
237 -> 831 [arrowhead = none ];
831 -> 241;

832 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
240 -> 832 [arrowhead = none ];
832 -> 243;

833 [label="SPLIT 2\nnew knowledge:\nT346 is ground", fontsize=14, style = filled, fillcolor = violet];
240 -> 833 [arrowhead = none ];
833 -> 245;

834 [label="INSTANCE with matching:\nT26 -> T346", fontsize=14, style = filled, fillcolor = lightgrey];
243 -> 834 [arrowhead = none , style=dashed];
834 -> 34[style=dashed];

835 [label="INSTANCE with matching:\nT1 -> s(T346)\nT2 -> T341\nT3 -> T343", fontsize=14, style = filled, fillcolor = lightgrey];
245 -> 835 [arrowhead = none , style=dashed];
835 -> 2[style=dashed];

836 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
251 -> 836 [arrowhead = none ];
836 -> 253;

837 [label="EVAL with clause\ndelete(X671, tree(X671, X672, X673), tree(X674, X672, X675)) :- delmin(X673, X674, X675).\nand substitutionT1 -> T438,\nX671 -> T438,\nX672 -> T439,\nX673 -> T440,\nT2 -> tree(T438, T439, T440),\nX674 -> T443,\nX675 -> T444,\nT3 -> tree(T443, T439, T444),\nT441 -> T443,\nT442 -> T444", fontsize=14, style = filled, fillcolor = lightblue];
252 -> 837 [arrowhead = none ];
837 -> 322;

838 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
252 -> 838 [arrowhead = none ];
838 -> 323;

839 [label="EVAL with clause\ndelete(X532, tree(X532, X533, X534), tree(X535, X533, X536)) :- delmin(X534, X535, X536).\nand substitutionT353 -> T359,\nX532 -> T359,\nT354 -> T360,\nX533 -> T360,\nX534 -> void,\nX535 -> T363,\nX536 -> T364,\nT3 -> tree(T363, T360, T364),\nT361 -> T363,\nT362 -> T364", fontsize=14, style = filled, fillcolor = lightblue];
253 -> 839 [arrowhead = none ];
839 -> 256;

840 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
253 -> 840 [arrowhead = none ];
840 -> 257;

841 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
256 -> 841 [arrowhead = none ];
841 -> 260;

842 [label="EVAL with clause\ndelete(X600, tree(X601, X602, X603), tree(X601, X604, X603)) :- ','(less(X600, X601), delete(X600, X602, X604)).\nand substitutionT353 -> T398,\nX600 -> T398,\nX601 -> T398,\nT354 -> T399,\nX602 -> T399,\nX603 -> void,\nX604 -> T401,\nT3 -> tree(T398, T401, void),\nT400 -> T401", fontsize=14, style = filled, fillcolor = lightblue];
257 -> 842 [arrowhead = none ];
842 -> 289;

843 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
257 -> 843 [arrowhead = none ];
843 -> 290;

844 [label="BACKTRACK\nfor clause: delmin(tree(Y, void, Right), Y, Right)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
260 -> 844 [arrowhead = none ];
844 -> 262;

845 [label="BACKTRACK\nfor clause: delmin(tree(X, Left, X1), Y, tree(X, Left1, X2)) :- delmin(Left, Y, Left1)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
262 -> 845 [arrowhead = none ];
845 -> 263;

846 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
263 -> 846 [arrowhead = none ];
846 -> 264;

847 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
264 -> 847 [arrowhead = none ];
847 -> 267;

848 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
264 -> 848 [arrowhead = none ];
848 -> 268;

849 [label="EVAL with clause\ndelete(X565, tree(X566, X567, X568), tree(X566, X569, X568)) :- ','(less(X565, X566), delete(X565, X567, X569)).\nand substitutionT359 -> T377,\nX565 -> T377,\nX566 -> T377,\nT360 -> T378,\nX567 -> T378,\nX568 -> void,\nX569 -> T380,\nT3 -> tree(T377, T380, void),\nT379 -> T380", fontsize=14, style = filled, fillcolor = lightblue];
267 -> 849 [arrowhead = none ];
849 -> 270;

850 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
267 -> 850 [arrowhead = none ];
850 -> 271;

851 [label="EVAL with clause\ndelete(X588, tree(X589, X590, X591), tree(X589, X590, X592)) :- ','(less(X589, X588), delete(X588, X591, X592)).\nand substitutionT359 -> T391,\nX588 -> T391,\nX589 -> T391,\nT360 -> T392,\nX590 -> T392,\nX591 -> void,\nX592 -> T394,\nT3 -> tree(T391, T392, T394),\nT393 -> T394", fontsize=14, style = filled, fillcolor = lightblue];
268 -> 851 [arrowhead = none ];
851 -> 281;

852 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
268 -> 852 [arrowhead = none ];
852 -> 282;

853 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
270 -> 853 [arrowhead = none ];
853 -> 276;

854 [label="SPLIT 2\nnew knowledge:\nT377 is ground", fontsize=14, style = filled, fillcolor = violet];
270 -> 854 [arrowhead = none ];
854 -> 277;

855 [label="INSTANCE with matching:\nT26 -> T377", fontsize=14, style = filled, fillcolor = lightgrey];
276 -> 855 [arrowhead = none , style=dashed];
855 -> 34[style=dashed];

856 [label="INSTANCE with matching:\nT1 -> T377\nT2 -> T378\nT3 -> T380", fontsize=14, style = filled, fillcolor = lightgrey];
277 -> 856 [arrowhead = none , style=dashed];
856 -> 2[style=dashed];

857 [label="INSTANCE with matching:\nT26 -> T391\nT28 -> T394", fontsize=14, style = filled, fillcolor = lightgrey];
281 -> 857 [arrowhead = none , style=dashed];
857 -> 29[style=dashed];

858 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
289 -> 858 [arrowhead = none ];
858 -> 291;

859 [label="EVAL with clause\ndelete(X646, tree(X647, X648, X649), tree(X647, X648, X650)) :- ','(less(X647, X646), delete(X646, X649, X650)).\nand substitutionT353 -> T424,\nX646 -> T424,\nX647 -> T424,\nT354 -> T425,\nX648 -> T425,\nX649 -> void,\nX650 -> T427,\nT3 -> tree(T424, T425, T427),\nT426 -> T427", fontsize=14, style = filled, fillcolor = lightblue];
290 -> 859 [arrowhead = none ];
859 -> 312;

860 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
290 -> 860 [arrowhead = none ];
860 -> 315;

861 [label="BACKTRACK\nfor clause: less(0, s(X3))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
291 -> 861 [arrowhead = none ];
861 -> 292;

862 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
292 -> 862 [arrowhead = none ];
862 -> 293;

863 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
292 -> 863 [arrowhead = none ];
863 -> 294;

864 [label="EVAL with clause\nless(s(X614), s(X615)) :- less(X614, X615).\nand substitutionX614 -> T406,\nT398 -> s(T406),\nX615 -> T406", fontsize=14, style = filled, fillcolor = lightblue];
293 -> 864 [arrowhead = none ];
864 -> 296;

865 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
293 -> 865 [arrowhead = none ];
865 -> 297;

866 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
294 -> 866 [arrowhead = none ];
866 -> 307;

867 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
296 -> 867 [arrowhead = none ];
867 -> 302;

868 [label="SPLIT 2\nnew knowledge:\nT406 is ground", fontsize=14, style = filled, fillcolor = violet];
296 -> 868 [arrowhead = none ];
868 -> 304;

869 [label="INSTANCE with matching:\nT26 -> T406", fontsize=14, style = filled, fillcolor = lightgrey];
302 -> 869 [arrowhead = none , style=dashed];
869 -> 34[style=dashed];

870 [label="INSTANCE with matching:\nT1 -> s(T406)\nT2 -> T399\nT3 -> T401", fontsize=14, style = filled, fillcolor = lightgrey];
304 -> 870 [arrowhead = none , style=dashed];
870 -> 2[style=dashed];

871 [label="EVAL with clause\ndelete(X634, tree(X635, X636, X637), tree(X635, X636, X638)) :- ','(less(X635, X634), delete(X634, X637, X638)).\nand substitutionT398 -> T417,\nX634 -> T417,\nX635 -> T417,\nT399 -> T418,\nX636 -> T418,\nX637 -> void,\nX638 -> T420,\nT3 -> tree(T417, T418, T420),\nT419 -> T420", fontsize=14, style = filled, fillcolor = lightblue];
307 -> 871 [arrowhead = none ];
871 -> 308;

872 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
307 -> 872 [arrowhead = none ];
872 -> 309;

873 [label="INSTANCE with matching:\nT26 -> T417\nT28 -> T420", fontsize=14, style = filled, fillcolor = lightgrey];
308 -> 873 [arrowhead = none , style=dashed];
873 -> 29[style=dashed];

874 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
312 -> 874 [arrowhead = none ];
874 -> 316;

875 [label="BACKTRACK\nfor clause: less(0, s(X3))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
316 -> 875 [arrowhead = none ];
875 -> 317;

876 [label="EVAL with clause\nless(s(X656), s(X657)) :- less(X656, X657).\nand substitutionX656 -> T430,\nT424 -> s(T430),\nX657 -> T430", fontsize=14, style = filled, fillcolor = lightblue];
317 -> 876 [arrowhead = none ];
876 -> 318;

877 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
317 -> 877 [arrowhead = none ];
877 -> 319;

878 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
318 -> 878 [arrowhead = none ];
878 -> 320;

879 [label="SPLIT 2\nnew knowledge:\nT430 is ground", fontsize=14, style = filled, fillcolor = violet];
318 -> 879 [arrowhead = none ];
879 -> 321;

880 [label="INSTANCE with matching:\nT26 -> T430", fontsize=14, style = filled, fillcolor = lightgrey];
320 -> 880 [arrowhead = none , style=dashed];
880 -> 34[style=dashed];

881 [label="INSTANCE with matching:\nT1 -> s(T430)\nT2 -> void\nT3 -> T427", fontsize=14, style = filled, fillcolor = lightgrey];
321 -> 881 [arrowhead = none , style=dashed];
881 -> 2[style=dashed];

882 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
322 -> 882 [arrowhead = none ];
882 -> 324;

883 [label="EVAL with clause\ndelete(X861, tree(X862, X863, X864), tree(X862, X865, X864)) :- ','(less(X861, X862), delete(X861, X863, X865)).\nand substitutionT1 -> T607,\nX861 -> T607,\nX862 -> T608,\nX863 -> T609,\nX864 -> T610,\nT2 -> tree(T608, T609, T610),\nX865 -> T612,\nT3 -> tree(T608, T612, T610),\nT611 -> T612", fontsize=14, style = filled, fillcolor = lightblue];
323 -> 883 [arrowhead = none ];
883 -> 446;

884 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
323 -> 884 [arrowhead = none ];
884 -> 447;

885 [label="EVAL with clause\ndelmin(tree(X680, void, X681), X680, X681).\nand substitutionX680 -> T449,\nX681 -> T450,\nT440 -> tree(T449, void, T450),\nT443 -> T449,\nT444 -> T450", fontsize=14, style = filled, fillcolor = lightblue];
324 -> 885 [arrowhead = none ];
885 -> 325;

886 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
324 -> 886 [arrowhead = none ];
886 -> 326;

887 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
325 -> 887 [arrowhead = none ];
887 -> 327;

888 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
326 -> 888 [arrowhead = none ];
888 -> 341;

889 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
326 -> 889 [arrowhead = none ];
889 -> 342;

890 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
327 -> 890 [arrowhead = none ];
890 -> 328;

891 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
327 -> 891 [arrowhead = none ];
891 -> 329;

892 [label="EVAL with clause\ndelmin(tree(X706, X707, X708), X709, tree(X706, X710, X711)) :- delmin(X707, X709, X710).\nand substitutionT449 -> T471,\nX706 -> T471,\nX707 -> void,\nT450 -> T472,\nX708 -> T472,\nT443 -> T476,\nX709 -> T476,\nX710 -> T477,\nX711 -> T475,\nT444 -> tree(T471, T477, T475),\nT473 -> T476,\nT474 -> T477", fontsize=14, style = filled, fillcolor = lightblue];
328 -> 892 [arrowhead = none ];
892 -> 330;

893 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
328 -> 893 [arrowhead = none ];
893 -> 331;

894 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
329 -> 894 [arrowhead = none ];
894 -> 332;

895 [label="INSTANCE with matching:\nT109 -> T476\nT110 -> T477", fontsize=14, style = filled, fillcolor = lightgrey];
330 -> 895 [arrowhead = none , style=dashed];
895 -> 117[style=dashed];

896 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
332 -> 896 [arrowhead = none ];
896 -> 333;

897 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
332 -> 897 [arrowhead = none ];
897 -> 334;

898 [label="EVAL with clause\ndelete(X736, tree(X737, X738, X739), tree(X737, X740, X739)) :- ','(less(X736, X737), delete(X736, X738, X740)).\nand substitutionT438 -> T498,\nX736 -> T498,\nX737 -> T498,\nT439 -> T499,\nX738 -> T499,\nT449 -> T500,\nT450 -> T501,\nX739 -> tree(T500, void, T501),\nX740 -> T503,\nT3 -> tree(T498, T503, tree(T500, void, T501)),\nT502 -> T503", fontsize=14, style = filled, fillcolor = lightblue];
333 -> 898 [arrowhead = none ];
898 -> 335;

899 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
333 -> 899 [arrowhead = none ];
899 -> 336;

900 [label="EVAL with clause\ndelete(X759, tree(X760, X761, X762), tree(X760, X761, X763)) :- ','(less(X760, X759), delete(X759, X762, X763)).\nand substitutionT438 -> T518,\nX759 -> T518,\nX760 -> T518,\nT439 -> T519,\nX761 -> T519,\nT449 -> T520,\nT450 -> T521,\nX762 -> tree(T520, void, T521),\nX763 -> T523,\nT3 -> tree(T518, T519, T523),\nT522 -> T523", fontsize=14, style = filled, fillcolor = lightblue];
334 -> 900 [arrowhead = none ];
900 -> 339;

901 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
334 -> 901 [arrowhead = none ];
901 -> 340;

902 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
335 -> 902 [arrowhead = none ];
902 -> 337;

903 [label="SPLIT 2\nnew knowledge:\nT498 is ground", fontsize=14, style = filled, fillcolor = violet];
335 -> 903 [arrowhead = none ];
903 -> 338;

904 [label="INSTANCE with matching:\nT26 -> T498", fontsize=14, style = filled, fillcolor = lightgrey];
337 -> 904 [arrowhead = none , style=dashed];
904 -> 34[style=dashed];

905 [label="INSTANCE with matching:\nT1 -> T498\nT2 -> T499\nT3 -> T503", fontsize=14, style = filled, fillcolor = lightgrey];
338 -> 905 [arrowhead = none , style=dashed];
905 -> 2[style=dashed];

906 [label="INSTANCE with matching:\nT140 -> T518\nT141 -> T520\nT142 -> T521\nT144 -> T523", fontsize=14, style = filled, fillcolor = lightgrey];
339 -> 906 [arrowhead = none , style=dashed];
906 -> 132[style=dashed];

907 [label="EVAL with clause\ndelmin(tree(X790, X791, X792), X793, tree(X790, X794, X795)) :- delmin(X791, X793, X794).\nand substitutionX790 -> T548,\nX791 -> T549,\nX792 -> T550,\nT440 -> tree(T548, T549, T550),\nT443 -> T554,\nX793 -> T554,\nX794 -> T555,\nX795 -> T553,\nT444 -> tree(T548, T555, T553),\nT551 -> T554,\nT552 -> T555", fontsize=14, style = filled, fillcolor = lightblue];
341 -> 907 [arrowhead = none ];
907 -> 343;

908 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
341 -> 908 [arrowhead = none ];
908 -> 344;

909 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
342 -> 909 [arrowhead = none ];
909 -> 387;

910 [label="INSTANCE with matching:\nT174 -> T549\nT179 -> T554\nT180 -> T555\nT173 -> T548\nT175 -> T550\nT76 -> T443\nT77 -> T444\nX168 -> X680\nX169 -> X681", fontsize=14, style = filled, fillcolor = lightgrey];
343 -> 910 [arrowhead = none , style=dashed];
910 -> 146[style=dashed];

911 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
387 -> 911 [arrowhead = none ];
911 -> 388;

912 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
387 -> 912 [arrowhead = none ];
912 -> 389;

913 [label="EVAL with clause\ndelete(X820, tree(X821, X822, X823), tree(X821, X824, X823)) :- ','(less(X820, X821), delete(X820, X822, X824)).\nand substitutionT438 -> T576,\nX820 -> T576,\nX821 -> T576,\nT439 -> T577,\nX822 -> T577,\nT440 -> T578,\nX823 -> T578,\nX824 -> T580,\nT3 -> tree(T576, T580, T578),\nT579 -> T580", fontsize=14, style = filled, fillcolor = lightblue];
388 -> 913 [arrowhead = none ];
913 -> 390;

914 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
388 -> 914 [arrowhead = none ];
914 -> 391;

915 [label="EVAL with clause\ndelete(X843, tree(X844, X845, X846), tree(X844, X845, X847)) :- ','(less(X844, X843), delete(X843, X846, X847)).\nand substitutionT438 -> T593,\nX843 -> T593,\nX844 -> T593,\nT439 -> T594,\nX845 -> T594,\nT440 -> T595,\nX846 -> T595,\nX847 -> T597,\nT3 -> tree(T593, T594, T597),\nT596 -> T597", fontsize=14, style = filled, fillcolor = lightblue];
389 -> 915 [arrowhead = none ];
915 -> 394;

916 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
389 -> 916 [arrowhead = none ];
916 -> 395;

917 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
390 -> 917 [arrowhead = none ];
917 -> 392;

918 [label="SPLIT 2\nnew knowledge:\nT576 is ground", fontsize=14, style = filled, fillcolor = violet];
390 -> 918 [arrowhead = none ];
918 -> 393;

919 [label="INSTANCE with matching:\nT26 -> T576", fontsize=14, style = filled, fillcolor = lightgrey];
392 -> 919 [arrowhead = none , style=dashed];
919 -> 34[style=dashed];

920 [label="INSTANCE with matching:\nT1 -> T576\nT2 -> T577\nT3 -> T580", fontsize=14, style = filled, fillcolor = lightgrey];
393 -> 920 [arrowhead = none , style=dashed];
920 -> 2[style=dashed];

921 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
394 -> 921 [arrowhead = none ];
921 -> 439;

922 [label="SPLIT 2\nnew knowledge:\nT593 is ground", fontsize=14, style = filled, fillcolor = violet];
394 -> 922 [arrowhead = none ];
922 -> 441;

923 [label="INSTANCE with matching:\nT26 -> T593", fontsize=14, style = filled, fillcolor = lightgrey];
439 -> 923 [arrowhead = none , style=dashed];
923 -> 34[style=dashed];

924 [label="INSTANCE with matching:\nT1 -> T593\nT2 -> T595\nT3 -> T597", fontsize=14, style = filled, fillcolor = lightgrey];
441 -> 924 [arrowhead = none , style=dashed];
924 -> 2[style=dashed];

925 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
446 -> 925 [arrowhead = none ];
925 -> 448;

926 [label="EVAL with clause\ndelete(X1057, tree(X1058, X1059, X1060), tree(X1058, X1059, X1061)) :- ','(less(X1058, X1057), delete(X1057, X1060, X1061)).\nand substitutionT1 -> T775,\nX1057 -> T775,\nX1058 -> T776,\nX1059 -> T777,\nX1060 -> T778,\nT2 -> tree(T776, T777, T778),\nX1061 -> T780,\nT3 -> tree(T776, T777, T780),\nT779 -> T780", fontsize=14, style = filled, fillcolor = lightblue];
447 -> 926 [arrowhead = none ];
926 -> 682;

927 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
447 -> 927 [arrowhead = none ];
927 -> 683;

928 [label="EVAL with clause\nless(0, s(X868)).\nand substitutionT607 -> 0,\nX868 -> T615,\nT608 -> s(T615)", fontsize=14, style = filled, fillcolor = lightblue];
448 -> 928 [arrowhead = none ];
928 -> 449;

929 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
448 -> 929 [arrowhead = none ];
929 -> 450;

930 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
449 -> 930 [arrowhead = none ];
930 -> 459;

931 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
449 -> 931 [arrowhead = none ];
931 -> 460;

932 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
450 -> 932 [arrowhead = none ];
932 -> 499;

933 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
450 -> 933 [arrowhead = none ];
933 -> 500;

934 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T609\nT3 -> T612", fontsize=14, style = filled, fillcolor = lightgrey];
459 -> 934 [arrowhead = none , style=dashed];
934 -> 2[style=dashed];

935 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
460 -> 935 [arrowhead = none ];
935 -> 461;

936 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
461 -> 936 [arrowhead = none ];
936 -> 462;

937 [label="EVAL with clause\ndelete(X889, tree(X890, X891, X892), tree(X890, X891, X893)) :- ','(less(X890, X889), delete(X889, X892, X893)).\nand substitutionX889 -> 0,\nT615 -> T628,\nX890 -> s(T628),\nT609 -> T629,\nX891 -> T629,\nT610 -> T630,\nX892 -> T630,\nX893 -> T632,\nT3 -> tree(s(T628), T629, T632),\nT631 -> T632", fontsize=14, style = filled, fillcolor = lightblue];
462 -> 937 [arrowhead = none ];
937 -> 487;

938 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
462 -> 938 [arrowhead = none ];
938 -> 489;

939 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
487 -> 939 [arrowhead = none ];
939 -> 494;

940 [label="SPLIT 2\nnew knowledge:\nT628 is ground", fontsize=14, style = filled, fillcolor = violet];
487 -> 940 [arrowhead = none ];
940 -> 495;

941 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
494 -> 941 [arrowhead = none ];
941 -> 496;

942 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T630\nT3 -> T632", fontsize=14, style = filled, fillcolor = lightgrey];
495 -> 942 [arrowhead = none , style=dashed];
942 -> 2[style=dashed];

943 [label="BACKTRACK\nfor clause: less(0, s(X3))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
496 -> 943 [arrowhead = none ];
943 -> 497;

944 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
497 -> 944 [arrowhead = none ];
944 -> 498;

945 [label="EVAL with clause\nless(s(X913), s(X914)) :- less(X913, X914).\nand substitutionX913 -> T644,\nT607 -> s(T644),\nX914 -> T645,\nT608 -> s(T645)", fontsize=14, style = filled, fillcolor = lightblue];
499 -> 945 [arrowhead = none ];
945 -> 501;

946 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
499 -> 946 [arrowhead = none ];
946 -> 502;

947 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
500 -> 947 [arrowhead = none ];
947 -> 677;

948 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
501 -> 948 [arrowhead = none ];
948 -> 503;

949 [label="SPLIT 2\nnew knowledge:\nT644 is ground\nT645 is ground", fontsize=14, style = filled, fillcolor = violet];
501 -> 949 [arrowhead = none ];
949 -> 504;

950 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
503 -> 950 [arrowhead = none ];
950 -> 505;

951 [label="INSTANCE with matching:\nT1 -> s(T644)\nT2 -> T609\nT3 -> T612", fontsize=14, style = filled, fillcolor = lightgrey];
504 -> 951 [arrowhead = none , style=dashed];
951 -> 2[style=dashed];

952 [label="EVAL with clause\nless(0, s(X921)).\nand substitutionT644 -> 0,\nX921 -> T652,\nT645 -> s(T652)", fontsize=14, style = filled, fillcolor = lightblue];
505 -> 952 [arrowhead = none ];
952 -> 506;

953 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
505 -> 953 [arrowhead = none ];
953 -> 507;

954 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
506 -> 954 [arrowhead = none ];
954 -> 508;

955 [label="EVAL with clause\nless(s(X928), s(X929)) :- less(X928, X929).\nand substitutionX928 -> T657,\nT644 -> s(T657),\nX929 -> T658,\nT645 -> s(T658)", fontsize=14, style = filled, fillcolor = lightblue];
507 -> 955 [arrowhead = none ];
955 -> 510;

956 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
507 -> 956 [arrowhead = none ];
956 -> 511;

957 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
508 -> 957 [arrowhead = none ];
957 -> 509;

958 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
510 -> 958 [arrowhead = none ];
958 -> 512;

959 [label="EVAL with clause\nless(0, s(X934)).\nand substitutionT657 -> 0,\nX934 -> T663,\nT658 -> s(T663)", fontsize=14, style = filled, fillcolor = lightblue];
512 -> 959 [arrowhead = none ];
959 -> 513;

960 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
512 -> 960 [arrowhead = none ];
960 -> 514;

961 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
513 -> 961 [arrowhead = none ];
961 -> 515;

962 [label="EVAL with clause\nless(s(X941), s(X942)) :- less(X941, X942).\nand substitutionX941 -> T668,\nT657 -> s(T668),\nX942 -> T669,\nT658 -> s(T669)", fontsize=14, style = filled, fillcolor = lightblue];
514 -> 962 [arrowhead = none ];
962 -> 517;

963 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
514 -> 963 [arrowhead = none ];
963 -> 518;

964 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
515 -> 964 [arrowhead = none ];
964 -> 516;

965 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
517 -> 965 [arrowhead = none ];
965 -> 519;

966 [label="EVAL with clause\nless(0, s(X947)).\nand substitutionT668 -> 0,\nX947 -> T674,\nT669 -> s(T674)", fontsize=14, style = filled, fillcolor = lightblue];
519 -> 966 [arrowhead = none ];
966 -> 520;

967 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
519 -> 967 [arrowhead = none ];
967 -> 521;

968 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
520 -> 968 [arrowhead = none ];
968 -> 522;

969 [label="EVAL with clause\nless(s(X954), s(X955)) :- less(X954, X955).\nand substitutionX954 -> T679,\nT668 -> s(T679),\nX955 -> T680,\nT669 -> s(T680)", fontsize=14, style = filled, fillcolor = lightblue];
521 -> 969 [arrowhead = none ];
969 -> 524;

970 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
521 -> 970 [arrowhead = none ];
970 -> 525;

971 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
522 -> 971 [arrowhead = none ];
971 -> 523;

972 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
524 -> 972 [arrowhead = none ];
972 -> 526;

973 [label="EVAL with clause\nless(0, s(X960)).\nand substitutionT679 -> 0,\nX960 -> T685,\nT680 -> s(T685)", fontsize=14, style = filled, fillcolor = lightblue];
526 -> 973 [arrowhead = none ];
973 -> 527;

974 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
526 -> 974 [arrowhead = none ];
974 -> 528;

975 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
527 -> 975 [arrowhead = none ];
975 -> 529;

976 [label="EVAL with clause\nless(s(X967), s(X968)) :- less(X967, X968).\nand substitutionX967 -> T690,\nT679 -> s(T690),\nX968 -> T691,\nT680 -> s(T691)", fontsize=14, style = filled, fillcolor = lightblue];
528 -> 976 [arrowhead = none ];
976 -> 531;

977 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
528 -> 977 [arrowhead = none ];
977 -> 532;

978 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
529 -> 978 [arrowhead = none ];
978 -> 530;

979 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
531 -> 979 [arrowhead = none ];
979 -> 533;

980 [label="EVAL with clause\nless(0, s(X973)).\nand substitutionT690 -> 0,\nX973 -> T696,\nT691 -> s(T696)", fontsize=14, style = filled, fillcolor = lightblue];
533 -> 980 [arrowhead = none ];
980 -> 534;

981 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
533 -> 981 [arrowhead = none ];
981 -> 535;

982 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
534 -> 982 [arrowhead = none ];
982 -> 536;

983 [label="EVAL with clause\nless(s(X980), s(X981)) :- less(X980, X981).\nand substitutionX980 -> T701,\nT690 -> s(T701),\nX981 -> T702,\nT691 -> s(T702)", fontsize=14, style = filled, fillcolor = lightblue];
535 -> 983 [arrowhead = none ];
983 -> 538;

984 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
535 -> 984 [arrowhead = none ];
984 -> 539;

985 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
536 -> 985 [arrowhead = none ];
985 -> 537;

986 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
538 -> 986 [arrowhead = none ];
986 -> 540;

987 [label="EVAL with clause\nless(0, s(X986)).\nand substitutionT701 -> 0,\nX986 -> T707,\nT702 -> s(T707)", fontsize=14, style = filled, fillcolor = lightblue];
540 -> 987 [arrowhead = none ];
987 -> 541;

988 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
540 -> 988 [arrowhead = none ];
988 -> 542;

989 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
541 -> 989 [arrowhead = none ];
989 -> 543;

990 [label="EVAL with clause\nless(s(X993), s(X994)) :- less(X993, X994).\nand substitutionX993 -> T712,\nT701 -> s(T712),\nX994 -> T713,\nT702 -> s(T713)", fontsize=14, style = filled, fillcolor = lightblue];
542 -> 990 [arrowhead = none ];
990 -> 545;

991 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
542 -> 991 [arrowhead = none ];
991 -> 546;

992 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
543 -> 992 [arrowhead = none ];
992 -> 544;

993 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
545 -> 993 [arrowhead = none ];
993 -> 547;

994 [label="EVAL with clause\nless(0, s(X999)).\nand substitutionT712 -> 0,\nX999 -> T718,\nT713 -> s(T718)", fontsize=14, style = filled, fillcolor = lightblue];
547 -> 994 [arrowhead = none ];
994 -> 548;

995 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
547 -> 995 [arrowhead = none ];
995 -> 549;

996 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
548 -> 996 [arrowhead = none ];
996 -> 550;

997 [label="EVAL with clause\nless(s(X1006), s(X1007)) :- less(X1006, X1007).\nand substitutionX1006 -> T723,\nT712 -> s(T723),\nX1007 -> T724,\nT713 -> s(T724)", fontsize=14, style = filled, fillcolor = lightblue];
549 -> 997 [arrowhead = none ];
997 -> 552;

998 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
549 -> 998 [arrowhead = none ];
998 -> 553;

999 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
550 -> 999 [arrowhead = none ];
999 -> 551;

1000 [label="GENERALIZATION\nT727 <-- s(s(s(s(s(s(s(T723)))))))\nT728 <-- s(s(s(s(s(s(s(T724)))))))\n\nNew Knowledge:\nT727 is ground\nT728 is ground", fontsize=14, style = filled, fillcolor = violet];
552 -> 1000 [arrowhead = none ];
1000 -> 554;

1001 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
554 -> 1001 [arrowhead = none ];
1001 -> 555;

1002 [label="EVAL with clause\nless(0, s(X1014)).\nand substitutionT723 -> 0,\nX1014 -> T733,\nT724 -> s(T733)", fontsize=14, style = filled, fillcolor = lightblue];
555 -> 1002 [arrowhead = none ];
1002 -> 556;

1003 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
555 -> 1003 [arrowhead = none ];
1003 -> 557;

1004 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
556 -> 1004 [arrowhead = none ];
1004 -> 558;

1005 [label="EVAL with clause\nless(s(X1021), s(X1022)) :- less(X1021, X1022).\nand substitutionX1021 -> T738,\nT723 -> s(T738),\nX1022 -> T739,\nT724 -> s(T739)", fontsize=14, style = filled, fillcolor = lightblue];
557 -> 1005 [arrowhead = none ];
1005 -> 560;

1006 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
557 -> 1006 [arrowhead = none ];
1006 -> 561;

1007 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
558 -> 1007 [arrowhead = none ];
1007 -> 559;

1008 [label="INSTANCE with matching:\nT723 -> T738\nT724 -> T739", fontsize=14, style = filled, fillcolor = lightgrey];
560 -> 1008 [arrowhead = none , style=dashed];
1008 -> 554[style=dashed];

1009 [label="EVAL with clause\ndelete(X1039, tree(X1040, X1041, X1042), tree(X1040, X1041, X1043)) :- ','(less(X1040, X1039), delete(X1039, X1042, X1043)).\nand substitutionT607 -> T756,\nX1039 -> T756,\nT608 -> T757,\nX1040 -> T757,\nT609 -> T758,\nX1041 -> T758,\nT610 -> T759,\nX1042 -> T759,\nX1043 -> T761,\nT3 -> tree(T757, T758, T761),\nT760 -> T761", fontsize=14, style = filled, fillcolor = lightblue];
677 -> 1009 [arrowhead = none ];
1009 -> 678;

1010 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
677 -> 1010 [arrowhead = none ];
1010 -> 679;

1011 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
678 -> 1011 [arrowhead = none ];
1011 -> 680;

1012 [label="SPLIT 2\nnew knowledge:\nT757 is ground\nT756 is ground", fontsize=14, style = filled, fillcolor = violet];
678 -> 1012 [arrowhead = none ];
1012 -> 681;

1013 [label="INSTANCE with matching:\nT723 -> T757\nT724 -> T756", fontsize=14, style = filled, fillcolor = lightgrey];
680 -> 1013 [arrowhead = none , style=dashed];
1013 -> 554[style=dashed];

1014 [label="INSTANCE with matching:\nT1 -> T756\nT2 -> T759\nT3 -> T761", fontsize=14, style = filled, fillcolor = lightgrey];
681 -> 1014 [arrowhead = none , style=dashed];
1014 -> 2[style=dashed];

1015 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
682 -> 1015 [arrowhead = none ];
1015 -> 684;

1016 [label="EVAL with clause\nless(0, s(X1064)).\nand substitutionT776 -> 0,\nX1064 -> T783,\nT775 -> s(T783)", fontsize=14, style = filled, fillcolor = lightblue];
684 -> 1016 [arrowhead = none ];
1016 -> 685;

1017 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
684 -> 1017 [arrowhead = none ];
1017 -> 686;

1018 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
685 -> 1018 [arrowhead = none ];
1018 -> 687;

1019 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
685 -> 1019 [arrowhead = none ];
1019 -> 688;

1020 [label="EVAL with clause\nless(s(X1079), s(X1080)) :- less(X1079, X1080).\nand substitutionX1079 -> T796,\nT776 -> s(T796),\nX1080 -> T797,\nT775 -> s(T797)", fontsize=14, style = filled, fillcolor = lightblue];
686 -> 1020 [arrowhead = none ];
1020 -> 690;

1021 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
686 -> 1021 [arrowhead = none ];
1021 -> 691;

1022 [label="INSTANCE with matching:\nT1 -> s(T783)\nT2 -> T778\nT3 -> T780", fontsize=14, style = filled, fillcolor = lightgrey];
687 -> 1022 [arrowhead = none , style=dashed];
1022 -> 2[style=dashed];

1023 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
688 -> 1023 [arrowhead = none ];
1023 -> 689;

1024 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
690 -> 1024 [arrowhead = none ];
1024 -> 692;

1025 [label="SPLIT 2\nnew knowledge:\nT796 is ground\nT797 is ground", fontsize=14, style = filled, fillcolor = violet];
690 -> 1025 [arrowhead = none ];
1025 -> 693;

1026 [label="INSTANCE with matching:\nT723 -> T796\nT724 -> T797", fontsize=14, style = filled, fillcolor = lightgrey];
692 -> 1026 [arrowhead = none , style=dashed];
1026 -> 554[style=dashed];

1027 [label="INSTANCE with matching:\nT1 -> s(T797)\nT2 -> T778\nT3 -> T780", fontsize=14, style = filled, fillcolor = lightgrey];
693 -> 1027 [arrowhead = none , style=dashed];
1027 -> 2[style=dashed];

}

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F2_IN(z0, tree(z0, void, void)) → c2(U1'(f24_in(z0), z0, tree(z0, void, void)), F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(U2'(f63_in(z0), z0, tree(z0, void, void)), F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c4(U3'(f72_in(z0), s(z0), tree(s(z0), void, void)), F72_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(U4'(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2))), F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(U5'(f109_in(z1, z0), z0, tree(z0, void, z1)), F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(U6'(f201_in(z0, z1), z0, tree(z0, void, z1)), F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(U7'(f240_in(z0, z1), s(z0), tree(s(z0), void, z1)), F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(U8'(f264_in(z0, z1), z0, tree(z0, z1, void)), F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(U9'(f292_in(z0, z1), z0, tree(z0, z1, void)), F292_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), z1, void)) → c13(U10'(f318_in(z0), s(z0), tree(s(z0), z1, void)), F318_IN(z0))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(U11'(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3))), F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(U12'(f326_in(z2, z0, z1), z0, tree(z0, z1, z2)), F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(U13'(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(U14'(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(U15'(f685_in(z0, z2), s(z0), tree(0, z1, z2)), F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(U16'(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55(U17'(f117_in, tree(z0, void, z1)))
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57(U18'(f117_in, tree(z0, tree(z1, void, z2), z3)))
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(U19'(f146_in(z2), tree(z0, tree(z1, z2, z3), z4)), F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(U20'(f554_in(z0, z1), s(z0), s(z1)), F554_IN(z0, z1))
F34_IN(s(z0)) → c65(U21'(f34_in(z0), s(z0)), F34_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c74(U22'(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))), F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c76(U23'(f146_in(z1), tree(z0, z1, z2)), F146_IN(z1))
F342_IN(z0, z1, z2) → c78(U24'(f387_in(z0, z1, z2), z0, z1, z2), F387_IN(z0, z1, z2))
F140_IN(tree(z0, z1, z2)) → c81(U25'(f146_in(z1), tree(z0, z1, z2)), F146_IN(z1))
F141_IN(z0, z1) → c83(U26'(f176_in(z0, z1), z0, z1), F176_IN(z0, z1))
F328_IN(z0, z1) → c86(U27'(f117_in, z0, z1))
F329_IN(z0, z1, z2, z3) → c88(U28'(f332_in(z0, z1, z2, z3), z0, z1, z2, z3), F332_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2) → c91(U29'(f487_in(z0, z2), z0, z1, z2), F487_IN(z0, z2))
F499_IN(s(z0), s(z1), z2) → c93(U30'(f501_in(z0, z1, z2), s(z0), s(z1), z2), F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(U31'(f678_in(z1, z0, z3), z0, z1, z2, z3), F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97(U32'(f117_in, z0, z1))
F113_IN(z0, z1, z2) → c99(U33'(f122_in(z0, z1, z2), z0, z1, z2), F122_IN(z0, z1, z2))
F202_IN(s(z0)) → c102(U34'(f206_in(z0), s(z0)), F206_IN(z0))
F203_IN(z0, z1) → c104(U35'(f219_in(z0, z1), z0, z1), F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(U36'(f296_in(z0, z1), s(z0), z1), F296_IN(z0, z1))
F294_IN(z0, z1) → c108(U37'(f29_in(z0), z0, z1), F29_IN(z0))
F388_IN(z0, z1, z2) → c110(U38'(f390_in(z0, z1), z0, z1, z2), F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(U39'(f394_in(z0, z2), z0, z1, z2), F394_IN(z0, z2))
F68_IN(s(z0)) → c114(U40'(f72_in(z0), s(z0)), F72_IN(z0))
F69_IN(z0) → c116(U41'(f29_in(z0), z0), F29_IN(z0))
F177_IN(z0, z1) → c118(U42'(f29_in(z0), z0, z1), F29_IN(z0))
F178_IN(z0, z1) → c120(U43'(f185_in(z0, z1), z0, z1), F185_IN(z0, z1))
F267_IN(z0, z1) → c122(U44'(f270_in(z0, z1), z0, z1), F270_IN(z0, z1))
F268_IN(z0, z1) → c124(U45'(f29_in(z0), z0, z1), F29_IN(z0))
F333_IN(z0, z1, z2, z3) → c126(U46'(f335_in(z0, z1), z0, z1, z2, z3), F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(U47'(f132_in(z0, z2, z3), z0, z1, z2, z3), F132_IN(z0, z2, z3))
F27_IN(z0) → c130(U48'(f29_in(z0), z0), F29_IN(z0))
F28_IN(z0) → c132(U49'(f29_in(z0), z0), F29_IN(z0))
F124_IN(z0, z1, z2) → c134(U50'(f29_in(z0), z0, z1, z2), F29_IN(z0))
F125_IN(z0, z1, z2) → c136(U51'(f132_in(z0, z1, z2), z0, z1, z2), F132_IN(z0, z1, z2))
F29_IN(z0) → c138(U52'(f34_in(z0), z0), F34_IN(z0))
U52'(f34_out1, z0) → c139(U53'(f2_in(z0, void), z0), F2_IN(z0, void))
F72_IN(z0) → c141(U54'(f34_in(z0), z0), F34_IN(z0))
U54'(f34_out1, z0) → c142(U55'(f2_in(s(z0), void), z0), F2_IN(s(z0), void))
F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
U56'(f34_out1, z0, z1, z2) → c145(U57'(f2_in(z0, tree(z1, void, z2)), z0, z1, z2), F2_IN(z0, tree(z1, void, z2)))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
U58'(f34_out1, z0, z1) → c148(U59'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F206_IN(z0) → c150(U60'(f34_in(z0), z0), F34_IN(z0))
U60'(f34_out1, z0) → c151(U61'(f2_in(s(z0), void), z0), F2_IN(s(z0), void))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
U62'(f34_out1, z0, z1) → c154(U63'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
U64'(f34_out1, z0, z1) → c157(U65'(f2_in(s(z0), z1), z0, z1), F2_IN(s(z0), z1))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
U66'(f34_out1, z0, z1) → c160(U67'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
U68'(f34_out1, z0, z1) → c163(U69'(f2_in(s(z0), z1), z0, z1), F2_IN(s(z0), z1))
F318_IN(z0) → c165(U70'(f34_in(z0), z0), F34_IN(z0))
U70'(f34_out1, z0) → c166(U71'(f2_in(s(z0), void), z0), F2_IN(s(z0), void))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
U72'(f34_out1, z0, z1) → c169(U73'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
U74'(f34_out1, z0, z1) → c172(U75'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
U76'(f34_out1, z0, z1) → c175(U77'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F487_IN(z0, z1) → c177(U78'(f494_in(z0), z0, z1))
U78'(f494_out1, z0, z1) → c178(U79'(f2_in(0, z1), z0, z1), F2_IN(0, z1))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
U80'(f503_out1, z0, z1, z2) → c181(U81'(f2_in(s(z0), z2), z0, z1, z2), F2_IN(s(z0), z2))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
U82'(f554_out1, z0, z1, z2) → c184(U83'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
U84'(f554_out1, z0, z1, z2) → c187(U85'(f2_in(s(z1), z2), z0, z1, z2), F2_IN(s(z1), z2))
F24_IN(z0) → c189(U86'(f27_in(z0), f28_in(z0), z0), F27_IN(z0), F28_IN(z0))
F63_IN(z0) → c192(U87'(f68_in(z0), f69_in(z0), z0), F68_IN(z0), F69_IN(z0))
F109_IN(z0, z1) → c195(U88'(f140_in(z0), f141_in(z1, z0), z0, z1), F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(U89'(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2), F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(U90'(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2), F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(U91'(f177_in(z0, z1), f178_in(z0, z1), z0, z1), F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(U92'(f202_in(z0), f203_in(z0, z1), z0, z1), F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(U93'(f267_in(z0, z1), f268_in(z0, z1), z0, z1), F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(U94'(f293_in(z0, z1), f294_in(z0, z1), z0, z1), F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(U95'(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2), F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(U96'(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3), F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(U97'(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3), F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(U98'(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2), F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(U99'(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(U100'(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3), F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(U101'(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1), F2_IN(s(z0), z1))

S tuples:

F2_IN(z0, tree(z0, void, void)) → c2(U1'(f24_in(z0), z0, tree(z0, void, void)), F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c3(U2'(f63_in(z0), z0, tree(z0, void, void)), F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c4(U3'(f72_in(z0), s(z0), tree(s(z0), void, void)), F72_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(U4'(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2))), F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(U5'(f109_in(z1, z0), z0, tree(z0, void, z1)), F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(U6'(f201_in(z0, z1), z0, tree(z0, void, z1)), F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(U7'(f240_in(z0, z1), s(z0), tree(s(z0), void, z1)), F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(U8'(f264_in(z0, z1), z0, tree(z0, z1, void)), F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(U9'(f292_in(z0, z1), z0, tree(z0, z1, void)), F292_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), z1, void)) → c13(U10'(f318_in(z0), s(z0), tree(s(z0), z1, void)), F318_IN(z0))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(U11'(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3))), F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(U12'(f326_in(z2, z0, z1), z0, tree(z0, z1, z2)), F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(U13'(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(U14'(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(U15'(f685_in(z0, z2), s(z0), tree(0, z1, z2)), F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(U16'(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55(U17'(f117_in, tree(z0, void, z1)))
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57(U18'(f117_in, tree(z0, tree(z1, void, z2), z3)))
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(U19'(f146_in(z2), tree(z0, tree(z1, z2, z3), z4)), F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(U20'(f554_in(z0, z1), s(z0), s(z1)), F554_IN(z0, z1))
F34_IN(s(z0)) → c65(U21'(f34_in(z0), s(z0)), F34_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c74(U22'(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))), F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c76(U23'(f146_in(z1), tree(z0, z1, z2)), F146_IN(z1))
F342_IN(z0, z1, z2) → c78(U24'(f387_in(z0, z1, z2), z0, z1, z2), F387_IN(z0, z1, z2))
F140_IN(tree(z0, z1, z2)) → c81(U25'(f146_in(z1), tree(z0, z1, z2)), F146_IN(z1))
F141_IN(z0, z1) → c83(U26'(f176_in(z0, z1), z0, z1), F176_IN(z0, z1))
F328_IN(z0, z1) → c86(U27'(f117_in, z0, z1))
F329_IN(z0, z1, z2, z3) → c88(U28'(f332_in(z0, z1, z2, z3), z0, z1, z2, z3), F332_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2) → c91(U29'(f487_in(z0, z2), z0, z1, z2), F487_IN(z0, z2))
F499_IN(s(z0), s(z1), z2) → c93(U30'(f501_in(z0, z1, z2), s(z0), s(z1), z2), F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(U31'(f678_in(z1, z0, z3), z0, z1, z2, z3), F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97(U32'(f117_in, z0, z1))
F113_IN(z0, z1, z2) → c99(U33'(f122_in(z0, z1, z2), z0, z1, z2), F122_IN(z0, z1, z2))
F202_IN(s(z0)) → c102(U34'(f206_in(z0), s(z0)), F206_IN(z0))
F203_IN(z0, z1) → c104(U35'(f219_in(z0, z1), z0, z1), F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(U36'(f296_in(z0, z1), s(z0), z1), F296_IN(z0, z1))
F294_IN(z0, z1) → c108(U37'(f29_in(z0), z0, z1), F29_IN(z0))
F388_IN(z0, z1, z2) → c110(U38'(f390_in(z0, z1), z0, z1, z2), F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(U39'(f394_in(z0, z2), z0, z1, z2), F394_IN(z0, z2))
F68_IN(s(z0)) → c114(U40'(f72_in(z0), s(z0)), F72_IN(z0))
F69_IN(z0) → c116(U41'(f29_in(z0), z0), F29_IN(z0))
F177_IN(z0, z1) → c118(U42'(f29_in(z0), z0, z1), F29_IN(z0))
F178_IN(z0, z1) → c120(U43'(f185_in(z0, z1), z0, z1), F185_IN(z0, z1))
F267_IN(z0, z1) → c122(U44'(f270_in(z0, z1), z0, z1), F270_IN(z0, z1))
F268_IN(z0, z1) → c124(U45'(f29_in(z0), z0, z1), F29_IN(z0))
F333_IN(z0, z1, z2, z3) → c126(U46'(f335_in(z0, z1), z0, z1, z2, z3), F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(U47'(f132_in(z0, z2, z3), z0, z1, z2, z3), F132_IN(z0, z2, z3))
F27_IN(z0) → c130(U48'(f29_in(z0), z0), F29_IN(z0))
F28_IN(z0) → c132(U49'(f29_in(z0), z0), F29_IN(z0))
F124_IN(z0, z1, z2) → c134(U50'(f29_in(z0), z0, z1, z2), F29_IN(z0))
F125_IN(z0, z1, z2) → c136(U51'(f132_in(z0, z1, z2), z0, z1, z2), F132_IN(z0, z1, z2))
F29_IN(z0) → c138(U52'(f34_in(z0), z0), F34_IN(z0))
U52'(f34_out1, z0) → c139(U53'(f2_in(z0, void), z0), F2_IN(z0, void))
F72_IN(z0) → c141(U54'(f34_in(z0), z0), F34_IN(z0))
U54'(f34_out1, z0) → c142(U55'(f2_in(s(z0), void), z0), F2_IN(s(z0), void))
F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
U56'(f34_out1, z0, z1, z2) → c145(U57'(f2_in(z0, tree(z1, void, z2)), z0, z1, z2), F2_IN(z0, tree(z1, void, z2)))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
U58'(f34_out1, z0, z1) → c148(U59'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F206_IN(z0) → c150(U60'(f34_in(z0), z0), F34_IN(z0))
U60'(f34_out1, z0) → c151(U61'(f2_in(s(z0), void), z0), F2_IN(s(z0), void))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
U62'(f34_out1, z0, z1) → c154(U63'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
U64'(f34_out1, z0, z1) → c157(U65'(f2_in(s(z0), z1), z0, z1), F2_IN(s(z0), z1))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
U66'(f34_out1, z0, z1) → c160(U67'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
U68'(f34_out1, z0, z1) → c163(U69'(f2_in(s(z0), z1), z0, z1), F2_IN(s(z0), z1))
F318_IN(z0) → c165(U70'(f34_in(z0), z0), F34_IN(z0))
U70'(f34_out1, z0) → c166(U71'(f2_in(s(z0), void), z0), F2_IN(s(z0), void))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
U72'(f34_out1, z0, z1) → c169(U73'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
U74'(f34_out1, z0, z1) → c172(U75'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
U76'(f34_out1, z0, z1) → c175(U77'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F487_IN(z0, z1) → c177(U78'(f494_in(z0), z0, z1))
U78'(f494_out1, z0, z1) → c178(U79'(f2_in(0, z1), z0, z1), F2_IN(0, z1))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
U80'(f503_out1, z0, z1, z2) → c181(U81'(f2_in(s(z0), z2), z0, z1, z2), F2_IN(s(z0), z2))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
U82'(f554_out1, z0, z1, z2) → c184(U83'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
U84'(f554_out1, z0, z1, z2) → c187(U85'(f2_in(s(z1), z2), z0, z1, z2), F2_IN(s(z1), z2))
F24_IN(z0) → c189(U86'(f27_in(z0), f28_in(z0), z0), F27_IN(z0), F28_IN(z0))
F63_IN(z0) → c192(U87'(f68_in(z0), f69_in(z0), z0), F68_IN(z0), F69_IN(z0))
F109_IN(z0, z1) → c195(U88'(f140_in(z0), f141_in(z1, z0), z0, z1), F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(U89'(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2), F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(U90'(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2), F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(U91'(f177_in(z0, z1), f178_in(z0, z1), z0, z1), F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(U92'(f202_in(z0), f203_in(z0, z1), z0, z1), F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(U93'(f267_in(z0, z1), f268_in(z0, z1), z0, z1), F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(U94'(f293_in(z0, z1), f294_in(z0, z1), z0, z1), F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(U95'(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2), F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(U96'(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3), F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(U97'(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3), F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(U98'(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2), F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(U99'(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(U100'(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3), F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(U101'(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1), F2_IN(s(z0), z1))

K tuples:none
Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F2_IN, F146_IN, F554_IN, F34_IN, F503_IN, F341_IN, F342_IN, F140_IN, F141_IN, F328_IN, F329_IN, F460_IN, F499_IN, F500_IN, F112_IN, F113_IN, F202_IN, F203_IN, F293_IN, F294_IN, F388_IN, F389_IN, F68_IN, F69_IN, F177_IN, F178_IN, F267_IN, F268_IN, F333_IN, F334_IN, F27_IN, F28_IN, F124_IN, F125_IN, F29_IN, U52', F72_IN, U54', F132_IN, U56', F185_IN, U58', F206_IN, U60', F219_IN, U62', F240_IN, U64', F270_IN, U66', F296_IN, U68', F318_IN, U70', F335_IN, U72', F390_IN, U74', F394_IN, U76', F487_IN, U78', F501_IN, U80', F678_IN, U82', F690_IN, U84', F24_IN, F63_IN, F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN

Compound Symbols:

c2, c3, c4, c6, c7, c8, c9, c11, c12, c13, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c74, c76, c78, c81, c83, c86, c88, c91, c93, c95, c97, c99, c102, c104, c106, c108, c110, c112, c114, c116, c118, c120, c122, c124, c126, c128, c130, c132, c134, c136, c138, c139, c141, c142, c144, c145, c147, c148, c150, c151, c153, c154, c156, c157, c159, c160, c162, c163, c165, c166, c168, c169, c171, c172, c174, c175, c177, c178, c180, c181, c183, c184, c186, c187, c189, c192, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239

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

Split RHS of tuples not part of any SCC

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(U4'(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2))), F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(U5'(f109_in(z1, z0), z0, tree(z0, void, z1)), F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(U6'(f201_in(z0, z1), z0, tree(z0, void, z1)), F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(U7'(f240_in(z0, z1), s(z0), tree(s(z0), void, z1)), F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(U8'(f264_in(z0, z1), z0, tree(z0, z1, void)), F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(U9'(f292_in(z0, z1), z0, tree(z0, z1, void)), F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(U11'(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3))), F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(U12'(f326_in(z2, z0, z1), z0, tree(z0, z1, z2)), F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(U13'(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(U14'(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(U15'(f685_in(z0, z2), s(z0), tree(0, z1, z2)), F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(U16'(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55(U17'(f117_in, tree(z0, void, z1)))
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57(U18'(f117_in, tree(z0, tree(z1, void, z2), z3)))
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(U19'(f146_in(z2), tree(z0, tree(z1, z2, z3), z4)), F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(U20'(f554_in(z0, z1), s(z0), s(z1)), F554_IN(z0, z1))
F34_IN(s(z0)) → c65(U21'(f34_in(z0), s(z0)), F34_IN(z0))
F342_IN(z0, z1, z2) → c78(U24'(f387_in(z0, z1, z2), z0, z1, z2), F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(U26'(f176_in(z0, z1), z0, z1), F176_IN(z0, z1))
F328_IN(z0, z1) → c86(U27'(f117_in, z0, z1))
F329_IN(z0, z1, z2, z3) → c88(U28'(f332_in(z0, z1, z2, z3), z0, z1, z2, z3), F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(U30'(f501_in(z0, z1, z2), s(z0), s(z1), z2), F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(U31'(f678_in(z1, z0, z3), z0, z1, z2, z3), F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97(U32'(f117_in, z0, z1))
F113_IN(z0, z1, z2) → c99(U33'(f122_in(z0, z1, z2), z0, z1, z2), F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(U35'(f219_in(z0, z1), z0, z1), F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(U36'(f296_in(z0, z1), s(z0), z1), F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(U38'(f390_in(z0, z1), z0, z1, z2), F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(U39'(f394_in(z0, z2), z0, z1, z2), F394_IN(z0, z2))
F178_IN(z0, z1) → c120(U43'(f185_in(z0, z1), z0, z1), F185_IN(z0, z1))
F267_IN(z0, z1) → c122(U44'(f270_in(z0, z1), z0, z1), F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(U46'(f335_in(z0, z1), z0, z1, z2, z3), F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(U47'(f132_in(z0, z2, z3), z0, z1, z2, z3), F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(U51'(f132_in(z0, z1, z2), z0, z1, z2), F132_IN(z0, z1, z2))
F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
U56'(f34_out1, z0, z1, z2) → c145(U57'(f2_in(z0, tree(z1, void, z2)), z0, z1, z2), F2_IN(z0, tree(z1, void, z2)))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
U58'(f34_out1, z0, z1) → c148(U59'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
U62'(f34_out1, z0, z1) → c154(U63'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
U64'(f34_out1, z0, z1) → c157(U65'(f2_in(s(z0), z1), z0, z1), F2_IN(s(z0), z1))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
U66'(f34_out1, z0, z1) → c160(U67'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
U68'(f34_out1, z0, z1) → c163(U69'(f2_in(s(z0), z1), z0, z1), F2_IN(s(z0), z1))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
U72'(f34_out1, z0, z1) → c169(U73'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
U74'(f34_out1, z0, z1) → c172(U75'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
U76'(f34_out1, z0, z1) → c175(U77'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F487_IN(z0, z1) → c177(U78'(f494_in(z0), z0, z1))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
U80'(f503_out1, z0, z1, z2) → c181(U81'(f2_in(s(z0), z2), z0, z1, z2), F2_IN(s(z0), z2))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
U82'(f554_out1, z0, z1, z2) → c184(U83'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
U84'(f554_out1, z0, z1, z2) → c187(U85'(f2_in(s(z1), z2), z0, z1, z2), F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(U88'(f140_in(z0), f141_in(z1, z0), z0, z1), F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(U89'(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2), F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(U90'(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2), F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(U91'(f177_in(z0, z1), f178_in(z0, z1), z0, z1), F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(U92'(f202_in(z0), f203_in(z0, z1), z0, z1), F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(U93'(f267_in(z0, z1), f268_in(z0, z1), z0, z1), F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(U94'(f293_in(z0, z1), f294_in(z0, z1), z0, z1), F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(U95'(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2), F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(U96'(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3), F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(U97'(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3), F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(U98'(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2), F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(U99'(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(U100'(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3), F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(U101'(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c(U1'(f24_in(z0), z0, tree(z0, void, void)))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(U2'(f63_in(z0), z0, tree(z0, void, void)))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(U3'(f72_in(z0), s(z0), tree(s(z0), void, void)))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(U10'(f318_in(z0), s(z0), tree(s(z0), z1, void)))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(U22'(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(U23'(f146_in(z1), tree(z0, z1, z2)))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(U25'(f146_in(z1), tree(z0, z1, z2)))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(U29'(f487_in(z0, z2), z0, z1, z2))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(U34'(f206_in(z0), s(z0)))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(U37'(f29_in(z0), z0, z1))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(U40'(f72_in(z0), s(z0)))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(U41'(f29_in(z0), z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(U42'(f29_in(z0), z0, z1))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(U45'(f29_in(z0), z0, z1))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(U48'(f29_in(z0), z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(U49'(f29_in(z0), z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(U50'(f29_in(z0), z0, z1, z2))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
U52'(f34_out1, z0) → c(U53'(f2_in(z0, void), z0))
U52'(f34_out1, z0) → c(F2_IN(z0, void))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
U54'(f34_out1, z0) → c(U55'(f2_in(s(z0), void), z0))
U54'(f34_out1, z0) → c(F2_IN(s(z0), void))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
U60'(f34_out1, z0) → c(U61'(f2_in(s(z0), void), z0))
U60'(f34_out1, z0) → c(F2_IN(s(z0), void))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U70'(f34_out1, z0) → c(U71'(f2_in(s(z0), void), z0))
U70'(f34_out1, z0) → c(F2_IN(s(z0), void))
U78'(f494_out1, z0, z1) → c(U79'(f2_in(0, z1), z0, z1))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(U86'(f27_in(z0), f28_in(z0), z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(U87'(f68_in(z0), f69_in(z0), z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))

S tuples:

F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(U4'(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2))), F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(U5'(f109_in(z1, z0), z0, tree(z0, void, z1)), F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(U6'(f201_in(z0, z1), z0, tree(z0, void, z1)), F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(U7'(f240_in(z0, z1), s(z0), tree(s(z0), void, z1)), F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(U8'(f264_in(z0, z1), z0, tree(z0, z1, void)), F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(U9'(f292_in(z0, z1), z0, tree(z0, z1, void)), F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(U11'(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3))), F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(U12'(f326_in(z2, z0, z1), z0, tree(z0, z1, z2)), F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(U13'(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(U14'(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(U15'(f685_in(z0, z2), s(z0), tree(0, z1, z2)), F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(U16'(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55(U17'(f117_in, tree(z0, void, z1)))
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57(U18'(f117_in, tree(z0, tree(z1, void, z2), z3)))
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(U19'(f146_in(z2), tree(z0, tree(z1, z2, z3), z4)), F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(U20'(f554_in(z0, z1), s(z0), s(z1)), F554_IN(z0, z1))
F34_IN(s(z0)) → c65(U21'(f34_in(z0), s(z0)), F34_IN(z0))
F342_IN(z0, z1, z2) → c78(U24'(f387_in(z0, z1, z2), z0, z1, z2), F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(U26'(f176_in(z0, z1), z0, z1), F176_IN(z0, z1))
F328_IN(z0, z1) → c86(U27'(f117_in, z0, z1))
F329_IN(z0, z1, z2, z3) → c88(U28'(f332_in(z0, z1, z2, z3), z0, z1, z2, z3), F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(U30'(f501_in(z0, z1, z2), s(z0), s(z1), z2), F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(U31'(f678_in(z1, z0, z3), z0, z1, z2, z3), F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97(U32'(f117_in, z0, z1))
F113_IN(z0, z1, z2) → c99(U33'(f122_in(z0, z1, z2), z0, z1, z2), F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(U35'(f219_in(z0, z1), z0, z1), F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(U36'(f296_in(z0, z1), s(z0), z1), F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(U38'(f390_in(z0, z1), z0, z1, z2), F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(U39'(f394_in(z0, z2), z0, z1, z2), F394_IN(z0, z2))
F178_IN(z0, z1) → c120(U43'(f185_in(z0, z1), z0, z1), F185_IN(z0, z1))
F267_IN(z0, z1) → c122(U44'(f270_in(z0, z1), z0, z1), F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(U46'(f335_in(z0, z1), z0, z1, z2, z3), F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(U47'(f132_in(z0, z2, z3), z0, z1, z2, z3), F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(U51'(f132_in(z0, z1, z2), z0, z1, z2), F132_IN(z0, z1, z2))
F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
U56'(f34_out1, z0, z1, z2) → c145(U57'(f2_in(z0, tree(z1, void, z2)), z0, z1, z2), F2_IN(z0, tree(z1, void, z2)))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
U58'(f34_out1, z0, z1) → c148(U59'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
U62'(f34_out1, z0, z1) → c154(U63'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
U64'(f34_out1, z0, z1) → c157(U65'(f2_in(s(z0), z1), z0, z1), F2_IN(s(z0), z1))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
U66'(f34_out1, z0, z1) → c160(U67'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
U68'(f34_out1, z0, z1) → c163(U69'(f2_in(s(z0), z1), z0, z1), F2_IN(s(z0), z1))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
U72'(f34_out1, z0, z1) → c169(U73'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
U74'(f34_out1, z0, z1) → c172(U75'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
U76'(f34_out1, z0, z1) → c175(U77'(f2_in(z0, z1), z0, z1), F2_IN(z0, z1))
F487_IN(z0, z1) → c177(U78'(f494_in(z0), z0, z1))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
U80'(f503_out1, z0, z1, z2) → c181(U81'(f2_in(s(z0), z2), z0, z1, z2), F2_IN(s(z0), z2))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
U82'(f554_out1, z0, z1, z2) → c184(U83'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
U84'(f554_out1, z0, z1, z2) → c187(U85'(f2_in(s(z1), z2), z0, z1, z2), F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(U88'(f140_in(z0), f141_in(z1, z0), z0, z1), F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(U89'(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2), F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(U90'(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2), F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(U91'(f177_in(z0, z1), f178_in(z0, z1), z0, z1), F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(U92'(f202_in(z0), f203_in(z0, z1), z0, z1), F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(U93'(f267_in(z0, z1), f268_in(z0, z1), z0, z1), F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(U94'(f293_in(z0, z1), f294_in(z0, z1), z0, z1), F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(U95'(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2), F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(U96'(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3), F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(U97'(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3), F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(U98'(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2), F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(U99'(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(U100'(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3), F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(U101'(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c(U1'(f24_in(z0), z0, tree(z0, void, void)))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(U2'(f63_in(z0), z0, tree(z0, void, void)))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(U3'(f72_in(z0), s(z0), tree(s(z0), void, void)))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(U10'(f318_in(z0), s(z0), tree(s(z0), z1, void)))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(U22'(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(U23'(f146_in(z1), tree(z0, z1, z2)))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(U25'(f146_in(z1), tree(z0, z1, z2)))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(U29'(f487_in(z0, z2), z0, z1, z2))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(U34'(f206_in(z0), s(z0)))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(U37'(f29_in(z0), z0, z1))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(U40'(f72_in(z0), s(z0)))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(U41'(f29_in(z0), z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(U42'(f29_in(z0), z0, z1))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(U45'(f29_in(z0), z0, z1))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(U48'(f29_in(z0), z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(U49'(f29_in(z0), z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(U50'(f29_in(z0), z0, z1, z2))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
U52'(f34_out1, z0) → c(U53'(f2_in(z0, void), z0))
U52'(f34_out1, z0) → c(F2_IN(z0, void))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
U54'(f34_out1, z0) → c(U55'(f2_in(s(z0), void), z0))
U54'(f34_out1, z0) → c(F2_IN(s(z0), void))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
U60'(f34_out1, z0) → c(U61'(f2_in(s(z0), void), z0))
U60'(f34_out1, z0) → c(F2_IN(s(z0), void))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U70'(f34_out1, z0) → c(U71'(f2_in(s(z0), void), z0))
U70'(f34_out1, z0) → c(F2_IN(s(z0), void))
U78'(f494_out1, z0, z1) → c(U79'(f2_in(0, z1), z0, z1))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(U86'(f27_in(z0), f28_in(z0), z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(U87'(f68_in(z0), f69_in(z0), z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))

K tuples:none
Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F2_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, F132_IN, U56', F185_IN, U58', F219_IN, U62', F240_IN, U64', F270_IN, U66', F296_IN, U68', F335_IN, U72', F390_IN, U74', F394_IN, U76', F487_IN, F501_IN, U80', F678_IN, U82', F690_IN, U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, U52', F72_IN, U54', F206_IN, U60', F318_IN, U70', U78', F24_IN, F63_IN

Compound Symbols:

c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c144, c145, c147, c148, c153, c154, c156, c157, c159, c160, c162, c163, c168, c169, c171, c172, c174, c175, c177, c180, c181, c183, c184, c186, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

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

Removed 89 trailing tuple parts

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

K tuples:none
Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(39) CdtKnowledgeProof (EQUIVALENT transformation)

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

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
F24_IN(z0) → c
F63_IN(z0) → c

K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(41) 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.

U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))

We considered the (Usable) Rules:

f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1

And the Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

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

POL(0) = 0   
POL(F109_IN(x₁, x₂)) = 0   
POL(F110_IN(x₁, x₂, x₃)) = 0   
POL(F112_IN(x₁, x₂)) = 0   
POL(F113_IN(x₁, x₂, x₃)) = 0   
POL(F122_IN(x₁, x₂, x₃)) = 0   
POL(F124_IN(x₁, x₂, x₃)) = 0   
POL(F125_IN(x₁, x₂, x₃)) = 0   
POL(F132_IN(x₁, x₂, x₃)) = 0   
POL(F140_IN(x₁)) = 0   
POL(F141_IN(x₁, x₂)) = 0   
POL(F146_IN(x₁)) = 0   
POL(F176_IN(x₁, x₂)) = 0   
POL(F177_IN(x₁, x₂)) = 0   
POL(F178_IN(x₁, x₂)) = 0   
POL(F185_IN(x₁, x₂)) = 0   
POL(F201_IN(x₁, x₂)) = 0   
POL(F202_IN(x₁)) = 0   
POL(F203_IN(x₁, x₂)) = 0   
POL(F206_IN(x₁)) = 0   
POL(F219_IN(x₁, x₂)) = 0   
POL(F240_IN(x₁, x₂)) = 0   
POL(F24_IN(x₁)) = 0   
POL(F264_IN(x₁, x₂)) = 0   
POL(F267_IN(x₁, x₂)) = 0   
POL(F268_IN(x₁, x₂)) = 0   
POL(F270_IN(x₁, x₂)) = 0   
POL(F27_IN(x₁)) = 0   
POL(F28_IN(x₁)) = 0   
POL(F292_IN(x₁, x₂)) = 0   
POL(F293_IN(x₁, x₂)) = 0   
POL(F294_IN(x₁, x₂)) = 0   
POL(F296_IN(x₁, x₂)) = 0   
POL(F29_IN(x₁)) = 0   
POL(F2_IN(x₁, x₂)) = 0   
POL(F318_IN(x₁)) = 0   
POL(F326_IN(x₁, x₂, x₃)) = 0   
POL(F327_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F328_IN(x₁, x₂)) = 0   
POL(F329_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F332_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F333_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F334_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F335_IN(x₁, x₂)) = 0   
POL(F341_IN(x₁)) = 0   
POL(F342_IN(x₁, x₂, x₃)) = 0   
POL(F34_IN(x₁)) = 0   
POL(F387_IN(x₁, x₂, x₃)) = 0   
POL(F388_IN(x₁, x₂, x₃)) = 0   
POL(F389_IN(x₁, x₂, x₃)) = 0   
POL(F390_IN(x₁, x₂)) = 0   
POL(F394_IN(x₁, x₂)) = 0   
POL(F449_IN(x₁, x₂, x₃)) = 0   
POL(F450_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F460_IN(x₁, x₂, x₃)) = 0   
POL(F487_IN(x₁, x₂)) = 0   
POL(F499_IN(x₁, x₂, x₃)) = 0   
POL(F500_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F501_IN(x₁, x₂, x₃)) = 0   
POL(F503_IN(x₁, x₂)) = 0   
POL(F554_IN(x₁, x₂)) = 0   
POL(F63_IN(x₁)) = 0   
POL(F678_IN(x₁, x₂, x₃)) = 0   
POL(F685_IN(x₁, x₂)) = 0   
POL(F68_IN(x₁)) = 0   
POL(F690_IN(x₁, x₂, x₃)) = 0   
POL(F69_IN(x₁)) = 0   
POL(F72_IN(x₁)) = 0   
POL(U20(x₁, x₂, x₃)) = 0   
POL(U21(x₁, x₂)) = x₁   
POL(U22(x₁, x₂, x₃)) = 0   
POL(U52'(x₁, x₂)) = 0   
POL(U54'(x₁, x₂)) = 0   
POL(U56'(x₁, x₂, x₃, x₄)) = [2]x₁   
POL(U58'(x₁, x₂, x₃)) = [2]x₁   
POL(U60'(x₁, x₂)) = 0   
POL(U62'(x₁, x₂, x₃)) = 0   
POL(U64'(x₁, x₂, x₃)) = 0   
POL(U66'(x₁, x₂, x₃)) = [2]x₁   
POL(U68'(x₁, x₂, x₃)) = x₁   
POL(U70'(x₁, x₂)) = 0   
POL(U72'(x₁, x₂, x₃)) = x₁   
POL(U74'(x₁, x₂, x₃)) = 0   
POL(U76'(x₁, x₂, x₃)) = 0   
POL(U78'(x₁, x₂, x₃)) = [2]x₃   
POL(U80'(x₁, x₂, x₃, x₄)) = 0   
POL(U82'(x₁, x₂, x₃, x₄)) = 0   
POL(U84'(x₁, x₂, x₃, x₄)) = 0   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c104(x₁)) = x₁   
POL(c106(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c110(x₁)) = x₁   
POL(c112(x₁)) = x₁   
POL(c12(x₁)) = x₁   
POL(c120(x₁)) = x₁   
POL(c122(x₁)) = x₁   
POL(c126(x₁)) = x₁   
POL(c128(x₁)) = x₁   
POL(c136(x₁)) = x₁   
POL(c144(x₁, x₂)) = x₁ + x₂   
POL(c145(x₁)) = x₁   
POL(c147(x₁, x₂)) = x₁ + x₂   
POL(c148(x₁)) = x₁   
POL(c15(x₁)) = x₁   
POL(c153(x₁, x₂)) = x₁ + x₂   
POL(c154(x₁)) = x₁   
POL(c156(x₁, x₂)) = x₁ + x₂   
POL(c157(x₁)) = x₁   
POL(c159(x₁, x₂)) = x₁ + x₂   
POL(c16(x₁)) = x₁   
POL(c160(x₁)) = x₁   
POL(c162(x₁, x₂)) = x₁ + x₂   
POL(c163(x₁)) = x₁   
POL(c168(x₁, x₂)) = x₁ + x₂   
POL(c169(x₁)) = x₁   
POL(c17(x₁)) = x₁   
POL(c171(x₁, x₂)) = x₁ + x₂   
POL(c172(x₁)) = x₁   
POL(c174(x₁, x₂)) = x₁ + x₂   
POL(c175(x₁)) = x₁   
POL(c177) = 0   
POL(c18(x₁)) = x₁   
POL(c180(x₁, x₂)) = x₁ + x₂   
POL(c181(x₁)) = x₁   
POL(c183(x₁, x₂)) = x₁ + x₂   
POL(c184(x₁)) = x₁   
POL(c186(x₁, x₂)) = x₁ + x₂   
POL(c187(x₁)) = x₁   
POL(c19(x₁)) = x₁   
POL(c195(x₁, x₂)) = x₁ + x₂   
POL(c199(x₁, x₂)) = x₁ + x₂   
POL(c20(x₁)) = x₁   
POL(c203(x₁, x₂)) = x₁ + x₂   
POL(c206(x₁, x₂)) = x₁ + x₂   
POL(c209(x₁, x₂)) = x₁ + x₂   
POL(c212(x₁, x₂)) = x₁ + x₂   
POL(c215(x₁, x₂)) = x₁ + x₂   
POL(c218(x₁, x₂)) = x₁ + x₂   
POL(c222(x₁, x₂)) = x₁ + x₂   
POL(c226(x₁, x₂)) = x₁ + x₂   
POL(c229(x₁, x₂)) = x₁ + x₂   
POL(c232(x₁, x₂)) = x₁ + x₂   
POL(c236(x₁, x₂)) = x₁ + x₂   
POL(c239(x₁)) = x₁   
POL(c55) = 0   
POL(c57) = 0   
POL(c58(x₁)) = x₁   
POL(c6(x₁)) = x₁   
POL(c63(x₁)) = x₁   
POL(c65(x₁)) = x₁   
POL(c7(x₁)) = x₁   
POL(c78(x₁)) = x₁   
POL(c8(x₁)) = x₁   
POL(c83(x₁)) = x₁   
POL(c86) = 0   
POL(c88(x₁)) = x₁   
POL(c9(x₁)) = x₁   
POL(c93(x₁)) = x₁   
POL(c95(x₁)) = x₁   
POL(c97) = 0   
POL(c99(x₁)) = x₁   
POL(f34_in(x₁)) = 0   
POL(f34_out1) = [2]   
POL(f494_out1) = 0   
POL(f503_in(x₁, x₂)) = 0   
POL(f503_out1) = 0   
POL(f554_in(x₁, x₂)) = 0   
POL(f554_out1) = 0   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = 0   
POL(void) = 0   

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
F24_IN(z0) → c
F63_IN(z0) → c

K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(43) 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.

U52'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c

We considered the (Usable) Rules:

f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1

And the Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

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

POL(0) = 0   
POL(F109_IN(x₁, x₂)) = 0   
POL(F110_IN(x₁, x₂, x₃)) = 0   
POL(F112_IN(x₁, x₂)) = 0   
POL(F113_IN(x₁, x₂, x₃)) = 0   
POL(F122_IN(x₁, x₂, x₃)) = 0   
POL(F124_IN(x₁, x₂, x₃)) = 0   
POL(F125_IN(x₁, x₂, x₃)) = 0   
POL(F132_IN(x₁, x₂, x₃)) = 0   
POL(F140_IN(x₁)) = 0   
POL(F141_IN(x₁, x₂)) = 0   
POL(F146_IN(x₁)) = 0   
POL(F176_IN(x₁, x₂)) = 0   
POL(F177_IN(x₁, x₂)) = 0   
POL(F178_IN(x₁, x₂)) = 0   
POL(F185_IN(x₁, x₂)) = 0   
POL(F201_IN(x₁, x₂)) = 0   
POL(F202_IN(x₁)) = 0   
POL(F203_IN(x₁, x₂)) = 0   
POL(F206_IN(x₁)) = 0   
POL(F219_IN(x₁, x₂)) = 0   
POL(F240_IN(x₁, x₂)) = 0   
POL(F24_IN(x₁)) = 0   
POL(F264_IN(x₁, x₂)) = 0   
POL(F267_IN(x₁, x₂)) = 0   
POL(F268_IN(x₁, x₂)) = 0   
POL(F270_IN(x₁, x₂)) = 0   
POL(F27_IN(x₁)) = 0   
POL(F28_IN(x₁)) = 0   
POL(F292_IN(x₁, x₂)) = 0   
POL(F293_IN(x₁, x₂)) = 0   
POL(F294_IN(x₁, x₂)) = 0   
POL(F296_IN(x₁, x₂)) = 0   
POL(F29_IN(x₁)) = 0   
POL(F2_IN(x₁, x₂)) = 0   
POL(F318_IN(x₁)) = 0   
POL(F326_IN(x₁, x₂, x₃)) = 0   
POL(F327_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F328_IN(x₁, x₂)) = 0   
POL(F329_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F332_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F333_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F334_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F335_IN(x₁, x₂)) = 0   
POL(F341_IN(x₁)) = 0   
POL(F342_IN(x₁, x₂, x₃)) = 0   
POL(F34_IN(x₁)) = 0   
POL(F387_IN(x₁, x₂, x₃)) = 0   
POL(F388_IN(x₁, x₂, x₃)) = 0   
POL(F389_IN(x₁, x₂, x₃)) = 0   
POL(F390_IN(x₁, x₂)) = 0   
POL(F394_IN(x₁, x₂)) = 0   
POL(F449_IN(x₁, x₂, x₃)) = 0   
POL(F450_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F460_IN(x₁, x₂, x₃)) = 0   
POL(F487_IN(x₁, x₂)) = 0   
POL(F499_IN(x₁, x₂, x₃)) = 0   
POL(F500_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F501_IN(x₁, x₂, x₃)) = 0   
POL(F503_IN(x₁, x₂)) = 0   
POL(F554_IN(x₁, x₂)) = 0   
POL(F63_IN(x₁)) = 0   
POL(F678_IN(x₁, x₂, x₃)) = 0   
POL(F685_IN(x₁, x₂)) = 0   
POL(F68_IN(x₁)) = 0   
POL(F690_IN(x₁, x₂, x₃)) = 0   
POL(F69_IN(x₁)) = 0   
POL(F72_IN(x₁)) = 0   
POL(U20(x₁, x₂, x₃)) = 0   
POL(U21(x₁, x₂)) = [2]x₁   
POL(U22(x₁, x₂, x₃)) = 0   
POL(U52'(x₁, x₂)) = [2]x₁   
POL(U54'(x₁, x₂)) = 0   
POL(U56'(x₁, x₂, x₃, x₄)) = 0   
POL(U58'(x₁, x₂, x₃)) = [3]x₁   
POL(U60'(x₁, x₂)) = [2]x₁   
POL(U62'(x₁, x₂, x₃)) = 0   
POL(U64'(x₁, x₂, x₃)) = 0   
POL(U66'(x₁, x₂, x₃)) = [2]x₁   
POL(U68'(x₁, x₂, x₃)) = [2]x₁   
POL(U70'(x₁, x₂)) = [2]x₁   
POL(U72'(x₁, x₂, x₃)) = 0   
POL(U74'(x₁, x₂, x₃)) = 0   
POL(U76'(x₁, x₂, x₃)) = 0   
POL(U78'(x₁, x₂, x₃)) = [3]x₃   
POL(U80'(x₁, x₂, x₃, x₄)) = 0   
POL(U82'(x₁, x₂, x₃, x₄)) = 0   
POL(U84'(x₁, x₂, x₃, x₄)) = 0   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c104(x₁)) = x₁   
POL(c106(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c110(x₁)) = x₁   
POL(c112(x₁)) = x₁   
POL(c12(x₁)) = x₁   
POL(c120(x₁)) = x₁   
POL(c122(x₁)) = x₁   
POL(c126(x₁)) = x₁   
POL(c128(x₁)) = x₁   
POL(c136(x₁)) = x₁   
POL(c144(x₁, x₂)) = x₁ + x₂   
POL(c145(x₁)) = x₁   
POL(c147(x₁, x₂)) = x₁ + x₂   
POL(c148(x₁)) = x₁   
POL(c15(x₁)) = x₁   
POL(c153(x₁, x₂)) = x₁ + x₂   
POL(c154(x₁)) = x₁   
POL(c156(x₁, x₂)) = x₁ + x₂   
POL(c157(x₁)) = x₁   
POL(c159(x₁, x₂)) = x₁ + x₂   
POL(c16(x₁)) = x₁   
POL(c160(x₁)) = x₁   
POL(c162(x₁, x₂)) = x₁ + x₂   
POL(c163(x₁)) = x₁   
POL(c168(x₁, x₂)) = x₁ + x₂   
POL(c169(x₁)) = x₁   
POL(c17(x₁)) = x₁   
POL(c171(x₁, x₂)) = x₁ + x₂   
POL(c172(x₁)) = x₁   
POL(c174(x₁, x₂)) = x₁ + x₂   
POL(c175(x₁)) = x₁   
POL(c177) = 0   
POL(c18(x₁)) = x₁   
POL(c180(x₁, x₂)) = x₁ + x₂   
POL(c181(x₁)) = x₁   
POL(c183(x₁, x₂)) = x₁ + x₂   
POL(c184(x₁)) = x₁   
POL(c186(x₁, x₂)) = x₁ + x₂   
POL(c187(x₁)) = x₁   
POL(c19(x₁)) = x₁   
POL(c195(x₁, x₂)) = x₁ + x₂   
POL(c199(x₁, x₂)) = x₁ + x₂   
POL(c20(x₁)) = x₁   
POL(c203(x₁, x₂)) = x₁ + x₂   
POL(c206(x₁, x₂)) = x₁ + x₂   
POL(c209(x₁, x₂)) = x₁ + x₂   
POL(c212(x₁, x₂)) = x₁ + x₂   
POL(c215(x₁, x₂)) = x₁ + x₂   
POL(c218(x₁, x₂)) = x₁ + x₂   
POL(c222(x₁, x₂)) = x₁ + x₂   
POL(c226(x₁, x₂)) = x₁ + x₂   
POL(c229(x₁, x₂)) = x₁ + x₂   
POL(c232(x₁, x₂)) = x₁ + x₂   
POL(c236(x₁, x₂)) = x₁ + x₂   
POL(c239(x₁)) = x₁   
POL(c55) = 0   
POL(c57) = 0   
POL(c58(x₁)) = x₁   
POL(c6(x₁)) = x₁   
POL(c63(x₁)) = x₁   
POL(c65(x₁)) = x₁   
POL(c7(x₁)) = x₁   
POL(c78(x₁)) = x₁   
POL(c8(x₁)) = x₁   
POL(c83(x₁)) = x₁   
POL(c86) = 0   
POL(c88(x₁)) = x₁   
POL(c9(x₁)) = x₁   
POL(c93(x₁)) = x₁   
POL(c95(x₁)) = x₁   
POL(c97) = 0   
POL(c99(x₁)) = x₁   
POL(f34_in(x₁)) = 0   
POL(f34_out1) = [2]   
POL(f494_out1) = 0   
POL(f503_in(x₁, x₂)) = 0   
POL(f503_out1) = 0   
POL(f554_in(x₁, x₂)) = 0   
POL(f554_out1) = 0   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = 0   
POL(void) = 0   

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U54'(f34_out1, z0) → c
F24_IN(z0) → c
F63_IN(z0) → c

K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U52'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(45) 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.

U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
U54'(f34_out1, z0) → c

We considered the (Usable) Rules:

f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1

And the Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

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

POL(0) = 0   
POL(F109_IN(x₁, x₂)) = 0   
POL(F110_IN(x₁, x₂, x₃)) = 0   
POL(F112_IN(x₁, x₂)) = 0   
POL(F113_IN(x₁, x₂, x₃)) = 0   
POL(F122_IN(x₁, x₂, x₃)) = 0   
POL(F124_IN(x₁, x₂, x₃)) = 0   
POL(F125_IN(x₁, x₂, x₃)) = 0   
POL(F132_IN(x₁, x₂, x₃)) = 0   
POL(F140_IN(x₁)) = 0   
POL(F141_IN(x₁, x₂)) = 0   
POL(F146_IN(x₁)) = 0   
POL(F176_IN(x₁, x₂)) = 0   
POL(F177_IN(x₁, x₂)) = 0   
POL(F178_IN(x₁, x₂)) = 0   
POL(F185_IN(x₁, x₂)) = 0   
POL(F201_IN(x₁, x₂)) = 0   
POL(F202_IN(x₁)) = 0   
POL(F203_IN(x₁, x₂)) = 0   
POL(F206_IN(x₁)) = 0   
POL(F219_IN(x₁, x₂)) = 0   
POL(F240_IN(x₁, x₂)) = 0   
POL(F24_IN(x₁)) = 0   
POL(F264_IN(x₁, x₂)) = 0   
POL(F267_IN(x₁, x₂)) = 0   
POL(F268_IN(x₁, x₂)) = 0   
POL(F270_IN(x₁, x₂)) = 0   
POL(F27_IN(x₁)) = 0   
POL(F28_IN(x₁)) = 0   
POL(F292_IN(x₁, x₂)) = 0   
POL(F293_IN(x₁, x₂)) = 0   
POL(F294_IN(x₁, x₂)) = 0   
POL(F296_IN(x₁, x₂)) = 0   
POL(F29_IN(x₁)) = 0   
POL(F2_IN(x₁, x₂)) = 0   
POL(F318_IN(x₁)) = 0   
POL(F326_IN(x₁, x₂, x₃)) = 0   
POL(F327_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F328_IN(x₁, x₂)) = 0   
POL(F329_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F332_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F333_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F334_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F335_IN(x₁, x₂)) = 0   
POL(F341_IN(x₁)) = 0   
POL(F342_IN(x₁, x₂, x₃)) = 0   
POL(F34_IN(x₁)) = 0   
POL(F387_IN(x₁, x₂, x₃)) = 0   
POL(F388_IN(x₁, x₂, x₃)) = 0   
POL(F389_IN(x₁, x₂, x₃)) = 0   
POL(F390_IN(x₁, x₂)) = 0   
POL(F394_IN(x₁, x₂)) = 0   
POL(F449_IN(x₁, x₂, x₃)) = 0   
POL(F450_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F460_IN(x₁, x₂, x₃)) = 0   
POL(F487_IN(x₁, x₂)) = 0   
POL(F499_IN(x₁, x₂, x₃)) = 0   
POL(F500_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F501_IN(x₁, x₂, x₃)) = 0   
POL(F503_IN(x₁, x₂)) = 0   
POL(F554_IN(x₁, x₂)) = 0   
POL(F63_IN(x₁)) = 0   
POL(F678_IN(x₁, x₂, x₃)) = 0   
POL(F685_IN(x₁, x₂)) = 0   
POL(F68_IN(x₁)) = 0   
POL(F690_IN(x₁, x₂, x₃)) = 0   
POL(F69_IN(x₁)) = 0   
POL(F72_IN(x₁)) = 0   
POL(U20(x₁, x₂, x₃)) = 0   
POL(U21(x₁, x₂)) = x₁   
POL(U22(x₁, x₂, x₃)) = 0   
POL(U52'(x₁, x₂)) = 0   
POL(U54'(x₁, x₂)) = [2]x₁   
POL(U56'(x₁, x₂, x₃, x₄)) = 0   
POL(U58'(x₁, x₂, x₃)) = [2]x₁   
POL(U60'(x₁, x₂)) = 0   
POL(U62'(x₁, x₂, x₃)) = 0   
POL(U64'(x₁, x₂, x₃)) = 0   
POL(U66'(x₁, x₂, x₃)) = [2]x₁   
POL(U68'(x₁, x₂, x₃)) = 0   
POL(U70'(x₁, x₂)) = 0   
POL(U72'(x₁, x₂, x₃)) = 0   
POL(U74'(x₁, x₂, x₃)) = 0   
POL(U76'(x₁, x₂, x₃)) = [2]x₁   
POL(U78'(x₁, x₂, x₃)) = 0   
POL(U80'(x₁, x₂, x₃, x₄)) = 0   
POL(U82'(x₁, x₂, x₃, x₄)) = 0   
POL(U84'(x₁, x₂, x₃, x₄)) = 0   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c104(x₁)) = x₁   
POL(c106(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c110(x₁)) = x₁   
POL(c112(x₁)) = x₁   
POL(c12(x₁)) = x₁   
POL(c120(x₁)) = x₁   
POL(c122(x₁)) = x₁   
POL(c126(x₁)) = x₁   
POL(c128(x₁)) = x₁   
POL(c136(x₁)) = x₁   
POL(c144(x₁, x₂)) = x₁ + x₂   
POL(c145(x₁)) = x₁   
POL(c147(x₁, x₂)) = x₁ + x₂   
POL(c148(x₁)) = x₁   
POL(c15(x₁)) = x₁   
POL(c153(x₁, x₂)) = x₁ + x₂   
POL(c154(x₁)) = x₁   
POL(c156(x₁, x₂)) = x₁ + x₂   
POL(c157(x₁)) = x₁   
POL(c159(x₁, x₂)) = x₁ + x₂   
POL(c16(x₁)) = x₁   
POL(c160(x₁)) = x₁   
POL(c162(x₁, x₂)) = x₁ + x₂   
POL(c163(x₁)) = x₁   
POL(c168(x₁, x₂)) = x₁ + x₂   
POL(c169(x₁)) = x₁   
POL(c17(x₁)) = x₁   
POL(c171(x₁, x₂)) = x₁ + x₂   
POL(c172(x₁)) = x₁   
POL(c174(x₁, x₂)) = x₁ + x₂   
POL(c175(x₁)) = x₁   
POL(c177) = 0   
POL(c18(x₁)) = x₁   
POL(c180(x₁, x₂)) = x₁ + x₂   
POL(c181(x₁)) = x₁   
POL(c183(x₁, x₂)) = x₁ + x₂   
POL(c184(x₁)) = x₁   
POL(c186(x₁, x₂)) = x₁ + x₂   
POL(c187(x₁)) = x₁   
POL(c19(x₁)) = x₁   
POL(c195(x₁, x₂)) = x₁ + x₂   
POL(c199(x₁, x₂)) = x₁ + x₂   
POL(c20(x₁)) = x₁   
POL(c203(x₁, x₂)) = x₁ + x₂   
POL(c206(x₁, x₂)) = x₁ + x₂   
POL(c209(x₁, x₂)) = x₁ + x₂   
POL(c212(x₁, x₂)) = x₁ + x₂   
POL(c215(x₁, x₂)) = x₁ + x₂   
POL(c218(x₁, x₂)) = x₁ + x₂   
POL(c222(x₁, x₂)) = x₁ + x₂   
POL(c226(x₁, x₂)) = x₁ + x₂   
POL(c229(x₁, x₂)) = x₁ + x₂   
POL(c232(x₁, x₂)) = x₁ + x₂   
POL(c236(x₁, x₂)) = x₁ + x₂   
POL(c239(x₁)) = x₁   
POL(c55) = 0   
POL(c57) = 0   
POL(c58(x₁)) = x₁   
POL(c6(x₁)) = x₁   
POL(c63(x₁)) = x₁   
POL(c65(x₁)) = x₁   
POL(c7(x₁)) = x₁   
POL(c78(x₁)) = x₁   
POL(c8(x₁)) = x₁   
POL(c83(x₁)) = x₁   
POL(c86) = 0   
POL(c88(x₁)) = x₁   
POL(c9(x₁)) = x₁   
POL(c93(x₁)) = x₁   
POL(c95(x₁)) = x₁   
POL(c97) = 0   
POL(c99(x₁)) = x₁   
POL(f34_in(x₁)) = 0   
POL(f34_out1) = [2]   
POL(f494_out1) = 0   
POL(f503_in(x₁, x₂)) = 0   
POL(f503_out1) = 0   
POL(f554_in(x₁, x₂)) = 0   
POL(f554_out1) = 0   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = 0   
POL(void) = 0   

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
F24_IN(z0) → c
F63_IN(z0) → c

K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U52'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
U54'(f34_out1, z0) → c

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(47) 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.

U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))

We considered the (Usable) Rules:

f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1

And the Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

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

POL(0) = 0   
POL(F109_IN(x₁, x₂)) = 0   
POL(F110_IN(x₁, x₂, x₃)) = 0   
POL(F112_IN(x₁, x₂)) = 0   
POL(F113_IN(x₁, x₂, x₃)) = 0   
POL(F122_IN(x₁, x₂, x₃)) = 0   
POL(F124_IN(x₁, x₂, x₃)) = 0   
POL(F125_IN(x₁, x₂, x₃)) = 0   
POL(F132_IN(x₁, x₂, x₃)) = 0   
POL(F140_IN(x₁)) = 0   
POL(F141_IN(x₁, x₂)) = 0   
POL(F146_IN(x₁)) = 0   
POL(F176_IN(x₁, x₂)) = 0   
POL(F177_IN(x₁, x₂)) = 0   
POL(F178_IN(x₁, x₂)) = 0   
POL(F185_IN(x₁, x₂)) = 0   
POL(F201_IN(x₁, x₂)) = 0   
POL(F202_IN(x₁)) = 0   
POL(F203_IN(x₁, x₂)) = 0   
POL(F206_IN(x₁)) = 0   
POL(F219_IN(x₁, x₂)) = 0   
POL(F240_IN(x₁, x₂)) = 0   
POL(F24_IN(x₁)) = 0   
POL(F264_IN(x₁, x₂)) = 0   
POL(F267_IN(x₁, x₂)) = 0   
POL(F268_IN(x₁, x₂)) = 0   
POL(F270_IN(x₁, x₂)) = 0   
POL(F27_IN(x₁)) = 0   
POL(F28_IN(x₁)) = 0   
POL(F292_IN(x₁, x₂)) = 0   
POL(F293_IN(x₁, x₂)) = 0   
POL(F294_IN(x₁, x₂)) = 0   
POL(F296_IN(x₁, x₂)) = 0   
POL(F29_IN(x₁)) = 0   
POL(F2_IN(x₁, x₂)) = 0   
POL(F318_IN(x₁)) = 0   
POL(F326_IN(x₁, x₂, x₃)) = 0   
POL(F327_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F328_IN(x₁, x₂)) = 0   
POL(F329_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F332_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F333_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F334_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F335_IN(x₁, x₂)) = 0   
POL(F341_IN(x₁)) = 0   
POL(F342_IN(x₁, x₂, x₃)) = 0   
POL(F34_IN(x₁)) = 0   
POL(F387_IN(x₁, x₂, x₃)) = 0   
POL(F388_IN(x₁, x₂, x₃)) = 0   
POL(F389_IN(x₁, x₂, x₃)) = 0   
POL(F390_IN(x₁, x₂)) = 0   
POL(F394_IN(x₁, x₂)) = 0   
POL(F449_IN(x₁, x₂, x₃)) = 0   
POL(F450_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F460_IN(x₁, x₂, x₃)) = 0   
POL(F487_IN(x₁, x₂)) = 0   
POL(F499_IN(x₁, x₂, x₃)) = 0   
POL(F500_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F501_IN(x₁, x₂, x₃)) = 0   
POL(F503_IN(x₁, x₂)) = 0   
POL(F554_IN(x₁, x₂)) = 0   
POL(F63_IN(x₁)) = 0   
POL(F678_IN(x₁, x₂, x₃)) = 0   
POL(F685_IN(x₁, x₂)) = 0   
POL(F68_IN(x₁)) = 0   
POL(F690_IN(x₁, x₂, x₃)) = 0   
POL(F69_IN(x₁)) = 0   
POL(F72_IN(x₁)) = 0   
POL(U20(x₁, x₂, x₃)) = 0   
POL(U21(x₁, x₂)) = [2]x₁   
POL(U22(x₁, x₂, x₃)) = 0   
POL(U52'(x₁, x₂)) = 0   
POL(U54'(x₁, x₂)) = 0   
POL(U56'(x₁, x₂, x₃, x₄)) = 0   
POL(U58'(x₁, x₂, x₃)) = 0   
POL(U60'(x₁, x₂)) = 0   
POL(U62'(x₁, x₂, x₃)) = [2]x₁   
POL(U64'(x₁, x₂, x₃)) = 0   
POL(U66'(x₁, x₂, x₃)) = 0   
POL(U68'(x₁, x₂, x₃)) = 0   
POL(U70'(x₁, x₂)) = 0   
POL(U72'(x₁, x₂, x₃)) = [2]x₁   
POL(U74'(x₁, x₂, x₃)) = [2]x₁   
POL(U76'(x₁, x₂, x₃)) = 0   
POL(U78'(x₁, x₂, x₃)) = [2]x₃   
POL(U80'(x₁, x₂, x₃, x₄)) = 0   
POL(U82'(x₁, x₂, x₃, x₄)) = 0   
POL(U84'(x₁, x₂, x₃, x₄)) = 0   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c104(x₁)) = x₁   
POL(c106(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c110(x₁)) = x₁   
POL(c112(x₁)) = x₁   
POL(c12(x₁)) = x₁   
POL(c120(x₁)) = x₁   
POL(c122(x₁)) = x₁   
POL(c126(x₁)) = x₁   
POL(c128(x₁)) = x₁   
POL(c136(x₁)) = x₁   
POL(c144(x₁, x₂)) = x₁ + x₂   
POL(c145(x₁)) = x₁   
POL(c147(x₁, x₂)) = x₁ + x₂   
POL(c148(x₁)) = x₁   
POL(c15(x₁)) = x₁   
POL(c153(x₁, x₂)) = x₁ + x₂   
POL(c154(x₁)) = x₁   
POL(c156(x₁, x₂)) = x₁ + x₂   
POL(c157(x₁)) = x₁   
POL(c159(x₁, x₂)) = x₁ + x₂   
POL(c16(x₁)) = x₁   
POL(c160(x₁)) = x₁   
POL(c162(x₁, x₂)) = x₁ + x₂   
POL(c163(x₁)) = x₁   
POL(c168(x₁, x₂)) = x₁ + x₂   
POL(c169(x₁)) = x₁   
POL(c17(x₁)) = x₁   
POL(c171(x₁, x₂)) = x₁ + x₂   
POL(c172(x₁)) = x₁   
POL(c174(x₁, x₂)) = x₁ + x₂   
POL(c175(x₁)) = x₁   
POL(c177) = 0   
POL(c18(x₁)) = x₁   
POL(c180(x₁, x₂)) = x₁ + x₂   
POL(c181(x₁)) = x₁   
POL(c183(x₁, x₂)) = x₁ + x₂   
POL(c184(x₁)) = x₁   
POL(c186(x₁, x₂)) = x₁ + x₂   
POL(c187(x₁)) = x₁   
POL(c19(x₁)) = x₁   
POL(c195(x₁, x₂)) = x₁ + x₂   
POL(c199(x₁, x₂)) = x₁ + x₂   
POL(c20(x₁)) = x₁   
POL(c203(x₁, x₂)) = x₁ + x₂   
POL(c206(x₁, x₂)) = x₁ + x₂   
POL(c209(x₁, x₂)) = x₁ + x₂   
POL(c212(x₁, x₂)) = x₁ + x₂   
POL(c215(x₁, x₂)) = x₁ + x₂   
POL(c218(x₁, x₂)) = x₁ + x₂   
POL(c222(x₁, x₂)) = x₁ + x₂   
POL(c226(x₁, x₂)) = x₁ + x₂   
POL(c229(x₁, x₂)) = x₁ + x₂   
POL(c232(x₁, x₂)) = x₁ + x₂   
POL(c236(x₁, x₂)) = x₁ + x₂   
POL(c239(x₁)) = x₁   
POL(c55) = 0   
POL(c57) = 0   
POL(c58(x₁)) = x₁   
POL(c6(x₁)) = x₁   
POL(c63(x₁)) = x₁   
POL(c65(x₁)) = x₁   
POL(c7(x₁)) = x₁   
POL(c78(x₁)) = x₁   
POL(c8(x₁)) = x₁   
POL(c83(x₁)) = x₁   
POL(c86) = 0   
POL(c88(x₁)) = x₁   
POL(c9(x₁)) = x₁   
POL(c93(x₁)) = x₁   
POL(c95(x₁)) = x₁   
POL(c97) = 0   
POL(c99(x₁)) = x₁   
POL(f34_in(x₁)) = 0   
POL(f34_out1) = [2]   
POL(f494_out1) = 0   
POL(f503_in(x₁, x₂)) = 0   
POL(f503_out1) = 0   
POL(f554_in(x₁, x₂)) = 0   
POL(f554_out1) = 0   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = 0   
POL(void) = 0   

(48) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
F24_IN(z0) → c
F63_IN(z0) → c

K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U52'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
U54'(f34_out1, z0) → c
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(49) 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.

U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))

We considered the (Usable) Rules:

f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1

And the Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

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

POL(0) = 0   
POL(F109_IN(x₁, x₂)) = 0   
POL(F110_IN(x₁, x₂, x₃)) = 0   
POL(F112_IN(x₁, x₂)) = 0   
POL(F113_IN(x₁, x₂, x₃)) = 0   
POL(F122_IN(x₁, x₂, x₃)) = 0   
POL(F124_IN(x₁, x₂, x₃)) = 0   
POL(F125_IN(x₁, x₂, x₃)) = 0   
POL(F132_IN(x₁, x₂, x₃)) = 0   
POL(F140_IN(x₁)) = 0   
POL(F141_IN(x₁, x₂)) = 0   
POL(F146_IN(x₁)) = 0   
POL(F176_IN(x₁, x₂)) = 0   
POL(F177_IN(x₁, x₂)) = 0   
POL(F178_IN(x₁, x₂)) = 0   
POL(F185_IN(x₁, x₂)) = 0   
POL(F201_IN(x₁, x₂)) = 0   
POL(F202_IN(x₁)) = 0   
POL(F203_IN(x₁, x₂)) = 0   
POL(F206_IN(x₁)) = 0   
POL(F219_IN(x₁, x₂)) = 0   
POL(F240_IN(x₁, x₂)) = 0   
POL(F24_IN(x₁)) = 0   
POL(F264_IN(x₁, x₂)) = 0   
POL(F267_IN(x₁, x₂)) = 0   
POL(F268_IN(x₁, x₂)) = 0   
POL(F270_IN(x₁, x₂)) = 0   
POL(F27_IN(x₁)) = 0   
POL(F28_IN(x₁)) = 0   
POL(F292_IN(x₁, x₂)) = 0   
POL(F293_IN(x₁, x₂)) = 0   
POL(F294_IN(x₁, x₂)) = 0   
POL(F296_IN(x₁, x₂)) = 0   
POL(F29_IN(x₁)) = 0   
POL(F2_IN(x₁, x₂)) = 0   
POL(F318_IN(x₁)) = 0   
POL(F326_IN(x₁, x₂, x₃)) = 0   
POL(F327_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F328_IN(x₁, x₂)) = 0   
POL(F329_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F332_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F333_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F334_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F335_IN(x₁, x₂)) = 0   
POL(F341_IN(x₁)) = 0   
POL(F342_IN(x₁, x₂, x₃)) = 0   
POL(F34_IN(x₁)) = 0   
POL(F387_IN(x₁, x₂, x₃)) = 0   
POL(F388_IN(x₁, x₂, x₃)) = 0   
POL(F389_IN(x₁, x₂, x₃)) = 0   
POL(F390_IN(x₁, x₂)) = 0   
POL(F394_IN(x₁, x₂)) = 0   
POL(F449_IN(x₁, x₂, x₃)) = 0   
POL(F450_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F460_IN(x₁, x₂, x₃)) = 0   
POL(F487_IN(x₁, x₂)) = 0   
POL(F499_IN(x₁, x₂, x₃)) = 0   
POL(F500_IN(x₁, x₂, x₃, x₄)) = 0   
POL(F501_IN(x₁, x₂, x₃)) = 0   
POL(F503_IN(x₁, x₂)) = 0   
POL(F554_IN(x₁, x₂)) = 0   
POL(F63_IN(x₁)) = 0   
POL(F678_IN(x₁, x₂, x₃)) = 0   
POL(F685_IN(x₁, x₂)) = 0   
POL(F68_IN(x₁)) = 0   
POL(F690_IN(x₁, x₂, x₃)) = 0   
POL(F69_IN(x₁)) = 0   
POL(F72_IN(x₁)) = 0   
POL(U20(x₁, x₂, x₃)) = 0   
POL(U21(x₁, x₂)) = [2]x₁   
POL(U22(x₁, x₂, x₃)) = 0   
POL(U52'(x₁, x₂)) = 0   
POL(U54'(x₁, x₂)) = 0   
POL(U56'(x₁, x₂, x₃, x₄)) = 0   
POL(U58'(x₁, x₂, x₃)) = 0   
POL(U60'(x₁, x₂)) = 0   
POL(U62'(x₁, x₂, x₃)) = 0   
POL(U64'(x₁, x₂, x₃)) = x₁   
POL(U66'(x₁, x₂, x₃)) = 0   
POL(U68'(x₁, x₂, x₃)) = 0   
POL(U70'(x₁, x₂)) = 0   
POL(U72'(x₁, x₂, x₃)) = 0   
POL(U74'(x₁, x₂, x₃)) = 0   
POL(U76'(x₁, x₂, x₃)) = 0   
POL(U78'(x₁, x₂, x₃)) = [1]   
POL(U80'(x₁, x₂, x₃, x₄)) = 0   
POL(U82'(x₁, x₂, x₃, x₄)) = 0   
POL(U84'(x₁, x₂, x₃, x₄)) = 0   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c104(x₁)) = x₁   
POL(c106(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c110(x₁)) = x₁   
POL(c112(x₁)) = x₁   
POL(c12(x₁)) = x₁   
POL(c120(x₁)) = x₁   
POL(c122(x₁)) = x₁   
POL(c126(x₁)) = x₁   
POL(c128(x₁)) = x₁   
POL(c136(x₁)) = x₁   
POL(c144(x₁, x₂)) = x₁ + x₂   
POL(c145(x₁)) = x₁   
POL(c147(x₁, x₂)) = x₁ + x₂   
POL(c148(x₁)) = x₁   
POL(c15(x₁)) = x₁   
POL(c153(x₁, x₂)) = x₁ + x₂   
POL(c154(x₁)) = x₁   
POL(c156(x₁, x₂)) = x₁ + x₂   
POL(c157(x₁)) = x₁   
POL(c159(x₁, x₂)) = x₁ + x₂   
POL(c16(x₁)) = x₁   
POL(c160(x₁)) = x₁   
POL(c162(x₁, x₂)) = x₁ + x₂   
POL(c163(x₁)) = x₁   
POL(c168(x₁, x₂)) = x₁ + x₂   
POL(c169(x₁)) = x₁   
POL(c17(x₁)) = x₁   
POL(c171(x₁, x₂)) = x₁ + x₂   
POL(c172(x₁)) = x₁   
POL(c174(x₁, x₂)) = x₁ + x₂   
POL(c175(x₁)) = x₁   
POL(c177) = 0   
POL(c18(x₁)) = x₁   
POL(c180(x₁, x₂)) = x₁ + x₂   
POL(c181(x₁)) = x₁   
POL(c183(x₁, x₂)) = x₁ + x₂   
POL(c184(x₁)) = x₁   
POL(c186(x₁, x₂)) = x₁ + x₂   
POL(c187(x₁)) = x₁   
POL(c19(x₁)) = x₁   
POL(c195(x₁, x₂)) = x₁ + x₂   
POL(c199(x₁, x₂)) = x₁ + x₂   
POL(c20(x₁)) = x₁   
POL(c203(x₁, x₂)) = x₁ + x₂   
POL(c206(x₁, x₂)) = x₁ + x₂   
POL(c209(x₁, x₂)) = x₁ + x₂   
POL(c212(x₁, x₂)) = x₁ + x₂   
POL(c215(x₁, x₂)) = x₁ + x₂   
POL(c218(x₁, x₂)) = x₁ + x₂   
POL(c222(x₁, x₂)) = x₁ + x₂   
POL(c226(x₁, x₂)) = x₁ + x₂   
POL(c229(x₁, x₂)) = x₁ + x₂   
POL(c232(x₁, x₂)) = x₁ + x₂   
POL(c236(x₁, x₂)) = x₁ + x₂   
POL(c239(x₁)) = x₁   
POL(c55) = 0   
POL(c57) = 0   
POL(c58(x₁)) = x₁   
POL(c6(x₁)) = x₁   
POL(c63(x₁)) = x₁   
POL(c65(x₁)) = x₁   
POL(c7(x₁)) = x₁   
POL(c78(x₁)) = x₁   
POL(c8(x₁)) = x₁   
POL(c83(x₁)) = x₁   
POL(c86) = 0   
POL(c88(x₁)) = x₁   
POL(c9(x₁)) = x₁   
POL(c93(x₁)) = x₁   
POL(c95(x₁)) = x₁   
POL(c97) = 0   
POL(c99(x₁)) = x₁   
POL(f34_in(x₁)) = 0   
POL(f34_out1) = [1]   
POL(f494_out1) = 0   
POL(f503_in(x₁, x₂)) = 0   
POL(f503_out1) = 0   
POL(f554_in(x₁, x₂)) = 0   
POL(f554_out1) = 0   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = 0   
POL(void) = 0   

(50) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
F24_IN(z0) → c
F63_IN(z0) → c

K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U52'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
U54'(f34_out1, z0) → c
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(51) 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.

F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F68_IN(s(z0)) → c
F63_IN(z0) → c

We considered the (Usable) Rules:

f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1

And the Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

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

POL(0) = 0   
POL(F109_IN(x₁, x₂)) = x₁   
POL(F110_IN(x₁, x₂, x₃)) = [1] + x₂   
POL(F112_IN(x₁, x₂)) = 0   
POL(F113_IN(x₁, x₂, x₃)) = x₃   
POL(F122_IN(x₁, x₂, x₃)) = x₃   
POL(F124_IN(x₁, x₂, x₃)) = 0   
POL(F125_IN(x₁, x₂, x₃)) = x₃   
POL(F132_IN(x₁, x₂, x₃)) = x₃   
POL(F140_IN(x₁)) = 0   
POL(F141_IN(x₁, x₂)) = x₂   
POL(F146_IN(x₁)) = 0   
POL(F176_IN(x₁, x₂)) = x₂   
POL(F177_IN(x₁, x₂)) = 0   
POL(F178_IN(x₁, x₂)) = x₂   
POL(F185_IN(x₁, x₂)) = x₂   
POL(F201_IN(x₁, x₂)) = x₂   
POL(F202_IN(x₁)) = 0   
POL(F203_IN(x₁, x₂)) = x₂   
POL(F206_IN(x₁)) = 0   
POL(F219_IN(x₁, x₂)) = x₂   
POL(F240_IN(x₁, x₂)) = [1] + x₂   
POL(F24_IN(x₁)) = 0   
POL(F264_IN(x₁, x₂)) = x₂   
POL(F267_IN(x₁, x₂)) = x₂   
POL(F268_IN(x₁, x₂)) = 0   
POL(F270_IN(x₁, x₂)) = x₂   
POL(F27_IN(x₁)) = 0   
POL(F28_IN(x₁)) = 0   
POL(F292_IN(x₁, x₂)) = x₂   
POL(F293_IN(x₁, x₂)) = x₂   
POL(F294_IN(x₁, x₂)) = 0   
POL(F296_IN(x₁, x₂)) = x₂   
POL(F29_IN(x₁)) = 0   
POL(F2_IN(x₁, x₂)) = x₂   
POL(F318_IN(x₁)) = [2]   
POL(F326_IN(x₁, x₂, x₃)) = x₁ + x₃   
POL(F327_IN(x₁, x₂, x₃, x₄)) = x₂ + x₄   
POL(F328_IN(x₁, x₂)) = 0   
POL(F329_IN(x₁, x₂, x₃, x₄)) = x₂ + x₄   
POL(F332_IN(x₁, x₂, x₃, x₄)) = x₂ + x₄   
POL(F333_IN(x₁, x₂, x₃, x₄)) = x₂   
POL(F334_IN(x₁, x₂, x₃, x₄)) = x₄   
POL(F335_IN(x₁, x₂)) = x₂   
POL(F341_IN(x₁)) = 0   
POL(F342_IN(x₁, x₂, x₃)) = x₂ + x₃   
POL(F34_IN(x₁)) = 0   
POL(F387_IN(x₁, x₂, x₃)) = x₂ + x₃   
POL(F388_IN(x₁, x₂, x₃)) = x₂   
POL(F389_IN(x₁, x₂, x₃)) = x₃   
POL(F390_IN(x₁, x₂)) = x₂   
POL(F394_IN(x₁, x₂)) = x₂   
POL(F449_IN(x₁, x₂, x₃)) = x₁   
POL(F450_IN(x₁, x₂, x₃, x₄)) = x₃ + x₄   
POL(F460_IN(x₁, x₂, x₃)) = 0   
POL(F487_IN(x₁, x₂)) = 0   
POL(F499_IN(x₁, x₂, x₃)) = x₃   
POL(F500_IN(x₁, x₂, x₃, x₄)) = x₄   
POL(F501_IN(x₁, x₂, x₃)) = x₃   
POL(F503_IN(x₁, x₂)) = 0   
POL(F554_IN(x₁, x₂)) = 0   
POL(F63_IN(x₁)) = [2]   
POL(F678_IN(x₁, x₂, x₃)) = x₃   
POL(F685_IN(x₁, x₂)) = x₂   
POL(F68_IN(x₁)) = [1]   
POL(F690_IN(x₁, x₂, x₃)) = x₃   
POL(F69_IN(x₁)) = 0   
POL(F72_IN(x₁)) = 0   
POL(U20(x₁, x₂, x₃)) = 0   
POL(U21(x₁, x₂)) = [2]x₁   
POL(U22(x₁, x₂, x₃)) = 0   
POL(U52'(x₁, x₂)) = 0   
POL(U54'(x₁, x₂)) = 0   
POL(U56'(x₁, x₂, x₃, x₄)) = x₁ + x₄   
POL(U58'(x₁, x₂, x₃)) = x₃   
POL(U60'(x₁, x₂)) = 0   
POL(U62'(x₁, x₂, x₃)) = x₃   
POL(U64'(x₁, x₂, x₃)) = x₃   
POL(U66'(x₁, x₂, x₃)) = x₃   
POL(U68'(x₁, x₂, x₃)) = x₃   
POL(U70'(x₁, x₂)) = 0   
POL(U72'(x₁, x₂, x₃)) = x₃   
POL(U74'(x₁, x₂, x₃)) = x₃   
POL(U76'(x₁, x₂, x₃)) = x₃   
POL(U78'(x₁, x₂, x₃)) = [2]x₁ + x₃   
POL(U80'(x₁, x₂, x₃, x₄)) = x₄   
POL(U82'(x₁, x₂, x₃, x₄)) = x₄   
POL(U84'(x₁, x₂, x₃, x₄)) = x₄   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c104(x₁)) = x₁   
POL(c106(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c110(x₁)) = x₁   
POL(c112(x₁)) = x₁   
POL(c12(x₁)) = x₁   
POL(c120(x₁)) = x₁   
POL(c122(x₁)) = x₁   
POL(c126(x₁)) = x₁   
POL(c128(x₁)) = x₁   
POL(c136(x₁)) = x₁   
POL(c144(x₁, x₂)) = x₁ + x₂   
POL(c145(x₁)) = x₁   
POL(c147(x₁, x₂)) = x₁ + x₂   
POL(c148(x₁)) = x₁   
POL(c15(x₁)) = x₁   
POL(c153(x₁, x₂)) = x₁ + x₂   
POL(c154(x₁)) = x₁   
POL(c156(x₁, x₂)) = x₁ + x₂   
POL(c157(x₁)) = x₁   
POL(c159(x₁, x₂)) = x₁ + x₂   
POL(c16(x₁)) = x₁   
POL(c160(x₁)) = x₁   
POL(c162(x₁, x₂)) = x₁ + x₂   
POL(c163(x₁)) = x₁   
POL(c168(x₁, x₂)) = x₁ + x₂   
POL(c169(x₁)) = x₁   
POL(c17(x₁)) = x₁   
POL(c171(x₁, x₂)) = x₁ + x₂   
POL(c172(x₁)) = x₁   
POL(c174(x₁, x₂)) = x₁ + x₂   
POL(c175(x₁)) = x₁   
POL(c177) = 0   
POL(c18(x₁)) = x₁   
POL(c180(x₁, x₂)) = x₁ + x₂   
POL(c181(x₁)) = x₁   
POL(c183(x₁, x₂)) = x₁ + x₂   
POL(c184(x₁)) = x₁   
POL(c186(x₁, x₂)) = x₁ + x₂   
POL(c187(x₁)) = x₁   
POL(c19(x₁)) = x₁   
POL(c195(x₁, x₂)) = x₁ + x₂   
POL(c199(x₁, x₂)) = x₁ + x₂   
POL(c20(x₁)) = x₁   
POL(c203(x₁, x₂)) = x₁ + x₂   
POL(c206(x₁, x₂)) = x₁ + x₂   
POL(c209(x₁, x₂)) = x₁ + x₂   
POL(c212(x₁, x₂)) = x₁ + x₂   
POL(c215(x₁, x₂)) = x₁ + x₂   
POL(c218(x₁, x₂)) = x₁ + x₂   
POL(c222(x₁, x₂)) = x₁ + x₂   
POL(c226(x₁, x₂)) = x₁ + x₂   
POL(c229(x₁, x₂)) = x₁ + x₂   
POL(c232(x₁, x₂)) = x₁ + x₂   
POL(c236(x₁, x₂)) = x₁ + x₂   
POL(c239(x₁)) = x₁   
POL(c55) = 0   
POL(c57) = 0   
POL(c58(x₁)) = x₁   
POL(c6(x₁)) = x₁   
POL(c63(x₁)) = x₁   
POL(c65(x₁)) = x₁   
POL(c7(x₁)) = x₁   
POL(c78(x₁)) = x₁   
POL(c8(x₁)) = x₁   
POL(c83(x₁)) = x₁   
POL(c86) = 0   
POL(c88(x₁)) = x₁   
POL(c9(x₁)) = x₁   
POL(c93(x₁)) = x₁   
POL(c95(x₁)) = x₁   
POL(c97) = 0   
POL(c99(x₁)) = x₁   
POL(f34_in(x₁)) = 0   
POL(f34_out1) = [2]   
POL(f494_out1) = [2]   
POL(f503_in(x₁, x₂)) = 0   
POL(f503_out1) = 0   
POL(f554_in(x₁, x₂)) = 0   
POL(f554_out1) = 0   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = x₂ + x₃   
POL(void) = [2]   

(52) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
F24_IN(z0) → c

K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U52'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
U54'(f34_out1, z0) → c
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F68_IN(s(z0)) → c
F63_IN(z0) → c

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(53) CdtKnowledgeProof (EQUIVALENT transformation)

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

F69_IN(z0) → c(F29_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F140_IN(tree(z0, z1, z2)) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F69_IN(z0) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
F24_IN(z0) → c
U54'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
F27_IN(z0) → c(F29_IN(z0))
F27_IN(z0) → c
F28_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F140_IN(tree(z0, z1, z2)) → c
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
F124_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c(F206_IN(z0))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F202_IN(s(z0)) → c
F268_IN(z0, z1) → c(F29_IN(z0))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F268_IN(z0, z1) → c
F294_IN(z0, z1) → c(F29_IN(z0))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F294_IN(z0, z1) → c
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F177_IN(z0, z1) → c(F29_IN(z0))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F177_IN(z0, z1) → c
U60'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
U52'(f34_out1, z0) → c
U52'(f34_out1, z0) → c
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))

(54) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c

K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U52'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
U54'(f34_out1, z0) → c
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F68_IN(s(z0)) → c
F63_IN(z0) → c
F69_IN(z0) → c(F29_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F140_IN(tree(z0, z1, z2)) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F69_IN(z0) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
F24_IN(z0) → c
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F268_IN(z0, z1) → c(F29_IN(z0))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F294_IN(z0, z1) → c(F29_IN(z0))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F177_IN(z0, z1) → c(F29_IN(z0))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F177_IN(z0, z1) → c
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(55) 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(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))

We considered the (Usable) Rules:

f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1

And the Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

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

POL(0) = [1]   
POL(F109_IN(x₁, x₂)) = x₁ + x₂   
POL(F110_IN(x₁, x₂, x₃)) = x₁ + x₂ + x₃   
POL(F112_IN(x₁, x₂)) = 0   
POL(F113_IN(x₁, x₂, x₃)) = x₂ + x₃   
POL(F122_IN(x₁, x₂, x₃)) = x₂ + x₃   
POL(F124_IN(x₁, x₂, x₃)) = 0   
POL(F125_IN(x₁, x₂, x₃)) = x₂ + x₃   
POL(F132_IN(x₁, x₂, x₃)) = x₂ + x₃   
POL(F140_IN(x₁)) = 0   
POL(F141_IN(x₁, x₂)) = x₂   
POL(F146_IN(x₁)) = 0   
POL(F176_IN(x₁, x₂)) = x₂   
POL(F177_IN(x₁, x₂)) = 0   
POL(F178_IN(x₁, x₂)) = x₂   
POL(F185_IN(x₁, x₂)) = x₂   
POL(F201_IN(x₁, x₂)) = x₂   
POL(F202_IN(x₁)) = 0   
POL(F203_IN(x₁, x₂)) = x₂   
POL(F206_IN(x₁)) = 0   
POL(F219_IN(x₁, x₂)) = x₂   
POL(F240_IN(x₁, x₂)) = x₂   
POL(F24_IN(x₁)) = x₁   
POL(F264_IN(x₁, x₂)) = x₁ + x₂   
POL(F267_IN(x₁, x₂)) = x₂   
POL(F268_IN(x₁, x₂)) = 0   
POL(F270_IN(x₁, x₂)) = x₂   
POL(F27_IN(x₁)) = 0   
POL(F28_IN(x₁)) = x₁   
POL(F292_IN(x₁, x₂)) = x₁ + x₂   
POL(F293_IN(x₁, x₂)) = x₂   
POL(F294_IN(x₁, x₂)) = 0   
POL(F296_IN(x₁, x₂)) = x₂   
POL(F29_IN(x₁)) = 0   
POL(F2_IN(x₁, x₂)) = x₂   
POL(F318_IN(x₁)) = 0   
POL(F326_IN(x₁, x₂, x₃)) = x₁ + x₂ + x₃   
POL(F327_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄   
POL(F328_IN(x₁, x₂)) = 0   
POL(F329_IN(x₁, x₂, x₃, x₄)) = x₂ + x₃ + x₄   
POL(F332_IN(x₁, x₂, x₃, x₄)) = x₂ + x₃ + x₄   
POL(F333_IN(x₁, x₂, x₃, x₄)) = x₂   
POL(F334_IN(x₁, x₂, x₃, x₄)) = x₃ + x₄   
POL(F335_IN(x₁, x₂)) = x₂   
POL(F341_IN(x₁)) = 0   
POL(F342_IN(x₁, x₂, x₃)) = x₂ + x₃   
POL(F34_IN(x₁)) = 0   
POL(F387_IN(x₁, x₂, x₃)) = x₂ + x₃   
POL(F388_IN(x₁, x₂, x₃)) = x₂   
POL(F389_IN(x₁, x₂, x₃)) = x₃   
POL(F390_IN(x₁, x₂)) = x₂   
POL(F394_IN(x₁, x₂)) = x₂   
POL(F449_IN(x₁, x₂, x₃)) = x₁ + x₃   
POL(F450_IN(x₁, x₂, x₃, x₄)) = x₂ + x₃ + x₄   
POL(F460_IN(x₁, x₂, x₃)) = 0   
POL(F487_IN(x₁, x₂)) = 0   
POL(F499_IN(x₁, x₂, x₃)) = x₃   
POL(F500_IN(x₁, x₂, x₃, x₄)) = x₄   
POL(F501_IN(x₁, x₂, x₃)) = x₃   
POL(F503_IN(x₁, x₂)) = 0   
POL(F554_IN(x₁, x₂)) = 0   
POL(F63_IN(x₁)) = x₁   
POL(F678_IN(x₁, x₂, x₃)) = x₃   
POL(F685_IN(x₁, x₂)) = x₂   
POL(F68_IN(x₁)) = x₁   
POL(F690_IN(x₁, x₂, x₃)) = x₃   
POL(F69_IN(x₁)) = x₁   
POL(F72_IN(x₁)) = 0   
POL(U20(x₁, x₂, x₃)) = 0   
POL(U21(x₁, x₂)) = 0   
POL(U22(x₁, x₂, x₃)) = 0   
POL(U52'(x₁, x₂)) = 0   
POL(U54'(x₁, x₂)) = 0   
POL(U56'(x₁, x₂, x₃, x₄)) = x₃ + x₄   
POL(U58'(x₁, x₂, x₃)) = x₃   
POL(U60'(x₁, x₂)) = 0   
POL(U62'(x₁, x₂, x₃)) = x₃   
POL(U64'(x₁, x₂, x₃)) = x₃   
POL(U66'(x₁, x₂, x₃)) = x₃   
POL(U68'(x₁, x₂, x₃)) = x₃   
POL(U70'(x₁, x₂)) = 0   
POL(U72'(x₁, x₂, x₃)) = x₃   
POL(U74'(x₁, x₂, x₃)) = x₃   
POL(U76'(x₁, x₂, x₃)) = x₃   
POL(U78'(x₁, x₂, x₃)) = [2]x₃   
POL(U80'(x₁, x₂, x₃, x₄)) = x₄   
POL(U82'(x₁, x₂, x₃, x₄)) = x₄   
POL(U84'(x₁, x₂, x₃, x₄)) = x₄   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c104(x₁)) = x₁   
POL(c106(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c110(x₁)) = x₁   
POL(c112(x₁)) = x₁   
POL(c12(x₁)) = x₁   
POL(c120(x₁)) = x₁   
POL(c122(x₁)) = x₁   
POL(c126(x₁)) = x₁   
POL(c128(x₁)) = x₁   
POL(c136(x₁)) = x₁   
POL(c144(x₁, x₂)) = x₁ + x₂   
POL(c145(x₁)) = x₁   
POL(c147(x₁, x₂)) = x₁ + x₂   
POL(c148(x₁)) = x₁   
POL(c15(x₁)) = x₁   
POL(c153(x₁, x₂)) = x₁ + x₂   
POL(c154(x₁)) = x₁   
POL(c156(x₁, x₂)) = x₁ + x₂   
POL(c157(x₁)) = x₁   
POL(c159(x₁, x₂)) = x₁ + x₂   
POL(c16(x₁)) = x₁   
POL(c160(x₁)) = x₁   
POL(c162(x₁, x₂)) = x₁ + x₂   
POL(c163(x₁)) = x₁   
POL(c168(x₁, x₂)) = x₁ + x₂   
POL(c169(x₁)) = x₁   
POL(c17(x₁)) = x₁   
POL(c171(x₁, x₂)) = x₁ + x₂   
POL(c172(x₁)) = x₁   
POL(c174(x₁, x₂)) = x₁ + x₂   
POL(c175(x₁)) = x₁   
POL(c177) = 0   
POL(c18(x₁)) = x₁   
POL(c180(x₁, x₂)) = x₁ + x₂   
POL(c181(x₁)) = x₁   
POL(c183(x₁, x₂)) = x₁ + x₂   
POL(c184(x₁)) = x₁   
POL(c186(x₁, x₂)) = x₁ + x₂   
POL(c187(x₁)) = x₁   
POL(c19(x₁)) = x₁   
POL(c195(x₁, x₂)) = x₁ + x₂   
POL(c199(x₁, x₂)) = x₁ + x₂   
POL(c20(x₁)) = x₁   
POL(c203(x₁, x₂)) = x₁ + x₂   
POL(c206(x₁, x₂)) = x₁ + x₂   
POL(c209(x₁, x₂)) = x₁ + x₂   
POL(c212(x₁, x₂)) = x₁ + x₂   
POL(c215(x₁, x₂)) = x₁ + x₂   
POL(c218(x₁, x₂)) = x₁ + x₂   
POL(c222(x₁, x₂)) = x₁ + x₂   
POL(c226(x₁, x₂)) = x₁ + x₂   
POL(c229(x₁, x₂)) = x₁ + x₂   
POL(c232(x₁, x₂)) = x₁ + x₂   
POL(c236(x₁, x₂)) = x₁ + x₂   
POL(c239(x₁)) = x₁   
POL(c55) = 0   
POL(c57) = 0   
POL(c58(x₁)) = x₁   
POL(c6(x₁)) = x₁   
POL(c63(x₁)) = x₁   
POL(c65(x₁)) = x₁   
POL(c7(x₁)) = x₁   
POL(c78(x₁)) = x₁   
POL(c8(x₁)) = x₁   
POL(c83(x₁)) = x₁   
POL(c86) = 0   
POL(c88(x₁)) = x₁   
POL(c9(x₁)) = x₁   
POL(c93(x₁)) = x₁   
POL(c95(x₁)) = x₁   
POL(c97) = 0   
POL(c99(x₁)) = x₁   
POL(f34_in(x₁)) = 0   
POL(f34_out1) = 0   
POL(f494_out1) = 0   
POL(f503_in(x₁, x₂)) = 0   
POL(f503_out1) = 0   
POL(f554_in(x₁, x₂)) = 0   
POL(f554_out1) = 0   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = x₁ + x₂ + x₃   
POL(void) = 0   

(56) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c

K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U52'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
U54'(f34_out1, z0) → c
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F68_IN(s(z0)) → c
F63_IN(z0) → c
F69_IN(z0) → c(F29_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F140_IN(tree(z0, z1, z2)) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F69_IN(z0) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
F24_IN(z0) → c
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F268_IN(z0, z1) → c(F29_IN(z0))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F294_IN(z0, z1) → c(F29_IN(z0))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F177_IN(z0, z1) → c(F29_IN(z0))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F177_IN(z0, z1) → c
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(57) CdtKnowledgeProof (EQUIVALENT transformation)

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

F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c

(58) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c

K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U52'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
U54'(f34_out1, z0) → c
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F68_IN(s(z0)) → c
F63_IN(z0) → c
F69_IN(z0) → c(F29_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F140_IN(tree(z0, z1, z2)) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F69_IN(z0) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
F24_IN(z0) → c
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F268_IN(z0, z1) → c(F29_IN(z0))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F294_IN(z0, z1) → c(F29_IN(z0))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F177_IN(z0, z1) → c(F29_IN(z0))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F177_IN(z0, z1) → c
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(59) 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.

F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))

We considered the (Usable) Rules:

f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1

And the Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

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

POL(0) = 0   
POL(F109_IN(x₁, x₂)) = [1] + [2]x₁   
POL(F110_IN(x₁, x₂, x₃)) = [2]x₂   
POL(F112_IN(x₁, x₂)) = 0   
POL(F113_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F122_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F124_IN(x₁, x₂, x₃)) = 0   
POL(F125_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F132_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F140_IN(x₁)) = 0   
POL(F141_IN(x₁, x₂)) = [2]x₂   
POL(F146_IN(x₁)) = 0   
POL(F176_IN(x₁, x₂)) = [2]x₂   
POL(F177_IN(x₁, x₂)) = 0   
POL(F178_IN(x₁, x₂)) = [2]x₂   
POL(F185_IN(x₁, x₂)) = [2]x₂   
POL(F201_IN(x₁, x₂)) = [2]x₂   
POL(F202_IN(x₁)) = 0   
POL(F203_IN(x₁, x₂)) = [2]x₂   
POL(F206_IN(x₁)) = 0   
POL(F219_IN(x₁, x₂)) = [2]x₂   
POL(F240_IN(x₁, x₂)) = [2]x₂   
POL(F24_IN(x₁)) = [2]   
POL(F264_IN(x₁, x₂)) = [3] + [2]x₂   
POL(F267_IN(x₁, x₂)) = [2]x₂   
POL(F268_IN(x₁, x₂)) = 0   
POL(F270_IN(x₁, x₂)) = [2]x₂   
POL(F27_IN(x₁)) = 0   
POL(F28_IN(x₁)) = [2]   
POL(F292_IN(x₁, x₂)) = [3] + [2]x₂   
POL(F293_IN(x₁, x₂)) = [2]x₂   
POL(F294_IN(x₁, x₂)) = 0   
POL(F296_IN(x₁, x₂)) = [2]x₂   
POL(F29_IN(x₁)) = 0   
POL(F2_IN(x₁, x₂)) = [2]x₂   
POL(F318_IN(x₁)) = 0   
POL(F326_IN(x₁, x₂, x₃)) = [2] + [2]x₁ + [2]x₃   
POL(F327_IN(x₁, x₂, x₃, x₄)) = [3] + [2]x₂ + [2]x₄   
POL(F328_IN(x₁, x₂)) = [1]   
POL(F329_IN(x₁, x₂, x₃, x₄)) = [2]x₂ + [2]x₄   
POL(F332_IN(x₁, x₂, x₃, x₄)) = [2]x₂ + [2]x₄   
POL(F333_IN(x₁, x₂, x₃, x₄)) = [2]x₂   
POL(F334_IN(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(F335_IN(x₁, x₂)) = [2]x₂   
POL(F341_IN(x₁)) = 0   
POL(F342_IN(x₁, x₂, x₃)) = [2]x₂ + [2]x₃   
POL(F34_IN(x₁)) = 0   
POL(F387_IN(x₁, x₂, x₃)) = [2]x₂ + [2]x₃   
POL(F388_IN(x₁, x₂, x₃)) = [2]x₂   
POL(F389_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F390_IN(x₁, x₂)) = [2]x₂   
POL(F394_IN(x₁, x₂)) = [2]x₂   
POL(F449_IN(x₁, x₂, x₃)) = [2]x₁ + x₃   
POL(F450_IN(x₁, x₂, x₃, x₄)) = [2]x₃ + [2]x₄   
POL(F460_IN(x₁, x₂, x₃)) = 0   
POL(F487_IN(x₁, x₂)) = 0   
POL(F499_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F500_IN(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(F501_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F503_IN(x₁, x₂)) = 0   
POL(F554_IN(x₁, x₂)) = 0   
POL(F63_IN(x₁)) = [3]   
POL(F678_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F685_IN(x₁, x₂)) = [1] + [2]x₂   
POL(F68_IN(x₁)) = 0   
POL(F690_IN(x₁, x₂, x₃)) = [2] + [2]x₃   
POL(F69_IN(x₁)) = [1]   
POL(F72_IN(x₁)) = 0   
POL(U20(x₁, x₂, x₃)) = 0   
POL(U21(x₁, x₂)) = x₁   
POL(U22(x₁, x₂, x₃)) = [1]   
POL(U52'(x₁, x₂)) = 0   
POL(U54'(x₁, x₂)) = 0   
POL(U56'(x₁, x₂, x₃, x₄)) = [3]x₁ + [2]x₄   
POL(U58'(x₁, x₂, x₃)) = [2]x₃   
POL(U60'(x₁, x₂)) = 0   
POL(U62'(x₁, x₂, x₃)) = [2]x₃   
POL(U64'(x₁, x₂, x₃)) = [2]x₃   
POL(U66'(x₁, x₂, x₃)) = [2]x₁ + [2]x₃   
POL(U68'(x₁, x₂, x₃)) = [2]x₃   
POL(U70'(x₁, x₂)) = 0   
POL(U72'(x₁, x₂, x₃)) = [2]x₁ + [2]x₃   
POL(U74'(x₁, x₂, x₃)) = [2]x₃   
POL(U76'(x₁, x₂, x₃)) = x₁ + [2]x₃   
POL(U78'(x₁, x₂, x₃)) = [2]x₃   
POL(U80'(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(U82'(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(U84'(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c104(x₁)) = x₁   
POL(c106(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c110(x₁)) = x₁   
POL(c112(x₁)) = x₁   
POL(c12(x₁)) = x₁   
POL(c120(x₁)) = x₁   
POL(c122(x₁)) = x₁   
POL(c126(x₁)) = x₁   
POL(c128(x₁)) = x₁   
POL(c136(x₁)) = x₁   
POL(c144(x₁, x₂)) = x₁ + x₂   
POL(c145(x₁)) = x₁   
POL(c147(x₁, x₂)) = x₁ + x₂   
POL(c148(x₁)) = x₁   
POL(c15(x₁)) = x₁   
POL(c153(x₁, x₂)) = x₁ + x₂   
POL(c154(x₁)) = x₁   
POL(c156(x₁, x₂)) = x₁ + x₂   
POL(c157(x₁)) = x₁   
POL(c159(x₁, x₂)) = x₁ + x₂   
POL(c16(x₁)) = x₁   
POL(c160(x₁)) = x₁   
POL(c162(x₁, x₂)) = x₁ + x₂   
POL(c163(x₁)) = x₁   
POL(c168(x₁, x₂)) = x₁ + x₂   
POL(c169(x₁)) = x₁   
POL(c17(x₁)) = x₁   
POL(c171(x₁, x₂)) = x₁ + x₂   
POL(c172(x₁)) = x₁   
POL(c174(x₁, x₂)) = x₁ + x₂   
POL(c175(x₁)) = x₁   
POL(c177) = 0   
POL(c18(x₁)) = x₁   
POL(c180(x₁, x₂)) = x₁ + x₂   
POL(c181(x₁)) = x₁   
POL(c183(x₁, x₂)) = x₁ + x₂   
POL(c184(x₁)) = x₁   
POL(c186(x₁, x₂)) = x₁ + x₂   
POL(c187(x₁)) = x₁   
POL(c19(x₁)) = x₁   
POL(c195(x₁, x₂)) = x₁ + x₂   
POL(c199(x₁, x₂)) = x₁ + x₂   
POL(c20(x₁)) = x₁   
POL(c203(x₁, x₂)) = x₁ + x₂   
POL(c206(x₁, x₂)) = x₁ + x₂   
POL(c209(x₁, x₂)) = x₁ + x₂   
POL(c212(x₁, x₂)) = x₁ + x₂   
POL(c215(x₁, x₂)) = x₁ + x₂   
POL(c218(x₁, x₂)) = x₁ + x₂   
POL(c222(x₁, x₂)) = x₁ + x₂   
POL(c226(x₁, x₂)) = x₁ + x₂   
POL(c229(x₁, x₂)) = x₁ + x₂   
POL(c232(x₁, x₂)) = x₁ + x₂   
POL(c236(x₁, x₂)) = x₁ + x₂   
POL(c239(x₁)) = x₁   
POL(c55) = 0   
POL(c57) = 0   
POL(c58(x₁)) = x₁   
POL(c6(x₁)) = x₁   
POL(c63(x₁)) = x₁   
POL(c65(x₁)) = x₁   
POL(c7(x₁)) = x₁   
POL(c78(x₁)) = x₁   
POL(c8(x₁)) = x₁   
POL(c83(x₁)) = x₁   
POL(c86) = 0   
POL(c88(x₁)) = x₁   
POL(c9(x₁)) = x₁   
POL(c93(x₁)) = x₁   
POL(c95(x₁)) = x₁   
POL(c97) = 0   
POL(c99(x₁)) = x₁   
POL(f34_in(x₁)) = 0   
POL(f34_out1) = [3]   
POL(f494_out1) = 0   
POL(f503_in(x₁, x₂)) = [1]   
POL(f503_out1) = 0   
POL(f554_in(x₁, x₂)) = 0   
POL(f554_out1) = 0   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = [2] + x₂ + x₃   
POL(void) = [2]   

(60) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c

K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U52'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
U54'(f34_out1, z0) → c
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F68_IN(s(z0)) → c
F63_IN(z0) → c
F69_IN(z0) → c(F29_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F140_IN(tree(z0, z1, z2)) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F69_IN(z0) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
F24_IN(z0) → c
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F268_IN(z0, z1) → c(F29_IN(z0))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F294_IN(z0, z1) → c(F29_IN(z0))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F177_IN(z0, z1) → c(F29_IN(z0))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F177_IN(z0, z1) → c
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(61) CdtKnowledgeProof (EQUIVALENT transformation)

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

F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F341_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(z0, tree(z0, void, void)) → c
F460_IN(z0, z1, z2) → c
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F487_IN(z0, z1) → c177
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c

(62) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))

K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U52'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
U54'(f34_out1, z0) → c
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F68_IN(s(z0)) → c
F63_IN(z0) → c
F69_IN(z0) → c(F29_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F140_IN(tree(z0, z1, z2)) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F69_IN(z0) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
F24_IN(z0) → c
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F268_IN(z0, z1) → c(F29_IN(z0))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F294_IN(z0, z1) → c(F29_IN(z0))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F177_IN(z0, z1) → c(F29_IN(z0))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F177_IN(z0, z1) → c
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F341_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F487_IN(z0, z1) → c177
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(63) 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.

F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57

We considered the (Usable) Rules:

f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1

And the Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

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

POL(0) = 0   
POL(F109_IN(x₁, x₂)) = [1] + x₁   
POL(F110_IN(x₁, x₂, x₃)) = [1] + x₂   
POL(F112_IN(x₁, x₂)) = 0   
POL(F113_IN(x₁, x₂, x₃)) = x₃   
POL(F122_IN(x₁, x₂, x₃)) = x₃   
POL(F124_IN(x₁, x₂, x₃)) = 0   
POL(F125_IN(x₁, x₂, x₃)) = x₃   
POL(F132_IN(x₁, x₂, x₃)) = x₃   
POL(F140_IN(x₁)) = [1]   
POL(F141_IN(x₁, x₂)) = x₂   
POL(F146_IN(x₁)) = [1]   
POL(F176_IN(x₁, x₂)) = x₂   
POL(F177_IN(x₁, x₂)) = 0   
POL(F178_IN(x₁, x₂)) = x₂   
POL(F185_IN(x₁, x₂)) = x₂   
POL(F201_IN(x₁, x₂)) = x₂   
POL(F202_IN(x₁)) = 0   
POL(F203_IN(x₁, x₂)) = x₂   
POL(F206_IN(x₁)) = 0   
POL(F219_IN(x₁, x₂)) = x₂   
POL(F240_IN(x₁, x₂)) = [1] + x₂   
POL(F24_IN(x₁)) = 0   
POL(F264_IN(x₁, x₂)) = [1] + x₂   
POL(F267_IN(x₁, x₂)) = x₂   
POL(F268_IN(x₁, x₂)) = 0   
POL(F270_IN(x₁, x₂)) = x₂   
POL(F27_IN(x₁)) = 0   
POL(F28_IN(x₁)) = 0   
POL(F292_IN(x₁, x₂)) = [1] + x₂   
POL(F293_IN(x₁, x₂)) = x₂   
POL(F294_IN(x₁, x₂)) = [1]   
POL(F296_IN(x₁, x₂)) = x₂   
POL(F29_IN(x₁)) = 0   
POL(F2_IN(x₁, x₂)) = x₂   
POL(F318_IN(x₁)) = [1]   
POL(F326_IN(x₁, x₂, x₃)) = [1] + x₁ + x₃   
POL(F327_IN(x₁, x₂, x₃, x₄)) = x₂ + x₄   
POL(F328_IN(x₁, x₂)) = 0   
POL(F329_IN(x₁, x₂, x₃, x₄)) = x₂ + x₄   
POL(F332_IN(x₁, x₂, x₃, x₄)) = x₂ + x₄   
POL(F333_IN(x₁, x₂, x₃, x₄)) = x₂   
POL(F334_IN(x₁, x₂, x₃, x₄)) = x₄   
POL(F335_IN(x₁, x₂)) = x₂   
POL(F341_IN(x₁)) = [1]   
POL(F342_IN(x₁, x₂, x₃)) = x₂ + x₃   
POL(F34_IN(x₁)) = 0   
POL(F387_IN(x₁, x₂, x₃)) = x₂ + x₃   
POL(F388_IN(x₁, x₂, x₃)) = x₂   
POL(F389_IN(x₁, x₂, x₃)) = x₃   
POL(F390_IN(x₁, x₂)) = x₂   
POL(F394_IN(x₁, x₂)) = x₂   
POL(F449_IN(x₁, x₂, x₃)) = [1] + x₁   
POL(F450_IN(x₁, x₂, x₃, x₄)) = x₃ + x₄   
POL(F460_IN(x₁, x₂, x₃)) = [1]   
POL(F487_IN(x₁, x₂)) = [1]   
POL(F499_IN(x₁, x₂, x₃)) = x₃   
POL(F500_IN(x₁, x₂, x₃, x₄)) = x₄   
POL(F501_IN(x₁, x₂, x₃)) = x₃   
POL(F503_IN(x₁, x₂)) = 0   
POL(F554_IN(x₁, x₂)) = 0   
POL(F63_IN(x₁)) = [1]   
POL(F678_IN(x₁, x₂, x₃)) = x₃   
POL(F685_IN(x₁, x₂)) = [1] + x₂   
POL(F68_IN(x₁)) = [1]   
POL(F690_IN(x₁, x₂, x₃)) = [1] + x₃   
POL(F69_IN(x₁)) = 0   
POL(F72_IN(x₁)) = [1]   
POL(U20(x₁, x₂, x₃)) = 0   
POL(U21(x₁, x₂)) = x₁   
POL(U22(x₁, x₂, x₃)) = 0   
POL(U52'(x₁, x₂)) = 0   
POL(U54'(x₁, x₂)) = 0   
POL(U56'(x₁, x₂, x₃, x₄)) = [2]x₁ + x₄   
POL(U58'(x₁, x₂, x₃)) = x₃   
POL(U60'(x₁, x₂)) = 0   
POL(U62'(x₁, x₂, x₃)) = x₃   
POL(U64'(x₁, x₂, x₃)) = [2]x₁ + x₃   
POL(U66'(x₁, x₂, x₃)) = x₃   
POL(U68'(x₁, x₂, x₃)) = x₃   
POL(U70'(x₁, x₂)) = 0   
POL(U72'(x₁, x₂, x₃)) = x₃   
POL(U74'(x₁, x₂, x₃)) = [2]x₁ + x₃   
POL(U76'(x₁, x₂, x₃)) = x₃   
POL(U78'(x₁, x₂, x₃)) = [2]x₃   
POL(U80'(x₁, x₂, x₃, x₄)) = x₄   
POL(U82'(x₁, x₂, x₃, x₄)) = x₄   
POL(U84'(x₁, x₂, x₃, x₄)) = x₄   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c104(x₁)) = x₁   
POL(c106(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c110(x₁)) = x₁   
POL(c112(x₁)) = x₁   
POL(c12(x₁)) = x₁   
POL(c120(x₁)) = x₁   
POL(c122(x₁)) = x₁   
POL(c126(x₁)) = x₁   
POL(c128(x₁)) = x₁   
POL(c136(x₁)) = x₁   
POL(c144(x₁, x₂)) = x₁ + x₂   
POL(c145(x₁)) = x₁   
POL(c147(x₁, x₂)) = x₁ + x₂   
POL(c148(x₁)) = x₁   
POL(c15(x₁)) = x₁   
POL(c153(x₁, x₂)) = x₁ + x₂   
POL(c154(x₁)) = x₁   
POL(c156(x₁, x₂)) = x₁ + x₂   
POL(c157(x₁)) = x₁   
POL(c159(x₁, x₂)) = x₁ + x₂   
POL(c16(x₁)) = x₁   
POL(c160(x₁)) = x₁   
POL(c162(x₁, x₂)) = x₁ + x₂   
POL(c163(x₁)) = x₁   
POL(c168(x₁, x₂)) = x₁ + x₂   
POL(c169(x₁)) = x₁   
POL(c17(x₁)) = x₁   
POL(c171(x₁, x₂)) = x₁ + x₂   
POL(c172(x₁)) = x₁   
POL(c174(x₁, x₂)) = x₁ + x₂   
POL(c175(x₁)) = x₁   
POL(c177) = 0   
POL(c18(x₁)) = x₁   
POL(c180(x₁, x₂)) = x₁ + x₂   
POL(c181(x₁)) = x₁   
POL(c183(x₁, x₂)) = x₁ + x₂   
POL(c184(x₁)) = x₁   
POL(c186(x₁, x₂)) = x₁ + x₂   
POL(c187(x₁)) = x₁   
POL(c19(x₁)) = x₁   
POL(c195(x₁, x₂)) = x₁ + x₂   
POL(c199(x₁, x₂)) = x₁ + x₂   
POL(c20(x₁)) = x₁   
POL(c203(x₁, x₂)) = x₁ + x₂   
POL(c206(x₁, x₂)) = x₁ + x₂   
POL(c209(x₁, x₂)) = x₁ + x₂   
POL(c212(x₁, x₂)) = x₁ + x₂   
POL(c215(x₁, x₂)) = x₁ + x₂   
POL(c218(x₁, x₂)) = x₁ + x₂   
POL(c222(x₁, x₂)) = x₁ + x₂   
POL(c226(x₁, x₂)) = x₁ + x₂   
POL(c229(x₁, x₂)) = x₁ + x₂   
POL(c232(x₁, x₂)) = x₁ + x₂   
POL(c236(x₁, x₂)) = x₁ + x₂   
POL(c239(x₁)) = x₁   
POL(c55) = 0   
POL(c57) = 0   
POL(c58(x₁)) = x₁   
POL(c6(x₁)) = x₁   
POL(c63(x₁)) = x₁   
POL(c65(x₁)) = x₁   
POL(c7(x₁)) = x₁   
POL(c78(x₁)) = x₁   
POL(c8(x₁)) = x₁   
POL(c83(x₁)) = x₁   
POL(c86) = 0   
POL(c88(x₁)) = x₁   
POL(c9(x₁)) = x₁   
POL(c93(x₁)) = x₁   
POL(c95(x₁)) = x₁   
POL(c97) = 0   
POL(c99(x₁)) = x₁   
POL(f34_in(x₁)) = 0   
POL(f34_out1) = [1]   
POL(f494_out1) = 0   
POL(f503_in(x₁, x₂)) = 0   
POL(f503_out1) = 0   
POL(f554_in(x₁, x₂)) = 0   
POL(f554_out1) = 0   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = [1] + x₂ + x₃   
POL(void) = 0   

(64) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))

K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U52'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
U54'(f34_out1, z0) → c
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F68_IN(s(z0)) → c
F63_IN(z0) → c
F69_IN(z0) → c(F29_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F140_IN(tree(z0, z1, z2)) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F69_IN(z0) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
F24_IN(z0) → c
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F268_IN(z0, z1) → c(F29_IN(z0))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F294_IN(z0, z1) → c(F29_IN(z0))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F177_IN(z0, z1) → c(F29_IN(z0))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F177_IN(z0, z1) → c
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F341_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F487_IN(z0, z1) → c177
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(65) 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.

F34_IN(s(z0)) → c65(F34_IN(z0))

We considered the (Usable) Rules:

f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1

And the Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

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

POL(0) = 0   
POL(F109_IN(x₁, x₂)) = [3]x₁ + [3]x₂   
POL(F110_IN(x₁, x₂, x₃)) = [3]x₁ + [3]x₂ + [3]x₃   
POL(F112_IN(x₁, x₂)) = 0   
POL(F113_IN(x₁, x₂, x₃)) = [3]x₁ + [3]x₂ + [3]x₃   
POL(F122_IN(x₁, x₂, x₃)) = [3]x₁ + [3]x₂ + [3]x₃   
POL(F124_IN(x₁, x₂, x₃)) = x₁   
POL(F125_IN(x₁, x₂, x₃)) = [2]x₁ + [3]x₂ + [3]x₃   
POL(F132_IN(x₁, x₂, x₃)) = [2]x₁ + [3]x₂ + [3]x₃   
POL(F140_IN(x₁)) = 0   
POL(F141_IN(x₁, x₂)) = [3]x₁ + [3]x₂   
POL(F146_IN(x₁)) = 0   
POL(F176_IN(x₁, x₂)) = [3]x₁ + [3]x₂   
POL(F177_IN(x₁, x₂)) = [2]x₁   
POL(F178_IN(x₁, x₂)) = x₁ + [3]x₂   
POL(F185_IN(x₁, x₂)) = x₁ + [3]x₂   
POL(F201_IN(x₁, x₂)) = [3]x₁ + [3]x₂   
POL(F202_IN(x₁)) = [2]x₁   
POL(F203_IN(x₁, x₂)) = x₁ + [3]x₂   
POL(F206_IN(x₁)) = [2] + [2]x₁   
POL(F219_IN(x₁, x₂)) = x₁ + [3]x₂   
POL(F240_IN(x₁, x₂)) = [1] + x₁ + [3]x₂   
POL(F24_IN(x₁)) = [2]x₁   
POL(F264_IN(x₁, x₂)) = [2]x₁ + [3]x₂   
POL(F267_IN(x₁, x₂)) = x₁ + [3]x₂   
POL(F268_IN(x₁, x₂)) = x₁   
POL(F270_IN(x₁, x₂)) = x₁ + [3]x₂   
POL(F27_IN(x₁)) = x₁   
POL(F28_IN(x₁)) = x₁   
POL(F292_IN(x₁, x₂)) = [3]x₁ + [3]x₂   
POL(F293_IN(x₁, x₂)) = [2]x₁ + [3]x₂   
POL(F294_IN(x₁, x₂)) = x₁   
POL(F296_IN(x₁, x₂)) = [3] + [2]x₁ + [3]x₂   
POL(F29_IN(x₁)) = x₁   
POL(F2_IN(x₁, x₂)) = [3]x₂   
POL(F318_IN(x₁)) = [3]x₁   
POL(F326_IN(x₁, x₂, x₃)) = [3]x₁ + [3]x₂ + [3]x₃   
POL(F327_IN(x₁, x₂, x₃, x₄)) = [3]x₁ + [3]x₂ + [3]x₃ + [3]x₄   
POL(F328_IN(x₁, x₂)) = 0   
POL(F329_IN(x₁, x₂, x₃, x₄)) = [3]x₁ + [3]x₂ + [3]x₃ + [3]x₄   
POL(F332_IN(x₁, x₂, x₃, x₄)) = [3]x₁ + [3]x₂ + [3]x₃ + [3]x₄   
POL(F333_IN(x₁, x₂, x₃, x₄)) = x₁ + [3]x₂   
POL(F334_IN(x₁, x₂, x₃, x₄)) = [2]x₁ + [3]x₃ + [3]x₄   
POL(F335_IN(x₁, x₂)) = x₁ + [3]x₂   
POL(F341_IN(x₁)) = 0   
POL(F342_IN(x₁, x₂, x₃)) = [2]x₁ + [3]x₂ + [3]x₃   
POL(F34_IN(x₁)) = x₁   
POL(F387_IN(x₁, x₂, x₃)) = [2]x₁ + [3]x₂ + [3]x₃   
POL(F388_IN(x₁, x₂, x₃)) = x₁ + [3]x₂   
POL(F389_IN(x₁, x₂, x₃)) = x₁ + [3]x₃   
POL(F390_IN(x₁, x₂)) = x₁ + [3]x₂   
POL(F394_IN(x₁, x₂)) = x₁ + [3]x₂   
POL(F449_IN(x₁, x₂, x₃)) = [3] + [3]x₁ + x₂ + x₃   
POL(F450_IN(x₁, x₂, x₃, x₄)) = [2]x₂ + [3]x₃ + [3]x₄   
POL(F460_IN(x₁, x₂, x₃)) = [1] + x₁ + x₃   
POL(F487_IN(x₁, x₂)) = 0   
POL(F499_IN(x₁, x₂, x₃)) = [2]x₂ + [3]x₃   
POL(F500_IN(x₁, x₂, x₃, x₄)) = [3]x₄   
POL(F501_IN(x₁, x₂, x₃)) = x₂ + [3]x₃   
POL(F503_IN(x₁, x₂)) = 0   
POL(F554_IN(x₁, x₂)) = 0   
POL(F63_IN(x₁)) = [2]x₁   
POL(F678_IN(x₁, x₂, x₃)) = [3]x₃   
POL(F685_IN(x₁, x₂)) = [3]x₂   
POL(F68_IN(x₁)) = x₁   
POL(F690_IN(x₁, x₂, x₃)) = [3] + [2]x₁ + [3]x₃   
POL(F69_IN(x₁)) = x₁   
POL(F72_IN(x₁)) = [1] + x₁   
POL(U20(x₁, x₂, x₃)) = 0   
POL(U21(x₁, x₂)) = 0   
POL(U22(x₁, x₂, x₃)) = 0   
POL(U52'(x₁, x₂)) = x₂   
POL(U54'(x₁, x₂)) = x₂   
POL(U56'(x₁, x₂, x₃, x₄)) = x₂ + [3]x₃ + [3]x₄   
POL(U58'(x₁, x₂, x₃)) = [3]x₃   
POL(U60'(x₁, x₂)) = [2] + [2]x₂   
POL(U62'(x₁, x₂, x₃)) = [3]x₃   
POL(U64'(x₁, x₂, x₃)) = [1] + [3]x₃   
POL(U66'(x₁, x₂, x₃)) = [3]x₃   
POL(U68'(x₁, x₂, x₃)) = x₂ + [3]x₃   
POL(U70'(x₁, x₂)) = x₂   
POL(U72'(x₁, x₂, x₃)) = [3]x₃   
POL(U74'(x₁, x₂, x₃)) = [3]x₃   
POL(U76'(x₁, x₂, x₃)) = [3]x₃   
POL(U78'(x₁, x₂, x₃)) = x₁ + [3]x₃   
POL(U80'(x₁, x₂, x₃, x₄)) = [3]x₄   
POL(U82'(x₁, x₂, x₃, x₄)) = [3]x₄   
POL(U84'(x₁, x₂, x₃, x₄)) = [3]x₄   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c104(x₁)) = x₁   
POL(c106(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c110(x₁)) = x₁   
POL(c112(x₁)) = x₁   
POL(c12(x₁)) = x₁   
POL(c120(x₁)) = x₁   
POL(c122(x₁)) = x₁   
POL(c126(x₁)) = x₁   
POL(c128(x₁)) = x₁   
POL(c136(x₁)) = x₁   
POL(c144(x₁, x₂)) = x₁ + x₂   
POL(c145(x₁)) = x₁   
POL(c147(x₁, x₂)) = x₁ + x₂   
POL(c148(x₁)) = x₁   
POL(c15(x₁)) = x₁   
POL(c153(x₁, x₂)) = x₁ + x₂   
POL(c154(x₁)) = x₁   
POL(c156(x₁, x₂)) = x₁ + x₂   
POL(c157(x₁)) = x₁   
POL(c159(x₁, x₂)) = x₁ + x₂   
POL(c16(x₁)) = x₁   
POL(c160(x₁)) = x₁   
POL(c162(x₁, x₂)) = x₁ + x₂   
POL(c163(x₁)) = x₁   
POL(c168(x₁, x₂)) = x₁ + x₂   
POL(c169(x₁)) = x₁   
POL(c17(x₁)) = x₁   
POL(c171(x₁, x₂)) = x₁ + x₂   
POL(c172(x₁)) = x₁   
POL(c174(x₁, x₂)) = x₁ + x₂   
POL(c175(x₁)) = x₁   
POL(c177) = 0   
POL(c18(x₁)) = x₁   
POL(c180(x₁, x₂)) = x₁ + x₂   
POL(c181(x₁)) = x₁   
POL(c183(x₁, x₂)) = x₁ + x₂   
POL(c184(x₁)) = x₁   
POL(c186(x₁, x₂)) = x₁ + x₂   
POL(c187(x₁)) = x₁   
POL(c19(x₁)) = x₁   
POL(c195(x₁, x₂)) = x₁ + x₂   
POL(c199(x₁, x₂)) = x₁ + x₂   
POL(c20(x₁)) = x₁   
POL(c203(x₁, x₂)) = x₁ + x₂   
POL(c206(x₁, x₂)) = x₁ + x₂   
POL(c209(x₁, x₂)) = x₁ + x₂   
POL(c212(x₁, x₂)) = x₁ + x₂   
POL(c215(x₁, x₂)) = x₁ + x₂   
POL(c218(x₁, x₂)) = x₁ + x₂   
POL(c222(x₁, x₂)) = x₁ + x₂   
POL(c226(x₁, x₂)) = x₁ + x₂   
POL(c229(x₁, x₂)) = x₁ + x₂   
POL(c232(x₁, x₂)) = x₁ + x₂   
POL(c236(x₁, x₂)) = x₁ + x₂   
POL(c239(x₁)) = x₁   
POL(c55) = 0   
POL(c57) = 0   
POL(c58(x₁)) = x₁   
POL(c6(x₁)) = x₁   
POL(c63(x₁)) = x₁   
POL(c65(x₁)) = x₁   
POL(c7(x₁)) = x₁   
POL(c78(x₁)) = x₁   
POL(c8(x₁)) = x₁   
POL(c83(x₁)) = x₁   
POL(c86) = 0   
POL(c88(x₁)) = x₁   
POL(c9(x₁)) = x₁   
POL(c93(x₁)) = x₁   
POL(c95(x₁)) = x₁   
POL(c97) = 0   
POL(c99(x₁)) = x₁   
POL(f34_in(x₁)) = 0   
POL(f34_out1) = 0   
POL(f494_out1) = [2]   
POL(f503_in(x₁, x₂)) = 0   
POL(f503_out1) = 0   
POL(f554_in(x₁, x₂)) = 0   
POL(f554_out1) = 0   
POL(s(x₁)) = [2] + x₁   
POL(tree(x₁, x₂, x₃)) = x₁ + x₂ + x₃   
POL(void) = 0   

(66) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))

K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U52'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
U54'(f34_out1, z0) → c
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F68_IN(s(z0)) → c
F63_IN(z0) → c
F69_IN(z0) → c(F29_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F140_IN(tree(z0, z1, z2)) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F69_IN(z0) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
F24_IN(z0) → c
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F268_IN(z0, z1) → c(F29_IN(z0))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F294_IN(z0, z1) → c(F29_IN(z0))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F177_IN(z0, z1) → c(F29_IN(z0))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F177_IN(z0, z1) → c
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F341_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F487_IN(z0, z1) → c177
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F34_IN(s(z0)) → c65(F34_IN(z0))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(67) 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.

F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))

We considered the (Usable) Rules:

f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1

And the Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

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

POL(0) = 0   
POL(F109_IN(x₁, x₂)) = [1] + x₂ + x₂² + x₁·x₂   
POL(F110_IN(x₁, x₂, x₃)) = [1] + x₃ + x₂·x₃ + x₁·x₃   
POL(F112_IN(x₁, x₂)) = 0   
POL(F113_IN(x₁, x₂, x₃)) = x₁ + x₁·x₃ + x₁·x₂   
POL(F122_IN(x₁, x₂, x₃)) = x₁ + x₁·x₃ + x₁·x₂   
POL(F124_IN(x₁, x₂, x₃)) = 0   
POL(F125_IN(x₁, x₂, x₃)) = x₁ + x₁·x₃ + x₁·x₂   
POL(F132_IN(x₁, x₂, x₃)) = x₁ + x₁·x₃ + x₁·x₂   
POL(F140_IN(x₁)) = 0   
POL(F141_IN(x₁, x₂)) = [1] + x₁·x₂ + x₁²   
POL(F146_IN(x₁)) = 0   
POL(F176_IN(x₁, x₂)) = [1] + x₁·x₂ + x₁²   
POL(F177_IN(x₁, x₂)) = 0   
POL(F178_IN(x₁, x₂)) = [1] + x₁·x₂ + x₁²   
POL(F185_IN(x₁, x₂)) = [1] + x₁·x₂ + x₁²   
POL(F201_IN(x₁, x₂)) = [1] + x₁ + x₁·x₂ + x₁²   
POL(F202_IN(x₁)) = 0   
POL(F203_IN(x₁, x₂)) = [1] + x₁ + x₁·x₂ + x₁²   
POL(F206_IN(x₁)) = 0   
POL(F219_IN(x₁, x₂)) = [1] + x₁·x₂ + x₁²   
POL(F240_IN(x₁, x₂)) = [1] + x₁ + x₂ + x₁·x₂ + x₁²   
POL(F24_IN(x₁)) = 0   
POL(F264_IN(x₁, x₂)) = [1] + x₁ + x₁·x₂ + x₁²   
POL(F267_IN(x₁, x₂)) = [1] + x₁·x₂ + x₁²   
POL(F268_IN(x₁, x₂)) = 0   
POL(F270_IN(x₁, x₂)) = [1] + x₁·x₂ + x₁²   
POL(F27_IN(x₁)) = 0   
POL(F28_IN(x₁)) = 0   
POL(F292_IN(x₁, x₂)) = [1] + x₁·x₂ + x₁²   
POL(F293_IN(x₁, x₂)) = x₁·x₂ + x₁²   
POL(F294_IN(x₁, x₂)) = 0   
POL(F296_IN(x₁, x₂)) = [1] + x₂ + x₁·x₂   
POL(F29_IN(x₁)) = 0   
POL(F2_IN(x₁, x₂)) = [1] + x₁·x₂   
POL(F318_IN(x₁)) = [1] + x₁ + x₁²   
POL(F326_IN(x₁, x₂, x₃)) = [1] + x₂ + x₂·x₃ + x₁·x₂ + x₂²   
POL(F327_IN(x₁, x₂, x₃, x₄)) = [1] + x₃ + x₃·x₄ + x₁·x₃ + x₃² + x₂·x₃   
POL(F328_IN(x₁, x₂)) = 0   
POL(F329_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₁·x₄ + x₁² + x₁·x₂ + x₁·x₃   
POL(F332_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₁·x₄ + x₁² + x₁·x₂ + x₁·x₃   
POL(F333_IN(x₁, x₂, x₃, x₄)) = [1] + x₁² + x₁·x₂   
POL(F334_IN(x₁, x₂, x₃, x₄)) = x₁ + x₁·x₄ + x₁·x₃   
POL(F335_IN(x₁, x₂)) = [1] + x₁·x₂ + x₁²   
POL(F341_IN(x₁)) = 0   
POL(F342_IN(x₁, x₂, x₃)) = [1] + x₁ + x₁·x₃ + x₁² + x₁·x₂   
POL(F34_IN(x₁)) = 0   
POL(F387_IN(x₁, x₂, x₃)) = [1] + x₁ + x₁·x₃ + x₁² + x₁·x₂   
POL(F388_IN(x₁, x₂, x₃)) = [1] + x₁·x₂   
POL(F389_IN(x₁, x₂, x₃)) = x₁·x₃   
POL(F390_IN(x₁, x₂)) = [1] + x₁·x₂   
POL(F394_IN(x₁, x₂)) = x₁·x₂   
POL(F449_IN(x₁, x₂, x₃)) = [1]   
POL(F450_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₁·x₄ + x₁·x₂ + x₁·x₃   
POL(F460_IN(x₁, x₂, x₃)) = 0   
POL(F487_IN(x₁, x₂)) = 0   
POL(F499_IN(x₁, x₂, x₃)) = x₁·x₃ + x₁·x₂   
POL(F500_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₁·x₄   
POL(F501_IN(x₁, x₂, x₃)) = [1] + x₁ + x₂ + x₃ + x₁·x₃   
POL(F503_IN(x₁, x₂)) = x₁ + x₂   
POL(F554_IN(x₁, x₂)) = x₂   
POL(F63_IN(x₁)) = [1] + x₁ + x₁²   
POL(F678_IN(x₁, x₂, x₃)) = [1] + x₂ + x₂·x₃   
POL(F685_IN(x₁, x₂)) = [1] + x₂ + x₁·x₂   
POL(F68_IN(x₁)) = 0   
POL(F690_IN(x₁, x₂, x₃)) = [1] + x₂ + x₃ + x₂·x₃   
POL(F69_IN(x₁)) = 0   
POL(F72_IN(x₁)) = 0   
POL(U20(x₁, x₂, x₃)) = 0   
POL(U21(x₁, x₂)) = x₁   
POL(U22(x₁, x₂, x₃)) = [1] + x₂ + x₃ + x₃² + x₂·x₃ + x₂²   
POL(U52'(x₁, x₂)) = 0   
POL(U54'(x₁, x₂)) = 0   
POL(U56'(x₁, x₂, x₃, x₄)) = x₂ + x₂·x₄ + x₁² + x₁·x₂ + x₂·x₃   
POL(U58'(x₁, x₂, x₃)) = [1] + x₂·x₃ + x₂²   
POL(U60'(x₁, x₂)) = 0   
POL(U62'(x₁, x₂, x₃)) = [1] + x₂·x₃ + x₂²   
POL(U64'(x₁, x₂, x₃)) = [1] + x₃ + x₂·x₃ + x₂²   
POL(U66'(x₁, x₂, x₃)) = [1] + x₂·x₃ + x₂²   
POL(U68'(x₁, x₂, x₃)) = [1] + x₃ + x₂·x₃   
POL(U70'(x₁, x₂)) = 0   
POL(U72'(x₁, x₂, x₃)) = [1] + x₂·x₃ + x₂²   
POL(U74'(x₁, x₂, x₃)) = [1] + x₂·x₃   
POL(U76'(x₁, x₂, x₃)) = x₁ + x₂·x₃ + x₁·x₃   
POL(U78'(x₁, x₂, x₃)) = x₃ + x₁·x₃ + x₁²   
POL(U80'(x₁, x₂, x₃, x₄)) = [1] + x₄ + x₂·x₄   
POL(U82'(x₁, x₂, x₃, x₄)) = [1] + x₃·x₄ + x₁² + x₁·x₂ + x₁·x₃   
POL(U84'(x₁, x₂, x₃, x₄)) = [1] + x₄ + x₃·x₄   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c104(x₁)) = x₁   
POL(c106(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c110(x₁)) = x₁   
POL(c112(x₁)) = x₁   
POL(c12(x₁)) = x₁   
POL(c120(x₁)) = x₁   
POL(c122(x₁)) = x₁   
POL(c126(x₁)) = x₁   
POL(c128(x₁)) = x₁   
POL(c136(x₁)) = x₁   
POL(c144(x₁, x₂)) = x₁ + x₂   
POL(c145(x₁)) = x₁   
POL(c147(x₁, x₂)) = x₁ + x₂   
POL(c148(x₁)) = x₁   
POL(c15(x₁)) = x₁   
POL(c153(x₁, x₂)) = x₁ + x₂   
POL(c154(x₁)) = x₁   
POL(c156(x₁, x₂)) = x₁ + x₂   
POL(c157(x₁)) = x₁   
POL(c159(x₁, x₂)) = x₁ + x₂   
POL(c16(x₁)) = x₁   
POL(c160(x₁)) = x₁   
POL(c162(x₁, x₂)) = x₁ + x₂   
POL(c163(x₁)) = x₁   
POL(c168(x₁, x₂)) = x₁ + x₂   
POL(c169(x₁)) = x₁   
POL(c17(x₁)) = x₁   
POL(c171(x₁, x₂)) = x₁ + x₂   
POL(c172(x₁)) = x₁   
POL(c174(x₁, x₂)) = x₁ + x₂   
POL(c175(x₁)) = x₁   
POL(c177) = 0   
POL(c18(x₁)) = x₁   
POL(c180(x₁, x₂)) = x₁ + x₂   
POL(c181(x₁)) = x₁   
POL(c183(x₁, x₂)) = x₁ + x₂   
POL(c184(x₁)) = x₁   
POL(c186(x₁, x₂)) = x₁ + x₂   
POL(c187(x₁)) = x₁   
POL(c19(x₁)) = x₁   
POL(c195(x₁, x₂)) = x₁ + x₂   
POL(c199(x₁, x₂)) = x₁ + x₂   
POL(c20(x₁)) = x₁   
POL(c203(x₁, x₂)) = x₁ + x₂   
POL(c206(x₁, x₂)) = x₁ + x₂   
POL(c209(x₁, x₂)) = x₁ + x₂   
POL(c212(x₁, x₂)) = x₁ + x₂   
POL(c215(x₁, x₂)) = x₁ + x₂   
POL(c218(x₁, x₂)) = x₁ + x₂   
POL(c222(x₁, x₂)) = x₁ + x₂   
POL(c226(x₁, x₂)) = x₁ + x₂   
POL(c229(x₁, x₂)) = x₁ + x₂   
POL(c232(x₁, x₂)) = x₁ + x₂   
POL(c236(x₁, x₂)) = x₁ + x₂   
POL(c239(x₁)) = x₁   
POL(c55) = 0   
POL(c57) = 0   
POL(c58(x₁)) = x₁   
POL(c6(x₁)) = x₁   
POL(c63(x₁)) = x₁   
POL(c65(x₁)) = x₁   
POL(c7(x₁)) = x₁   
POL(c78(x₁)) = x₁   
POL(c8(x₁)) = x₁   
POL(c83(x₁)) = x₁   
POL(c86) = 0   
POL(c88(x₁)) = x₁   
POL(c9(x₁)) = x₁   
POL(c93(x₁)) = x₁   
POL(c95(x₁)) = x₁   
POL(c97) = 0   
POL(c99(x₁)) = x₁   
POL(f34_in(x₁)) = 0   
POL(f34_out1) = [1]   
POL(f494_out1) = [1]   
POL(f503_in(x₁, x₂)) = [1] + x₁ + x₂ + x₂² + x₁·x₂ + x₁²   
POL(f503_out1) = 0   
POL(f554_in(x₁, x₂)) = 0   
POL(f554_out1) = 0   
POL(s(x₁)) = [1] + x₁   
POL(tree(x₁, x₂, x₃)) = [1] + x₁ + x₂ + x₃   
POL(void) = [1]   

(68) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:

F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))

K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U52'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
U54'(f34_out1, z0) → c
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F68_IN(s(z0)) → c
F63_IN(z0) → c
F69_IN(z0) → c(F29_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F140_IN(tree(z0, z1, z2)) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F69_IN(z0) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
F24_IN(z0) → c
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F268_IN(z0, z1) → c(F29_IN(z0))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F294_IN(z0, z1) → c(F29_IN(z0))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F177_IN(z0, z1) → c(F29_IN(z0))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F177_IN(z0, z1) → c
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F341_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F487_IN(z0, z1) → c177
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F34_IN(s(z0)) → c65(F34_IN(z0))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(69) 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.

F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))

We considered the (Usable) Rules:

f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1

And the Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

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

POL(0) = 0   
POL(F109_IN(x₁, x₂)) = [1] + x₁   
POL(F110_IN(x₁, x₂, x₃)) = [1] + x₂   
POL(F112_IN(x₁, x₂)) = 0   
POL(F113_IN(x₁, x₂, x₃)) = [1] + x₃   
POL(F122_IN(x₁, x₂, x₃)) = [1] + x₃   
POL(F124_IN(x₁, x₂, x₃)) = 0   
POL(F125_IN(x₁, x₂, x₃)) = [1] + x₃   
POL(F132_IN(x₁, x₂, x₃)) = [1] + x₃   
POL(F140_IN(x₁)) = x₁   
POL(F141_IN(x₁, x₂)) = 0   
POL(F146_IN(x₁)) = x₁   
POL(F176_IN(x₁, x₂)) = 0   
POL(F177_IN(x₁, x₂)) = 0   
POL(F178_IN(x₁, x₂)) = 0   
POL(F185_IN(x₁, x₂)) = 0   
POL(F201_IN(x₁, x₂)) = [1] + x₂   
POL(F202_IN(x₁)) = 0   
POL(F203_IN(x₁, x₂)) = [1] + x₂   
POL(F206_IN(x₁)) = 0   
POL(F219_IN(x₁, x₂)) = x₂   
POL(F240_IN(x₁, x₂)) = x₂   
POL(F24_IN(x₁)) = 0   
POL(F264_IN(x₁, x₂)) = [1] + x₂   
POL(F267_IN(x₁, x₂)) = x₂   
POL(F268_IN(x₁, x₂)) = 0   
POL(F270_IN(x₁, x₂)) = x₂   
POL(F27_IN(x₁)) = 0   
POL(F28_IN(x₁)) = 0   
POL(F292_IN(x₁, x₂)) = [1] + x₂   
POL(F293_IN(x₁, x₂)) = x₂   
POL(F294_IN(x₁, x₂)) = 0   
POL(F296_IN(x₁, x₂)) = x₂   
POL(F29_IN(x₁)) = 0   
POL(F2_IN(x₁, x₂)) = x₂   
POL(F318_IN(x₁)) = 0   
POL(F326_IN(x₁, x₂, x₃)) = [1] + x₁ + x₃   
POL(F327_IN(x₁, x₂, x₃, x₄)) = [1] + x₂ + x₄   
POL(F328_IN(x₁, x₂)) = 0   
POL(F329_IN(x₁, x₂, x₃, x₄)) = [1] + x₂ + x₄   
POL(F332_IN(x₁, x₂, x₃, x₄)) = [1] + x₂ + x₄   
POL(F333_IN(x₁, x₂, x₃, x₄)) = x₂   
POL(F334_IN(x₁, x₂, x₃, x₄)) = [1] + x₄   
POL(F335_IN(x₁, x₂)) = x₂   
POL(F341_IN(x₁)) = x₁   
POL(F342_IN(x₁, x₂, x₃)) = x₂   
POL(F34_IN(x₁)) = 0   
POL(F387_IN(x₁, x₂, x₃)) = x₂   
POL(F388_IN(x₁, x₂, x₃)) = x₂   
POL(F389_IN(x₁, x₂, x₃)) = 0   
POL(F390_IN(x₁, x₂)) = x₂   
POL(F394_IN(x₁, x₂)) = 0   
POL(F449_IN(x₁, x₂, x₃)) = x₁ + x₃   
POL(F450_IN(x₁, x₂, x₃, x₄)) = [1] + x₃ + x₄   
POL(F460_IN(x₁, x₂, x₃)) = 0   
POL(F487_IN(x₁, x₂)) = 0   
POL(F499_IN(x₁, x₂, x₃)) = x₃   
POL(F500_IN(x₁, x₂, x₃, x₄)) = [1] + x₄   
POL(F501_IN(x₁, x₂, x₃)) = x₃   
POL(F503_IN(x₁, x₂)) = 0   
POL(F554_IN(x₁, x₂)) = 0   
POL(F63_IN(x₁)) = [1]   
POL(F678_IN(x₁, x₂, x₃)) = [1] + x₃   
POL(F685_IN(x₁, x₂)) = x₂   
POL(F68_IN(x₁)) = 0   
POL(F690_IN(x₁, x₂, x₃)) = x₃   
POL(F69_IN(x₁)) = 0   
POL(F72_IN(x₁)) = 0   
POL(U20(x₁, x₂, x₃)) = 0   
POL(U21(x₁, x₂)) = x₁²   
POL(U22(x₁, x₂, x₃)) = [1] + x₃ + x₃² + x₂·x₃ + x₂²   
POL(U52'(x₁, x₂)) = 0   
POL(U54'(x₁, x₂)) = 0   
POL(U56'(x₁, x₂, x₃, x₄)) = [1] + x₄   
POL(U58'(x₁, x₂, x₃)) = x₁·x₃   
POL(U60'(x₁, x₂)) = 0   
POL(U62'(x₁, x₂, x₃)) = x₃   
POL(U64'(x₁, x₂, x₃)) = x₃   
POL(U66'(x₁, x₂, x₃)) = x₃   
POL(U68'(x₁, x₂, x₃)) = x₃   
POL(U70'(x₁, x₂)) = 0   
POL(U72'(x₁, x₂, x₃)) = x₃   
POL(U74'(x₁, x₂, x₃)) = x₃   
POL(U76'(x₁, x₂, x₃)) = x₁·x₃   
POL(U78'(x₁, x₂, x₃)) = x₁·x₃   
POL(U80'(x₁, x₂, x₃, x₄)) = x₄   
POL(U82'(x₁, x₂, x₃, x₄)) = [1] + x₄   
POL(U84'(x₁, x₂, x₃, x₄)) = x₄   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c104(x₁)) = x₁   
POL(c106(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c110(x₁)) = x₁   
POL(c112(x₁)) = x₁   
POL(c12(x₁)) = x₁   
POL(c120(x₁)) = x₁   
POL(c122(x₁)) = x₁   
POL(c126(x₁)) = x₁   
POL(c128(x₁)) = x₁   
POL(c136(x₁)) = x₁   
POL(c144(x₁, x₂)) = x₁ + x₂   
POL(c145(x₁)) = x₁   
POL(c147(x₁, x₂)) = x₁ + x₂   
POL(c148(x₁)) = x₁   
POL(c15(x₁)) = x₁   
POL(c153(x₁, x₂)) = x₁ + x₂   
POL(c154(x₁)) = x₁   
POL(c156(x₁, x₂)) = x₁ + x₂   
POL(c157(x₁)) = x₁   
POL(c159(x₁, x₂)) = x₁ + x₂   
POL(c16(x₁)) = x₁   
POL(c160(x₁)) = x₁   
POL(c162(x₁, x₂)) = x₁ + x₂   
POL(c163(x₁)) = x₁   
POL(c168(x₁, x₂)) = x₁ + x₂   
POL(c169(x₁)) = x₁   
POL(c17(x₁)) = x₁   
POL(c171(x₁, x₂)) = x₁ + x₂   
POL(c172(x₁)) = x₁   
POL(c174(x₁, x₂)) = x₁ + x₂   
POL(c175(x₁)) = x₁   
POL(c177) = 0   
POL(c18(x₁)) = x₁   
POL(c180(x₁, x₂)) = x₁ + x₂   
POL(c181(x₁)) = x₁   
POL(c183(x₁, x₂)) = x₁ + x₂   
POL(c184(x₁)) = x₁   
POL(c186(x₁, x₂)) = x₁ + x₂   
POL(c187(x₁)) = x₁   
POL(c19(x₁)) = x₁   
POL(c195(x₁, x₂)) = x₁ + x₂   
POL(c199(x₁, x₂)) = x₁ + x₂   
POL(c20(x₁)) = x₁   
POL(c203(x₁, x₂)) = x₁ + x₂   
POL(c206(x₁, x₂)) = x₁ + x₂   
POL(c209(x₁, x₂)) = x₁ + x₂   
POL(c212(x₁, x₂)) = x₁ + x₂   
POL(c215(x₁, x₂)) = x₁ + x₂   
POL(c218(x₁, x₂)) = x₁ + x₂   
POL(c222(x₁, x₂)) = x₁ + x₂   
POL(c226(x₁, x₂)) = x₁ + x₂   
POL(c229(x₁, x₂)) = x₁ + x₂   
POL(c232(x₁, x₂)) = x₁ + x₂   
POL(c236(x₁, x₂)) = x₁ + x₂   
POL(c239(x₁)) = x₁   
POL(c55) = 0   
POL(c57) = 0   
POL(c58(x₁)) = x₁   
POL(c6(x₁)) = x₁   
POL(c63(x₁)) = x₁   
POL(c65(x₁)) = x₁   
POL(c7(x₁)) = x₁   
POL(c78(x₁)) = x₁   
POL(c8(x₁)) = x₁   
POL(c83(x₁)) = x₁   
POL(c86) = 0   
POL(c88(x₁)) = x₁   
POL(c9(x₁)) = x₁   
POL(c93(x₁)) = x₁   
POL(c95(x₁)) = x₁   
POL(c97) = 0   
POL(c99(x₁)) = x₁   
POL(f34_in(x₁)) = 0   
POL(f34_out1) = [1]   
POL(f494_out1) = [1]   
POL(f503_in(x₁, x₂)) = [1] + x₁ + x₂ + x₂² + x₁·x₂ + x₁²   
POL(f503_out1) = 0   
POL(f554_in(x₁, x₂)) = [1] + x₂ + x₂² + x₁·x₂ + x₁²   
POL(f554_out1) = 0   
POL(s(x₁)) = [1] + x₁   
POL(tree(x₁, x₂, x₃)) = [1] + x₂ + x₃   
POL(void) = 0   

(70) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, tree(z0, void, z1)) → f2_out1
f2_in(z0, tree(z0, void, void)) → f2_out1
f2_in(z0, tree(z0, void, void)) → U1(f24_in(z0), z0, tree(z0, void, void))
f2_in(z0, tree(z0, void, void)) → U2(f63_in(z0), z0, tree(z0, void, void))
f2_in(s(z0), tree(s(z0), void, void)) → U3(f72_in(z0), s(z0), tree(s(z0), void, void))
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
f2_in(z0, tree(z0, void, tree(z1, void, z2))) → U4(f110_in(z1, z2, z0), z0, tree(z0, void, tree(z1, void, z2)))
f2_in(z0, tree(z0, void, z1)) → U5(f109_in(z1, z0), z0, tree(z0, void, z1))
f2_in(z0, tree(z0, void, z1)) → U6(f201_in(z0, z1), z0, tree(z0, void, z1))
f2_in(s(z0), tree(s(z0), void, z1)) → U7(f240_in(z0, z1), s(z0), tree(s(z0), void, z1))
f2_in(z0, tree(z0, z1, void)) → f2_out1
f2_in(z0, tree(z0, z1, void)) → U8(f264_in(z0, z1), z0, tree(z0, z1, void))
f2_in(z0, tree(z0, z1, void)) → U9(f292_in(z0, z1), z0, tree(z0, z1, void))
f2_in(s(z0), tree(s(z0), z1, void)) → U10(f318_in(z0), s(z0), tree(s(z0), z1, void))
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
f2_in(z0, tree(z0, z1, tree(z2, void, z3))) → U11(f327_in(z2, z3, z0, z1), z0, tree(z0, z1, tree(z2, void, z3)))
f2_in(z0, tree(z0, z1, z2)) → U12(f326_in(z2, z0, z1), z0, tree(z0, z1, z2))
f2_in(0, tree(s(z0), z1, z2)) → U13(f449_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U14(f450_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U15(f685_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U16(f690_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f24_out1, z0, tree(z0, void, void)) → f2_out1
U1(f24_out2, z0, tree(z0, void, void)) → f2_out1
U2(f63_out1, z0, tree(z0, void, void)) → f2_out1
U2(f63_out3, z0, tree(z0, void, void)) → f2_out1
U3(f72_out1, s(z0), tree(s(z0), void, void)) → f2_out1
U4(f110_out1(z0), z1, tree(z1, void, tree(z2, void, z3))) → f2_out1
U4(f110_out3, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U4(f110_out4, z0, tree(z0, void, tree(z1, void, z2))) → f2_out1
U5(f109_out1(z0), z1, tree(z1, void, z2)) → f2_out1
U5(f109_out3, z0, tree(z0, void, z1)) → f2_out1
U5(f109_out4, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out1, z0, tree(z0, void, z1)) → f2_out1
U6(f201_out3, z0, tree(z0, void, z1)) → f2_out1
U7(f240_out1, s(z0), tree(s(z0), void, z1)) → f2_out1
U8(f264_out1, z0, tree(z0, z1, void)) → f2_out1
U8(f264_out2, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out1, z0, tree(z0, z1, void)) → f2_out1
U9(f292_out3, z0, tree(z0, z1, void)) → f2_out1
U10(f318_out1, s(z0), tree(s(z0), z1, void)) → f2_out1
U11(f327_out1(z0), z1, tree(z1, z2, tree(z3, void, z4))) → f2_out1
U11(f327_out3, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U11(f327_out4, z0, tree(z0, z1, tree(z2, void, z3))) → f2_out1
U12(f326_out1(z0), z1, tree(z1, z2, z3)) → f2_out1
U12(f326_out3, z0, tree(z0, z1, z2)) → f2_out1
U12(f326_out4, z0, tree(z0, z1, z2)) → f2_out1
U13(f449_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U13(f449_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U14(f450_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f450_out3, z0, tree(z1, z2, z3)) → f2_out1
U15(f685_out1, s(z0), tree(0, z1, z2)) → f2_out1
U15(f685_out2, s(z0), tree(0, z1, z2)) → f2_out1
U16(f690_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f146_in(tree(z0, void, z1)) → f146_out1(z0)
f146_in(tree(z0, void, z1)) → U17(f117_in, tree(z0, void, z1))
f146_in(tree(z0, tree(z1, void, z2), z3)) → f146_out1(z1)
f146_in(tree(z0, tree(z1, void, z2), z3)) → U18(f117_in, tree(z0, tree(z1, void, z2), z3))
f146_in(tree(z0, tree(z1, z2, z3), z4)) → U19(f146_in(z2), tree(z0, tree(z1, z2, z3), z4))
U17(f117_out1(z0), tree(z1, void, z2)) → f146_out1(z0)
U18(f117_out1(z0), tree(z1, tree(z2, void, z3), z4)) → f146_out1(z0)
U19(f146_out1(z0), tree(z1, tree(z2, z3, z4), z5)) → f146_out1(z0)
f554_in(0, s(z0)) → f554_out1
f554_in(s(z0), s(z1)) → U20(f554_in(z0, z1), s(z0), s(z1))
U20(f554_out1, s(z0), s(z1)) → f554_out1
f34_in(s(z0)) → U21(f34_in(z0), s(z0))
U21(f34_out1, s(z0)) → f34_out1
f503_in(0, s(z0)) → f503_out1
f503_in(s(0), s(s(z0))) → f503_out1
f503_in(s(s(0)), s(s(s(z0)))) → f503_out1
f503_in(s(s(s(0))), s(s(s(s(z0))))) → f503_out1
f503_in(s(s(s(s(0)))), s(s(s(s(s(z0)))))) → f503_out1
f503_in(s(s(s(s(s(0))))), s(s(s(s(s(s(z0))))))) → f503_out1
f503_in(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(z0)))))))) → f503_out1
f503_in(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → U22(f554_in(z0, z1), s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1))))))))
U22(f554_out1, s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → f503_out1
f341_in(tree(z0, z1, z2)) → U23(f146_in(z1), tree(z0, z1, z2))
U23(f146_out1(z0), tree(z1, z2, z3)) → f341_out1(z0)
f342_in(z0, z1, z2) → U24(f387_in(z0, z1, z2), z0, z1, z2)
U24(f387_out1, z0, z1, z2) → f342_out2
U24(f387_out2, z0, z1, z2) → f342_out3
f140_in(tree(z0, z1, z2)) → U25(f146_in(z1), tree(z0, z1, z2))
U25(f146_out1(z0), tree(z1, z2, z3)) → f140_out1(z0)
f141_in(z0, z1) → U26(f176_in(z0, z1), z0, z1)
U26(f176_out1, z0, z1) → f141_out2
U26(f176_out2, z0, z1) → f141_out3
f328_in(z0, z1) → U27(f117_in, z0, z1)
U27(f117_out1(z0), z1, z2) → f328_out1(z0)
f329_in(z0, z1, z2, z3) → U28(f332_in(z0, z1, z2, z3), z0, z1, z2, z3)
U28(f332_out1, z0, z1, z2, z3) → f329_out2
U28(f332_out2, z0, z1, z2, z3) → f329_out3
f460_in(z0, z1, z2) → U29(f487_in(z0, z2), z0, z1, z2)
U29(f487_out1, z0, z1, z2) → f460_out3
f499_in(s(z0), s(z1), z2) → U30(f501_in(z0, z1, z2), s(z0), s(z1), z2)
U30(f501_out1, s(z0), s(z1), z2) → f499_out1
f500_in(z0, z1, z2, z3) → U31(f678_in(z1, z0, z3), z0, z1, z2, z3)
U31(f678_out1, z0, z1, z2, z3) → f500_out2
f112_in(z0, z1) → U32(f117_in, z0, z1)
U32(f117_out1(z0), z1, z2) → f112_out1(z0)
f113_in(z0, z1, z2) → U33(f122_in(z0, z1, z2), z0, z1, z2)
U33(f122_out1, z0, z1, z2) → f113_out2
U33(f122_out2, z0, z1, z2) → f113_out3
f202_in(s(z0)) → U34(f206_in(z0), s(z0))
U34(f206_out1, s(z0)) → f202_out1
f203_in(z0, z1) → U35(f219_in(z0, z1), z0, z1)
U35(f219_out1, z0, z1) → f203_out2
f293_in(s(z0), z1) → U36(f296_in(z0, z1), s(z0), z1)
U36(f296_out1, s(z0), z1) → f293_out1
f294_in(z0, z1) → U37(f29_in(z0), z0, z1)
U37(f29_out1, z0, z1) → f294_out2
f388_in(z0, z1, z2) → U38(f390_in(z0, z1), z0, z1, z2)
U38(f390_out1, z0, z1, z2) → f388_out1
f389_in(z0, z1, z2) → U39(f394_in(z0, z2), z0, z1, z2)
U39(f394_out1, z0, z1, z2) → f389_out1
f68_in(s(z0)) → U40(f72_in(z0), s(z0))
U40(f72_out1, s(z0)) → f68_out1
f69_in(z0) → U41(f29_in(z0), z0)
U41(f29_out1, z0) → f69_out2
f177_in(z0, z1) → U42(f29_in(z0), z0, z1)
U42(f29_out1, z0, z1) → f177_out1
f178_in(z0, z1) → U43(f185_in(z0, z1), z0, z1)
U43(f185_out1, z0, z1) → f178_out1
f267_in(z0, z1) → U44(f270_in(z0, z1), z0, z1)
U44(f270_out1, z0, z1) → f267_out1
f268_in(z0, z1) → U45(f29_in(z0), z0, z1)
U45(f29_out1, z0, z1) → f268_out1
f333_in(z0, z1, z2, z3) → U46(f335_in(z0, z1), z0, z1, z2, z3)
U46(f335_out1, z0, z1, z2, z3) → f333_out1
f334_in(z0, z1, z2, z3) → U47(f132_in(z0, z2, z3), z0, z1, z2, z3)
U47(f132_out1, z0, z1, z2, z3) → f334_out1
f27_in(z0) → U48(f29_in(z0), z0)
U48(f29_out1, z0) → f27_out1
f28_in(z0) → U49(f29_in(z0), z0)
U49(f29_out1, z0) → f28_out1
f124_in(z0, z1, z2) → U50(f29_in(z0), z0, z1, z2)
U50(f29_out1, z0, z1, z2) → f124_out1
f125_in(z0, z1, z2) → U51(f132_in(z0, z1, z2), z0, z1, z2)
U51(f132_out1, z0, z1, z2) → f125_out1
f29_in(z0) → U52(f34_in(z0), z0)
U52(f34_out1, z0) → U53(f2_in(z0, void), z0)
U53(f2_out1, z0) → f29_out1
f72_in(z0) → U54(f34_in(z0), z0)
U54(f34_out1, z0) → U55(f2_in(s(z0), void), z0)
U55(f2_out1, z0) → f72_out1
f132_in(z0, z1, z2) → U56(f34_in(z0), z0, z1, z2)
U56(f34_out1, z0, z1, z2) → U57(f2_in(z0, tree(z1, void, z2)), z0, z1, z2)
U57(f2_out1, z0, z1, z2) → f132_out1
f185_in(z0, z1) → U58(f34_in(z0), z0, z1)
U58(f34_out1, z0, z1) → U59(f2_in(z0, z1), z0, z1)
U59(f2_out1, z0, z1) → f185_out1
f206_in(z0) → U60(f34_in(z0), z0)
U60(f34_out1, z0) → U61(f2_in(s(z0), void), z0)
U61(f2_out1, z0) → f206_out1
f219_in(z0, z1) → U62(f34_in(z0), z0, z1)
U62(f34_out1, z0, z1) → U63(f2_in(z0, z1), z0, z1)
U63(f2_out1, z0, z1) → f219_out1
f240_in(z0, z1) → U64(f34_in(z0), z0, z1)
U64(f34_out1, z0, z1) → U65(f2_in(s(z0), z1), z0, z1)
U65(f2_out1, z0, z1) → f240_out1
f270_in(z0, z1) → U66(f34_in(z0), z0, z1)
U66(f34_out1, z0, z1) → U67(f2_in(z0, z1), z0, z1)
U67(f2_out1, z0, z1) → f270_out1
f296_in(z0, z1) → U68(f34_in(z0), z0, z1)
U68(f34_out1, z0, z1) → U69(f2_in(s(z0), z1), z0, z1)
U69(f2_out1, z0, z1) → f296_out1
f318_in(z0) → U70(f34_in(z0), z0)
U70(f34_out1, z0) → U71(f2_in(s(z0), void), z0)
U71(f2_out1, z0) → f318_out1
f335_in(z0, z1) → U72(f34_in(z0), z0, z1)
U72(f34_out1, z0, z1) → U73(f2_in(z0, z1), z0, z1)
U73(f2_out1, z0, z1) → f335_out1
f390_in(z0, z1) → U74(f34_in(z0), z0, z1)
U74(f34_out1, z0, z1) → U75(f2_in(z0, z1), z0, z1)
U75(f2_out1, z0, z1) → f390_out1
f394_in(z0, z1) → U76(f34_in(z0), z0, z1)
U76(f34_out1, z0, z1) → U77(f2_in(z0, z1), z0, z1)
U77(f2_out1, z0, z1) → f394_out1
f487_in(z0, z1) → U78(f494_in(z0), z0, z1)
U78(f494_out1, z0, z1) → U79(f2_in(0, z1), z0, z1)
U79(f2_out1, z0, z1) → f487_out1
f501_in(z0, z1, z2) → U80(f503_in(z0, z1), z0, z1, z2)
U80(f503_out1, z0, z1, z2) → U81(f2_in(s(z0), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f501_out1
f678_in(z0, z1, z2) → U82(f554_in(z0, z1), z0, z1, z2)
U82(f554_out1, z0, z1, z2) → U83(f2_in(z1, z2), z0, z1, z2)
U83(f2_out1, z0, z1, z2) → f678_out1
f690_in(z0, z1, z2) → U84(f554_in(z0, z1), z0, z1, z2)
U84(f554_out1, z0, z1, z2) → U85(f2_in(s(z1), z2), z0, z1, z2)
U85(f2_out1, z0, z1, z2) → f690_out1
f24_in(z0) → U86(f27_in(z0), f28_in(z0), z0)
U86(f27_out1, z0, z1) → f24_out1
U86(z0, f28_out1, z1) → f24_out2
f63_in(z0) → U87(f68_in(z0), f69_in(z0), z0)
U87(f68_out1, z0, z1) → f63_out1
U87(z0, f69_out2, z1) → f63_out3
f109_in(z0, z1) → U88(f140_in(z0), f141_in(z1, z0), z0, z1)
U88(f140_out1(z0), z1, z2, z3) → f109_out1(z0)
U88(z0, f141_out2, z1, z2) → f109_out3
U88(z0, f141_out3, z1, z2) → f109_out4
f110_in(z0, z1, z2) → U89(f112_in(z0, z1), f113_in(z2, z0, z1), z0, z1, z2)
U89(f112_out1(z0), z1, z2, z3, z4) → f110_out1(z0)
U89(z0, f113_out2, z1, z2, z3) → f110_out3
U89(z0, f113_out3, z1, z2, z3) → f110_out4
f122_in(z0, z1, z2) → U90(f124_in(z0, z1, z2), f125_in(z0, z1, z2), z0, z1, z2)
U90(f124_out1, z0, z1, z2, z3) → f122_out1
U90(z0, f125_out1, z1, z2, z3) → f122_out2
f176_in(z0, z1) → U91(f177_in(z0, z1), f178_in(z0, z1), z0, z1)
U91(f177_out1, z0, z1, z2) → f176_out1
U91(z0, f178_out1, z1, z2) → f176_out2
f201_in(z0, z1) → U92(f202_in(z0), f203_in(z0, z1), z0, z1)
U92(f202_out1, z0, z1, z2) → f201_out1
U92(z0, f203_out2, z1, z2) → f201_out3
f264_in(z0, z1) → U93(f267_in(z0, z1), f268_in(z0, z1), z0, z1)
U93(f267_out1, z0, z1, z2) → f264_out1
U93(z0, f268_out1, z1, z2) → f264_out2
f292_in(z0, z1) → U94(f293_in(z0, z1), f294_in(z0, z1), z0, z1)
U94(f293_out1, z0, z1, z2) → f292_out1
U94(z0, f294_out2, z1, z2) → f292_out3
f326_in(z0, z1, z2) → U95(f341_in(z0), f342_in(z1, z2, z0), z0, z1, z2)
U95(f341_out1(z0), z1, z2, z3, z4) → f326_out1(z0)
U95(z0, f342_out2, z1, z2, z3) → f326_out3
U95(z0, f342_out3, z1, z2, z3) → f326_out4
f327_in(z0, z1, z2, z3) → U96(f328_in(z0, z1), f329_in(z2, z3, z0, z1), z0, z1, z2, z3)
U96(f328_out1(z0), z1, z2, z3, z4, z5) → f327_out1(z0)
U96(z0, f329_out2, z1, z2, z3, z4) → f327_out3
U96(z0, f329_out3, z1, z2, z3, z4) → f327_out4
f332_in(z0, z1, z2, z3) → U97(f333_in(z0, z1, z2, z3), f334_in(z0, z1, z2, z3), z0, z1, z2, z3)
U97(f333_out1, z0, z1, z2, z3, z4) → f332_out1
U97(z0, f334_out1, z1, z2, z3, z4) → f332_out2
f387_in(z0, z1, z2) → U98(f388_in(z0, z1, z2), f389_in(z0, z1, z2), z0, z1, z2)
U98(f388_out1, z0, z1, z2, z3) → f387_out1
U98(z0, f389_out1, z1, z2, z3) → f387_out2
f449_in(z0, z1, z2) → U99(f2_in(0, z0), f460_in(z1, z0, z2), z0, z1, z2)
U99(f2_out1, z0, z1, z2, z3) → f449_out1
U99(z0, f460_out1, z1, z2, z3) → f449_out2
U99(z0, f460_out3, z1, z2, z3) → f449_out4
f450_in(z0, z1, z2, z3) → U100(f499_in(z0, z1, z2), f500_in(z0, z1, z2, z3), z0, z1, z2, z3)
U100(f499_out1, z0, z1, z2, z3, z4) → f450_out1
U100(z0, f500_out2, z1, z2, z3, z4) → f450_out3
f685_in(z0, z1) → U101(f2_in(s(z0), z1), f688_in(z0, z1), z0, z1)
U101(f2_out1, z0, z1, z2) → f685_out1
U101(z0, f688_out1, z1, z2) → f685_out2

Tuples:

F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F294_IN(z0, z1) → c(F29_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F69_IN(z0) → c(F29_IN(z0))
F177_IN(z0, z1) → c(F29_IN(z0))
F268_IN(z0, z1) → c(F29_IN(z0))
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F34_IN(s(z0)) → c65(F34_IN(z0))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
F487_IN(z0, z1) → c177
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
F341_IN(tree(z0, z1, z2)) → c
F140_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F68_IN(s(z0)) → c
F69_IN(z0) → c
F177_IN(z0, z1) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
U52'(f34_out1, z0) → c
U54'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U78'(f494_out1, z0, z1) → c
F24_IN(z0) → c
F63_IN(z0) → c

S tuples:none
K tuples:

U78'(f494_out1, z0, z1) → c(F2_IN(0, z1))
U78'(f494_out1, z0, z1) → c
U56'(f34_out1, z0, z1, z2) → c145(F2_IN(z0, tree(z1, void, z2)))
U58'(f34_out1, z0, z1) → c148(F2_IN(z0, z1))
U66'(f34_out1, z0, z1) → c160(F2_IN(z0, z1))
U68'(f34_out1, z0, z1) → c163(F2_IN(s(z0), z1))
U72'(f34_out1, z0, z1) → c169(F2_IN(z0, z1))
U52'(f34_out1, z0) → c
U60'(f34_out1, z0) → c
U70'(f34_out1, z0) → c
U76'(f34_out1, z0, z1) → c175(F2_IN(z0, z1))
U54'(f34_out1, z0) → c
U62'(f34_out1, z0, z1) → c154(F2_IN(z0, z1))
U74'(f34_out1, z0, z1) → c172(F2_IN(z0, z1))
U64'(f34_out1, z0, z1) → c157(F2_IN(s(z0), z1))
F240_IN(z0, z1) → c156(U64'(f34_in(z0), z0, z1), F34_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F24_IN(z0))
F2_IN(z0, tree(z0, void, void)) → c(F63_IN(z0))
F2_IN(s(z0), tree(s(z0), void, void)) → c(F72_IN(z0))
F68_IN(s(z0)) → c(F72_IN(z0))
F318_IN(z0) → c(U70'(f34_in(z0), z0))
F318_IN(z0) → c(F34_IN(z0))
F63_IN(z0) → c(F68_IN(z0))
F63_IN(z0) → c(F69_IN(z0))
F2_IN(z0, tree(z0, void, tree(z1, void, z2))) → c6(F110_IN(z1, z2, z0))
F2_IN(z0, tree(z0, void, z1)) → c7(F109_IN(z1, z0))
F2_IN(z0, tree(z0, void, z1)) → c8(F201_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), void, z1)) → c9(F240_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c11(F264_IN(z0, z1))
F2_IN(z0, tree(z0, z1, void)) → c12(F292_IN(z0, z1))
F2_IN(z0, tree(z0, z1, tree(z2, void, z3))) → c15(F327_IN(z2, z3, z0, z1))
F110_IN(z0, z1, z2) → c199(F112_IN(z0, z1), F113_IN(z2, z0, z1))
F2_IN(z0, tree(z0, void, void)) → c
F2_IN(s(z0), tree(s(z0), void, void)) → c
F2_IN(s(z0), tree(s(z0), z1, void)) → c
F68_IN(s(z0)) → c
F63_IN(z0) → c
F69_IN(z0) → c(F29_IN(z0))
F72_IN(z0) → c(U54'(f34_in(z0), z0))
F72_IN(z0) → c(F34_IN(z0))
F24_IN(z0) → c(F27_IN(z0))
F24_IN(z0) → c(F28_IN(z0))
F112_IN(z0, z1) → c97
F113_IN(z0, z1, z2) → c99(F122_IN(z0, z1, z2))
F109_IN(z0, z1) → c195(F140_IN(z0), F141_IN(z1, z0))
F122_IN(z0, z1, z2) → c203(F124_IN(z0, z1, z2), F125_IN(z0, z1, z2))
F201_IN(z0, z1) → c209(F202_IN(z0), F203_IN(z0, z1))
F264_IN(z0, z1) → c212(F267_IN(z0, z1), F268_IN(z0, z1))
F292_IN(z0, z1) → c215(F293_IN(z0, z1), F294_IN(z0, z1))
F327_IN(z0, z1, z2, z3) → c222(F328_IN(z0, z1), F329_IN(z2, z3, z0, z1))
F140_IN(tree(z0, z1, z2)) → c
F202_IN(s(z0)) → c
F294_IN(z0, z1) → c
F69_IN(z0) → c
F268_IN(z0, z1) → c
F27_IN(z0) → c
F28_IN(z0) → c
F124_IN(z0, z1, z2) → c
F24_IN(z0) → c
F27_IN(z0) → c(F29_IN(z0))
F28_IN(z0) → c(F29_IN(z0))
F140_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F141_IN(z0, z1) → c83(F176_IN(z0, z1))
F124_IN(z0, z1, z2) → c(F29_IN(z0))
F125_IN(z0, z1, z2) → c136(F132_IN(z0, z1, z2))
F202_IN(s(z0)) → c(F206_IN(z0))
F203_IN(z0, z1) → c104(F219_IN(z0, z1))
F268_IN(z0, z1) → c(F29_IN(z0))
F267_IN(z0, z1) → c122(F270_IN(z0, z1))
F294_IN(z0, z1) → c(F29_IN(z0))
F293_IN(s(z0), z1) → c106(F296_IN(z0, z1))
F328_IN(z0, z1) → c86
F329_IN(z0, z1, z2, z3) → c88(F332_IN(z0, z1, z2, z3))
F176_IN(z0, z1) → c206(F177_IN(z0, z1), F178_IN(z0, z1))
F206_IN(z0) → c(U60'(f34_in(z0), z0))
F206_IN(z0) → c(F34_IN(z0))
F219_IN(z0, z1) → c153(U62'(f34_in(z0), z0, z1), F34_IN(z0))
F270_IN(z0, z1) → c159(U66'(f34_in(z0), z0, z1), F34_IN(z0))
F296_IN(z0, z1) → c162(U68'(f34_in(z0), z0, z1), F34_IN(z0))
F332_IN(z0, z1, z2, z3) → c226(F333_IN(z0, z1, z2, z3), F334_IN(z0, z1, z2, z3))
F177_IN(z0, z1) → c(F29_IN(z0))
F178_IN(z0, z1) → c120(F185_IN(z0, z1))
F177_IN(z0, z1) → c
F333_IN(z0, z1, z2, z3) → c126(F335_IN(z0, z1))
F334_IN(z0, z1, z2, z3) → c128(F132_IN(z0, z2, z3))
F29_IN(z0) → c(U52'(f34_in(z0), z0))
F29_IN(z0) → c(F34_IN(z0))
F185_IN(z0, z1) → c147(U58'(f34_in(z0), z0, z1), F34_IN(z0))
F335_IN(z0, z1) → c168(U72'(f34_in(z0), z0, z1), F34_IN(z0))
F132_IN(z0, z1, z2) → c144(U56'(f34_in(z0), z0, z1, z2), F34_IN(z0))
F2_IN(s(z0), tree(0, z1, z2)) → c19(F685_IN(z0, z2))
F685_IN(z0, z1) → c239(F2_IN(s(z0), z1))
F690_IN(z0, z1, z2) → c186(U84'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F2_IN(s(z0), tree(s(z0), z1, void)) → c(F318_IN(z0))
F2_IN(z0, tree(z0, z1, z2)) → c16(F326_IN(z2, z0, z1))
F2_IN(0, tree(s(z0), z1, z2)) → c17(F449_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c18(F450_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c20(F690_IN(z1, z0, z3))
F326_IN(z0, z1, z2) → c218(F341_IN(z0), F342_IN(z1, z2, z0))
F341_IN(tree(z0, z1, z2)) → c(F146_IN(z1))
F342_IN(z0, z1, z2) → c78(F387_IN(z0, z1, z2))
U84'(f554_out1, z0, z1, z2) → c187(F2_IN(s(z1), z2))
F387_IN(z0, z1, z2) → c229(F388_IN(z0, z1, z2), F389_IN(z0, z1, z2))
F449_IN(z0, z1, z2) → c232(F2_IN(0, z0), F460_IN(z1, z0, z2))
F450_IN(z0, z1, z2, z3) → c236(F499_IN(z0, z1, z2), F500_IN(z0, z1, z2, z3))
F341_IN(tree(z0, z1, z2)) → c
F460_IN(z0, z1, z2) → c
F388_IN(z0, z1, z2) → c110(F390_IN(z0, z1))
F389_IN(z0, z1, z2) → c112(F394_IN(z0, z2))
F460_IN(z0, z1, z2) → c(F487_IN(z0, z2))
F499_IN(s(z0), s(z1), z2) → c93(F501_IN(z0, z1, z2))
F500_IN(z0, z1, z2, z3) → c95(F678_IN(z1, z0, z3))
F390_IN(z0, z1) → c171(U74'(f34_in(z0), z0, z1), F34_IN(z0))
F394_IN(z0, z1) → c174(U76'(f34_in(z0), z0, z1), F34_IN(z0))
F487_IN(z0, z1) → c177
F501_IN(z0, z1, z2) → c180(U80'(f503_in(z0, z1), z0, z1, z2), F503_IN(z0, z1))
F678_IN(z0, z1, z2) → c183(U82'(f554_in(z0, z1), z0, z1, z2), F554_IN(z0, z1))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c(F554_IN(z0, z1))
U80'(f503_out1, z0, z1, z2) → c181(F2_IN(s(z0), z2))
F503_IN(s(s(s(s(s(s(s(z0))))))), s(s(s(s(s(s(s(z1)))))))) → c
U82'(f554_out1, z0, z1, z2) → c184(F2_IN(z1, z2))
F146_IN(tree(z0, void, z1)) → c55
F146_IN(tree(z0, tree(z1, void, z2), z3)) → c57
F34_IN(s(z0)) → c65(F34_IN(z0))
F554_IN(s(z0), s(z1)) → c63(F554_IN(z0, z1))
F146_IN(tree(z0, tree(z1, z2, z3), z4)) → c58(F146_IN(z2))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, f146_in, U17, U18, U19, f554_in, U20, f34_in, U21, f503_in, U22, f341_in, U23, f342_in, U24, f140_in, U25, f141_in, U26, f328_in, U27, f329_in, U28, f460_in, U29, f499_in, U30, f500_in, U31, f112_in, U32, f113_in, U33, f202_in, U34, f203_in, U35, f293_in, U36, f294_in, U37, f388_in, U38, f389_in, U39, f68_in, U40, f69_in, U41, f177_in, U42, f178_in, U43, f267_in, U44, f268_in, U45, f333_in, U46, f334_in, U47, f27_in, U48, f28_in, U49, f124_in, U50, f125_in, U51, f29_in, U52, U53, f72_in, U54, U55, f132_in, U56, U57, f185_in, U58, U59, f206_in, U60, U61, f219_in, U62, U63, f240_in, U64, U65, f270_in, U66, U67, f296_in, U68, U69, f318_in, U70, U71, f335_in, U72, U73, f390_in, U74, U75, f394_in, U76, U77, f487_in, U78, U79, f501_in, U80, U81, f678_in, U82, U83, f690_in, U84, U85, f24_in, U86, f63_in, U87, f109_in, U88, f110_in, U89, f122_in, U90, f176_in, U91, f201_in, U92, f264_in, U93, f292_in, U94, f326_in, U95, f327_in, U96, f332_in, U97, f387_in, U98, f449_in, U99, f450_in, U100, f685_in, U101

Defined Pair Symbols:

F132_IN, F185_IN, F219_IN, F240_IN, F270_IN, F296_IN, F335_IN, F390_IN, F394_IN, F501_IN, F678_IN, F690_IN, F2_IN, F503_IN, F341_IN, F140_IN, F460_IN, F202_IN, F294_IN, F68_IN, F69_IN, F177_IN, F268_IN, F27_IN, F28_IN, F124_IN, F29_IN, F72_IN, F206_IN, F318_IN, U78', F24_IN, F63_IN, F146_IN, F554_IN, F34_IN, F342_IN, F141_IN, F328_IN, F329_IN, F499_IN, F500_IN, F112_IN, F113_IN, F203_IN, F293_IN, F388_IN, F389_IN, F178_IN, F267_IN, F333_IN, F334_IN, F125_IN, U56', U58', U62', U64', U66', U68', U72', U74', U76', F487_IN, U80', U82', U84', F109_IN, F110_IN, F122_IN, F176_IN, F201_IN, F264_IN, F292_IN, F326_IN, F327_IN, F332_IN, F387_IN, F449_IN, F450_IN, F685_IN, U52', U54', U60', U70'

Compound Symbols:

c144, c147, c153, c156, c159, c162, c168, c171, c174, c180, c183, c186, c, c6, c7, c8, c9, c11, c12, c15, c16, c17, c18, c19, c20, c55, c57, c58, c63, c65, c78, c83, c86, c88, c93, c95, c97, c99, c104, c106, c110, c112, c120, c122, c126, c128, c136, c145, c148, c154, c157, c160, c163, c169, c172, c175, c177, c181, c184, c187, c195, c199, c203, c206, c209, c212, c215, c218, c222, c226, c229, c232, c236, c239, c

(71) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

(72) BOUNDS(O(1), O(1))