Runtime Complexity of the query pattern
delete(g,a,g)
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,a,g)

(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,a,g)

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

Built complexity over-approximating cdt problems from derivation graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: delete(T1, T2, T3)\n\nT1 is ground\nT3 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\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: true | delete(T8, T2, T9), SCOPE: 1, CLAUSE: 1 | delete(T8, T2, T9), SCOPE: 1, CLAUSE: 4 | delete(T8, T2, T9), SCOPE: 1, CLAUSE: 5 | delete(T8, T2, T9), 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\nT3 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];
9 [label="9: delete(T8, T2, T9), SCOPE: 1, CLAUSE: 1 | delete(T8, T2, T9), SCOPE: 1, CLAUSE: 4 | delete(T8, T2, T9), SCOPE: 1, CLAUSE: 5 | delete(T8, T2, T9), SCOPE: 1, CLAUSE: 6\n\nT8 is ground\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: true | delete(T14, T2, T15), SCOPE: 1, CLAUSE: 4 | delete(T14, T2, T15), SCOPE: 1, CLAUSE: 5 | delete(T14, T2, T15), SCOPE: 1, CLAUSE: 6\n\nT14 is ground\nT15 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: delete(T8, T2, T9), SCOPE: 1, CLAUSE: 4 | delete(T8, T2, T9), SCOPE: 1, CLAUSE: 5 | delete(T8, T2, T9), SCOPE: 1, CLAUSE: 6\n\nT8 is ground\nT9 is ground\nX14 is free\nX15 is free\ndelete(T8, T2, T9) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: delete(T14, T2, T15), SCOPE: 1, CLAUSE: 4 | delete(T14, T2, T15), SCOPE: 1, CLAUSE: 5 | delete(T14, T2, T15), SCOPE: 1, CLAUSE: 6\n\nT14 is ground\nT15 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: delete(T14, T2, T15), SCOPE: 1, CLAUSE: 4\n\nT14 is ground\nT15 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: delete(T14, T2, T15), SCOPE: 1, CLAUSE: 5 | delete(T14, T2, T15), SCOPE: 1, CLAUSE: 6\n\nT14 is ground\nT15 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: delmin(T41, T39, T40)\n\nT39 is ground\nT40 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: delmin(T41, T39, T40), SCOPE: 2, CLAUSE: 2 | delmin(T41, T39, T40), SCOPE: 2, CLAUSE: 7\n\nT39 is ground\nT40 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: true | delmin(T41, T50, T51), SCOPE: 2, CLAUSE: 7\n\nT50 is ground\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: delmin(T41, T39, T40), SCOPE: 2, CLAUSE: 7\n\nT39 is ground\nT40 is ground\nX49 is free\nX50 is free\ndelmin(T41, T39, T40) !=? delmin(tree(X49, void, X50), X49, X50)", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: delmin(T41, T50, T51), SCOPE: 2, CLAUSE: 7\n\nT50 is ground\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: delmin(T70, T67, T68)\n\nT67 is ground\nT68 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: delmin(T93, T90, T91)\n\nT90 is ground\nT87 is ground\nT91 is ground\nT92 is ground\nX49 is free\nX50 is free\ndelmin(T41, T90, tree(T87, T91, T92)) !=? delmin(tree(X49, void, X50), X49, X50)", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: delete(T14, T2, T15), SCOPE: 1, CLAUSE: 5\n\nT14 is ground\nT15 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: delete(T14, T2, T15), SCOPE: 1, CLAUSE: 6\n\nT14 is ground\nT15 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(less(T118, T119), delete(T118, T123, T122))\n\nT118 is ground\nT119 is ground\nT122 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: less(T118, T119)\n\nT118 is ground\nT119 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: delete(T118, T123, T122)\n\nT118 is ground\nT122 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: less(T118, T119), SCOPE: 3, CLAUSE: 3 | less(T118, T119), SCOPE: 3, CLAUSE: 8\n\nT118 is ground\nT119 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: true | less(0, s(T130)), SCOPE: 3, CLAUSE: 8\n\nT130 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: less(T118, T119), SCOPE: 3, CLAUSE: 8\n\nT118 is ground\nT119 is ground\nX126 is free\nless(T118, T119) !=? less(0, s(X126))", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: less(0, s(T130)), SCOPE: 3, CLAUSE: 8\n\nT130 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: less(T135, T136)\n\nT135 is ground\nT136 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: ','(less(T154, T153), delete(T153, T158, T157))\n\nT153 is ground\nT154 is ground\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: less(T154, T153)\n\nT153 is ground\nT154 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: delete(T153, T158, T157)\n\nT153 is ground\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: delete(T8, T2, T9), SCOPE: 1, CLAUSE: 4\n\nT8 is ground\nT9 is ground\nX14 is free\nX15 is free\ndelete(T8, T2, T9) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: delete(T8, T2, T9), SCOPE: 1, CLAUSE: 5 | delete(T8, T2, T9), SCOPE: 1, CLAUSE: 6\n\nT8 is ground\nT9 is ground\nX14 is free\nX15 is free\ndelete(T8, T2, T9) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: delmin(T192, T190, T191)\n\nT187 is ground\nT190 is ground\nT188 is ground\nT191 is ground\nX14 is free\nX15 is free\ndelete(T187, T2, tree(T190, T188, T191)) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: delete(T8, T2, T9), SCOPE: 1, CLAUSE: 5\n\nT8 is ground\nT9 is ground\nX14 is free\nX15 is free\ndelete(T8, T2, T9) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: delete(T8, T2, T9), SCOPE: 1, CLAUSE: 6\n\nT8 is ground\nT9 is ground\nX14 is free\nX15 is free\ndelete(T8, T2, T9) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: ','(less(T217, T218), delete(T217, T222, T221))\n\nT217 is ground\nT218 is ground\nT221 is ground\nT220 is ground\nX14 is free\nX15 is free\ndelete(T217, T2, tree(T218, T221, T220)) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: ','(less(T236, T235), delete(T235, T240, T239))\n\nT235 is ground\nT236 is ground\nT237 is ground\nT239 is ground\nX14 is free\nX15 is free\ndelete(T235, T2, tree(T236, T237, T239)) !=? delete(X14, tree(X14, X15, void), X15)", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: true | delete(T247, T2, T248), SCOPE: 1, CLAUSE: 4 | delete(T247, T2, T248), SCOPE: 1, CLAUSE: 5 | delete(T247, T2, T248), SCOPE: 1, CLAUSE: 6\n\nT247 is ground\nT248 is ground\nX8 is free\nX9 is free\ndelete(T247, T2, T248) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: 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\nT3 is ground\nX8 is free\nX9 is free\nX241 is free\nX242 is free\ndelete(T1, T2, T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T1, T2, T3) !=? delete(X241, tree(X241, X242, void), X242)", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: delete(T247, T2, T248), SCOPE: 1, CLAUSE: 4 | delete(T247, T2, T248), SCOPE: 1, CLAUSE: 5 | delete(T247, T2, T248), SCOPE: 1, CLAUSE: 6\n\nT247 is ground\nT248 is ground\nX8 is free\nX9 is free\ndelete(T247, T2, T248) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: delete(T247, T2, T248), SCOPE: 1, CLAUSE: 4\n\nT247 is ground\nT248 is ground\nX8 is free\nX9 is free\ndelete(T247, T2, T248) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: delete(T247, T2, T248), SCOPE: 1, CLAUSE: 5 | delete(T247, T2, T248), SCOPE: 1, CLAUSE: 6\n\nT247 is ground\nT248 is ground\nX8 is free\nX9 is free\ndelete(T247, T2, T248) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: delmin(T274, T272, T273)\n\nT269 is ground\nT272 is ground\nT270 is ground\nT273 is ground\nX8 is free\nX9 is free\ndelete(T269, T2, tree(T272, T270, T273)) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: delete(T247, T2, T248), SCOPE: 1, CLAUSE: 5\n\nT247 is ground\nT248 is ground\nX8 is free\nX9 is free\ndelete(T247, T2, T248) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: delete(T247, T2, T248), SCOPE: 1, CLAUSE: 6\n\nT247 is ground\nT248 is ground\nX8 is free\nX9 is free\ndelete(T247, T2, T248) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: ','(less(T299, T300), delete(T299, T304, T303))\n\nT299 is ground\nT300 is ground\nT303 is ground\nT302 is ground\nX8 is free\nX9 is free\ndelete(T299, T2, tree(T300, T303, T302)) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: ','(less(T318, T317), delete(T317, T322, T321))\n\nT317 is ground\nT318 is ground\nT319 is ground\nT321 is ground\nX8 is free\nX9 is free\ndelete(T317, T2, tree(T318, T319, T321)) !=? delete(X8, tree(X8, void, X9), X9)", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT1 is ground\nT3 is ground\nX8 is free\nX9 is free\nX241 is free\nX242 is free\ndelete(T1, T2, T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T1, T2, T3) !=? delete(X241, tree(X241, X242, void), X242)", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 5 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 6\n\nT1 is ground\nT3 is ground\nX8 is free\nX9 is free\nX241 is free\nX242 is free\ndelete(T1, T2, T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T1, T2, T3) !=? delete(X241, tree(X241, X242, void), X242)", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: delmin(T350, T348, T349)\n\nT345 is ground\nT348 is ground\nT346 is ground\nT349 is ground\nX8 is free\nX9 is free\nX241 is free\nX242 is free\ndelete(T345, T2, tree(T348, T346, T349)) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T345, T2, tree(T348, T346, T349)) !=? delete(X241, tree(X241, X242, void), X242)", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 5\n\nT1 is ground\nT3 is ground\nX8 is free\nX9 is free\nX241 is free\nX242 is free\ndelete(T1, T2, T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T1, T2, T3) !=? delete(X241, tree(X241, X242, void), X242)", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 6\n\nT1 is ground\nT3 is ground\nX8 is free\nX9 is free\nX241 is free\nX242 is free\ndelete(T1, T2, T3) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T1, T2, T3) !=? delete(X241, tree(X241, X242, void), X242)", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: ','(less(T375, T376), delete(T375, T380, T379))\n\nT375 is ground\nT376 is ground\nT379 is ground\nT378 is ground\nX8 is free\nX9 is free\nX241 is free\nX242 is free\ndelete(T375, T2, tree(T376, T379, T378)) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T375, T2, tree(T376, T379, T378)) !=? delete(X241, tree(X241, X242, void), X242)", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: ','(less(T394, T393), delete(T393, T398, T397))\n\nT393 is ground\nT394 is ground\nT395 is ground\nT397 is ground\nX8 is free\nX9 is free\nX241 is free\nX242 is free\ndelete(T393, T2, tree(T394, T395, T397)) !=? delete(X8, tree(X8, void, X9), X9)\ndelete(T393, T2, tree(T394, T395, T397)) !=? delete(X241, tree(X241, X242, void), X242)", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 151 [arrowhead = none ];
151 -> 4;

152 [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];
4 -> 152 [arrowhead = none ];
152 -> 5;

153 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 153 [arrowhead = none ];
153 -> 7;

154 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 154 [arrowhead = none ];
154 -> 9;

155 [label="EVAL with clause\ndelete(X241, tree(X241, X242, void), X242).\nand substitutionT1 -> T247,\nX241 -> T247,\nX242 -> T248,\nT2 -> tree(T247, T248, void),\nT3 -> T248", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 155 [arrowhead = none ];
155 -> 101;

156 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 156 [arrowhead = none ];
156 -> 102;

157 [label="EVAL with clause\ndelete(X14, tree(X14, X15, void), X15).\nand substitutionT8 -> T14,\nX14 -> T14,\nX15 -> T15,\nT2 -> tree(T14, T15, void),\nT9 -> T15", fontsize=14, style = filled, fillcolor = lightblue];
9 -> 157 [arrowhead = none ];
157 -> 11;

158 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
9 -> 158 [arrowhead = none ];
158 -> 13;

159 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 159 [arrowhead = none ];
159 -> 14;

160 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 160 [arrowhead = none ];
160 -> 82;

161 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 161 [arrowhead = none ];
161 -> 83;

162 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 162 [arrowhead = none ];
162 -> 17;

163 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 163 [arrowhead = none ];
163 -> 18;

164 [label="EVAL with clause\ndelete(X36, tree(X36, X37, X38), tree(X39, X37, X40)) :- delmin(X38, X39, X40).\nand substitutionT14 -> T36,\nX36 -> T36,\nX37 -> T37,\nX38 -> T41,\nT2 -> tree(T36, T37, T41),\nX39 -> T39,\nX40 -> T40,\nT15 -> tree(T39, T37, T40),\nT38 -> T41", fontsize=14, style = filled, fillcolor = lightblue];
17 -> 164 [arrowhead = none ];
164 -> 24;

165 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 165 [arrowhead = none ];
165 -> 26;

166 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
18 -> 166 [arrowhead = none ];
166 -> 47;

167 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
18 -> 167 [arrowhead = none ];
167 -> 48;

168 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
24 -> 168 [arrowhead = none ];
168 -> 29;

169 [label="EVAL with clause\ndelmin(tree(X49, void, X50), X49, X50).\nand substitutionX49 -> T50,\nX50 -> T51,\nT41 -> tree(T50, void, T51),\nT39 -> T50,\nT40 -> T51", fontsize=14, style = filled, fillcolor = lightblue];
29 -> 169 [arrowhead = none ];
169 -> 30;

170 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
29 -> 170 [arrowhead = none ];
170 -> 31;

171 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 171 [arrowhead = none ];
171 -> 32;

172 [label="EVAL with clause\ndelmin(tree(X85, X86, X87), X88, tree(X85, X89, X90)) :- delmin(X86, X88, X89).\nand substitutionX85 -> T87,\nX86 -> T93,\nX87 -> T89,\nT41 -> tree(T87, T93, T89),\nT39 -> T90,\nX88 -> T90,\nX89 -> T91,\nX90 -> T92,\nT40 -> tree(T87, T91, T92),\nT88 -> T93", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 172 [arrowhead = none ];
172 -> 43;

173 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
31 -> 173 [arrowhead = none ];
173 -> 44;

174 [label="EVAL with clause\ndelmin(tree(X63, X64, X65), X66, tree(X63, X67, X68)) :- delmin(X64, X66, X67).\nand substitutionX63 -> T64,\nX64 -> T70,\nX65 -> T66,\nT41 -> tree(T64, T70, T66),\nT50 -> T67,\nX66 -> T67,\nX67 -> T68,\nX68 -> T69,\nT51 -> tree(T64, T68, T69),\nT65 -> T70", fontsize=14, style = filled, fillcolor = lightblue];
32 -> 174 [arrowhead = none ];
174 -> 39;

175 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
32 -> 175 [arrowhead = none ];
175 -> 40;

176 [label="INSTANCE with matching:\nT41 -> T70\nT39 -> T67\nT40 -> T68", fontsize=14, style = filled, fillcolor = lightgrey];
39 -> 176 [arrowhead = none , style=dashed];
176 -> 24[style=dashed];

177 [label="INSTANCE with matching:\nT41 -> T93\nT39 -> T90\nT40 -> T91", fontsize=14, style = filled, fillcolor = lightgrey];
43 -> 177 [arrowhead = none , style=dashed];
177 -> 24[style=dashed];

178 [label="EVAL with clause\ndelete(X115, tree(X116, X117, X118), tree(X116, X119, X118)) :- ','(less(X115, X116), delete(X115, X117, X119)).\nand substitutionT14 -> T118,\nX115 -> T118,\nX116 -> T119,\nX117 -> T123,\nX118 -> T121,\nT2 -> tree(T119, T123, T121),\nX119 -> T122,\nT15 -> tree(T119, T122, T121),\nT120 -> T123", fontsize=14, style = filled, fillcolor = lightblue];
47 -> 178 [arrowhead = none ];
178 -> 50;

179 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
47 -> 179 [arrowhead = none ];
179 -> 51;

180 [label="EVAL with clause\ndelete(X151, tree(X152, X153, X154), tree(X152, X153, X155)) :- ','(less(X152, X151), delete(X151, X154, X155)).\nand substitutionT14 -> T153,\nX151 -> T153,\nX152 -> T154,\nX153 -> T155,\nX154 -> T158,\nT2 -> tree(T154, T155, T158),\nX155 -> T157,\nT15 -> tree(T154, T155, T157),\nT156 -> T158", fontsize=14, style = filled, fillcolor = lightblue];
48 -> 180 [arrowhead = none ];
180 -> 74;

181 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
48 -> 181 [arrowhead = none ];
181 -> 75;

182 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
50 -> 182 [arrowhead = none ];
182 -> 54;

183 [label="SPLIT 2\nnew knowledge:\nT118 is ground\nT119 is ground", fontsize=14, style = filled, fillcolor = violet];
50 -> 183 [arrowhead = none ];
183 -> 55;

184 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
54 -> 184 [arrowhead = none ];
184 -> 56;

185 [label="INSTANCE with matching:\nT1 -> T118\nT2 -> T123\nT3 -> T122", fontsize=14, style = filled, fillcolor = lightgrey];
55 -> 185 [arrowhead = none , style=dashed];
185 -> 1[style=dashed];

186 [label="EVAL with clause\nless(0, s(X126)).\nand substitutionT118 -> 0,\nX126 -> T130,\nT119 -> s(T130)", fontsize=14, style = filled, fillcolor = lightblue];
56 -> 186 [arrowhead = none ];
186 -> 57;

187 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
56 -> 187 [arrowhead = none ];
187 -> 58;

188 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
57 -> 188 [arrowhead = none ];
188 -> 59;

189 [label="EVAL with clause\nless(s(X133), s(X134)) :- less(X133, X134).\nand substitutionX133 -> T135,\nT118 -> s(T135),\nX134 -> T136,\nT119 -> s(T136)", fontsize=14, style = filled, fillcolor = lightblue];
58 -> 189 [arrowhead = none ];
189 -> 65;

190 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
58 -> 190 [arrowhead = none ];
190 -> 66;

191 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
59 -> 191 [arrowhead = none ];
191 -> 60;

192 [label="INSTANCE with matching:\nT118 -> T135\nT119 -> T136", fontsize=14, style = filled, fillcolor = lightgrey];
65 -> 192 [arrowhead = none , style=dashed];
192 -> 54[style=dashed];

193 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
74 -> 193 [arrowhead = none ];
193 -> 76;

194 [label="SPLIT 2\nnew knowledge:\nT154 is ground\nT153 is ground", fontsize=14, style = filled, fillcolor = violet];
74 -> 194 [arrowhead = none ];
194 -> 77;

195 [label="INSTANCE with matching:\nT118 -> T154\nT119 -> T153", fontsize=14, style = filled, fillcolor = lightgrey];
76 -> 195 [arrowhead = none , style=dashed];
195 -> 54[style=dashed];

196 [label="INSTANCE with matching:\nT1 -> T153\nT2 -> T158\nT3 -> T157", fontsize=14, style = filled, fillcolor = lightgrey];
77 -> 196 [arrowhead = none , style=dashed];
196 -> 1[style=dashed];

197 [label="EVAL with clause\ndelete(X184, tree(X184, X185, X186), tree(X187, X185, X188)) :- delmin(X186, X187, X188).\nand substitutionT8 -> T187,\nX184 -> T187,\nX185 -> T188,\nX186 -> T192,\nT2 -> tree(T187, T188, T192),\nX187 -> T190,\nX188 -> T191,\nT9 -> tree(T190, T188, T191),\nT189 -> T192", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 197 [arrowhead = none ];
197 -> 84;

198 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
82 -> 198 [arrowhead = none ];
198 -> 85;

199 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
83 -> 199 [arrowhead = none ];
199 -> 88;

200 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
83 -> 200 [arrowhead = none ];
200 -> 89;

201 [label="INSTANCE with matching:\nT41 -> T192\nT39 -> T190\nT40 -> T191", fontsize=14, style = filled, fillcolor = lightgrey];
84 -> 201 [arrowhead = none , style=dashed];
201 -> 24[style=dashed];

202 [label="EVAL with clause\ndelete(X213, tree(X214, X215, X216), tree(X214, X217, X216)) :- ','(less(X213, X214), delete(X213, X215, X217)).\nand substitutionT8 -> T217,\nX213 -> T217,\nX214 -> T218,\nX215 -> T222,\nX216 -> T220,\nT2 -> tree(T218, T222, T220),\nX217 -> T221,\nT9 -> tree(T218, T221, T220),\nT219 -> T222", fontsize=14, style = filled, fillcolor = lightblue];
88 -> 202 [arrowhead = none ];
202 -> 93;

203 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
88 -> 203 [arrowhead = none ];
203 -> 94;

204 [label="EVAL with clause\ndelete(X230, tree(X231, X232, X233), tree(X231, X232, X234)) :- ','(less(X231, X230), delete(X230, X233, X234)).\nand substitutionT8 -> T235,\nX230 -> T235,\nX231 -> T236,\nX232 -> T237,\nX233 -> T240,\nT2 -> tree(T236, T237, T240),\nX234 -> T239,\nT9 -> tree(T236, T237, T239),\nT238 -> T240", fontsize=14, style = filled, fillcolor = lightblue];
89 -> 204 [arrowhead = none ];
204 -> 97;

205 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
89 -> 205 [arrowhead = none ];
205 -> 98;

206 [label="INSTANCE with matching:\nT118 -> T217\nT119 -> T218\nT123 -> T222\nT122 -> T221", fontsize=14, style = filled, fillcolor = lightgrey];
93 -> 206 [arrowhead = none , style=dashed];
206 -> 50[style=dashed];

207 [label="INSTANCE with matching:\nT154 -> T236\nT153 -> T235\nT158 -> T240\nT157 -> T239", fontsize=14, style = filled, fillcolor = lightgrey];
97 -> 207 [arrowhead = none , style=dashed];
207 -> 74[style=dashed];

208 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
101 -> 208 [arrowhead = none ];
208 -> 103;

209 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
102 -> 209 [arrowhead = none ];
209 -> 130;

210 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
102 -> 210 [arrowhead = none ];
210 -> 132;

211 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
103 -> 211 [arrowhead = none ];
211 -> 104;

212 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
103 -> 212 [arrowhead = none ];
212 -> 106;

213 [label="EVAL with clause\ndelete(X263, tree(X263, X264, X265), tree(X266, X264, X267)) :- delmin(X265, X266, X267).\nand substitutionT247 -> T269,\nX263 -> T269,\nX264 -> T270,\nX265 -> T274,\nT2 -> tree(T269, T270, T274),\nX266 -> T272,\nX267 -> T273,\nT248 -> tree(T272, T270, T273),\nT271 -> T274", fontsize=14, style = filled, fillcolor = lightblue];
104 -> 213 [arrowhead = none ];
213 -> 108;

214 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
104 -> 214 [arrowhead = none ];
214 -> 109;

215 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
106 -> 215 [arrowhead = none ];
215 -> 115;

216 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
106 -> 216 [arrowhead = none ];
216 -> 116;

217 [label="INSTANCE with matching:\nT41 -> T274\nT39 -> T272\nT40 -> T273", fontsize=14, style = filled, fillcolor = lightgrey];
108 -> 217 [arrowhead = none , style=dashed];
217 -> 24[style=dashed];

218 [label="EVAL with clause\ndelete(X292, tree(X293, X294, X295), tree(X293, X296, X295)) :- ','(less(X292, X293), delete(X292, X294, X296)).\nand substitutionT247 -> T299,\nX292 -> T299,\nX293 -> T300,\nX294 -> T304,\nX295 -> T302,\nT2 -> tree(T300, T304, T302),\nX296 -> T303,\nT248 -> tree(T300, T303, T302),\nT301 -> T304", fontsize=14, style = filled, fillcolor = lightblue];
115 -> 218 [arrowhead = none ];
218 -> 119;

219 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
115 -> 219 [arrowhead = none ];
219 -> 121;

220 [label="EVAL with clause\ndelete(X309, tree(X310, X311, X312), tree(X310, X311, X313)) :- ','(less(X310, X309), delete(X309, X312, X313)).\nand substitutionT247 -> T317,\nX309 -> T317,\nX310 -> T318,\nX311 -> T319,\nX312 -> T322,\nT2 -> tree(T318, T319, T322),\nX313 -> T321,\nT248 -> tree(T318, T319, T321),\nT320 -> T322", fontsize=14, style = filled, fillcolor = lightblue];
116 -> 220 [arrowhead = none ];
220 -> 124;

221 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
116 -> 221 [arrowhead = none ];
221 -> 126;

222 [label="INSTANCE with matching:\nT118 -> T299\nT119 -> T300\nT123 -> T304\nT122 -> T303", fontsize=14, style = filled, fillcolor = lightgrey];
119 -> 222 [arrowhead = none , style=dashed];
222 -> 50[style=dashed];

223 [label="INSTANCE with matching:\nT154 -> T318\nT153 -> T317\nT158 -> T322\nT157 -> T321", fontsize=14, style = filled, fillcolor = lightgrey];
124 -> 223 [arrowhead = none , style=dashed];
223 -> 74[style=dashed];

224 [label="EVAL with clause\ndelete(X336, tree(X336, X337, X338), tree(X339, X337, X340)) :- delmin(X338, X339, X340).\nand substitutionT1 -> T345,\nX336 -> T345,\nX337 -> T346,\nX338 -> T350,\nT2 -> tree(T345, T346, T350),\nX339 -> T348,\nX340 -> T349,\nT3 -> tree(T348, T346, T349),\nT347 -> T350", fontsize=14, style = filled, fillcolor = lightblue];
130 -> 224 [arrowhead = none ];
224 -> 136;

225 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
130 -> 225 [arrowhead = none ];
225 -> 137;

226 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
132 -> 226 [arrowhead = none ];
226 -> 142;

227 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
132 -> 227 [arrowhead = none ];
227 -> 143;

228 [label="INSTANCE with matching:\nT41 -> T350\nT39 -> T348\nT40 -> T349", fontsize=14, style = filled, fillcolor = lightgrey];
136 -> 228 [arrowhead = none , style=dashed];
228 -> 24[style=dashed];

229 [label="EVAL with clause\ndelete(X365, tree(X366, X367, X368), tree(X366, X369, X368)) :- ','(less(X365, X366), delete(X365, X367, X369)).\nand substitutionT1 -> T375,\nX365 -> T375,\nX366 -> T376,\nX367 -> T380,\nX368 -> T378,\nT2 -> tree(T376, T380, T378),\nX369 -> T379,\nT3 -> tree(T376, T379, T378),\nT377 -> T380", fontsize=14, style = filled, fillcolor = lightblue];
142 -> 229 [arrowhead = none ];
229 -> 145;

230 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
142 -> 230 [arrowhead = none ];
230 -> 146;

231 [label="EVAL with clause\ndelete(X382, tree(X383, X384, X385), tree(X383, X384, X386)) :- ','(less(X383, X382), delete(X382, X385, X386)).\nand substitutionT1 -> T393,\nX382 -> T393,\nX383 -> T394,\nX384 -> T395,\nX385 -> T398,\nT2 -> tree(T394, T395, T398),\nX386 -> T397,\nT3 -> tree(T394, T395, T397),\nT396 -> T398", fontsize=14, style = filled, fillcolor = lightblue];
143 -> 231 [arrowhead = none ];
231 -> 149;

232 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
143 -> 232 [arrowhead = none ];
232 -> 150;

233 [label="INSTANCE with matching:\nT118 -> T375\nT119 -> T376\nT123 -> T380\nT122 -> T379", fontsize=14, style = filled, fillcolor = lightgrey];
145 -> 233 [arrowhead = none , style=dashed];
233 -> 50[style=dashed];

234 [label="INSTANCE with matching:\nT154 -> T394\nT153 -> T393\nT158 -> T398\nT157 -> T397", fontsize=14, style = filled, fillcolor = lightgrey];
149 -> 234 [arrowhead = none , style=dashed];
234 -> 74[style=dashed];

}

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → f1_out1
f1_in(z0, z1) → U1(f14_in(z0, z1), z0, z1)
f1_in(z0, z1) → U2(f13_in(z0, z1), z0, z1)
f1_in(z0, z1) → U3(f103_in(z0, z1), z0, z1)
f1_in(z0, z1) → U4(f102_in(z0, z1), z0, z1)
U1(f14_out1, z0, z1) → f1_out1
U1(f14_out2, z0, z1) → f1_out1
U1(f14_out3, z0, z1) → f1_out1
U2(f13_out1, z0, z1) → f1_out1
U2(f13_out2, z0, z1) → f1_out1
U2(f13_out3, z0, z1) → f1_out1
U3(f103_out1, z0, z1) → f1_out1
U3(f103_out2, z0, z1) → f1_out1
U3(f103_out3, z0, z1) → f1_out1
U4(f102_out1, z0, z1) → f1_out1
U4(f102_out2, z0, z1) → f1_out1
U4(f102_out3, z0, z1) → f1_out1
f24_in(z0, z1) → f24_out1
f24_in(z0, tree(z1, z2, z3)) → U5(f24_in(z0, z2), z0, tree(z1, z2, z3))
f24_in(z0, tree(z1, z2, z3)) → U6(f24_in(z0, z2), z0, tree(z1, z2, z3))
U5(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
U6(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
f54_in(0, s(z0)) → f54_out1
f54_in(s(z0), s(z1)) → U7(f54_in(z0, z1), s(z0), s(z1))
U7(f54_out1, s(z0), s(z1)) → f54_out1
f130_in(z0, tree(z1, z2, z3)) → U8(f24_in(z1, z3), z0, tree(z1, z2, z3))
U8(f24_out1, z0, tree(z1, z2, z3)) → f130_out1
f82_in(z0, tree(z1, z2, z3)) → U9(f24_in(z1, z3), z0, tree(z1, z2, z3))
U9(f24_out1, z0, tree(z1, z2, z3)) → f82_out1
f104_in(z0, tree(z1, z2, z3)) → U10(f24_in(z1, z3), z0, tree(z1, z2, z3))
U10(f24_out1, z0, tree(z1, z2, z3)) → f104_out1
f142_in(z0, tree(z1, z2, z3)) → U11(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U11(f50_out1, z0, tree(z1, z2, z3)) → f142_out1
f143_in(z0, tree(z1, z2, z3)) → U12(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U12(f74_out1, z0, tree(z1, z2, z3)) → f143_out1
f17_in(z0, tree(z1, z2, z3)) → U13(f24_in(z1, z3), z0, tree(z1, z2, z3))
U13(f24_out1, z0, tree(z1, z2, z3)) → f17_out1
f88_in(z0, tree(z1, z2, z3)) → U14(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U14(f50_out1, z0, tree(z1, z2, z3)) → f88_out1
f89_in(z0, tree(z1, z2, z3)) → U15(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U15(f74_out1, z0, tree(z1, z2, z3)) → f89_out1
f115_in(z0, tree(z1, z2, z3)) → U16(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f50_out1, z0, tree(z1, z2, z3)) → f115_out1
f116_in(z0, tree(z1, z2, z3)) → U17(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f74_out1, z0, tree(z1, z2, z3)) → f116_out1
f47_in(z0, tree(z1, z2, z3)) → U18(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U18(f50_out1, z0, tree(z1, z2, z3)) → f47_out1
f48_in(z0, tree(z1, z2, z3)) → U19(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U19(f74_out1, z0, tree(z1, z2, z3)) → f48_out1
f50_in(z0, z1, z2) → U20(f54_in(z0, z1), z0, z1, z2)
U20(f54_out1, z0, z1, z2) → U21(f1_in(z0, z2), z0, z1, z2)
U21(f1_out1, z0, z1, z2) → f50_out1
f74_in(z0, z1, z2) → U22(f54_in(z0, z1), z0, z1, z2)
U22(f54_out1, z0, z1, z2) → U23(f1_in(z1, z2), z0, z1, z2)
U23(f1_out1, z0, z1, z2) → f74_out1
f13_in(z0, z1) → U24(f82_in(z0, z1), f83_in(z0, z1), z0, z1)
U24(f82_out1, z0, z1, z2) → f13_out1
U24(z0, f83_out1, z1, z2) → f13_out2
U24(z0, f83_out2, z1, z2) → f13_out3
f14_in(z0, z1) → U25(f17_in(z0, z1), f18_in(z0, z1), z0, z1)
U25(f17_out1, z0, z1, z2) → f14_out1
U25(z0, f18_out1, z1, z2) → f14_out2
U25(z0, f18_out2, z1, z2) → f14_out3
f18_in(z0, z1) → U26(f47_in(z0, z1), f48_in(z0, z1), z0, z1)
U26(f47_out1, z0, z1, z2) → f18_out1
U26(z0, f48_out1, z1, z2) → f18_out2
f83_in(z0, z1) → U27(f88_in(z0, z1), f89_in(z0, z1), z0, z1)
U27(f88_out1, z0, z1, z2) → f83_out1
U27(z0, f89_out1, z1, z2) → f83_out2
f102_in(z0, z1) → U28(f130_in(z0, z1), f132_in(z0, z1), z0, z1)
U28(f130_out1, z0, z1, z2) → f102_out1
U28(z0, f132_out1, z1, z2) → f102_out2
U28(z0, f132_out2, z1, z2) → f102_out3
f103_in(z0, z1) → U29(f104_in(z0, z1), f106_in(z0, z1), z0, z1)
U29(f104_out1, z0, z1, z2) → f103_out1
U29(z0, f106_out1, z1, z2) → f103_out2
U29(z0, f106_out2, z1, z2) → f103_out3
f106_in(z0, z1) → U30(f115_in(z0, z1), f116_in(z0, z1), z0, z1)
U30(f115_out1, z0, z1, z2) → f106_out1
U30(z0, f116_out1, z1, z2) → f106_out2
f132_in(z0, z1) → U31(f142_in(z0, z1), f143_in(z0, z1), z0, z1)
U31(f142_out1, z0, z1, z2) → f132_out1
U31(z0, f143_out1, z1, z2) → f132_out2

Tuples:

F1_IN(z0, z1) → c1(U1'(f14_in(z0, z1), z0, z1), F14_IN(z0, z1))
F1_IN(z0, z1) → c2(U2'(f13_in(z0, z1), z0, z1), F13_IN(z0, z1))
F1_IN(z0, z1) → c3(U3'(f103_in(z0, z1), z0, z1), F103_IN(z0, z1))
F1_IN(z0, z1) → c4(U4'(f102_in(z0, z1), z0, z1), F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(U5'(f24_in(z0, z2), z0, tree(z1, z2, z3)), F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(U6'(f24_in(z0, z2), z0, tree(z1, z2, z3)), F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(U7'(f54_in(z0, z1), s(z0), s(z1)), F54_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c25(U8'(f24_in(z1, z3), z0, tree(z1, z2, z3)), F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c27(U9'(f24_in(z1, z3), z0, tree(z1, z2, z3)), F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c29(U10'(f24_in(z1, z3), z0, tree(z1, z2, z3)), F24_IN(z1, z3))
F142_IN(z0, tree(z1, z2, z3)) → c31(U11'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(U12'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F17_IN(z0, tree(z1, z2, z3)) → c35(U13'(f24_in(z1, z3), z0, tree(z1, z2, z3)), F24_IN(z1, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(U14'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(U15'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(U16'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(U17'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(U18'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(U19'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F50_IN(z0, z1, z2) → c49(U20'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
U20'(f54_out1, z0, z1, z2) → c50(U21'(f1_in(z0, z2), z0, z1, z2), F1_IN(z0, z2))
F74_IN(z0, z1, z2) → c52(U22'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
U22'(f54_out1, z0, z1, z2) → c53(U23'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F13_IN(z0, z1) → c55(U24'(f82_in(z0, z1), f83_in(z0, z1), z0, z1), F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(U25'(f17_in(z0, z1), f18_in(z0, z1), z0, z1), F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(U26'(f47_in(z0, z1), f48_in(z0, z1), z0, z1), F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(U27'(f88_in(z0, z1), f89_in(z0, z1), z0, z1), F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(U28'(f130_in(z0, z1), f132_in(z0, z1), z0, z1), F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(U29'(f104_in(z0, z1), f106_in(z0, z1), z0, z1), F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(U30'(f115_in(z0, z1), f116_in(z0, z1), z0, z1), F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(U31'(f142_in(z0, z1), f143_in(z0, z1), z0, z1), F142_IN(z0, z1), F143_IN(z0, z1))

S tuples:

F1_IN(z0, z1) → c1(U1'(f14_in(z0, z1), z0, z1), F14_IN(z0, z1))
F1_IN(z0, z1) → c2(U2'(f13_in(z0, z1), z0, z1), F13_IN(z0, z1))
F1_IN(z0, z1) → c3(U3'(f103_in(z0, z1), z0, z1), F103_IN(z0, z1))
F1_IN(z0, z1) → c4(U4'(f102_in(z0, z1), z0, z1), F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(U5'(f24_in(z0, z2), z0, tree(z1, z2, z3)), F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(U6'(f24_in(z0, z2), z0, tree(z1, z2, z3)), F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(U7'(f54_in(z0, z1), s(z0), s(z1)), F54_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c25(U8'(f24_in(z1, z3), z0, tree(z1, z2, z3)), F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c27(U9'(f24_in(z1, z3), z0, tree(z1, z2, z3)), F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c29(U10'(f24_in(z1, z3), z0, tree(z1, z2, z3)), F24_IN(z1, z3))
F142_IN(z0, tree(z1, z2, z3)) → c31(U11'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(U12'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F17_IN(z0, tree(z1, z2, z3)) → c35(U13'(f24_in(z1, z3), z0, tree(z1, z2, z3)), F24_IN(z1, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(U14'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(U15'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(U16'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(U17'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(U18'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(U19'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F50_IN(z0, z1, z2) → c49(U20'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
U20'(f54_out1, z0, z1, z2) → c50(U21'(f1_in(z0, z2), z0, z1, z2), F1_IN(z0, z2))
F74_IN(z0, z1, z2) → c52(U22'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
U22'(f54_out1, z0, z1, z2) → c53(U23'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F13_IN(z0, z1) → c55(U24'(f82_in(z0, z1), f83_in(z0, z1), z0, z1), F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(U25'(f17_in(z0, z1), f18_in(z0, z1), z0, z1), F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(U26'(f47_in(z0, z1), f48_in(z0, z1), z0, z1), F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(U27'(f88_in(z0, z1), f89_in(z0, z1), z0, z1), F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(U28'(f130_in(z0, z1), f132_in(z0, z1), z0, z1), F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(U29'(f104_in(z0, z1), f106_in(z0, z1), z0, z1), F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(U30'(f115_in(z0, z1), f116_in(z0, z1), z0, z1), F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(U31'(f142_in(z0, z1), f143_in(z0, z1), z0, z1), F142_IN(z0, z1), F143_IN(z0, z1))

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f24_in, U5, U6, f54_in, U7, f130_in, U8, f82_in, U9, f104_in, U10, f142_in, U11, f143_in, U12, f17_in, U13, f88_in, U14, f89_in, U15, f115_in, U16, f116_in, U17, f47_in, U18, f48_in, U19, f50_in, U20, U21, f74_in, U22, U23, f13_in, U24, f14_in, U25, f18_in, U26, f83_in, U27, f102_in, U28, f103_in, U29, f106_in, U30, f132_in, U31

Defined Pair Symbols:

F1_IN, F24_IN, F54_IN, F130_IN, F82_IN, F104_IN, F142_IN, F143_IN, F17_IN, F88_IN, F89_IN, F115_IN, F116_IN, F47_IN, F48_IN, F50_IN, U20', F74_IN, U22', F13_IN, F14_IN, F18_IN, F83_IN, F102_IN, F103_IN, F106_IN, F132_IN

Compound Symbols:

c1, c2, c3, c4, c18, c19, c23, c25, c27, c29, c31, c33, c35, c37, c39, c41, c43, c45, c47, c49, c50, c52, c53, c55, c59, c63, c66, c69, c73, c77, c80

(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, z1) → f1_out1
f1_in(z0, z1) → U1(f14_in(z0, z1), z0, z1)
f1_in(z0, z1) → U2(f13_in(z0, z1), z0, z1)
f1_in(z0, z1) → U3(f103_in(z0, z1), z0, z1)
f1_in(z0, z1) → U4(f102_in(z0, z1), z0, z1)
U1(f14_out1, z0, z1) → f1_out1
U1(f14_out2, z0, z1) → f1_out1
U1(f14_out3, z0, z1) → f1_out1
U2(f13_out1, z0, z1) → f1_out1
U2(f13_out2, z0, z1) → f1_out1
U2(f13_out3, z0, z1) → f1_out1
U3(f103_out1, z0, z1) → f1_out1
U3(f103_out2, z0, z1) → f1_out1
U3(f103_out3, z0, z1) → f1_out1
U4(f102_out1, z0, z1) → f1_out1
U4(f102_out2, z0, z1) → f1_out1
U4(f102_out3, z0, z1) → f1_out1
f24_in(z0, z1) → f24_out1
f24_in(z0, tree(z1, z2, z3)) → U5(f24_in(z0, z2), z0, tree(z1, z2, z3))
f24_in(z0, tree(z1, z2, z3)) → U6(f24_in(z0, z2), z0, tree(z1, z2, z3))
U5(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
U6(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
f54_in(0, s(z0)) → f54_out1
f54_in(s(z0), s(z1)) → U7(f54_in(z0, z1), s(z0), s(z1))
U7(f54_out1, s(z0), s(z1)) → f54_out1
f130_in(z0, tree(z1, z2, z3)) → U8(f24_in(z1, z3), z0, tree(z1, z2, z3))
U8(f24_out1, z0, tree(z1, z2, z3)) → f130_out1
f82_in(z0, tree(z1, z2, z3)) → U9(f24_in(z1, z3), z0, tree(z1, z2, z3))
U9(f24_out1, z0, tree(z1, z2, z3)) → f82_out1
f104_in(z0, tree(z1, z2, z3)) → U10(f24_in(z1, z3), z0, tree(z1, z2, z3))
U10(f24_out1, z0, tree(z1, z2, z3)) → f104_out1
f142_in(z0, tree(z1, z2, z3)) → U11(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U11(f50_out1, z0, tree(z1, z2, z3)) → f142_out1
f143_in(z0, tree(z1, z2, z3)) → U12(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U12(f74_out1, z0, tree(z1, z2, z3)) → f143_out1
f17_in(z0, tree(z1, z2, z3)) → U13(f24_in(z1, z3), z0, tree(z1, z2, z3))
U13(f24_out1, z0, tree(z1, z2, z3)) → f17_out1
f88_in(z0, tree(z1, z2, z3)) → U14(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U14(f50_out1, z0, tree(z1, z2, z3)) → f88_out1
f89_in(z0, tree(z1, z2, z3)) → U15(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U15(f74_out1, z0, tree(z1, z2, z3)) → f89_out1
f115_in(z0, tree(z1, z2, z3)) → U16(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f50_out1, z0, tree(z1, z2, z3)) → f115_out1
f116_in(z0, tree(z1, z2, z3)) → U17(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f74_out1, z0, tree(z1, z2, z3)) → f116_out1
f47_in(z0, tree(z1, z2, z3)) → U18(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U18(f50_out1, z0, tree(z1, z2, z3)) → f47_out1
f48_in(z0, tree(z1, z2, z3)) → U19(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U19(f74_out1, z0, tree(z1, z2, z3)) → f48_out1
f50_in(z0, z1, z2) → U20(f54_in(z0, z1), z0, z1, z2)
U20(f54_out1, z0, z1, z2) → U21(f1_in(z0, z2), z0, z1, z2)
U21(f1_out1, z0, z1, z2) → f50_out1
f74_in(z0, z1, z2) → U22(f54_in(z0, z1), z0, z1, z2)
U22(f54_out1, z0, z1, z2) → U23(f1_in(z1, z2), z0, z1, z2)
U23(f1_out1, z0, z1, z2) → f74_out1
f13_in(z0, z1) → U24(f82_in(z0, z1), f83_in(z0, z1), z0, z1)
U24(f82_out1, z0, z1, z2) → f13_out1
U24(z0, f83_out1, z1, z2) → f13_out2
U24(z0, f83_out2, z1, z2) → f13_out3
f14_in(z0, z1) → U25(f17_in(z0, z1), f18_in(z0, z1), z0, z1)
U25(f17_out1, z0, z1, z2) → f14_out1
U25(z0, f18_out1, z1, z2) → f14_out2
U25(z0, f18_out2, z1, z2) → f14_out3
f18_in(z0, z1) → U26(f47_in(z0, z1), f48_in(z0, z1), z0, z1)
U26(f47_out1, z0, z1, z2) → f18_out1
U26(z0, f48_out1, z1, z2) → f18_out2
f83_in(z0, z1) → U27(f88_in(z0, z1), f89_in(z0, z1), z0, z1)
U27(f88_out1, z0, z1, z2) → f83_out1
U27(z0, f89_out1, z1, z2) → f83_out2
f102_in(z0, z1) → U28(f130_in(z0, z1), f132_in(z0, z1), z0, z1)
U28(f130_out1, z0, z1, z2) → f102_out1
U28(z0, f132_out1, z1, z2) → f102_out2
U28(z0, f132_out2, z1, z2) → f102_out3
f103_in(z0, z1) → U29(f104_in(z0, z1), f106_in(z0, z1), z0, z1)
U29(f104_out1, z0, z1, z2) → f103_out1
U29(z0, f106_out1, z1, z2) → f103_out2
U29(z0, f106_out2, z1, z2) → f103_out3
f106_in(z0, z1) → U30(f115_in(z0, z1), f116_in(z0, z1), z0, z1)
U30(f115_out1, z0, z1, z2) → f106_out1
U30(z0, f116_out1, z1, z2) → f106_out2
f132_in(z0, z1) → U31(f142_in(z0, z1), f143_in(z0, z1), z0, z1)
U31(f142_out1, z0, z1, z2) → f132_out1
U31(z0, f143_out1, z1, z2) → f132_out2

Tuples:

F1_IN(z0, z1) → c1(U1'(f14_in(z0, z1), z0, z1), F14_IN(z0, z1))
F1_IN(z0, z1) → c2(U2'(f13_in(z0, z1), z0, z1), F13_IN(z0, z1))
F1_IN(z0, z1) → c3(U3'(f103_in(z0, z1), z0, z1), F103_IN(z0, z1))
F1_IN(z0, z1) → c4(U4'(f102_in(z0, z1), z0, z1), F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(U5'(f24_in(z0, z2), z0, tree(z1, z2, z3)), F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(U6'(f24_in(z0, z2), z0, tree(z1, z2, z3)), F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(U7'(f54_in(z0, z1), s(z0), s(z1)), F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(U11'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(U12'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(U14'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(U15'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(U16'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(U17'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(U18'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(U19'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F50_IN(z0, z1, z2) → c49(U20'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
U20'(f54_out1, z0, z1, z2) → c50(U21'(f1_in(z0, z2), z0, z1, z2), F1_IN(z0, z2))
F74_IN(z0, z1, z2) → c52(U22'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
U22'(f54_out1, z0, z1, z2) → c53(U23'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F13_IN(z0, z1) → c55(U24'(f82_in(z0, z1), f83_in(z0, z1), z0, z1), F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(U25'(f17_in(z0, z1), f18_in(z0, z1), z0, z1), F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(U26'(f47_in(z0, z1), f48_in(z0, z1), z0, z1), F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(U27'(f88_in(z0, z1), f89_in(z0, z1), z0, z1), F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(U28'(f130_in(z0, z1), f132_in(z0, z1), z0, z1), F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(U29'(f104_in(z0, z1), f106_in(z0, z1), z0, z1), F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(U30'(f115_in(z0, z1), f116_in(z0, z1), z0, z1), F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(U31'(f142_in(z0, z1), f143_in(z0, z1), z0, z1), F142_IN(z0, z1), F143_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c(U8'(f24_in(z1, z3), z0, tree(z1, z2, z3)))
F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(U9'(f24_in(z1, z3), z0, tree(z1, z2, z3)))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(U10'(f24_in(z1, z3), z0, tree(z1, z2, z3)))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(U13'(f24_in(z1, z3), z0, tree(z1, z2, z3)))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))

S tuples:

F1_IN(z0, z1) → c1(U1'(f14_in(z0, z1), z0, z1), F14_IN(z0, z1))
F1_IN(z0, z1) → c2(U2'(f13_in(z0, z1), z0, z1), F13_IN(z0, z1))
F1_IN(z0, z1) → c3(U3'(f103_in(z0, z1), z0, z1), F103_IN(z0, z1))
F1_IN(z0, z1) → c4(U4'(f102_in(z0, z1), z0, z1), F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(U5'(f24_in(z0, z2), z0, tree(z1, z2, z3)), F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(U6'(f24_in(z0, z2), z0, tree(z1, z2, z3)), F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(U7'(f54_in(z0, z1), s(z0), s(z1)), F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(U11'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(U12'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(U14'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(U15'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(U16'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(U17'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(U18'(f50_in(z0, z1, z2), z0, tree(z1, z2, z3)), F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(U19'(f74_in(z1, z0, z3), z0, tree(z1, z2, z3)), F74_IN(z1, z0, z3))
F50_IN(z0, z1, z2) → c49(U20'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
U20'(f54_out1, z0, z1, z2) → c50(U21'(f1_in(z0, z2), z0, z1, z2), F1_IN(z0, z2))
F74_IN(z0, z1, z2) → c52(U22'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
U22'(f54_out1, z0, z1, z2) → c53(U23'(f1_in(z1, z2), z0, z1, z2), F1_IN(z1, z2))
F13_IN(z0, z1) → c55(U24'(f82_in(z0, z1), f83_in(z0, z1), z0, z1), F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(U25'(f17_in(z0, z1), f18_in(z0, z1), z0, z1), F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(U26'(f47_in(z0, z1), f48_in(z0, z1), z0, z1), F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(U27'(f88_in(z0, z1), f89_in(z0, z1), z0, z1), F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(U28'(f130_in(z0, z1), f132_in(z0, z1), z0, z1), F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(U29'(f104_in(z0, z1), f106_in(z0, z1), z0, z1), F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(U30'(f115_in(z0, z1), f116_in(z0, z1), z0, z1), F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(U31'(f142_in(z0, z1), f143_in(z0, z1), z0, z1), F142_IN(z0, z1), F143_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c(U8'(f24_in(z1, z3), z0, tree(z1, z2, z3)))
F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(U9'(f24_in(z1, z3), z0, tree(z1, z2, z3)))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(U10'(f24_in(z1, z3), z0, tree(z1, z2, z3)))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(U13'(f24_in(z1, z3), z0, tree(z1, z2, z3)))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f24_in, U5, U6, f54_in, U7, f130_in, U8, f82_in, U9, f104_in, U10, f142_in, U11, f143_in, U12, f17_in, U13, f88_in, U14, f89_in, U15, f115_in, U16, f116_in, U17, f47_in, U18, f48_in, U19, f50_in, U20, U21, f74_in, U22, U23, f13_in, U24, f14_in, U25, f18_in, U26, f83_in, U27, f102_in, U28, f103_in, U29, f106_in, U30, f132_in, U31

Defined Pair Symbols:

F1_IN, F24_IN, F54_IN, F142_IN, F143_IN, F88_IN, F89_IN, F115_IN, F116_IN, F47_IN, F48_IN, F50_IN, U20', F74_IN, U22', F13_IN, F14_IN, F18_IN, F83_IN, F102_IN, F103_IN, F106_IN, F132_IN, F130_IN, F82_IN, F104_IN, F17_IN

Compound Symbols:

c1, c2, c3, c4, c18, c19, c23, c31, c33, c37, c39, c41, c43, c45, c47, c49, c50, c52, c53, c55, c59, c63, c66, c69, c73, c77, c80, c

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

Removed 29 trailing tuple parts

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → f1_out1
f1_in(z0, z1) → U1(f14_in(z0, z1), z0, z1)
f1_in(z0, z1) → U2(f13_in(z0, z1), z0, z1)
f1_in(z0, z1) → U3(f103_in(z0, z1), z0, z1)
f1_in(z0, z1) → U4(f102_in(z0, z1), z0, z1)
U1(f14_out1, z0, z1) → f1_out1
U1(f14_out2, z0, z1) → f1_out1
U1(f14_out3, z0, z1) → f1_out1
U2(f13_out1, z0, z1) → f1_out1
U2(f13_out2, z0, z1) → f1_out1
U2(f13_out3, z0, z1) → f1_out1
U3(f103_out1, z0, z1) → f1_out1
U3(f103_out2, z0, z1) → f1_out1
U3(f103_out3, z0, z1) → f1_out1
U4(f102_out1, z0, z1) → f1_out1
U4(f102_out2, z0, z1) → f1_out1
U4(f102_out3, z0, z1) → f1_out1
f24_in(z0, z1) → f24_out1
f24_in(z0, tree(z1, z2, z3)) → U5(f24_in(z0, z2), z0, tree(z1, z2, z3))
f24_in(z0, tree(z1, z2, z3)) → U6(f24_in(z0, z2), z0, tree(z1, z2, z3))
U5(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
U6(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
f54_in(0, s(z0)) → f54_out1
f54_in(s(z0), s(z1)) → U7(f54_in(z0, z1), s(z0), s(z1))
U7(f54_out1, s(z0), s(z1)) → f54_out1
f130_in(z0, tree(z1, z2, z3)) → U8(f24_in(z1, z3), z0, tree(z1, z2, z3))
U8(f24_out1, z0, tree(z1, z2, z3)) → f130_out1
f82_in(z0, tree(z1, z2, z3)) → U9(f24_in(z1, z3), z0, tree(z1, z2, z3))
U9(f24_out1, z0, tree(z1, z2, z3)) → f82_out1
f104_in(z0, tree(z1, z2, z3)) → U10(f24_in(z1, z3), z0, tree(z1, z2, z3))
U10(f24_out1, z0, tree(z1, z2, z3)) → f104_out1
f142_in(z0, tree(z1, z2, z3)) → U11(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U11(f50_out1, z0, tree(z1, z2, z3)) → f142_out1
f143_in(z0, tree(z1, z2, z3)) → U12(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U12(f74_out1, z0, tree(z1, z2, z3)) → f143_out1
f17_in(z0, tree(z1, z2, z3)) → U13(f24_in(z1, z3), z0, tree(z1, z2, z3))
U13(f24_out1, z0, tree(z1, z2, z3)) → f17_out1
f88_in(z0, tree(z1, z2, z3)) → U14(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U14(f50_out1, z0, tree(z1, z2, z3)) → f88_out1
f89_in(z0, tree(z1, z2, z3)) → U15(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U15(f74_out1, z0, tree(z1, z2, z3)) → f89_out1
f115_in(z0, tree(z1, z2, z3)) → U16(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f50_out1, z0, tree(z1, z2, z3)) → f115_out1
f116_in(z0, tree(z1, z2, z3)) → U17(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f74_out1, z0, tree(z1, z2, z3)) → f116_out1
f47_in(z0, tree(z1, z2, z3)) → U18(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U18(f50_out1, z0, tree(z1, z2, z3)) → f47_out1
f48_in(z0, tree(z1, z2, z3)) → U19(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U19(f74_out1, z0, tree(z1, z2, z3)) → f48_out1
f50_in(z0, z1, z2) → U20(f54_in(z0, z1), z0, z1, z2)
U20(f54_out1, z0, z1, z2) → U21(f1_in(z0, z2), z0, z1, z2)
U21(f1_out1, z0, z1, z2) → f50_out1
f74_in(z0, z1, z2) → U22(f54_in(z0, z1), z0, z1, z2)
U22(f54_out1, z0, z1, z2) → U23(f1_in(z1, z2), z0, z1, z2)
U23(f1_out1, z0, z1, z2) → f74_out1
f13_in(z0, z1) → U24(f82_in(z0, z1), f83_in(z0, z1), z0, z1)
U24(f82_out1, z0, z1, z2) → f13_out1
U24(z0, f83_out1, z1, z2) → f13_out2
U24(z0, f83_out2, z1, z2) → f13_out3
f14_in(z0, z1) → U25(f17_in(z0, z1), f18_in(z0, z1), z0, z1)
U25(f17_out1, z0, z1, z2) → f14_out1
U25(z0, f18_out1, z1, z2) → f14_out2
U25(z0, f18_out2, z1, z2) → f14_out3
f18_in(z0, z1) → U26(f47_in(z0, z1), f48_in(z0, z1), z0, z1)
U26(f47_out1, z0, z1, z2) → f18_out1
U26(z0, f48_out1, z1, z2) → f18_out2
f83_in(z0, z1) → U27(f88_in(z0, z1), f89_in(z0, z1), z0, z1)
U27(f88_out1, z0, z1, z2) → f83_out1
U27(z0, f89_out1, z1, z2) → f83_out2
f102_in(z0, z1) → U28(f130_in(z0, z1), f132_in(z0, z1), z0, z1)
U28(f130_out1, z0, z1, z2) → f102_out1
U28(z0, f132_out1, z1, z2) → f102_out2
U28(z0, f132_out2, z1, z2) → f102_out3
f103_in(z0, z1) → U29(f104_in(z0, z1), f106_in(z0, z1), z0, z1)
U29(f104_out1, z0, z1, z2) → f103_out1
U29(z0, f106_out1, z1, z2) → f103_out2
U29(z0, f106_out2, z1, z2) → f103_out3
f106_in(z0, z1) → U30(f115_in(z0, z1), f116_in(z0, z1), z0, z1)
U30(f115_out1, z0, z1, z2) → f106_out1
U30(z0, f116_out1, z1, z2) → f106_out2
f132_in(z0, z1) → U31(f142_in(z0, z1), f143_in(z0, z1), z0, z1)
U31(f142_out1, z0, z1, z2) → f132_out1
U31(z0, f143_out1, z1, z2) → f132_out2

Tuples:

F50_IN(z0, z1, z2) → c49(U20'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
F74_IN(z0, z1, z2) → c52(U22'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c
F82_IN(z0, tree(z1, z2, z3)) → c
F104_IN(z0, tree(z1, z2, z3)) → c
F17_IN(z0, tree(z1, z2, z3)) → c

S tuples:

F50_IN(z0, z1, z2) → c49(U20'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
F74_IN(z0, z1, z2) → c52(U22'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c
F82_IN(z0, tree(z1, z2, z3)) → c
F104_IN(z0, tree(z1, z2, z3)) → c
F17_IN(z0, tree(z1, z2, z3)) → c

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f24_in, U5, U6, f54_in, U7, f130_in, U8, f82_in, U9, f104_in, U10, f142_in, U11, f143_in, U12, f17_in, U13, f88_in, U14, f89_in, U15, f115_in, U16, f116_in, U17, f47_in, U18, f48_in, U19, f50_in, U20, U21, f74_in, U22, U23, f13_in, U24, f14_in, U25, f18_in, U26, f83_in, U27, f102_in, U28, f103_in, U29, f106_in, U30, f132_in, U31

Defined Pair Symbols:

F50_IN, F74_IN, F130_IN, F82_IN, F104_IN, F17_IN, F1_IN, F24_IN, F54_IN, F142_IN, F143_IN, F88_IN, F89_IN, F115_IN, F116_IN, F47_IN, F48_IN, U20', U22', F13_IN, F14_IN, F18_IN, F83_IN, F102_IN, F103_IN, F106_IN, F132_IN

Compound Symbols:

c49, c52, c, c1, c2, c3, c4, c18, c19, c23, c31, c33, c37, c39, c41, c43, c45, c47, c50, c53, c55, c59, c63, c66, c69, c73, c77, c80, c

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

Use narrowing to replace F50_IN(z0, z1, z2) → c49(U20'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1)) by

F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2), F54_IN(0, s(z0)))
F50_IN(s(z0), s(z1), x2) → c49(U20'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → f1_out1
f1_in(z0, z1) → U1(f14_in(z0, z1), z0, z1)
f1_in(z0, z1) → U2(f13_in(z0, z1), z0, z1)
f1_in(z0, z1) → U3(f103_in(z0, z1), z0, z1)
f1_in(z0, z1) → U4(f102_in(z0, z1), z0, z1)
U1(f14_out1, z0, z1) → f1_out1
U1(f14_out2, z0, z1) → f1_out1
U1(f14_out3, z0, z1) → f1_out1
U2(f13_out1, z0, z1) → f1_out1
U2(f13_out2, z0, z1) → f1_out1
U2(f13_out3, z0, z1) → f1_out1
U3(f103_out1, z0, z1) → f1_out1
U3(f103_out2, z0, z1) → f1_out1
U3(f103_out3, z0, z1) → f1_out1
U4(f102_out1, z0, z1) → f1_out1
U4(f102_out2, z0, z1) → f1_out1
U4(f102_out3, z0, z1) → f1_out1
f24_in(z0, z1) → f24_out1
f24_in(z0, tree(z1, z2, z3)) → U5(f24_in(z0, z2), z0, tree(z1, z2, z3))
f24_in(z0, tree(z1, z2, z3)) → U6(f24_in(z0, z2), z0, tree(z1, z2, z3))
U5(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
U6(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
f54_in(0, s(z0)) → f54_out1
f54_in(s(z0), s(z1)) → U7(f54_in(z0, z1), s(z0), s(z1))
U7(f54_out1, s(z0), s(z1)) → f54_out1
f130_in(z0, tree(z1, z2, z3)) → U8(f24_in(z1, z3), z0, tree(z1, z2, z3))
U8(f24_out1, z0, tree(z1, z2, z3)) → f130_out1
f82_in(z0, tree(z1, z2, z3)) → U9(f24_in(z1, z3), z0, tree(z1, z2, z3))
U9(f24_out1, z0, tree(z1, z2, z3)) → f82_out1
f104_in(z0, tree(z1, z2, z3)) → U10(f24_in(z1, z3), z0, tree(z1, z2, z3))
U10(f24_out1, z0, tree(z1, z2, z3)) → f104_out1
f142_in(z0, tree(z1, z2, z3)) → U11(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U11(f50_out1, z0, tree(z1, z2, z3)) → f142_out1
f143_in(z0, tree(z1, z2, z3)) → U12(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U12(f74_out1, z0, tree(z1, z2, z3)) → f143_out1
f17_in(z0, tree(z1, z2, z3)) → U13(f24_in(z1, z3), z0, tree(z1, z2, z3))
U13(f24_out1, z0, tree(z1, z2, z3)) → f17_out1
f88_in(z0, tree(z1, z2, z3)) → U14(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U14(f50_out1, z0, tree(z1, z2, z3)) → f88_out1
f89_in(z0, tree(z1, z2, z3)) → U15(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U15(f74_out1, z0, tree(z1, z2, z3)) → f89_out1
f115_in(z0, tree(z1, z2, z3)) → U16(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f50_out1, z0, tree(z1, z2, z3)) → f115_out1
f116_in(z0, tree(z1, z2, z3)) → U17(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f74_out1, z0, tree(z1, z2, z3)) → f116_out1
f47_in(z0, tree(z1, z2, z3)) → U18(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U18(f50_out1, z0, tree(z1, z2, z3)) → f47_out1
f48_in(z0, tree(z1, z2, z3)) → U19(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U19(f74_out1, z0, tree(z1, z2, z3)) → f48_out1
f50_in(z0, z1, z2) → U20(f54_in(z0, z1), z0, z1, z2)
U20(f54_out1, z0, z1, z2) → U21(f1_in(z0, z2), z0, z1, z2)
U21(f1_out1, z0, z1, z2) → f50_out1
f74_in(z0, z1, z2) → U22(f54_in(z0, z1), z0, z1, z2)
U22(f54_out1, z0, z1, z2) → U23(f1_in(z1, z2), z0, z1, z2)
U23(f1_out1, z0, z1, z2) → f74_out1
f13_in(z0, z1) → U24(f82_in(z0, z1), f83_in(z0, z1), z0, z1)
U24(f82_out1, z0, z1, z2) → f13_out1
U24(z0, f83_out1, z1, z2) → f13_out2
U24(z0, f83_out2, z1, z2) → f13_out3
f14_in(z0, z1) → U25(f17_in(z0, z1), f18_in(z0, z1), z0, z1)
U25(f17_out1, z0, z1, z2) → f14_out1
U25(z0, f18_out1, z1, z2) → f14_out2
U25(z0, f18_out2, z1, z2) → f14_out3
f18_in(z0, z1) → U26(f47_in(z0, z1), f48_in(z0, z1), z0, z1)
U26(f47_out1, z0, z1, z2) → f18_out1
U26(z0, f48_out1, z1, z2) → f18_out2
f83_in(z0, z1) → U27(f88_in(z0, z1), f89_in(z0, z1), z0, z1)
U27(f88_out1, z0, z1, z2) → f83_out1
U27(z0, f89_out1, z1, z2) → f83_out2
f102_in(z0, z1) → U28(f130_in(z0, z1), f132_in(z0, z1), z0, z1)
U28(f130_out1, z0, z1, z2) → f102_out1
U28(z0, f132_out1, z1, z2) → f102_out2
U28(z0, f132_out2, z1, z2) → f102_out3
f103_in(z0, z1) → U29(f104_in(z0, z1), f106_in(z0, z1), z0, z1)
U29(f104_out1, z0, z1, z2) → f103_out1
U29(z0, f106_out1, z1, z2) → f103_out2
U29(z0, f106_out2, z1, z2) → f103_out3
f106_in(z0, z1) → U30(f115_in(z0, z1), f116_in(z0, z1), z0, z1)
U30(f115_out1, z0, z1, z2) → f106_out1
U30(z0, f116_out1, z1, z2) → f106_out2
f132_in(z0, z1) → U31(f142_in(z0, z1), f143_in(z0, z1), z0, z1)
U31(f142_out1, z0, z1, z2) → f132_out1
U31(z0, f143_out1, z1, z2) → f132_out2

Tuples:

F74_IN(z0, z1, z2) → c52(U22'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c
F82_IN(z0, tree(z1, z2, z3)) → c
F104_IN(z0, tree(z1, z2, z3)) → c
F17_IN(z0, tree(z1, z2, z3)) → c
F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2), F54_IN(0, s(z0)))
F50_IN(s(z0), s(z1), x2) → c49(U20'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))

S tuples:

F74_IN(z0, z1, z2) → c52(U22'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c
F82_IN(z0, tree(z1, z2, z3)) → c
F104_IN(z0, tree(z1, z2, z3)) → c
F17_IN(z0, tree(z1, z2, z3)) → c
F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2), F54_IN(0, s(z0)))
F50_IN(s(z0), s(z1), x2) → c49(U20'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f24_in, U5, U6, f54_in, U7, f130_in, U8, f82_in, U9, f104_in, U10, f142_in, U11, f143_in, U12, f17_in, U13, f88_in, U14, f89_in, U15, f115_in, U16, f116_in, U17, f47_in, U18, f48_in, U19, f50_in, U20, U21, f74_in, U22, U23, f13_in, U24, f14_in, U25, f18_in, U26, f83_in, U27, f102_in, U28, f103_in, U29, f106_in, U30, f132_in, U31

Defined Pair Symbols:

F74_IN, F130_IN, F82_IN, F104_IN, F17_IN, F1_IN, F24_IN, F54_IN, F142_IN, F143_IN, F88_IN, F89_IN, F115_IN, F116_IN, F47_IN, F48_IN, U20', U22', F13_IN, F14_IN, F18_IN, F83_IN, F102_IN, F103_IN, F106_IN, F132_IN, F50_IN

Compound Symbols:

c52, c, c1, c2, c3, c4, c18, c19, c23, c31, c33, c37, c39, c41, c43, c45, c47, c50, c53, c55, c59, c63, c66, c69, c73, c77, c80, c, c49

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

Split RHS of tuples not part of any SCC

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → f1_out1
f1_in(z0, z1) → U1(f14_in(z0, z1), z0, z1)
f1_in(z0, z1) → U2(f13_in(z0, z1), z0, z1)
f1_in(z0, z1) → U3(f103_in(z0, z1), z0, z1)
f1_in(z0, z1) → U4(f102_in(z0, z1), z0, z1)
U1(f14_out1, z0, z1) → f1_out1
U1(f14_out2, z0, z1) → f1_out1
U1(f14_out3, z0, z1) → f1_out1
U2(f13_out1, z0, z1) → f1_out1
U2(f13_out2, z0, z1) → f1_out1
U2(f13_out3, z0, z1) → f1_out1
U3(f103_out1, z0, z1) → f1_out1
U3(f103_out2, z0, z1) → f1_out1
U3(f103_out3, z0, z1) → f1_out1
U4(f102_out1, z0, z1) → f1_out1
U4(f102_out2, z0, z1) → f1_out1
U4(f102_out3, z0, z1) → f1_out1
f24_in(z0, z1) → f24_out1
f24_in(z0, tree(z1, z2, z3)) → U5(f24_in(z0, z2), z0, tree(z1, z2, z3))
f24_in(z0, tree(z1, z2, z3)) → U6(f24_in(z0, z2), z0, tree(z1, z2, z3))
U5(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
U6(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
f54_in(0, s(z0)) → f54_out1
f54_in(s(z0), s(z1)) → U7(f54_in(z0, z1), s(z0), s(z1))
U7(f54_out1, s(z0), s(z1)) → f54_out1
f130_in(z0, tree(z1, z2, z3)) → U8(f24_in(z1, z3), z0, tree(z1, z2, z3))
U8(f24_out1, z0, tree(z1, z2, z3)) → f130_out1
f82_in(z0, tree(z1, z2, z3)) → U9(f24_in(z1, z3), z0, tree(z1, z2, z3))
U9(f24_out1, z0, tree(z1, z2, z3)) → f82_out1
f104_in(z0, tree(z1, z2, z3)) → U10(f24_in(z1, z3), z0, tree(z1, z2, z3))
U10(f24_out1, z0, tree(z1, z2, z3)) → f104_out1
f142_in(z0, tree(z1, z2, z3)) → U11(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U11(f50_out1, z0, tree(z1, z2, z3)) → f142_out1
f143_in(z0, tree(z1, z2, z3)) → U12(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U12(f74_out1, z0, tree(z1, z2, z3)) → f143_out1
f17_in(z0, tree(z1, z2, z3)) → U13(f24_in(z1, z3), z0, tree(z1, z2, z3))
U13(f24_out1, z0, tree(z1, z2, z3)) → f17_out1
f88_in(z0, tree(z1, z2, z3)) → U14(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U14(f50_out1, z0, tree(z1, z2, z3)) → f88_out1
f89_in(z0, tree(z1, z2, z3)) → U15(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U15(f74_out1, z0, tree(z1, z2, z3)) → f89_out1
f115_in(z0, tree(z1, z2, z3)) → U16(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f50_out1, z0, tree(z1, z2, z3)) → f115_out1
f116_in(z0, tree(z1, z2, z3)) → U17(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f74_out1, z0, tree(z1, z2, z3)) → f116_out1
f47_in(z0, tree(z1, z2, z3)) → U18(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U18(f50_out1, z0, tree(z1, z2, z3)) → f47_out1
f48_in(z0, tree(z1, z2, z3)) → U19(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U19(f74_out1, z0, tree(z1, z2, z3)) → f48_out1
f50_in(z0, z1, z2) → U20(f54_in(z0, z1), z0, z1, z2)
U20(f54_out1, z0, z1, z2) → U21(f1_in(z0, z2), z0, z1, z2)
U21(f1_out1, z0, z1, z2) → f50_out1
f74_in(z0, z1, z2) → U22(f54_in(z0, z1), z0, z1, z2)
U22(f54_out1, z0, z1, z2) → U23(f1_in(z1, z2), z0, z1, z2)
U23(f1_out1, z0, z1, z2) → f74_out1
f13_in(z0, z1) → U24(f82_in(z0, z1), f83_in(z0, z1), z0, z1)
U24(f82_out1, z0, z1, z2) → f13_out1
U24(z0, f83_out1, z1, z2) → f13_out2
U24(z0, f83_out2, z1, z2) → f13_out3
f14_in(z0, z1) → U25(f17_in(z0, z1), f18_in(z0, z1), z0, z1)
U25(f17_out1, z0, z1, z2) → f14_out1
U25(z0, f18_out1, z1, z2) → f14_out2
U25(z0, f18_out2, z1, z2) → f14_out3
f18_in(z0, z1) → U26(f47_in(z0, z1), f48_in(z0, z1), z0, z1)
U26(f47_out1, z0, z1, z2) → f18_out1
U26(z0, f48_out1, z1, z2) → f18_out2
f83_in(z0, z1) → U27(f88_in(z0, z1), f89_in(z0, z1), z0, z1)
U27(f88_out1, z0, z1, z2) → f83_out1
U27(z0, f89_out1, z1, z2) → f83_out2
f102_in(z0, z1) → U28(f130_in(z0, z1), f132_in(z0, z1), z0, z1)
U28(f130_out1, z0, z1, z2) → f102_out1
U28(z0, f132_out1, z1, z2) → f102_out2
U28(z0, f132_out2, z1, z2) → f102_out3
f103_in(z0, z1) → U29(f104_in(z0, z1), f106_in(z0, z1), z0, z1)
U29(f104_out1, z0, z1, z2) → f103_out1
U29(z0, f106_out1, z1, z2) → f103_out2
U29(z0, f106_out2, z1, z2) → f103_out3
f106_in(z0, z1) → U30(f115_in(z0, z1), f116_in(z0, z1), z0, z1)
U30(f115_out1, z0, z1, z2) → f106_out1
U30(z0, f116_out1, z1, z2) → f106_out2
f132_in(z0, z1) → U31(f142_in(z0, z1), f143_in(z0, z1), z0, z1)
U31(f142_out1, z0, z1, z2) → f132_out1
U31(z0, f143_out1, z1, z2) → f132_out2

Tuples:

F74_IN(z0, z1, z2) → c52(U22'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2), F54_IN(0, s(z0)))
F50_IN(s(z0), s(z1), x2) → c49(U20'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))

S tuples:

F74_IN(z0, z1, z2) → c52(U22'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2), F54_IN(0, s(z0)))
F50_IN(s(z0), s(z1), x2) → c49(U20'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f24_in, U5, U6, f54_in, U7, f130_in, U8, f82_in, U9, f104_in, U10, f142_in, U11, f143_in, U12, f17_in, U13, f88_in, U14, f89_in, U15, f115_in, U16, f116_in, U17, f47_in, U18, f48_in, U19, f50_in, U20, U21, f74_in, U22, U23, f13_in, U24, f14_in, U25, f18_in, U26, f83_in, U27, f102_in, U28, f103_in, U29, f106_in, U30, f132_in, U31

Defined Pair Symbols:

F74_IN, F130_IN, F82_IN, F104_IN, F17_IN, F1_IN, F24_IN, F54_IN, F142_IN, F143_IN, F88_IN, F89_IN, F115_IN, F116_IN, F47_IN, F48_IN, U20', U22', F13_IN, F14_IN, F18_IN, F83_IN, F102_IN, F103_IN, F106_IN, F132_IN, F50_IN

Compound Symbols:

c52, c, c1, c2, c3, c4, c18, c19, c23, c31, c33, c37, c39, c41, c43, c45, c47, c50, c53, c55, c59, c63, c66, c69, c73, c77, c80, c49

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

Removed 1 trailing tuple parts

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → f1_out1
f1_in(z0, z1) → U1(f14_in(z0, z1), z0, z1)
f1_in(z0, z1) → U2(f13_in(z0, z1), z0, z1)
f1_in(z0, z1) → U3(f103_in(z0, z1), z0, z1)
f1_in(z0, z1) → U4(f102_in(z0, z1), z0, z1)
U1(f14_out1, z0, z1) → f1_out1
U1(f14_out2, z0, z1) → f1_out1
U1(f14_out3, z0, z1) → f1_out1
U2(f13_out1, z0, z1) → f1_out1
U2(f13_out2, z0, z1) → f1_out1
U2(f13_out3, z0, z1) → f1_out1
U3(f103_out1, z0, z1) → f1_out1
U3(f103_out2, z0, z1) → f1_out1
U3(f103_out3, z0, z1) → f1_out1
U4(f102_out1, z0, z1) → f1_out1
U4(f102_out2, z0, z1) → f1_out1
U4(f102_out3, z0, z1) → f1_out1
f24_in(z0, z1) → f24_out1
f24_in(z0, tree(z1, z2, z3)) → U5(f24_in(z0, z2), z0, tree(z1, z2, z3))
f24_in(z0, tree(z1, z2, z3)) → U6(f24_in(z0, z2), z0, tree(z1, z2, z3))
U5(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
U6(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
f54_in(0, s(z0)) → f54_out1
f54_in(s(z0), s(z1)) → U7(f54_in(z0, z1), s(z0), s(z1))
U7(f54_out1, s(z0), s(z1)) → f54_out1
f130_in(z0, tree(z1, z2, z3)) → U8(f24_in(z1, z3), z0, tree(z1, z2, z3))
U8(f24_out1, z0, tree(z1, z2, z3)) → f130_out1
f82_in(z0, tree(z1, z2, z3)) → U9(f24_in(z1, z3), z0, tree(z1, z2, z3))
U9(f24_out1, z0, tree(z1, z2, z3)) → f82_out1
f104_in(z0, tree(z1, z2, z3)) → U10(f24_in(z1, z3), z0, tree(z1, z2, z3))
U10(f24_out1, z0, tree(z1, z2, z3)) → f104_out1
f142_in(z0, tree(z1, z2, z3)) → U11(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U11(f50_out1, z0, tree(z1, z2, z3)) → f142_out1
f143_in(z0, tree(z1, z2, z3)) → U12(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U12(f74_out1, z0, tree(z1, z2, z3)) → f143_out1
f17_in(z0, tree(z1, z2, z3)) → U13(f24_in(z1, z3), z0, tree(z1, z2, z3))
U13(f24_out1, z0, tree(z1, z2, z3)) → f17_out1
f88_in(z0, tree(z1, z2, z3)) → U14(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U14(f50_out1, z0, tree(z1, z2, z3)) → f88_out1
f89_in(z0, tree(z1, z2, z3)) → U15(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U15(f74_out1, z0, tree(z1, z2, z3)) → f89_out1
f115_in(z0, tree(z1, z2, z3)) → U16(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f50_out1, z0, tree(z1, z2, z3)) → f115_out1
f116_in(z0, tree(z1, z2, z3)) → U17(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f74_out1, z0, tree(z1, z2, z3)) → f116_out1
f47_in(z0, tree(z1, z2, z3)) → U18(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U18(f50_out1, z0, tree(z1, z2, z3)) → f47_out1
f48_in(z0, tree(z1, z2, z3)) → U19(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U19(f74_out1, z0, tree(z1, z2, z3)) → f48_out1
f50_in(z0, z1, z2) → U20(f54_in(z0, z1), z0, z1, z2)
U20(f54_out1, z0, z1, z2) → U21(f1_in(z0, z2), z0, z1, z2)
U21(f1_out1, z0, z1, z2) → f50_out1
f74_in(z0, z1, z2) → U22(f54_in(z0, z1), z0, z1, z2)
U22(f54_out1, z0, z1, z2) → U23(f1_in(z1, z2), z0, z1, z2)
U23(f1_out1, z0, z1, z2) → f74_out1
f13_in(z0, z1) → U24(f82_in(z0, z1), f83_in(z0, z1), z0, z1)
U24(f82_out1, z0, z1, z2) → f13_out1
U24(z0, f83_out1, z1, z2) → f13_out2
U24(z0, f83_out2, z1, z2) → f13_out3
f14_in(z0, z1) → U25(f17_in(z0, z1), f18_in(z0, z1), z0, z1)
U25(f17_out1, z0, z1, z2) → f14_out1
U25(z0, f18_out1, z1, z2) → f14_out2
U25(z0, f18_out2, z1, z2) → f14_out3
f18_in(z0, z1) → U26(f47_in(z0, z1), f48_in(z0, z1), z0, z1)
U26(f47_out1, z0, z1, z2) → f18_out1
U26(z0, f48_out1, z1, z2) → f18_out2
f83_in(z0, z1) → U27(f88_in(z0, z1), f89_in(z0, z1), z0, z1)
U27(f88_out1, z0, z1, z2) → f83_out1
U27(z0, f89_out1, z1, z2) → f83_out2
f102_in(z0, z1) → U28(f130_in(z0, z1), f132_in(z0, z1), z0, z1)
U28(f130_out1, z0, z1, z2) → f102_out1
U28(z0, f132_out1, z1, z2) → f102_out2
U28(z0, f132_out2, z1, z2) → f102_out3
f103_in(z0, z1) → U29(f104_in(z0, z1), f106_in(z0, z1), z0, z1)
U29(f104_out1, z0, z1, z2) → f103_out1
U29(z0, f106_out1, z1, z2) → f103_out2
U29(z0, f106_out2, z1, z2) → f103_out3
f106_in(z0, z1) → U30(f115_in(z0, z1), f116_in(z0, z1), z0, z1)
U30(f115_out1, z0, z1, z2) → f106_out1
U30(z0, f116_out1, z1, z2) → f106_out2
f132_in(z0, z1) → U31(f142_in(z0, z1), f143_in(z0, z1), z0, z1)
U31(f142_out1, z0, z1, z2) → f132_out1
U31(z0, f143_out1, z1, z2) → f132_out2

Tuples:

F74_IN(z0, z1, z2) → c52(U22'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F50_IN(s(z0), s(z1), x2) → c49(U20'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2))

S tuples:

F74_IN(z0, z1, z2) → c52(U22'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1))
F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F50_IN(s(z0), s(z1), x2) → c49(U20'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2))

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f24_in, U5, U6, f54_in, U7, f130_in, U8, f82_in, U9, f104_in, U10, f142_in, U11, f143_in, U12, f17_in, U13, f88_in, U14, f89_in, U15, f115_in, U16, f116_in, U17, f47_in, U18, f48_in, U19, f50_in, U20, U21, f74_in, U22, U23, f13_in, U24, f14_in, U25, f18_in, U26, f83_in, U27, f102_in, U28, f103_in, U29, f106_in, U30, f132_in, U31

Defined Pair Symbols:

F74_IN, F130_IN, F82_IN, F104_IN, F17_IN, F1_IN, F24_IN, F54_IN, F142_IN, F143_IN, F88_IN, F89_IN, F115_IN, F116_IN, F47_IN, F48_IN, U20', U22', F13_IN, F14_IN, F18_IN, F83_IN, F102_IN, F103_IN, F106_IN, F132_IN, F50_IN

Compound Symbols:

c52, c, c1, c2, c3, c4, c18, c19, c23, c31, c33, c37, c39, c41, c43, c45, c47, c50, c53, c55, c59, c63, c66, c69, c73, c77, c80, c49, c49

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

Use narrowing to replace F74_IN(z0, z1, z2) → c52(U22'(f54_in(z0, z1), z0, z1, z2), F54_IN(z0, z1)) by

F74_IN(0, s(z0), x2) → c52(U22'(f54_out1, 0, s(z0), x2), F54_IN(0, s(z0)))
F74_IN(s(z0), s(z1), x2) → c52(U22'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → f1_out1
f1_in(z0, z1) → U1(f14_in(z0, z1), z0, z1)
f1_in(z0, z1) → U2(f13_in(z0, z1), z0, z1)
f1_in(z0, z1) → U3(f103_in(z0, z1), z0, z1)
f1_in(z0, z1) → U4(f102_in(z0, z1), z0, z1)
U1(f14_out1, z0, z1) → f1_out1
U1(f14_out2, z0, z1) → f1_out1
U1(f14_out3, z0, z1) → f1_out1
U2(f13_out1, z0, z1) → f1_out1
U2(f13_out2, z0, z1) → f1_out1
U2(f13_out3, z0, z1) → f1_out1
U3(f103_out1, z0, z1) → f1_out1
U3(f103_out2, z0, z1) → f1_out1
U3(f103_out3, z0, z1) → f1_out1
U4(f102_out1, z0, z1) → f1_out1
U4(f102_out2, z0, z1) → f1_out1
U4(f102_out3, z0, z1) → f1_out1
f24_in(z0, z1) → f24_out1
f24_in(z0, tree(z1, z2, z3)) → U5(f24_in(z0, z2), z0, tree(z1, z2, z3))
f24_in(z0, tree(z1, z2, z3)) → U6(f24_in(z0, z2), z0, tree(z1, z2, z3))
U5(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
U6(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
f54_in(0, s(z0)) → f54_out1
f54_in(s(z0), s(z1)) → U7(f54_in(z0, z1), s(z0), s(z1))
U7(f54_out1, s(z0), s(z1)) → f54_out1
f130_in(z0, tree(z1, z2, z3)) → U8(f24_in(z1, z3), z0, tree(z1, z2, z3))
U8(f24_out1, z0, tree(z1, z2, z3)) → f130_out1
f82_in(z0, tree(z1, z2, z3)) → U9(f24_in(z1, z3), z0, tree(z1, z2, z3))
U9(f24_out1, z0, tree(z1, z2, z3)) → f82_out1
f104_in(z0, tree(z1, z2, z3)) → U10(f24_in(z1, z3), z0, tree(z1, z2, z3))
U10(f24_out1, z0, tree(z1, z2, z3)) → f104_out1
f142_in(z0, tree(z1, z2, z3)) → U11(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U11(f50_out1, z0, tree(z1, z2, z3)) → f142_out1
f143_in(z0, tree(z1, z2, z3)) → U12(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U12(f74_out1, z0, tree(z1, z2, z3)) → f143_out1
f17_in(z0, tree(z1, z2, z3)) → U13(f24_in(z1, z3), z0, tree(z1, z2, z3))
U13(f24_out1, z0, tree(z1, z2, z3)) → f17_out1
f88_in(z0, tree(z1, z2, z3)) → U14(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U14(f50_out1, z0, tree(z1, z2, z3)) → f88_out1
f89_in(z0, tree(z1, z2, z3)) → U15(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U15(f74_out1, z0, tree(z1, z2, z3)) → f89_out1
f115_in(z0, tree(z1, z2, z3)) → U16(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f50_out1, z0, tree(z1, z2, z3)) → f115_out1
f116_in(z0, tree(z1, z2, z3)) → U17(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f74_out1, z0, tree(z1, z2, z3)) → f116_out1
f47_in(z0, tree(z1, z2, z3)) → U18(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U18(f50_out1, z0, tree(z1, z2, z3)) → f47_out1
f48_in(z0, tree(z1, z2, z3)) → U19(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U19(f74_out1, z0, tree(z1, z2, z3)) → f48_out1
f50_in(z0, z1, z2) → U20(f54_in(z0, z1), z0, z1, z2)
U20(f54_out1, z0, z1, z2) → U21(f1_in(z0, z2), z0, z1, z2)
U21(f1_out1, z0, z1, z2) → f50_out1
f74_in(z0, z1, z2) → U22(f54_in(z0, z1), z0, z1, z2)
U22(f54_out1, z0, z1, z2) → U23(f1_in(z1, z2), z0, z1, z2)
U23(f1_out1, z0, z1, z2) → f74_out1
f13_in(z0, z1) → U24(f82_in(z0, z1), f83_in(z0, z1), z0, z1)
U24(f82_out1, z0, z1, z2) → f13_out1
U24(z0, f83_out1, z1, z2) → f13_out2
U24(z0, f83_out2, z1, z2) → f13_out3
f14_in(z0, z1) → U25(f17_in(z0, z1), f18_in(z0, z1), z0, z1)
U25(f17_out1, z0, z1, z2) → f14_out1
U25(z0, f18_out1, z1, z2) → f14_out2
U25(z0, f18_out2, z1, z2) → f14_out3
f18_in(z0, z1) → U26(f47_in(z0, z1), f48_in(z0, z1), z0, z1)
U26(f47_out1, z0, z1, z2) → f18_out1
U26(z0, f48_out1, z1, z2) → f18_out2
f83_in(z0, z1) → U27(f88_in(z0, z1), f89_in(z0, z1), z0, z1)
U27(f88_out1, z0, z1, z2) → f83_out1
U27(z0, f89_out1, z1, z2) → f83_out2
f102_in(z0, z1) → U28(f130_in(z0, z1), f132_in(z0, z1), z0, z1)
U28(f130_out1, z0, z1, z2) → f102_out1
U28(z0, f132_out1, z1, z2) → f102_out2
U28(z0, f132_out2, z1, z2) → f102_out3
f103_in(z0, z1) → U29(f104_in(z0, z1), f106_in(z0, z1), z0, z1)
U29(f104_out1, z0, z1, z2) → f103_out1
U29(z0, f106_out1, z1, z2) → f103_out2
U29(z0, f106_out2, z1, z2) → f103_out3
f106_in(z0, z1) → U30(f115_in(z0, z1), f116_in(z0, z1), z0, z1)
U30(f115_out1, z0, z1, z2) → f106_out1
U30(z0, f116_out1, z1, z2) → f106_out2
f132_in(z0, z1) → U31(f142_in(z0, z1), f143_in(z0, z1), z0, z1)
U31(f142_out1, z0, z1, z2) → f132_out1
U31(z0, f143_out1, z1, z2) → f132_out2

Tuples:

F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F50_IN(s(z0), s(z1), x2) → c49(U20'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2))
F74_IN(0, s(z0), x2) → c52(U22'(f54_out1, 0, s(z0), x2), F54_IN(0, s(z0)))
F74_IN(s(z0), s(z1), x2) → c52(U22'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))

S tuples:

F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F50_IN(s(z0), s(z1), x2) → c49(U20'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2))
F74_IN(0, s(z0), x2) → c52(U22'(f54_out1, 0, s(z0), x2), F54_IN(0, s(z0)))
F74_IN(s(z0), s(z1), x2) → c52(U22'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f24_in, U5, U6, f54_in, U7, f130_in, U8, f82_in, U9, f104_in, U10, f142_in, U11, f143_in, U12, f17_in, U13, f88_in, U14, f89_in, U15, f115_in, U16, f116_in, U17, f47_in, U18, f48_in, U19, f50_in, U20, U21, f74_in, U22, U23, f13_in, U24, f14_in, U25, f18_in, U26, f83_in, U27, f102_in, U28, f103_in, U29, f106_in, U30, f132_in, U31

Defined Pair Symbols:

F130_IN, F82_IN, F104_IN, F17_IN, F1_IN, F24_IN, F54_IN, F142_IN, F143_IN, F88_IN, F89_IN, F115_IN, F116_IN, F47_IN, F48_IN, U20', U22', F13_IN, F14_IN, F18_IN, F83_IN, F102_IN, F103_IN, F106_IN, F132_IN, F50_IN, F74_IN

Compound Symbols:

c, c1, c2, c3, c4, c18, c19, c23, c31, c33, c37, c39, c41, c43, c45, c47, c50, c53, c55, c59, c63, c66, c69, c73, c77, c80, c49, c49, c52

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

Removed 1 trailing tuple parts

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → f1_out1
f1_in(z0, z1) → U1(f14_in(z0, z1), z0, z1)
f1_in(z0, z1) → U2(f13_in(z0, z1), z0, z1)
f1_in(z0, z1) → U3(f103_in(z0, z1), z0, z1)
f1_in(z0, z1) → U4(f102_in(z0, z1), z0, z1)
U1(f14_out1, z0, z1) → f1_out1
U1(f14_out2, z0, z1) → f1_out1
U1(f14_out3, z0, z1) → f1_out1
U2(f13_out1, z0, z1) → f1_out1
U2(f13_out2, z0, z1) → f1_out1
U2(f13_out3, z0, z1) → f1_out1
U3(f103_out1, z0, z1) → f1_out1
U3(f103_out2, z0, z1) → f1_out1
U3(f103_out3, z0, z1) → f1_out1
U4(f102_out1, z0, z1) → f1_out1
U4(f102_out2, z0, z1) → f1_out1
U4(f102_out3, z0, z1) → f1_out1
f24_in(z0, z1) → f24_out1
f24_in(z0, tree(z1, z2, z3)) → U5(f24_in(z0, z2), z0, tree(z1, z2, z3))
f24_in(z0, tree(z1, z2, z3)) → U6(f24_in(z0, z2), z0, tree(z1, z2, z3))
U5(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
U6(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
f54_in(0, s(z0)) → f54_out1
f54_in(s(z0), s(z1)) → U7(f54_in(z0, z1), s(z0), s(z1))
U7(f54_out1, s(z0), s(z1)) → f54_out1
f130_in(z0, tree(z1, z2, z3)) → U8(f24_in(z1, z3), z0, tree(z1, z2, z3))
U8(f24_out1, z0, tree(z1, z2, z3)) → f130_out1
f82_in(z0, tree(z1, z2, z3)) → U9(f24_in(z1, z3), z0, tree(z1, z2, z3))
U9(f24_out1, z0, tree(z1, z2, z3)) → f82_out1
f104_in(z0, tree(z1, z2, z3)) → U10(f24_in(z1, z3), z0, tree(z1, z2, z3))
U10(f24_out1, z0, tree(z1, z2, z3)) → f104_out1
f142_in(z0, tree(z1, z2, z3)) → U11(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U11(f50_out1, z0, tree(z1, z2, z3)) → f142_out1
f143_in(z0, tree(z1, z2, z3)) → U12(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U12(f74_out1, z0, tree(z1, z2, z3)) → f143_out1
f17_in(z0, tree(z1, z2, z3)) → U13(f24_in(z1, z3), z0, tree(z1, z2, z3))
U13(f24_out1, z0, tree(z1, z2, z3)) → f17_out1
f88_in(z0, tree(z1, z2, z3)) → U14(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U14(f50_out1, z0, tree(z1, z2, z3)) → f88_out1
f89_in(z0, tree(z1, z2, z3)) → U15(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U15(f74_out1, z0, tree(z1, z2, z3)) → f89_out1
f115_in(z0, tree(z1, z2, z3)) → U16(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f50_out1, z0, tree(z1, z2, z3)) → f115_out1
f116_in(z0, tree(z1, z2, z3)) → U17(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f74_out1, z0, tree(z1, z2, z3)) → f116_out1
f47_in(z0, tree(z1, z2, z3)) → U18(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U18(f50_out1, z0, tree(z1, z2, z3)) → f47_out1
f48_in(z0, tree(z1, z2, z3)) → U19(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U19(f74_out1, z0, tree(z1, z2, z3)) → f48_out1
f50_in(z0, z1, z2) → U20(f54_in(z0, z1), z0, z1, z2)
U20(f54_out1, z0, z1, z2) → U21(f1_in(z0, z2), z0, z1, z2)
U21(f1_out1, z0, z1, z2) → f50_out1
f74_in(z0, z1, z2) → U22(f54_in(z0, z1), z0, z1, z2)
U22(f54_out1, z0, z1, z2) → U23(f1_in(z1, z2), z0, z1, z2)
U23(f1_out1, z0, z1, z2) → f74_out1
f13_in(z0, z1) → U24(f82_in(z0, z1), f83_in(z0, z1), z0, z1)
U24(f82_out1, z0, z1, z2) → f13_out1
U24(z0, f83_out1, z1, z2) → f13_out2
U24(z0, f83_out2, z1, z2) → f13_out3
f14_in(z0, z1) → U25(f17_in(z0, z1), f18_in(z0, z1), z0, z1)
U25(f17_out1, z0, z1, z2) → f14_out1
U25(z0, f18_out1, z1, z2) → f14_out2
U25(z0, f18_out2, z1, z2) → f14_out3
f18_in(z0, z1) → U26(f47_in(z0, z1), f48_in(z0, z1), z0, z1)
U26(f47_out1, z0, z1, z2) → f18_out1
U26(z0, f48_out1, z1, z2) → f18_out2
f83_in(z0, z1) → U27(f88_in(z0, z1), f89_in(z0, z1), z0, z1)
U27(f88_out1, z0, z1, z2) → f83_out1
U27(z0, f89_out1, z1, z2) → f83_out2
f102_in(z0, z1) → U28(f130_in(z0, z1), f132_in(z0, z1), z0, z1)
U28(f130_out1, z0, z1, z2) → f102_out1
U28(z0, f132_out1, z1, z2) → f102_out2
U28(z0, f132_out2, z1, z2) → f102_out3
f103_in(z0, z1) → U29(f104_in(z0, z1), f106_in(z0, z1), z0, z1)
U29(f104_out1, z0, z1, z2) → f103_out1
U29(z0, f106_out1, z1, z2) → f103_out2
U29(z0, f106_out2, z1, z2) → f103_out3
f106_in(z0, z1) → U30(f115_in(z0, z1), f116_in(z0, z1), z0, z1)
U30(f115_out1, z0, z1, z2) → f106_out1
U30(z0, f116_out1, z1, z2) → f106_out2
f132_in(z0, z1) → U31(f142_in(z0, z1), f143_in(z0, z1), z0, z1)
U31(f142_out1, z0, z1, z2) → f132_out1
U31(z0, f143_out1, z1, z2) → f132_out2

Tuples:

F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F50_IN(s(z0), s(z1), x2) → c49(U20'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2))
F74_IN(s(z0), s(z1), x2) → c52(U22'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F74_IN(0, s(z0), x2) → c52(U22'(f54_out1, 0, s(z0), x2))

S tuples:

F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F50_IN(s(z0), s(z1), x2) → c49(U20'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2))
F74_IN(s(z0), s(z1), x2) → c52(U22'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F74_IN(0, s(z0), x2) → c52(U22'(f54_out1, 0, s(z0), x2))

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f24_in, U5, U6, f54_in, U7, f130_in, U8, f82_in, U9, f104_in, U10, f142_in, U11, f143_in, U12, f17_in, U13, f88_in, U14, f89_in, U15, f115_in, U16, f116_in, U17, f47_in, U18, f48_in, U19, f50_in, U20, U21, f74_in, U22, U23, f13_in, U24, f14_in, U25, f18_in, U26, f83_in, U27, f102_in, U28, f103_in, U29, f106_in, U30, f132_in, U31

Defined Pair Symbols:

F130_IN, F82_IN, F104_IN, F17_IN, F1_IN, F24_IN, F54_IN, F142_IN, F143_IN, F88_IN, F89_IN, F115_IN, F116_IN, F47_IN, F48_IN, U20', U22', F13_IN, F14_IN, F18_IN, F83_IN, F102_IN, F103_IN, F106_IN, F132_IN, F50_IN, F74_IN

Compound Symbols:

c, c1, c2, c3, c4, c18, c19, c23, c31, c33, c37, c39, c41, c43, c45, c47, c50, c53, c55, c59, c63, c66, c69, c73, c77, c80, c49, c49, c52, c52

(19) 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.

F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2))

We considered the (Usable) Rules:

f54_in(0, s(z0)) → f54_out1
f54_in(s(z0), s(z1)) → U7(f54_in(z0, z1), s(z0), s(z1))
U7(f54_out1, s(z0), s(z1)) → f54_out1

And the Tuples:

F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F50_IN(s(z0), s(z1), x2) → c49(U20'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2))
F74_IN(s(z0), s(z1), x2) → c52(U22'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F74_IN(0, s(z0), x2) → c52(U22'(f54_out1, 0, s(z0), x2))

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

POL(0) = [1]   
POL(F102_IN(x₁, x₂)) = x₁·x₂ + x₁²   
POL(F103_IN(x₁, x₂)) = x₁·x₂ + x₁²   
POL(F104_IN(x₁, x₂)) = 0   
POL(F106_IN(x₁, x₂)) = x₁·x₂ + x₁²   
POL(F115_IN(x₁, x₂)) = x₁·x₂ + x₁²   
POL(F116_IN(x₁, x₂)) = 0   
POL(F130_IN(x₁, x₂)) = 0   
POL(F132_IN(x₁, x₂)) = x₁·x₂ + x₁²   
POL(F13_IN(x₁, x₂)) = x₁·x₂ + x₁²   
POL(F142_IN(x₁, x₂)) = x₁·x₂ + x₁²   
POL(F143_IN(x₁, x₂)) = 0   
POL(F14_IN(x₁, x₂)) = x₁·x₂ + x₁²   
POL(F17_IN(x₁, x₂)) = 0   
POL(F18_IN(x₁, x₂)) = x₁·x₂ + x₁²   
POL(F1_IN(x₁, x₂)) = x₁·x₂ + x₁²   
POL(F24_IN(x₁, x₂)) = 0   
POL(F47_IN(x₁, x₂)) = x₁·x₂ + x₁²   
POL(F48_IN(x₁, x₂)) = 0   
POL(F50_IN(x₁, x₂, x₃)) = x₁ + x₁·x₃ + x₁²   
POL(F54_IN(x₁, x₂)) = 0   
POL(F74_IN(x₁, x₂, x₃)) = 0   
POL(F82_IN(x₁, x₂)) = 0   
POL(F83_IN(x₁, x₂)) = x₁·x₂ + x₁²   
POL(F88_IN(x₁, x₂)) = x₁·x₂ + x₁²   
POL(F89_IN(x₁, x₂)) = 0   
POL(U20'(x₁, x₂, x₃, x₄)) = x₂·x₄ + x₁² + x₂²   
POL(U22'(x₁, x₂, x₃, x₄)) = x₃ + x₃·x₄ + x₁·x₂ + x₃²   
POL(U7(x₁, x₂, x₃)) = 0   
POL(c(x₁)) = x₁   
POL(c1(x₁)) = x₁   
POL(c18(x₁)) = x₁   
POL(c19(x₁)) = x₁   
POL(c2(x₁)) = x₁   
POL(c23(x₁)) = x₁   
POL(c3(x₁)) = x₁   
POL(c31(x₁)) = x₁   
POL(c33(x₁)) = x₁   
POL(c37(x₁)) = x₁   
POL(c39(x₁)) = x₁   
POL(c4(x₁)) = x₁   
POL(c41(x₁)) = x₁   
POL(c43(x₁)) = x₁   
POL(c45(x₁)) = x₁   
POL(c47(x₁)) = x₁   
POL(c49(x₁)) = x₁   
POL(c49(x₁, x₂)) = x₁ + x₂   
POL(c50(x₁)) = x₁   
POL(c52(x₁)) = x₁   
POL(c52(x₁, x₂)) = x₁ + x₂   
POL(c53(x₁)) = x₁   
POL(c55(x₁, x₂)) = x₁ + x₂   
POL(c59(x₁, x₂)) = x₁ + x₂   
POL(c63(x₁, x₂)) = x₁ + x₂   
POL(c66(x₁, x₂)) = x₁ + x₂   
POL(c69(x₁, x₂)) = x₁ + x₂   
POL(c73(x₁, x₂)) = x₁ + x₂   
POL(c77(x₁, x₂)) = x₁ + x₂   
POL(c80(x₁, x₂)) = x₁ + x₂   
POL(f54_in(x₁, x₂)) = [1]   
POL(f54_out1) = 0   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = [1] + x₁ + x₂ + x₃   

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → f1_out1
f1_in(z0, z1) → U1(f14_in(z0, z1), z0, z1)
f1_in(z0, z1) → U2(f13_in(z0, z1), z0, z1)
f1_in(z0, z1) → U3(f103_in(z0, z1), z0, z1)
f1_in(z0, z1) → U4(f102_in(z0, z1), z0, z1)
U1(f14_out1, z0, z1) → f1_out1
U1(f14_out2, z0, z1) → f1_out1
U1(f14_out3, z0, z1) → f1_out1
U2(f13_out1, z0, z1) → f1_out1
U2(f13_out2, z0, z1) → f1_out1
U2(f13_out3, z0, z1) → f1_out1
U3(f103_out1, z0, z1) → f1_out1
U3(f103_out2, z0, z1) → f1_out1
U3(f103_out3, z0, z1) → f1_out1
U4(f102_out1, z0, z1) → f1_out1
U4(f102_out2, z0, z1) → f1_out1
U4(f102_out3, z0, z1) → f1_out1
f24_in(z0, z1) → f24_out1
f24_in(z0, tree(z1, z2, z3)) → U5(f24_in(z0, z2), z0, tree(z1, z2, z3))
f24_in(z0, tree(z1, z2, z3)) → U6(f24_in(z0, z2), z0, tree(z1, z2, z3))
U5(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
U6(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
f54_in(0, s(z0)) → f54_out1
f54_in(s(z0), s(z1)) → U7(f54_in(z0, z1), s(z0), s(z1))
U7(f54_out1, s(z0), s(z1)) → f54_out1
f130_in(z0, tree(z1, z2, z3)) → U8(f24_in(z1, z3), z0, tree(z1, z2, z3))
U8(f24_out1, z0, tree(z1, z2, z3)) → f130_out1
f82_in(z0, tree(z1, z2, z3)) → U9(f24_in(z1, z3), z0, tree(z1, z2, z3))
U9(f24_out1, z0, tree(z1, z2, z3)) → f82_out1
f104_in(z0, tree(z1, z2, z3)) → U10(f24_in(z1, z3), z0, tree(z1, z2, z3))
U10(f24_out1, z0, tree(z1, z2, z3)) → f104_out1
f142_in(z0, tree(z1, z2, z3)) → U11(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U11(f50_out1, z0, tree(z1, z2, z3)) → f142_out1
f143_in(z0, tree(z1, z2, z3)) → U12(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U12(f74_out1, z0, tree(z1, z2, z3)) → f143_out1
f17_in(z0, tree(z1, z2, z3)) → U13(f24_in(z1, z3), z0, tree(z1, z2, z3))
U13(f24_out1, z0, tree(z1, z2, z3)) → f17_out1
f88_in(z0, tree(z1, z2, z3)) → U14(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U14(f50_out1, z0, tree(z1, z2, z3)) → f88_out1
f89_in(z0, tree(z1, z2, z3)) → U15(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U15(f74_out1, z0, tree(z1, z2, z3)) → f89_out1
f115_in(z0, tree(z1, z2, z3)) → U16(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f50_out1, z0, tree(z1, z2, z3)) → f115_out1
f116_in(z0, tree(z1, z2, z3)) → U17(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f74_out1, z0, tree(z1, z2, z3)) → f116_out1
f47_in(z0, tree(z1, z2, z3)) → U18(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U18(f50_out1, z0, tree(z1, z2, z3)) → f47_out1
f48_in(z0, tree(z1, z2, z3)) → U19(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U19(f74_out1, z0, tree(z1, z2, z3)) → f48_out1
f50_in(z0, z1, z2) → U20(f54_in(z0, z1), z0, z1, z2)
U20(f54_out1, z0, z1, z2) → U21(f1_in(z0, z2), z0, z1, z2)
U21(f1_out1, z0, z1, z2) → f50_out1
f74_in(z0, z1, z2) → U22(f54_in(z0, z1), z0, z1, z2)
U22(f54_out1, z0, z1, z2) → U23(f1_in(z1, z2), z0, z1, z2)
U23(f1_out1, z0, z1, z2) → f74_out1
f13_in(z0, z1) → U24(f82_in(z0, z1), f83_in(z0, z1), z0, z1)
U24(f82_out1, z0, z1, z2) → f13_out1
U24(z0, f83_out1, z1, z2) → f13_out2
U24(z0, f83_out2, z1, z2) → f13_out3
f14_in(z0, z1) → U25(f17_in(z0, z1), f18_in(z0, z1), z0, z1)
U25(f17_out1, z0, z1, z2) → f14_out1
U25(z0, f18_out1, z1, z2) → f14_out2
U25(z0, f18_out2, z1, z2) → f14_out3
f18_in(z0, z1) → U26(f47_in(z0, z1), f48_in(z0, z1), z0, z1)
U26(f47_out1, z0, z1, z2) → f18_out1
U26(z0, f48_out1, z1, z2) → f18_out2
f83_in(z0, z1) → U27(f88_in(z0, z1), f89_in(z0, z1), z0, z1)
U27(f88_out1, z0, z1, z2) → f83_out1
U27(z0, f89_out1, z1, z2) → f83_out2
f102_in(z0, z1) → U28(f130_in(z0, z1), f132_in(z0, z1), z0, z1)
U28(f130_out1, z0, z1, z2) → f102_out1
U28(z0, f132_out1, z1, z2) → f102_out2
U28(z0, f132_out2, z1, z2) → f102_out3
f103_in(z0, z1) → U29(f104_in(z0, z1), f106_in(z0, z1), z0, z1)
U29(f104_out1, z0, z1, z2) → f103_out1
U29(z0, f106_out1, z1, z2) → f103_out2
U29(z0, f106_out2, z1, z2) → f103_out3
f106_in(z0, z1) → U30(f115_in(z0, z1), f116_in(z0, z1), z0, z1)
U30(f115_out1, z0, z1, z2) → f106_out1
U30(z0, f116_out1, z1, z2) → f106_out2
f132_in(z0, z1) → U31(f142_in(z0, z1), f143_in(z0, z1), z0, z1)
U31(f142_out1, z0, z1, z2) → f132_out1
U31(z0, f143_out1, z1, z2) → f132_out2

Tuples:

F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F50_IN(s(z0), s(z1), x2) → c49(U20'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2))
F74_IN(s(z0), s(z1), x2) → c52(U22'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F74_IN(0, s(z0), x2) → c52(U22'(f54_out1, 0, s(z0), x2))

S tuples:

F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F50_IN(s(z0), s(z1), x2) → c49(U20'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F74_IN(s(z0), s(z1), x2) → c52(U22'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F74_IN(0, s(z0), x2) → c52(U22'(f54_out1, 0, s(z0), x2))

K tuples:

F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f24_in, U5, U6, f54_in, U7, f130_in, U8, f82_in, U9, f104_in, U10, f142_in, U11, f143_in, U12, f17_in, U13, f88_in, U14, f89_in, U15, f115_in, U16, f116_in, U17, f47_in, U18, f48_in, U19, f50_in, U20, U21, f74_in, U22, U23, f13_in, U24, f14_in, U25, f18_in, U26, f83_in, U27, f102_in, U28, f103_in, U29, f106_in, U30, f132_in, U31

Defined Pair Symbols:

F130_IN, F82_IN, F104_IN, F17_IN, F1_IN, F24_IN, F54_IN, F142_IN, F143_IN, F88_IN, F89_IN, F115_IN, F116_IN, F47_IN, F48_IN, U20', U22', F13_IN, F14_IN, F18_IN, F83_IN, F102_IN, F103_IN, F106_IN, F132_IN, F50_IN, F74_IN

Compound Symbols:

c, c1, c2, c3, c4, c18, c19, c23, c31, c33, c37, c39, c41, c43, c45, c47, c50, c53, c55, c59, c63, c66, c69, c73, c77, c80, c49, c49, c52, c52

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

Use narrowing to replace F50_IN(s(z0), s(z1), x2) → c49(U20'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1))) by

F50_IN(s(0), s(s(z0)), x2) → c49(U20'(U7(f54_out1, s(0), s(s(z0))), s(0), s(s(z0)), x2), F54_IN(s(0), s(s(z0))))
F50_IN(s(s(z0)), s(s(z1)), x2) → c49(U20'(U7(U7(f54_in(z0, z1), s(z0), s(z1)), s(s(z0)), s(s(z1))), s(s(z0)), s(s(z1)), x2), F54_IN(s(s(z0)), s(s(z1))))
F50_IN(s(x0), s(x1), x2) → c49(F54_IN(s(x0), s(x1)))

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → f1_out1
f1_in(z0, z1) → U1(f14_in(z0, z1), z0, z1)
f1_in(z0, z1) → U2(f13_in(z0, z1), z0, z1)
f1_in(z0, z1) → U3(f103_in(z0, z1), z0, z1)
f1_in(z0, z1) → U4(f102_in(z0, z1), z0, z1)
U1(f14_out1, z0, z1) → f1_out1
U1(f14_out2, z0, z1) → f1_out1
U1(f14_out3, z0, z1) → f1_out1
U2(f13_out1, z0, z1) → f1_out1
U2(f13_out2, z0, z1) → f1_out1
U2(f13_out3, z0, z1) → f1_out1
U3(f103_out1, z0, z1) → f1_out1
U3(f103_out2, z0, z1) → f1_out1
U3(f103_out3, z0, z1) → f1_out1
U4(f102_out1, z0, z1) → f1_out1
U4(f102_out2, z0, z1) → f1_out1
U4(f102_out3, z0, z1) → f1_out1
f24_in(z0, z1) → f24_out1
f24_in(z0, tree(z1, z2, z3)) → U5(f24_in(z0, z2), z0, tree(z1, z2, z3))
f24_in(z0, tree(z1, z2, z3)) → U6(f24_in(z0, z2), z0, tree(z1, z2, z3))
U5(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
U6(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
f54_in(0, s(z0)) → f54_out1
f54_in(s(z0), s(z1)) → U7(f54_in(z0, z1), s(z0), s(z1))
U7(f54_out1, s(z0), s(z1)) → f54_out1
f130_in(z0, tree(z1, z2, z3)) → U8(f24_in(z1, z3), z0, tree(z1, z2, z3))
U8(f24_out1, z0, tree(z1, z2, z3)) → f130_out1
f82_in(z0, tree(z1, z2, z3)) → U9(f24_in(z1, z3), z0, tree(z1, z2, z3))
U9(f24_out1, z0, tree(z1, z2, z3)) → f82_out1
f104_in(z0, tree(z1, z2, z3)) → U10(f24_in(z1, z3), z0, tree(z1, z2, z3))
U10(f24_out1, z0, tree(z1, z2, z3)) → f104_out1
f142_in(z0, tree(z1, z2, z3)) → U11(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U11(f50_out1, z0, tree(z1, z2, z3)) → f142_out1
f143_in(z0, tree(z1, z2, z3)) → U12(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U12(f74_out1, z0, tree(z1, z2, z3)) → f143_out1
f17_in(z0, tree(z1, z2, z3)) → U13(f24_in(z1, z3), z0, tree(z1, z2, z3))
U13(f24_out1, z0, tree(z1, z2, z3)) → f17_out1
f88_in(z0, tree(z1, z2, z3)) → U14(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U14(f50_out1, z0, tree(z1, z2, z3)) → f88_out1
f89_in(z0, tree(z1, z2, z3)) → U15(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U15(f74_out1, z0, tree(z1, z2, z3)) → f89_out1
f115_in(z0, tree(z1, z2, z3)) → U16(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f50_out1, z0, tree(z1, z2, z3)) → f115_out1
f116_in(z0, tree(z1, z2, z3)) → U17(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f74_out1, z0, tree(z1, z2, z3)) → f116_out1
f47_in(z0, tree(z1, z2, z3)) → U18(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U18(f50_out1, z0, tree(z1, z2, z3)) → f47_out1
f48_in(z0, tree(z1, z2, z3)) → U19(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U19(f74_out1, z0, tree(z1, z2, z3)) → f48_out1
f50_in(z0, z1, z2) → U20(f54_in(z0, z1), z0, z1, z2)
U20(f54_out1, z0, z1, z2) → U21(f1_in(z0, z2), z0, z1, z2)
U21(f1_out1, z0, z1, z2) → f50_out1
f74_in(z0, z1, z2) → U22(f54_in(z0, z1), z0, z1, z2)
U22(f54_out1, z0, z1, z2) → U23(f1_in(z1, z2), z0, z1, z2)
U23(f1_out1, z0, z1, z2) → f74_out1
f13_in(z0, z1) → U24(f82_in(z0, z1), f83_in(z0, z1), z0, z1)
U24(f82_out1, z0, z1, z2) → f13_out1
U24(z0, f83_out1, z1, z2) → f13_out2
U24(z0, f83_out2, z1, z2) → f13_out3
f14_in(z0, z1) → U25(f17_in(z0, z1), f18_in(z0, z1), z0, z1)
U25(f17_out1, z0, z1, z2) → f14_out1
U25(z0, f18_out1, z1, z2) → f14_out2
U25(z0, f18_out2, z1, z2) → f14_out3
f18_in(z0, z1) → U26(f47_in(z0, z1), f48_in(z0, z1), z0, z1)
U26(f47_out1, z0, z1, z2) → f18_out1
U26(z0, f48_out1, z1, z2) → f18_out2
f83_in(z0, z1) → U27(f88_in(z0, z1), f89_in(z0, z1), z0, z1)
U27(f88_out1, z0, z1, z2) → f83_out1
U27(z0, f89_out1, z1, z2) → f83_out2
f102_in(z0, z1) → U28(f130_in(z0, z1), f132_in(z0, z1), z0, z1)
U28(f130_out1, z0, z1, z2) → f102_out1
U28(z0, f132_out1, z1, z2) → f102_out2
U28(z0, f132_out2, z1, z2) → f102_out3
f103_in(z0, z1) → U29(f104_in(z0, z1), f106_in(z0, z1), z0, z1)
U29(f104_out1, z0, z1, z2) → f103_out1
U29(z0, f106_out1, z1, z2) → f103_out2
U29(z0, f106_out2, z1, z2) → f103_out3
f106_in(z0, z1) → U30(f115_in(z0, z1), f116_in(z0, z1), z0, z1)
U30(f115_out1, z0, z1, z2) → f106_out1
U30(z0, f116_out1, z1, z2) → f106_out2
f132_in(z0, z1) → U31(f142_in(z0, z1), f143_in(z0, z1), z0, z1)
U31(f142_out1, z0, z1, z2) → f132_out1
U31(z0, f143_out1, z1, z2) → f132_out2

Tuples:

F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2))
F74_IN(s(z0), s(z1), x2) → c52(U22'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F74_IN(0, s(z0), x2) → c52(U22'(f54_out1, 0, s(z0), x2))
F50_IN(s(0), s(s(z0)), x2) → c49(U20'(U7(f54_out1, s(0), s(s(z0))), s(0), s(s(z0)), x2), F54_IN(s(0), s(s(z0))))
F50_IN(s(s(z0)), s(s(z1)), x2) → c49(U20'(U7(U7(f54_in(z0, z1), s(z0), s(z1)), s(s(z0)), s(s(z1))), s(s(z0)), s(s(z1)), x2), F54_IN(s(s(z0)), s(s(z1))))
F50_IN(s(x0), s(x1), x2) → c49(F54_IN(s(x0), s(x1)))

S tuples:

F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F74_IN(s(z0), s(z1), x2) → c52(U22'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1)))
F74_IN(0, s(z0), x2) → c52(U22'(f54_out1, 0, s(z0), x2))
F50_IN(s(0), s(s(z0)), x2) → c49(U20'(U7(f54_out1, s(0), s(s(z0))), s(0), s(s(z0)), x2), F54_IN(s(0), s(s(z0))))
F50_IN(s(s(z0)), s(s(z1)), x2) → c49(U20'(U7(U7(f54_in(z0, z1), s(z0), s(z1)), s(s(z0)), s(s(z1))), s(s(z0)), s(s(z1)), x2), F54_IN(s(s(z0)), s(s(z1))))
F50_IN(s(x0), s(x1), x2) → c49(F54_IN(s(x0), s(x1)))

K tuples:

F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f24_in, U5, U6, f54_in, U7, f130_in, U8, f82_in, U9, f104_in, U10, f142_in, U11, f143_in, U12, f17_in, U13, f88_in, U14, f89_in, U15, f115_in, U16, f116_in, U17, f47_in, U18, f48_in, U19, f50_in, U20, U21, f74_in, U22, U23, f13_in, U24, f14_in, U25, f18_in, U26, f83_in, U27, f102_in, U28, f103_in, U29, f106_in, U30, f132_in, U31

Defined Pair Symbols:

F130_IN, F82_IN, F104_IN, F17_IN, F1_IN, F24_IN, F54_IN, F142_IN, F143_IN, F88_IN, F89_IN, F115_IN, F116_IN, F47_IN, F48_IN, U20', U22', F13_IN, F14_IN, F18_IN, F83_IN, F102_IN, F103_IN, F106_IN, F132_IN, F50_IN, F74_IN

Compound Symbols:

c, c1, c2, c3, c4, c18, c19, c23, c31, c33, c37, c39, c41, c43, c45, c47, c50, c53, c55, c59, c63, c66, c69, c73, c77, c80, c49, c52, c52, c49

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

Use narrowing to replace F74_IN(s(z0), s(z1), x2) → c52(U22'(U7(f54_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F54_IN(s(z0), s(z1))) by

F74_IN(s(0), s(s(z0)), x2) → c52(U22'(U7(f54_out1, s(0), s(s(z0))), s(0), s(s(z0)), x2), F54_IN(s(0), s(s(z0))))
F74_IN(s(s(z0)), s(s(z1)), x2) → c52(U22'(U7(U7(f54_in(z0, z1), s(z0), s(z1)), s(s(z0)), s(s(z1))), s(s(z0)), s(s(z1)), x2), F54_IN(s(s(z0)), s(s(z1))))
F74_IN(s(x0), s(x1), x2) → c52(F54_IN(s(x0), s(x1)))

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → f1_out1
f1_in(z0, z1) → U1(f14_in(z0, z1), z0, z1)
f1_in(z0, z1) → U2(f13_in(z0, z1), z0, z1)
f1_in(z0, z1) → U3(f103_in(z0, z1), z0, z1)
f1_in(z0, z1) → U4(f102_in(z0, z1), z0, z1)
U1(f14_out1, z0, z1) → f1_out1
U1(f14_out2, z0, z1) → f1_out1
U1(f14_out3, z0, z1) → f1_out1
U2(f13_out1, z0, z1) → f1_out1
U2(f13_out2, z0, z1) → f1_out1
U2(f13_out3, z0, z1) → f1_out1
U3(f103_out1, z0, z1) → f1_out1
U3(f103_out2, z0, z1) → f1_out1
U3(f103_out3, z0, z1) → f1_out1
U4(f102_out1, z0, z1) → f1_out1
U4(f102_out2, z0, z1) → f1_out1
U4(f102_out3, z0, z1) → f1_out1
f24_in(z0, z1) → f24_out1
f24_in(z0, tree(z1, z2, z3)) → U5(f24_in(z0, z2), z0, tree(z1, z2, z3))
f24_in(z0, tree(z1, z2, z3)) → U6(f24_in(z0, z2), z0, tree(z1, z2, z3))
U5(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
U6(f24_out1, z0, tree(z1, z2, z3)) → f24_out1
f54_in(0, s(z0)) → f54_out1
f54_in(s(z0), s(z1)) → U7(f54_in(z0, z1), s(z0), s(z1))
U7(f54_out1, s(z0), s(z1)) → f54_out1
f130_in(z0, tree(z1, z2, z3)) → U8(f24_in(z1, z3), z0, tree(z1, z2, z3))
U8(f24_out1, z0, tree(z1, z2, z3)) → f130_out1
f82_in(z0, tree(z1, z2, z3)) → U9(f24_in(z1, z3), z0, tree(z1, z2, z3))
U9(f24_out1, z0, tree(z1, z2, z3)) → f82_out1
f104_in(z0, tree(z1, z2, z3)) → U10(f24_in(z1, z3), z0, tree(z1, z2, z3))
U10(f24_out1, z0, tree(z1, z2, z3)) → f104_out1
f142_in(z0, tree(z1, z2, z3)) → U11(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U11(f50_out1, z0, tree(z1, z2, z3)) → f142_out1
f143_in(z0, tree(z1, z2, z3)) → U12(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U12(f74_out1, z0, tree(z1, z2, z3)) → f143_out1
f17_in(z0, tree(z1, z2, z3)) → U13(f24_in(z1, z3), z0, tree(z1, z2, z3))
U13(f24_out1, z0, tree(z1, z2, z3)) → f17_out1
f88_in(z0, tree(z1, z2, z3)) → U14(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U14(f50_out1, z0, tree(z1, z2, z3)) → f88_out1
f89_in(z0, tree(z1, z2, z3)) → U15(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U15(f74_out1, z0, tree(z1, z2, z3)) → f89_out1
f115_in(z0, tree(z1, z2, z3)) → U16(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U16(f50_out1, z0, tree(z1, z2, z3)) → f115_out1
f116_in(z0, tree(z1, z2, z3)) → U17(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U17(f74_out1, z0, tree(z1, z2, z3)) → f116_out1
f47_in(z0, tree(z1, z2, z3)) → U18(f50_in(z0, z1, z2), z0, tree(z1, z2, z3))
U18(f50_out1, z0, tree(z1, z2, z3)) → f47_out1
f48_in(z0, tree(z1, z2, z3)) → U19(f74_in(z1, z0, z3), z0, tree(z1, z2, z3))
U19(f74_out1, z0, tree(z1, z2, z3)) → f48_out1
f50_in(z0, z1, z2) → U20(f54_in(z0, z1), z0, z1, z2)
U20(f54_out1, z0, z1, z2) → U21(f1_in(z0, z2), z0, z1, z2)
U21(f1_out1, z0, z1, z2) → f50_out1
f74_in(z0, z1, z2) → U22(f54_in(z0, z1), z0, z1, z2)
U22(f54_out1, z0, z1, z2) → U23(f1_in(z1, z2), z0, z1, z2)
U23(f1_out1, z0, z1, z2) → f74_out1
f13_in(z0, z1) → U24(f82_in(z0, z1), f83_in(z0, z1), z0, z1)
U24(f82_out1, z0, z1, z2) → f13_out1
U24(z0, f83_out1, z1, z2) → f13_out2
U24(z0, f83_out2, z1, z2) → f13_out3
f14_in(z0, z1) → U25(f17_in(z0, z1), f18_in(z0, z1), z0, z1)
U25(f17_out1, z0, z1, z2) → f14_out1
U25(z0, f18_out1, z1, z2) → f14_out2
U25(z0, f18_out2, z1, z2) → f14_out3
f18_in(z0, z1) → U26(f47_in(z0, z1), f48_in(z0, z1), z0, z1)
U26(f47_out1, z0, z1, z2) → f18_out1
U26(z0, f48_out1, z1, z2) → f18_out2
f83_in(z0, z1) → U27(f88_in(z0, z1), f89_in(z0, z1), z0, z1)
U27(f88_out1, z0, z1, z2) → f83_out1
U27(z0, f89_out1, z1, z2) → f83_out2
f102_in(z0, z1) → U28(f130_in(z0, z1), f132_in(z0, z1), z0, z1)
U28(f130_out1, z0, z1, z2) → f102_out1
U28(z0, f132_out1, z1, z2) → f102_out2
U28(z0, f132_out2, z1, z2) → f102_out3
f103_in(z0, z1) → U29(f104_in(z0, z1), f106_in(z0, z1), z0, z1)
U29(f104_out1, z0, z1, z2) → f103_out1
U29(z0, f106_out1, z1, z2) → f103_out2
U29(z0, f106_out2, z1, z2) → f103_out3
f106_in(z0, z1) → U30(f115_in(z0, z1), f116_in(z0, z1), z0, z1)
U30(f115_out1, z0, z1, z2) → f106_out1
U30(z0, f116_out1, z1, z2) → f106_out2
f132_in(z0, z1) → U31(f142_in(z0, z1), f143_in(z0, z1), z0, z1)
U31(f142_out1, z0, z1, z2) → f132_out1
U31(z0, f143_out1, z1, z2) → f132_out2

Tuples:

F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2))
F74_IN(0, s(z0), x2) → c52(U22'(f54_out1, 0, s(z0), x2))
F50_IN(s(0), s(s(z0)), x2) → c49(U20'(U7(f54_out1, s(0), s(s(z0))), s(0), s(s(z0)), x2), F54_IN(s(0), s(s(z0))))
F50_IN(s(s(z0)), s(s(z1)), x2) → c49(U20'(U7(U7(f54_in(z0, z1), s(z0), s(z1)), s(s(z0)), s(s(z1))), s(s(z0)), s(s(z1)), x2), F54_IN(s(s(z0)), s(s(z1))))
F50_IN(s(x0), s(x1), x2) → c49(F54_IN(s(x0), s(x1)))
F74_IN(s(0), s(s(z0)), x2) → c52(U22'(U7(f54_out1, s(0), s(s(z0))), s(0), s(s(z0)), x2), F54_IN(s(0), s(s(z0))))
F74_IN(s(s(z0)), s(s(z1)), x2) → c52(U22'(U7(U7(f54_in(z0, z1), s(z0), s(z1)), s(s(z0)), s(s(z1))), s(s(z0)), s(s(z1)), x2), F54_IN(s(s(z0)), s(s(z1))))
F74_IN(s(x0), s(x1), x2) → c52(F54_IN(s(x0), s(x1)))

S tuples:

F130_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F82_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F104_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F17_IN(z0, tree(z1, z2, z3)) → c(F24_IN(z1, z3))
F1_IN(z0, z1) → c1(F14_IN(z0, z1))
F1_IN(z0, z1) → c2(F13_IN(z0, z1))
F1_IN(z0, z1) → c3(F103_IN(z0, z1))
F1_IN(z0, z1) → c4(F102_IN(z0, z1))
F24_IN(z0, tree(z1, z2, z3)) → c18(F24_IN(z0, z2))
F24_IN(z0, tree(z1, z2, z3)) → c19(F24_IN(z0, z2))
F54_IN(s(z0), s(z1)) → c23(F54_IN(z0, z1))
F142_IN(z0, tree(z1, z2, z3)) → c31(F50_IN(z0, z1, z2))
F143_IN(z0, tree(z1, z2, z3)) → c33(F74_IN(z1, z0, z3))
F88_IN(z0, tree(z1, z2, z3)) → c37(F50_IN(z0, z1, z2))
F89_IN(z0, tree(z1, z2, z3)) → c39(F74_IN(z1, z0, z3))
F115_IN(z0, tree(z1, z2, z3)) → c41(F50_IN(z0, z1, z2))
F116_IN(z0, tree(z1, z2, z3)) → c43(F74_IN(z1, z0, z3))
F47_IN(z0, tree(z1, z2, z3)) → c45(F50_IN(z0, z1, z2))
F48_IN(z0, tree(z1, z2, z3)) → c47(F74_IN(z1, z0, z3))
U20'(f54_out1, z0, z1, z2) → c50(F1_IN(z0, z2))
U22'(f54_out1, z0, z1, z2) → c53(F1_IN(z1, z2))
F13_IN(z0, z1) → c55(F82_IN(z0, z1), F83_IN(z0, z1))
F14_IN(z0, z1) → c59(F17_IN(z0, z1), F18_IN(z0, z1))
F18_IN(z0, z1) → c63(F47_IN(z0, z1), F48_IN(z0, z1))
F83_IN(z0, z1) → c66(F88_IN(z0, z1), F89_IN(z0, z1))
F102_IN(z0, z1) → c69(F130_IN(z0, z1), F132_IN(z0, z1))
F103_IN(z0, z1) → c73(F104_IN(z0, z1), F106_IN(z0, z1))
F106_IN(z0, z1) → c77(F115_IN(z0, z1), F116_IN(z0, z1))
F132_IN(z0, z1) → c80(F142_IN(z0, z1), F143_IN(z0, z1))
F74_IN(0, s(z0), x2) → c52(U22'(f54_out1, 0, s(z0), x2))
F50_IN(s(0), s(s(z0)), x2) → c49(U20'(U7(f54_out1, s(0), s(s(z0))), s(0), s(s(z0)), x2), F54_IN(s(0), s(s(z0))))
F50_IN(s(s(z0)), s(s(z1)), x2) → c49(U20'(U7(U7(f54_in(z0, z1), s(z0), s(z1)), s(s(z0)), s(s(z1))), s(s(z0)), s(s(z1)), x2), F54_IN(s(s(z0)), s(s(z1))))
F50_IN(s(x0), s(x1), x2) → c49(F54_IN(s(x0), s(x1)))
F74_IN(s(0), s(s(z0)), x2) → c52(U22'(U7(f54_out1, s(0), s(s(z0))), s(0), s(s(z0)), x2), F54_IN(s(0), s(s(z0))))
F74_IN(s(s(z0)), s(s(z1)), x2) → c52(U22'(U7(U7(f54_in(z0, z1), s(z0), s(z1)), s(s(z0)), s(s(z1))), s(s(z0)), s(s(z1)), x2), F54_IN(s(s(z0)), s(s(z1))))
F74_IN(s(x0), s(x1), x2) → c52(F54_IN(s(x0), s(x1)))

K tuples:

F50_IN(0, s(z0), x2) → c49(U20'(f54_out1, 0, s(z0), x2))

Defined Rule Symbols:

f1_in, U1, U2, U3, U4, f24_in, U5, U6, f54_in, U7, f130_in, U8, f82_in, U9, f104_in, U10, f142_in, U11, f143_in, U12, f17_in, U13, f88_in, U14, f89_in, U15, f115_in, U16, f116_in, U17, f47_in, U18, f48_in, U19, f50_in, U20, U21, f74_in, U22, U23, f13_in, U24, f14_in, U25, f18_in, U26, f83_in, U27, f102_in, U28, f103_in, U29, f106_in, U30, f132_in, U31

Defined Pair Symbols:

F130_IN, F82_IN, F104_IN, F17_IN, F1_IN, F24_IN, F54_IN, F142_IN, F143_IN, F88_IN, F89_IN, F115_IN, F116_IN, F47_IN, F48_IN, U20', U22', F13_IN, F14_IN, F18_IN, F83_IN, F102_IN, F103_IN, F106_IN, F132_IN, F50_IN, F74_IN

Compound Symbols:

c, c1, c2, c3, c4, c18, c19, c23, c31, c33, c37, c39, c41, c43, c45, c47, c50, c53, c55, c59, c63, c66, c69, c73, c77, c80, c49, c52, c49, c52

(25) 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\nT3 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\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: true | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 1 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 4 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 5 | delete(T6, T2, T7), 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\nT3 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];
10 [label="10: delete(T6, T2, T7), SCOPE: 1, CLAUSE: 1 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 4 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 5 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 6\n\nT6 is ground\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: true | delete(T10, T2, T11), SCOPE: 1, CLAUSE: 4 | delete(T10, T2, T11), SCOPE: 1, CLAUSE: 5 | delete(T10, T2, T11), SCOPE: 1, CLAUSE: 6\n\nT10 is ground\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: delete(T6, T2, T7), SCOPE: 1, CLAUSE: 4 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 5 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 6\n\nT6 is ground\nT7 is ground\nX10 is free\nX11 is free\ndelete(T6, T2, T7) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: delete(T10, T2, T11), SCOPE: 1, CLAUSE: 4 | delete(T10, T2, T11), SCOPE: 1, CLAUSE: 5 | delete(T10, T2, T11), SCOPE: 1, CLAUSE: 6\n\nT10 is ground\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: delmin(T22, T20, T21) | delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 5 | delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 6\n\nT17 is ground\nT20 is ground\nT18 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: delete(T10, T2, T11), SCOPE: 1, CLAUSE: 5 | delete(T10, T2, T11), SCOPE: 1, CLAUSE: 6\n\nT10 is ground\nT11 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T10, T2, T11) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: delmin(T22, T20, T21), SCOPE: 2, CLAUSE: 2 | delmin(T22, T20, T21), SCOPE: 2, CLAUSE: 7 | ?_2 | delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 5 | delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 6\n\nT17 is ground\nT20 is ground\nT18 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: true | delmin(T22, T27, T28), SCOPE: 2, CLAUSE: 7 | ?_2 | delete(T17, T2, tree(T27, T18, T28)), SCOPE: 1, CLAUSE: 5 | delete(T17, T2, tree(T27, T18, T28)), SCOPE: 1, CLAUSE: 6\n\nT17 is ground\nT18 is ground\nT27 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: delmin(T22, T20, T21), SCOPE: 2, CLAUSE: 7 | ?_2 | delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 5 | delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 6\n\nT17 is ground\nT20 is ground\nT18 is ground\nT21 is ground\nX26 is free\nX27 is free\ndelmin(T22, T20, T21) !=? delmin(tree(X26, void, X27), X26, X27)", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: delmin(T22, T27, T28), SCOPE: 2, CLAUSE: 7 | ?_2 | delete(T17, T2, tree(T27, T18, T28)), SCOPE: 1, CLAUSE: 5 | delete(T17, T2, tree(T27, T18, T28)), SCOPE: 1, CLAUSE: 6\n\nT17 is ground\nT18 is ground\nT27 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: delmin(T22, T27, T28), SCOPE: 2, CLAUSE: 7\n\nT27 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: ?_2 | delete(T17, T2, tree(T27, T18, T28)), SCOPE: 1, CLAUSE: 5 | delete(T17, T2, tree(T27, T18, T28)), SCOPE: 1, CLAUSE: 6\n\nT17 is ground\nT18 is ground\nT27 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: delmin(T59, T56, T57)\n\nT56 is ground\nT57 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: delmin(T59, T56, T57), SCOPE: 3, CLAUSE: 2 | delmin(T59, T56, T57), SCOPE: 3, CLAUSE: 7\n\nT56 is ground\nT57 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: true | delmin(T59, T68, T69), SCOPE: 3, CLAUSE: 7\n\nT68 is ground\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: delmin(T59, T56, T57), SCOPE: 3, CLAUSE: 7\n\nT56 is ground\nT57 is ground\nX66 is free\nX67 is free\ndelmin(T59, T56, T57) !=? delmin(tree(X66, void, X67), X66, X67)", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: delmin(T59, T68, T69), SCOPE: 3, CLAUSE: 7\n\nT68 is ground\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: delmin(T88, T85, T86)\n\nT85 is ground\nT86 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: delmin(T111, T108, T109)\n\nT108 is ground\nT105 is ground\nT109 is ground\nT110 is ground\nX66 is free\nX67 is free\ndelmin(T59, T108, tree(T105, T109, T110)) !=? delmin(tree(X66, void, X67), X66, X67)", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: delete(T17, T2, tree(T27, T18, T28)), SCOPE: 1, CLAUSE: 5 | delete(T17, T2, tree(T27, T18, T28)), SCOPE: 1, CLAUSE: 6\n\nT17 is ground\nT18 is ground\nT27 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: delete(T17, T2, tree(T27, T18, T28)), SCOPE: 1, CLAUSE: 5\n\nT17 is ground\nT18 is ground\nT27 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: delete(T17, T2, tree(T27, T18, T28)), SCOPE: 1, CLAUSE: 6\n\nT17 is ground\nT18 is ground\nT27 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(less(T136, T137), delete(T136, T141, T140))\n\nT136 is ground\nT137 is ground\nT140 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: less(T136, T137)\n\nT136 is ground\nT137 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: delete(T136, T141, T140)\n\nT136 is ground\nT140 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: less(T136, T137), SCOPE: 4, CLAUSE: 3 | less(T136, T137), SCOPE: 4, CLAUSE: 8\n\nT136 is ground\nT137 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: true | less(0, s(T148)), SCOPE: 4, CLAUSE: 8\n\nT148 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: less(T136, T137), SCOPE: 4, CLAUSE: 8\n\nT136 is ground\nT137 is ground\nX143 is free\nless(T136, T137) !=? less(0, s(X143))", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: less(0, s(T148)), SCOPE: 4, CLAUSE: 8\n\nT148 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: less(T153, T154)\n\nT153 is ground\nT154 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: ','(less(T172, T171), delete(T171, T176, T175))\n\nT171 is ground\nT172 is ground\nT175 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: less(T172, T171)\n\nT171 is ground\nT172 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: delete(T171, T176, T175)\n\nT171 is ground\nT175 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: delmin(T22, T20, T21), SCOPE: 2, CLAUSE: 7\n\nT20 is ground\nT21 is ground\nX26 is free\nX27 is free\ndelmin(T22, T20, T21) !=? delmin(tree(X26, void, X27), X26, X27)", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: ?_2 | delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 5 | delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 6\n\nT17 is ground\nT20 is ground\nT18 is ground\nT21 is ground\nX26 is free\nX27 is free\ndelmin(T22, T20, T21) !=? delmin(tree(X26, void, X27), X26, X27)", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: delmin(T215, T212, T213)\n\nT212 is ground\nT209 is ground\nT213 is ground\nT214 is ground\nX26 is free\nX27 is free\ndelmin(T22, T212, tree(T209, T213, T214)) !=? delmin(tree(X26, void, X27), X26, X27)", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 5 | delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 6\n\nT17 is ground\nT20 is ground\nT18 is ground\nT21 is ground\nX26 is free\nX27 is free\ndelmin(T22, T20, T21) !=? delmin(tree(X26, void, X27), X26, X27)", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 5\n\nT17 is ground\nT20 is ground\nT18 is ground\nT21 is ground\nX26 is free\nX27 is free\ndelmin(T22, T20, T21) !=? delmin(tree(X26, void, X27), X26, X27)", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: delete(T17, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 6\n\nT17 is ground\nT20 is ground\nT18 is ground\nT21 is ground\nX26 is free\nX27 is free\ndelmin(T22, T20, T21) !=? delmin(tree(X26, void, X27), X26, X27)", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: ','(less(T240, T241), delete(T240, T245, T244))\n\nT240 is ground\nT241 is ground\nT244 is ground\nT243 is ground\nX26 is free\nX27 is free\ndelmin(T22, T241, T243) !=? delmin(tree(X26, void, X27), X26, X27)", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: ','(less(T259, T258), delete(T258, T263, T262))\n\nT258 is ground\nT259 is ground\nT262 is ground\nX26 is free\nX27 is free\ndelmin(T22, T259, T262) !=? delmin(tree(X26, void, X27), X26, X27)", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: ','(less(T271, T272), delete(T271, T276, T275)) | delete(T271, T2, tree(T272, T275, T274)), SCOPE: 1, CLAUSE: 6\n\nT271 is ground\nT272 is ground\nT275 is ground\nT274 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T271, T2, tree(T272, T275, T274)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: delete(T10, T2, T11), SCOPE: 1, CLAUSE: 6\n\nT10 is ground\nT11 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX264 is free\nX265 is free\nX266 is free\nX267 is free\nX268 is free\ndelete(T10, T2, T11) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T10, T2, T11) !=? delete(X264, tree(X265, X266, X267), tree(X265, X268, X267))", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: ','(less(T271, T272), delete(T271, T276, T275)), SCOPE: 5, CLAUSE: 3 | ','(less(T271, T272), delete(T271, T276, T275)), SCOPE: 5, CLAUSE: 8 | ?_5 | delete(T271, T2, tree(T272, T275, T274)), SCOPE: 1, CLAUSE: 6\n\nT271 is ground\nT272 is ground\nT275 is ground\nT274 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T271, T2, tree(T272, T275, T274)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: delete(0, T276, T275) | ','(less(0, s(T279)), delete(0, T276, T275)), SCOPE: 5, CLAUSE: 8 | ?_5 | delete(0, T2, tree(s(T279), T275, T274)), SCOPE: 1, CLAUSE: 6\n\nT275 is ground\nT274 is ground\nT279 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(0, T2, tree(s(T279), T275, T274)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: ','(less(T271, T272), delete(T271, T276, T275)), SCOPE: 5, CLAUSE: 8 | ?_5 | delete(T271, T2, tree(T272, T275, T274)), SCOPE: 1, CLAUSE: 6\n\nT271 is ground\nT272 is ground\nT275 is ground\nT274 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX271 is free\ndelete(T271, T2, tree(T272, T275, T274)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\nless(T271, T272) !=? less(0, s(X271))", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: delete(0, T276, T275)\n\nT275 is ground\nT274 is ground\nT279 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(0, T2, tree(s(T279), T275, T274)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: ','(less(0, s(T279)), delete(0, T276, T275)), SCOPE: 5, CLAUSE: 8 | ?_5 | delete(0, T2, tree(s(T279), T275, T274)), SCOPE: 1, CLAUSE: 6\n\nT275 is ground\nT274 is ground\nT279 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(0, T2, tree(s(T279), T275, T274)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: ?_5 | delete(0, T2, tree(s(T279), T275, T274)), SCOPE: 1, CLAUSE: 6\n\nT275 is ground\nT274 is ground\nT279 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(0, T2, tree(s(T279), T275, T274)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: delete(0, T2, tree(s(T279), T275, T274)), SCOPE: 1, CLAUSE: 6\n\nT275 is ground\nT274 is ground\nT279 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(0, T2, tree(s(T279), T275, T274)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: ','(less(s(T297), 0), delete(0, T299, T298))\n\nT297 is ground\nT295 is ground\nT298 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(0, T2, tree(s(T297), T295, T298)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: less(s(T297), 0)\n\nT297 is ground\nT295 is ground\nT298 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(0, T2, tree(s(T297), T295, T298)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: delete(0, T299, T298)\n\nT297 is ground\nT295 is ground\nT298 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(0, T2, tree(s(T297), T295, T298)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: less(s(T297), 0), SCOPE: 6, CLAUSE: 3 | less(s(T297), 0), SCOPE: 6, CLAUSE: 8\n\nT297 is ground\nT295 is ground\nT298 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(0, T2, tree(s(T297), T295, T298)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: less(s(T297), 0), SCOPE: 6, CLAUSE: 8\n\nT297 is ground\nT295 is ground\nT298 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(0, T2, tree(s(T297), T295, T298)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: ','(less(T271, T272), delete(T271, T276, T275)), SCOPE: 5, CLAUSE: 8\n\nT271 is ground\nT272 is ground\nT275 is ground\nT274 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX271 is free\ndelete(T271, T2, tree(T272, T275, T274)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\nless(T271, T272) !=? less(0, s(X271))", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: ?_5 | delete(T271, T2, tree(T272, T275, T274)), SCOPE: 1, CLAUSE: 6\n\nT271 is ground\nT272 is ground\nT275 is ground\nT274 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX271 is free\ndelete(T271, T2, tree(T272, T275, T274)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\nless(T271, T272) !=? less(0, s(X271))", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: ','(less(T311, T312), delete(s(T311), T276, T275))\n\nT275 is ground\nT274 is ground\nT311 is ground\nT312 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(s(T311), T2, tree(s(T312), T275, T274)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: less(T311, T312)\n\nT275 is ground\nT274 is ground\nT311 is ground\nT312 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(s(T311), T2, tree(s(T312), T275, T274)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: delete(s(T311), T276, T275)\n\nT275 is ground\nT274 is ground\nT311 is ground\nT312 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(s(T311), T2, tree(s(T312), T275, T274)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: delete(T271, T2, tree(T272, T275, T274)), SCOPE: 1, CLAUSE: 6\n\nT271 is ground\nT272 is ground\nT275 is ground\nT274 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX271 is free\ndelete(T271, T2, tree(T272, T275, T274)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\nless(T271, T272) !=? less(0, s(X271))", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: ','(less(T332, T331), delete(T331, T336, T335))\n\nT331 is ground\nT332 is ground\nT333 is ground\nT335 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX271 is free\ndelete(T331, T2, tree(T332, T333, T335)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\nless(T331, T332) !=? less(0, s(X271))", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: ','(less(T345, T344), delete(T344, T349, T348))\n\nT344 is ground\nT345 is ground\nT346 is ground\nT348 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX264 is free\nX265 is free\nX266 is free\nX267 is free\nX268 is free\ndelete(T344, T2, tree(T345, T346, T348)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T344, T2, tree(T345, T346, T348)) !=? delete(X264, tree(X265, X266, X267), tree(X265, X268, X267))", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: ','(less(T345, T344), delete(T344, T349, T348)), SCOPE: 7, CLAUSE: 3 | ','(less(T345, T344), delete(T344, T349, T348)), SCOPE: 7, CLAUSE: 8\n\nT344 is ground\nT345 is ground\nT346 is ground\nT348 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX264 is free\nX265 is free\nX266 is free\nX267 is free\nX268 is free\ndelete(T344, T2, tree(T345, T346, T348)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T344, T2, tree(T345, T346, T348)) !=? delete(X264, tree(X265, X266, X267), tree(X265, X268, X267))", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: delete(s(T352), T349, T348) | ','(less(0, s(T352)), delete(s(T352), T349, T348)), SCOPE: 7, CLAUSE: 8\n\nT346 is ground\nT348 is ground\nT352 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX264 is free\nX265 is free\nX266 is free\nX267 is free\nX268 is free\ndelete(s(T352), T2, tree(0, T346, T348)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(s(T352), T2, tree(0, T346, T348)) !=? delete(X264, tree(X265, X266, X267), tree(X265, X268, X267))", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: ','(less(T345, T344), delete(T344, T349, T348)), SCOPE: 7, CLAUSE: 8\n\nT344 is ground\nT345 is ground\nT346 is ground\nT348 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX264 is free\nX265 is free\nX266 is free\nX267 is free\nX268 is free\nX355 is free\ndelete(T344, T2, tree(T345, T346, T348)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T344, T2, tree(T345, T346, T348)) !=? delete(X264, tree(X265, X266, X267), tree(X265, X268, X267))\nless(T345, T344) !=? less(0, s(X355))", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: delete(s(T352), T349, T348)\n\nT346 is ground\nT348 is ground\nT352 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX264 is free\nX265 is free\nX266 is free\nX267 is free\nX268 is free\ndelete(s(T352), T2, tree(0, T346, T348)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(s(T352), T2, tree(0, T346, T348)) !=? delete(X264, tree(X265, X266, X267), tree(X265, X268, X267))", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: ','(less(0, s(T352)), delete(s(T352), T349, T348)), SCOPE: 7, CLAUSE: 8\n\nT346 is ground\nT348 is ground\nT352 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX264 is free\nX265 is free\nX266 is free\nX267 is free\nX268 is free\ndelete(s(T352), T2, tree(0, T346, T348)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(s(T352), T2, tree(0, T346, T348)) !=? delete(X264, tree(X265, X266, X267), tree(X265, X268, X267))", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: ','(less(T365, T366), delete(s(T366), T349, T348))\n\nT346 is ground\nT348 is ground\nT365 is ground\nT366 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX264 is free\nX265 is free\nX266 is free\nX267 is free\nX268 is free\ndelete(s(T366), T2, tree(s(T365), T346, T348)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(s(T366), T2, tree(s(T365), T346, T348)) !=? delete(X264, tree(X265, X266, X267), tree(X265, X268, X267))", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: less(T365, T366)\n\nT346 is ground\nT348 is ground\nT365 is ground\nT366 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX264 is free\nX265 is free\nX266 is free\nX267 is free\nX268 is free\ndelete(s(T366), T2, tree(s(T365), T346, T348)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(s(T366), T2, tree(s(T365), T346, T348)) !=? delete(X264, tree(X265, X266, X267), tree(X265, X268, X267))", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: delete(s(T366), T349, T348)\n\nT346 is ground\nT348 is ground\nT365 is ground\nT366 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX264 is free\nX265 is free\nX266 is free\nX267 is free\nX268 is free\ndelete(s(T366), T2, tree(s(T365), T346, T348)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(s(T366), T2, tree(s(T365), T346, T348)) !=? delete(X264, tree(X265, X266, X267), tree(X265, X268, X267))", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: delmin(T385, T383, T384) | delete(T380, T2, tree(T383, T381, T384)), SCOPE: 1, CLAUSE: 5 | delete(T380, T2, tree(T383, T381, T384)), SCOPE: 1, CLAUSE: 6\n\nT380 is ground\nT383 is ground\nT381 is ground\nT384 is ground\nX10 is free\nX11 is free\ndelete(T380, T2, tree(T383, T381, T384)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: delete(T6, T2, T7), SCOPE: 1, CLAUSE: 5 | delete(T6, T2, T7), SCOPE: 1, CLAUSE: 6\n\nT6 is ground\nT7 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\ndelete(T6, T2, T7) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T6, T2, T7) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: delmin(T385, T383, T384), SCOPE: 8, CLAUSE: 2 | delmin(T385, T383, T384), SCOPE: 8, CLAUSE: 7 | ?_8 | delete(T380, T2, tree(T383, T381, T384)), SCOPE: 1, CLAUSE: 5 | delete(T380, T2, tree(T383, T381, T384)), SCOPE: 1, CLAUSE: 6\n\nT380 is ground\nT383 is ground\nT381 is ground\nT384 is ground\nX10 is free\nX11 is free\ndelete(T380, T2, tree(T383, T381, T384)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: true | delmin(T385, T390, T391), SCOPE: 8, CLAUSE: 7 | ?_8 | delete(T380, T2, tree(T390, T381, T391)), SCOPE: 1, CLAUSE: 5 | delete(T380, T2, tree(T390, T381, T391)), SCOPE: 1, CLAUSE: 6\n\nT380 is ground\nT381 is ground\nT390 is ground\nT391 is ground\nX10 is free\nX11 is free\ndelete(T380, T2, tree(T390, T381, T391)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: delmin(T385, T383, T384), SCOPE: 8, CLAUSE: 7 | ?_8 | delete(T380, T2, tree(T383, T381, T384)), SCOPE: 1, CLAUSE: 5 | delete(T380, T2, tree(T383, T381, T384)), SCOPE: 1, CLAUSE: 6\n\nT380 is ground\nT383 is ground\nT381 is ground\nT384 is ground\nX10 is free\nX11 is free\nX394 is free\nX395 is free\ndelete(T380, T2, tree(T383, T381, T384)) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T385, T383, T384) !=? delmin(tree(X394, void, X395), X394, X395)", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: delmin(T385, T390, T391), SCOPE: 8, CLAUSE: 7 | ?_8 | delete(T380, T2, tree(T390, T381, T391)), SCOPE: 1, CLAUSE: 5 | delete(T380, T2, tree(T390, T381, T391)), SCOPE: 1, CLAUSE: 6\n\nT380 is ground\nT381 is ground\nT390 is ground\nT391 is ground\nX10 is free\nX11 is free\ndelete(T380, T2, tree(T390, T381, T391)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: delmin(T385, T390, T391), SCOPE: 8, CLAUSE: 7\n\nT380 is ground\nT381 is ground\nT390 is ground\nT391 is ground\nX10 is free\nX11 is free\ndelete(T380, T2, tree(T390, T381, T391)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: ?_8 | delete(T380, T2, tree(T390, T381, T391)), SCOPE: 1, CLAUSE: 5 | delete(T380, T2, tree(T390, T381, T391)), SCOPE: 1, CLAUSE: 6\n\nT380 is ground\nT381 is ground\nT390 is ground\nT391 is ground\nX10 is free\nX11 is free\ndelete(T380, T2, tree(T390, T381, T391)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: delmin(T422, T419, T420)\n\nT380 is ground\nT381 is ground\nT419 is ground\nT416 is ground\nT420 is ground\nT421 is ground\nX10 is free\nX11 is free\ndelete(T380, T2, tree(T419, T381, tree(T416, T420, T421))) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: delete(T380, T2, tree(T390, T381, T391)), SCOPE: 1, CLAUSE: 5 | delete(T380, T2, tree(T390, T381, T391)), SCOPE: 1, CLAUSE: 6\n\nT380 is ground\nT381 is ground\nT390 is ground\nT391 is ground\nX10 is free\nX11 is free\ndelete(T380, T2, tree(T390, T381, T391)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: delete(T380, T2, tree(T390, T381, T391)), SCOPE: 1, CLAUSE: 5\n\nT380 is ground\nT381 is ground\nT390 is ground\nT391 is ground\nX10 is free\nX11 is free\ndelete(T380, T2, tree(T390, T381, T391)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: delete(T380, T2, tree(T390, T381, T391)), SCOPE: 1, CLAUSE: 6\n\nT380 is ground\nT381 is ground\nT390 is ground\nT391 is ground\nX10 is free\nX11 is free\ndelete(T380, T2, tree(T390, T381, T391)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: ','(less(T447, T448), delete(T447, T452, T451))\n\nT447 is ground\nT448 is ground\nT451 is ground\nT450 is ground\nX10 is free\nX11 is free\ndelete(T447, T2, tree(T448, T451, T450)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: ','(less(T466, T465), delete(T465, T470, T469))\n\nT465 is ground\nT466 is ground\nT467 is ground\nT469 is ground\nX10 is free\nX11 is free\ndelete(T465, T2, tree(T466, T467, T469)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: delmin(T385, T383, T384), SCOPE: 8, CLAUSE: 7\n\nT380 is ground\nT383 is ground\nT381 is ground\nT384 is ground\nX10 is free\nX11 is free\nX394 is free\nX395 is free\ndelete(T380, T2, tree(T383, T381, T384)) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T385, T383, T384) !=? delmin(tree(X394, void, X395), X394, X395)", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: ?_8 | delete(T380, T2, tree(T383, T381, T384)), SCOPE: 1, CLAUSE: 5 | delete(T380, T2, tree(T383, T381, T384)), SCOPE: 1, CLAUSE: 6\n\nT380 is ground\nT383 is ground\nT381 is ground\nT384 is ground\nX10 is free\nX11 is free\nX394 is free\nX395 is free\ndelete(T380, T2, tree(T383, T381, T384)) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T385, T383, T384) !=? delmin(tree(X394, void, X395), X394, X395)", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: delmin(T503, T500, T501)\n\nT380 is ground\nT381 is ground\nT500 is ground\nT497 is ground\nT501 is ground\nT502 is ground\nX10 is free\nX11 is free\nX394 is free\nX395 is free\ndelete(T380, T2, tree(T500, T381, tree(T497, T501, T502))) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T385, T500, tree(T497, T501, T502)) !=? delmin(tree(X394, void, X395), X394, X395)", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: delete(T380, T2, tree(T383, T381, T384)), SCOPE: 1, CLAUSE: 5 | delete(T380, T2, tree(T383, T381, T384)), SCOPE: 1, CLAUSE: 6\n\nT380 is ground\nT383 is ground\nT381 is ground\nT384 is ground\nX10 is free\nX11 is free\nX394 is free\nX395 is free\ndelete(T380, T2, tree(T383, T381, T384)) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T385, T383, T384) !=? delmin(tree(X394, void, X395), X394, X395)", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: delete(T380, T2, tree(T383, T381, T384)), SCOPE: 1, CLAUSE: 5\n\nT380 is ground\nT383 is ground\nT381 is ground\nT384 is ground\nX10 is free\nX11 is free\nX394 is free\nX395 is free\ndelete(T380, T2, tree(T383, T381, T384)) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T385, T383, T384) !=? delmin(tree(X394, void, X395), X394, X395)", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: delete(T380, T2, tree(T383, T381, T384)), SCOPE: 1, CLAUSE: 6\n\nT380 is ground\nT383 is ground\nT381 is ground\nT384 is ground\nX10 is free\nX11 is free\nX394 is free\nX395 is free\ndelete(T380, T2, tree(T383, T381, T384)) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T385, T383, T384) !=? delmin(tree(X394, void, X395), X394, X395)", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: ','(less(T528, T529), delete(T528, T533, T532))\n\nT528 is ground\nT529 is ground\nT532 is ground\nT531 is ground\nX10 is free\nX11 is free\nX394 is free\nX395 is free\ndelete(T528, T2, tree(T529, T532, T531)) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T385, T529, T531) !=? delmin(tree(X394, void, X395), X394, X395)", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: ','(less(T547, T546), delete(T546, T551, T550))\n\nT546 is ground\nT547 is ground\nT548 is ground\nT550 is ground\nX10 is free\nX11 is free\nX394 is free\nX395 is free\ndelete(T546, T2, tree(T547, T548, T550)) !=? delete(X10, tree(X10, X11, void), X11)\ndelmin(T385, T547, T550) !=? delmin(tree(X394, void, X395), X394, X395)", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
261 [label="261: ','(less(T559, T560), delete(T559, T564, T563)) | delete(T559, T2, tree(T560, T563, T562)), SCOPE: 1, CLAUSE: 6\n\nT559 is ground\nT560 is ground\nT563 is ground\nT562 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\ndelete(T559, T2, tree(T560, T563, T562)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T559, T2, tree(T560, T563, T562)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))", fontsize=16, style=filled, fillcolor=lightyellow];
262 [label="262: delete(T6, T2, T7), SCOPE: 1, CLAUSE: 6\n\nT6 is ground\nT7 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\nX557 is free\nX558 is free\nX559 is free\nX560 is free\nX561 is free\ndelete(T6, T2, T7) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T6, T2, T7) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))\ndelete(T6, T2, T7) !=? delete(X557, tree(X558, X559, X560), tree(X558, X561, X560))", fontsize=16, style=filled, fillcolor=lightyellow];
263 [label="263: ','(less(T559, T560), delete(T559, T564, T563)), SCOPE: 9, CLAUSE: 3 | ','(less(T559, T560), delete(T559, T564, T563)), SCOPE: 9, CLAUSE: 8 | ?_9 | delete(T559, T2, tree(T560, T563, T562)), SCOPE: 1, CLAUSE: 6\n\nT559 is ground\nT560 is ground\nT563 is ground\nT562 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\ndelete(T559, T2, tree(T560, T563, T562)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T559, T2, tree(T560, T563, T562)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))", fontsize=16, style=filled, fillcolor=lightyellow];
264 [label="264: delete(0, T564, T563) | ','(less(0, s(T567)), delete(0, T564, T563)), SCOPE: 9, CLAUSE: 8 | ?_9 | delete(0, T2, tree(s(T567), T563, T562)), SCOPE: 1, CLAUSE: 6\n\nT563 is ground\nT562 is ground\nT567 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\ndelete(0, T2, tree(s(T567), T563, T562)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(0, T2, tree(s(T567), T563, T562)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))", fontsize=16, style=filled, fillcolor=lightyellow];
265 [label="265: ','(less(T559, T560), delete(T559, T564, T563)), SCOPE: 9, CLAUSE: 8 | ?_9 | delete(T559, T2, tree(T560, T563, T562)), SCOPE: 1, CLAUSE: 6\n\nT559 is ground\nT560 is ground\nT563 is ground\nT562 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\nX564 is free\ndelete(T559, T2, tree(T560, T563, T562)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T559, T2, tree(T560, T563, T562)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))\nless(T559, T560) !=? less(0, s(X564))", fontsize=16, style=filled, fillcolor=lightyellow];
266 [label="266: delete(0, T564, T563)\n\nT563 is ground\nT562 is ground\nT567 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\ndelete(0, T2, tree(s(T567), T563, T562)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(0, T2, tree(s(T567), T563, T562)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))", fontsize=16, style=filled, fillcolor=lightyellow];
267 [label="267: ','(less(0, s(T567)), delete(0, T564, T563)), SCOPE: 9, CLAUSE: 8 | ?_9 | delete(0, T2, tree(s(T567), T563, T562)), SCOPE: 1, CLAUSE: 6\n\nT563 is ground\nT562 is ground\nT567 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\ndelete(0, T2, tree(s(T567), T563, T562)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(0, T2, tree(s(T567), T563, T562)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))", fontsize=16, style=filled, fillcolor=lightyellow];
274 [label="274: ?_9 | delete(0, T2, tree(s(T567), T563, T562)), SCOPE: 1, CLAUSE: 6\n\nT563 is ground\nT562 is ground\nT567 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\ndelete(0, T2, tree(s(T567), T563, T562)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(0, T2, tree(s(T567), T563, T562)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))", fontsize=16, style=filled, fillcolor=lightyellow];
275 [label="275: delete(0, T2, tree(s(T567), T563, T562)), SCOPE: 1, CLAUSE: 6\n\nT563 is ground\nT562 is ground\nT567 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\ndelete(0, T2, tree(s(T567), T563, T562)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(0, T2, tree(s(T567), T563, T562)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))", fontsize=16, style=filled, fillcolor=lightyellow];
293 [label="293: ','(less(s(T585), 0), delete(0, T587, T586))\n\nT585 is ground\nT583 is ground\nT586 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\ndelete(0, T2, tree(s(T585), T583, T586)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(0, T2, tree(s(T585), T583, T586)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))", fontsize=16, style=filled, fillcolor=lightyellow];
294 [label="294: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
301 [label="301: ','(less(T559, T560), delete(T559, T564, T563)), SCOPE: 9, CLAUSE: 8\n\nT559 is ground\nT560 is ground\nT563 is ground\nT562 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\nX564 is free\ndelete(T559, T2, tree(T560, T563, T562)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T559, T2, tree(T560, T563, T562)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))\nless(T559, T560) !=? less(0, s(X564))", fontsize=16, style=filled, fillcolor=lightyellow];
302 [label="302: ?_9 | delete(T559, T2, tree(T560, T563, T562)), SCOPE: 1, CLAUSE: 6\n\nT559 is ground\nT560 is ground\nT563 is ground\nT562 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\nX564 is free\ndelete(T559, T2, tree(T560, T563, T562)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T559, T2, tree(T560, T563, T562)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))\nless(T559, T560) !=? less(0, s(X564))", fontsize=16, style=filled, fillcolor=lightyellow];
303 [label="303: ','(less(T596, T597), delete(s(T596), T564, T563))\n\nT563 is ground\nT562 is ground\nT596 is ground\nT597 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\ndelete(s(T596), T2, tree(s(T597), T563, T562)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(s(T596), T2, tree(s(T597), T563, T562)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))", fontsize=16, style=filled, fillcolor=lightyellow];
304 [label="304: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
305 [label="305: delete(T559, T2, tree(T560, T563, T562)), SCOPE: 1, CLAUSE: 6\n\nT559 is ground\nT560 is ground\nT563 is ground\nT562 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\nX564 is free\ndelete(T559, T2, tree(T560, T563, T562)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T559, T2, tree(T560, T563, T562)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))\nless(T559, T560) !=? less(0, s(X564))", fontsize=16, style=filled, fillcolor=lightyellow];
306 [label="306: ','(less(T611, T610), delete(T610, T615, T614))\n\nT610 is ground\nT611 is ground\nT612 is ground\nT614 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\nX564 is free\ndelete(T610, T2, tree(T611, T612, T614)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T610, T2, tree(T611, T612, T614)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))\nless(T610, T611) !=? less(0, s(X564))", fontsize=16, style=filled, fillcolor=lightyellow];
307 [label="307: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
308 [label="308: ','(less(T624, T623), delete(T623, T628, T627))\n\nT623 is ground\nT624 is ground\nT625 is ground\nT627 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\nX557 is free\nX558 is free\nX559 is free\nX560 is free\nX561 is free\ndelete(T623, T2, tree(T624, T625, T627)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T623, T2, tree(T624, T625, T627)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))\ndelete(T623, T2, tree(T624, T625, T627)) !=? delete(X557, tree(X558, X559, X560), tree(X558, X561, X560))", fontsize=16, style=filled, fillcolor=lightyellow];
309 [label="309: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
310 [label="310: ','(less(T624, T623), delete(T623, T628, T627)), SCOPE: 10, CLAUSE: 3 | ','(less(T624, T623), delete(T623, T628, T627)), SCOPE: 10, CLAUSE: 8\n\nT623 is ground\nT624 is ground\nT625 is ground\nT627 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\nX557 is free\nX558 is free\nX559 is free\nX560 is free\nX561 is free\ndelete(T623, T2, tree(T624, T625, T627)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T623, T2, tree(T624, T625, T627)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))\ndelete(T623, T2, tree(T624, T625, T627)) !=? delete(X557, tree(X558, X559, X560), tree(X558, X561, X560))", fontsize=16, style=filled, fillcolor=lightyellow];
311 [label="311: delete(s(T631), T628, T627) | ','(less(0, s(T631)), delete(s(T631), T628, T627)), SCOPE: 10, CLAUSE: 8\n\nT625 is ground\nT627 is ground\nT631 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\nX557 is free\nX558 is free\nX559 is free\nX560 is free\nX561 is free\ndelete(s(T631), T2, tree(0, T625, T627)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(s(T631), T2, tree(0, T625, T627)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))\ndelete(s(T631), T2, tree(0, T625, T627)) !=? delete(X557, tree(X558, X559, X560), tree(X558, X561, X560))", fontsize=16, style=filled, fillcolor=lightyellow];
312 [label="312: ','(less(T624, T623), delete(T623, T628, T627)), SCOPE: 10, CLAUSE: 8\n\nT623 is ground\nT624 is ground\nT625 is ground\nT627 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\nX557 is free\nX558 is free\nX559 is free\nX560 is free\nX561 is free\nX633 is free\ndelete(T623, T2, tree(T624, T625, T627)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T623, T2, tree(T624, T625, T627)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))\ndelete(T623, T2, tree(T624, T625, T627)) !=? delete(X557, tree(X558, X559, X560), tree(X558, X561, X560))\nless(T624, T623) !=? less(0, s(X633))", fontsize=16, style=filled, fillcolor=lightyellow];
313 [label="313: delete(s(T631), T628, T627)\n\nT625 is ground\nT627 is ground\nT631 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\nX557 is free\nX558 is free\nX559 is free\nX560 is free\nX561 is free\ndelete(s(T631), T2, tree(0, T625, T627)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(s(T631), T2, tree(0, T625, T627)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))\ndelete(s(T631), T2, tree(0, T625, T627)) !=? delete(X557, tree(X558, X559, X560), tree(X558, X561, X560))", fontsize=16, style=filled, fillcolor=lightyellow];
314 [label="314: ','(less(0, s(T631)), delete(s(T631), T628, T627)), SCOPE: 10, CLAUSE: 8\n\nT625 is ground\nT627 is ground\nT631 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\nX557 is free\nX558 is free\nX559 is free\nX560 is free\nX561 is free\ndelete(s(T631), T2, tree(0, T625, T627)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(s(T631), T2, tree(0, T625, T627)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))\ndelete(s(T631), T2, tree(0, T625, T627)) !=? delete(X557, tree(X558, X559, X560), tree(X558, X561, X560))", fontsize=16, style=filled, fillcolor=lightyellow];
315 [label="315: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
316 [label="316: ','(less(T644, T645), delete(s(T645), T628, T627))\n\nT625 is ground\nT627 is ground\nT644 is ground\nT645 is ground\nX10 is free\nX11 is free\nX385 is free\nX386 is free\nX387 is free\nX388 is free\nX389 is free\nX557 is free\nX558 is free\nX559 is free\nX560 is free\nX561 is free\ndelete(s(T645), T2, tree(s(T644), T625, T627)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(s(T645), T2, tree(s(T644), T625, T627)) !=? delete(X385, tree(X385, X386, X387), tree(X388, X386, X389))\ndelete(s(T645), T2, tree(s(T644), T625, T627)) !=? delete(X557, tree(X558, X559, X560), tree(X558, X561, X560))", fontsize=16, style=filled, fillcolor=lightyellow];
317 [label="317: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
318 [label="318: true | delete(T650, T2, T651), SCOPE: 1, CLAUSE: 4 | delete(T650, T2, T651), SCOPE: 1, CLAUSE: 5 | delete(T650, T2, T651), SCOPE: 1, CLAUSE: 6\n\nT650 is ground\nT651 is ground\nX6 is free\nX7 is free\ndelete(T650, T2, T651) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
319 [label="319: 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\nT3 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X654, tree(X654, X655, void), X655)", fontsize=16, style=filled, fillcolor=lightyellow];
320 [label="320: delete(T650, T2, T651), SCOPE: 1, CLAUSE: 4 | delete(T650, T2, T651), SCOPE: 1, CLAUSE: 5 | delete(T650, T2, T651), SCOPE: 1, CLAUSE: 6\n\nT650 is ground\nT651 is ground\nX6 is free\nX7 is free\ndelete(T650, T2, T651) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
321 [label="321: delmin(T662, T660, T661) | delete(T657, T2, tree(T660, T658, T661)), SCOPE: 1, CLAUSE: 5 | delete(T657, T2, tree(T660, T658, T661)), SCOPE: 1, CLAUSE: 6\n\nT657 is ground\nT660 is ground\nT658 is ground\nT661 is ground\nX6 is free\nX7 is free\ndelete(T657, T2, tree(T660, T658, T661)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
322 [label="322: delete(T650, T2, T651), SCOPE: 1, CLAUSE: 5 | delete(T650, T2, T651), SCOPE: 1, CLAUSE: 6\n\nT650 is ground\nT651 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\ndelete(T650, T2, T651) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T650, T2, T651) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))", fontsize=16, style=filled, fillcolor=lightyellow];
323 [label="323: delmin(T662, T660, T661), SCOPE: 11, CLAUSE: 2 | delmin(T662, T660, T661), SCOPE: 11, CLAUSE: 7 | ?_11 | delete(T657, T2, tree(T660, T658, T661)), SCOPE: 1, CLAUSE: 5 | delete(T657, T2, tree(T660, T658, T661)), SCOPE: 1, CLAUSE: 6\n\nT657 is ground\nT660 is ground\nT658 is ground\nT661 is ground\nX6 is free\nX7 is free\ndelete(T657, T2, tree(T660, T658, T661)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
324 [label="324: true | delmin(T662, T667, T668), SCOPE: 11, CLAUSE: 7 | ?_11 | delete(T657, T2, tree(T667, T658, T668)), SCOPE: 1, CLAUSE: 5 | delete(T657, T2, tree(T667, T658, T668)), SCOPE: 1, CLAUSE: 6\n\nT657 is ground\nT658 is ground\nT667 is ground\nT668 is ground\nX6 is free\nX7 is free\ndelete(T657, T2, tree(T667, T658, T668)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
325 [label="325: delmin(T662, T660, T661), SCOPE: 11, CLAUSE: 7 | ?_11 | delete(T657, T2, tree(T660, T658, T661)), SCOPE: 1, CLAUSE: 5 | delete(T657, T2, tree(T660, T658, T661)), SCOPE: 1, CLAUSE: 6\n\nT657 is ground\nT660 is ground\nT658 is ground\nT661 is ground\nX6 is free\nX7 is free\nX670 is free\nX671 is free\ndelete(T657, T2, tree(T660, T658, T661)) !=? delete(X6, tree(X6, void, X7), X7)\ndelmin(T662, T660, T661) !=? delmin(tree(X670, void, X671), X670, X671)", fontsize=16, style=filled, fillcolor=lightyellow];
326 [label="326: delmin(T662, T667, T668), SCOPE: 11, CLAUSE: 7 | ?_11 | delete(T657, T2, tree(T667, T658, T668)), SCOPE: 1, CLAUSE: 5 | delete(T657, T2, tree(T667, T658, T668)), SCOPE: 1, CLAUSE: 6\n\nT657 is ground\nT658 is ground\nT667 is ground\nT668 is ground\nX6 is free\nX7 is free\ndelete(T657, T2, tree(T667, T658, T668)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
327 [label="327: delmin(T662, T667, T668), SCOPE: 11, CLAUSE: 7\n\nT657 is ground\nT658 is ground\nT667 is ground\nT668 is ground\nX6 is free\nX7 is free\ndelete(T657, T2, tree(T667, T658, T668)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
328 [label="328: ?_11 | delete(T657, T2, tree(T667, T658, T668)), SCOPE: 1, CLAUSE: 5 | delete(T657, T2, tree(T667, T658, T668)), SCOPE: 1, CLAUSE: 6\n\nT657 is ground\nT658 is ground\nT667 is ground\nT668 is ground\nX6 is free\nX7 is free\ndelete(T657, T2, tree(T667, T658, T668)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
329 [label="329: delmin(T699, T696, T697)\n\nT657 is ground\nT658 is ground\nT696 is ground\nT693 is ground\nT697 is ground\nT698 is ground\nX6 is free\nX7 is free\ndelete(T657, T2, tree(T696, T658, tree(T693, T697, T698))) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
330 [label="330: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
414 [label="414: delete(T657, T2, tree(T667, T658, T668)), SCOPE: 1, CLAUSE: 5 | delete(T657, T2, tree(T667, T658, T668)), SCOPE: 1, CLAUSE: 6\n\nT657 is ground\nT658 is ground\nT667 is ground\nT668 is ground\nX6 is free\nX7 is free\ndelete(T657, T2, tree(T667, T658, T668)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
415 [label="415: delete(T657, T2, tree(T667, T658, T668)), SCOPE: 1, CLAUSE: 5\n\nT657 is ground\nT658 is ground\nT667 is ground\nT668 is ground\nX6 is free\nX7 is free\ndelete(T657, T2, tree(T667, T658, T668)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
416 [label="416: delete(T657, T2, tree(T667, T658, T668)), SCOPE: 1, CLAUSE: 6\n\nT657 is ground\nT658 is ground\nT667 is ground\nT668 is ground\nX6 is free\nX7 is free\ndelete(T657, T2, tree(T667, T658, T668)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
417 [label="417: ','(less(T724, T725), delete(T724, T729, T728))\n\nT724 is ground\nT725 is ground\nT728 is ground\nT727 is ground\nX6 is free\nX7 is free\ndelete(T724, T2, tree(T725, T728, T727)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
418 [label="418: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
419 [label="419: ','(less(T743, T742), delete(T742, T747, T746))\n\nT742 is ground\nT743 is ground\nT744 is ground\nT746 is ground\nX6 is free\nX7 is free\ndelete(T742, T2, tree(T743, T744, T746)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
420 [label="420: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
422 [label="422: delmin(T662, T660, T661), SCOPE: 11, CLAUSE: 7\n\nT657 is ground\nT660 is ground\nT658 is ground\nT661 is ground\nX6 is free\nX7 is free\nX670 is free\nX671 is free\ndelete(T657, T2, tree(T660, T658, T661)) !=? delete(X6, tree(X6, void, X7), X7)\ndelmin(T662, T660, T661) !=? delmin(tree(X670, void, X671), X670, X671)", fontsize=16, style=filled, fillcolor=lightyellow];
424 [label="424: ?_11 | delete(T657, T2, tree(T660, T658, T661)), SCOPE: 1, CLAUSE: 5 | delete(T657, T2, tree(T660, T658, T661)), SCOPE: 1, CLAUSE: 6\n\nT657 is ground\nT660 is ground\nT658 is ground\nT661 is ground\nX6 is free\nX7 is free\nX670 is free\nX671 is free\ndelete(T657, T2, tree(T660, T658, T661)) !=? delete(X6, tree(X6, void, X7), X7)\ndelmin(T662, T660, T661) !=? delmin(tree(X670, void, X671), X670, X671)", fontsize=16, style=filled, fillcolor=lightyellow];
458 [label="458: delmin(T780, T777, T778)\n\nT657 is ground\nT658 is ground\nT777 is ground\nT774 is ground\nT778 is ground\nT779 is ground\nX6 is free\nX7 is free\nX670 is free\nX671 is free\ndelete(T657, T2, tree(T777, T658, tree(T774, T778, T779))) !=? delete(X6, tree(X6, void, X7), X7)\ndelmin(T662, T777, tree(T774, T778, T779)) !=? delmin(tree(X670, void, X671), X670, X671)", fontsize=16, style=filled, fillcolor=lightyellow];
459 [label="459: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
460 [label="460: delete(T657, T2, tree(T660, T658, T661)), SCOPE: 1, CLAUSE: 5 | delete(T657, T2, tree(T660, T658, T661)), SCOPE: 1, CLAUSE: 6\n\nT657 is ground\nT660 is ground\nT658 is ground\nT661 is ground\nX6 is free\nX7 is free\nX670 is free\nX671 is free\ndelete(T657, T2, tree(T660, T658, T661)) !=? delete(X6, tree(X6, void, X7), X7)\ndelmin(T662, T660, T661) !=? delmin(tree(X670, void, X671), X670, X671)", fontsize=16, style=filled, fillcolor=lightyellow];
461 [label="461: delete(T657, T2, tree(T660, T658, T661)), SCOPE: 1, CLAUSE: 5\n\nT657 is ground\nT660 is ground\nT658 is ground\nT661 is ground\nX6 is free\nX7 is free\nX670 is free\nX671 is free\ndelete(T657, T2, tree(T660, T658, T661)) !=? delete(X6, tree(X6, void, X7), X7)\ndelmin(T662, T660, T661) !=? delmin(tree(X670, void, X671), X670, X671)", fontsize=16, style=filled, fillcolor=lightyellow];
462 [label="462: delete(T657, T2, tree(T660, T658, T661)), SCOPE: 1, CLAUSE: 6\n\nT657 is ground\nT660 is ground\nT658 is ground\nT661 is ground\nX6 is free\nX7 is free\nX670 is free\nX671 is free\ndelete(T657, T2, tree(T660, T658, T661)) !=? delete(X6, tree(X6, void, X7), X7)\ndelmin(T662, T660, T661) !=? delmin(tree(X670, void, X671), X670, X671)", fontsize=16, style=filled, fillcolor=lightyellow];
463 [label="463: ','(less(T805, T806), delete(T805, T810, T809))\n\nT805 is ground\nT806 is ground\nT809 is ground\nT808 is ground\nX6 is free\nX7 is free\nX670 is free\nX671 is free\ndelete(T805, T2, tree(T806, T809, T808)) !=? delete(X6, tree(X6, void, X7), X7)\ndelmin(T662, T806, T808) !=? delmin(tree(X670, void, X671), X670, X671)", fontsize=16, style=filled, fillcolor=lightyellow];
464 [label="464: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
465 [label="465: ','(less(T824, T823), delete(T823, T828, T827))\n\nT823 is ground\nT824 is ground\nT825 is ground\nT827 is ground\nX6 is free\nX7 is free\nX670 is free\nX671 is free\ndelete(T823, T2, tree(T824, T825, T827)) !=? delete(X6, tree(X6, void, X7), X7)\ndelmin(T662, T824, T827) !=? delmin(tree(X670, void, X671), X670, X671)", fontsize=16, style=filled, fillcolor=lightyellow];
466 [label="466: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
467 [label="467: ','(less(T836, T837), delete(T836, T841, T840)) | delete(T836, T2, tree(T837, T840, T839)), SCOPE: 1, CLAUSE: 6\n\nT836 is ground\nT837 is ground\nT840 is ground\nT839 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\ndelete(T836, T2, tree(T837, T840, T839)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T836, T2, tree(T837, T840, T839)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))", fontsize=16, style=filled, fillcolor=lightyellow];
468 [label="468: delete(T650, T2, T651), SCOPE: 1, CLAUSE: 6\n\nT650 is ground\nT651 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\nX833 is free\nX834 is free\nX835 is free\nX836 is free\nX837 is free\ndelete(T650, T2, T651) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T650, T2, T651) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))\ndelete(T650, T2, T651) !=? delete(X833, tree(X834, X835, X836), tree(X834, X837, X836))", fontsize=16, style=filled, fillcolor=lightyellow];
469 [label="469: ','(less(T836, T837), delete(T836, T841, T840)), SCOPE: 12, CLAUSE: 3 | ','(less(T836, T837), delete(T836, T841, T840)), SCOPE: 12, CLAUSE: 8 | ?_12 | delete(T836, T2, tree(T837, T840, T839)), SCOPE: 1, CLAUSE: 6\n\nT836 is ground\nT837 is ground\nT840 is ground\nT839 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\ndelete(T836, T2, tree(T837, T840, T839)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T836, T2, tree(T837, T840, T839)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))", fontsize=16, style=filled, fillcolor=lightyellow];
470 [label="470: delete(0, T841, T840) | ','(less(0, s(T844)), delete(0, T841, T840)), SCOPE: 12, CLAUSE: 8 | ?_12 | delete(0, T2, tree(s(T844), T840, T839)), SCOPE: 1, CLAUSE: 6\n\nT840 is ground\nT839 is ground\nT844 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\ndelete(0, T2, tree(s(T844), T840, T839)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(0, T2, tree(s(T844), T840, T839)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))", fontsize=16, style=filled, fillcolor=lightyellow];
471 [label="471: ','(less(T836, T837), delete(T836, T841, T840)), SCOPE: 12, CLAUSE: 8 | ?_12 | delete(T836, T2, tree(T837, T840, T839)), SCOPE: 1, CLAUSE: 6\n\nT836 is ground\nT837 is ground\nT840 is ground\nT839 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\nX840 is free\ndelete(T836, T2, tree(T837, T840, T839)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T836, T2, tree(T837, T840, T839)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))\nless(T836, T837) !=? less(0, s(X840))", fontsize=16, style=filled, fillcolor=lightyellow];
475 [label="475: delete(0, T841, T840)\n\nT840 is ground\nT839 is ground\nT844 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\ndelete(0, T2, tree(s(T844), T840, T839)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(0, T2, tree(s(T844), T840, T839)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))", fontsize=16, style=filled, fillcolor=lightyellow];
476 [label="476: ','(less(0, s(T844)), delete(0, T841, T840)), SCOPE: 12, CLAUSE: 8 | ?_12 | delete(0, T2, tree(s(T844), T840, T839)), SCOPE: 1, CLAUSE: 6\n\nT840 is ground\nT839 is ground\nT844 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\ndelete(0, T2, tree(s(T844), T840, T839)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(0, T2, tree(s(T844), T840, T839)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))", fontsize=16, style=filled, fillcolor=lightyellow];
478 [label="478: ?_12 | delete(0, T2, tree(s(T844), T840, T839)), SCOPE: 1, CLAUSE: 6\n\nT840 is ground\nT839 is ground\nT844 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\ndelete(0, T2, tree(s(T844), T840, T839)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(0, T2, tree(s(T844), T840, T839)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))", fontsize=16, style=filled, fillcolor=lightyellow];
479 [label="479: delete(0, T2, tree(s(T844), T840, T839)), SCOPE: 1, CLAUSE: 6\n\nT840 is ground\nT839 is ground\nT844 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\ndelete(0, T2, tree(s(T844), T840, T839)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(0, T2, tree(s(T844), T840, T839)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))", fontsize=16, style=filled, fillcolor=lightyellow];
519 [label="519: ','(less(s(T862), 0), delete(0, T864, T863))\n\nT862 is ground\nT860 is ground\nT863 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\ndelete(0, T2, tree(s(T862), T860, T863)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(0, T2, tree(s(T862), T860, T863)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))", fontsize=16, style=filled, fillcolor=lightyellow];
520 [label="520: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
521 [label="521: ','(less(T836, T837), delete(T836, T841, T840)), SCOPE: 12, CLAUSE: 8\n\nT836 is ground\nT837 is ground\nT840 is ground\nT839 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\nX840 is free\ndelete(T836, T2, tree(T837, T840, T839)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T836, T2, tree(T837, T840, T839)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))\nless(T836, T837) !=? less(0, s(X840))", fontsize=16, style=filled, fillcolor=lightyellow];
522 [label="522: ?_12 | delete(T836, T2, tree(T837, T840, T839)), SCOPE: 1, CLAUSE: 6\n\nT836 is ground\nT837 is ground\nT840 is ground\nT839 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\nX840 is free\ndelete(T836, T2, tree(T837, T840, T839)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T836, T2, tree(T837, T840, T839)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))\nless(T836, T837) !=? less(0, s(X840))", fontsize=16, style=filled, fillcolor=lightyellow];
523 [label="523: ','(less(T873, T874), delete(s(T873), T841, T840))\n\nT840 is ground\nT839 is ground\nT873 is ground\nT874 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\ndelete(s(T873), T2, tree(s(T874), T840, T839)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T873), T2, tree(s(T874), T840, T839)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))", fontsize=16, style=filled, fillcolor=lightyellow];
524 [label="524: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
525 [label="525: delete(T836, T2, tree(T837, T840, T839)), SCOPE: 1, CLAUSE: 6\n\nT836 is ground\nT837 is ground\nT840 is ground\nT839 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\nX840 is free\ndelete(T836, T2, tree(T837, T840, T839)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T836, T2, tree(T837, T840, T839)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))\nless(T836, T837) !=? less(0, s(X840))", fontsize=16, style=filled, fillcolor=lightyellow];
526 [label="526: ','(less(T888, T887), delete(T887, T892, T891))\n\nT887 is ground\nT888 is ground\nT889 is ground\nT891 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\nX840 is free\ndelete(T887, T2, tree(T888, T889, T891)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T887, T2, tree(T888, T889, T891)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))\nless(T887, T888) !=? less(0, s(X840))", fontsize=16, style=filled, fillcolor=lightyellow];
527 [label="527: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
528 [label="528: ','(less(T901, T900), delete(T900, T905, T904))\n\nT900 is ground\nT901 is ground\nT902 is ground\nT904 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\nX833 is free\nX834 is free\nX835 is free\nX836 is free\nX837 is free\ndelete(T900, T2, tree(T901, T902, T904)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T900, T2, tree(T901, T902, T904)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))\ndelete(T900, T2, tree(T901, T902, T904)) !=? delete(X833, tree(X834, X835, X836), tree(X834, X837, X836))", fontsize=16, style=filled, fillcolor=lightyellow];
529 [label="529: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
530 [label="530: ','(less(T901, T900), delete(T900, T905, T904)), SCOPE: 13, CLAUSE: 3 | ','(less(T901, T900), delete(T900, T905, T904)), SCOPE: 13, CLAUSE: 8\n\nT900 is ground\nT901 is ground\nT902 is ground\nT904 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\nX833 is free\nX834 is free\nX835 is free\nX836 is free\nX837 is free\ndelete(T900, T2, tree(T901, T902, T904)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T900, T2, tree(T901, T902, T904)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))\ndelete(T900, T2, tree(T901, T902, T904)) !=? delete(X833, tree(X834, X835, X836), tree(X834, X837, X836))", fontsize=16, style=filled, fillcolor=lightyellow];
531 [label="531: delete(s(T908), T905, T904) | ','(less(0, s(T908)), delete(s(T908), T905, T904)), SCOPE: 13, CLAUSE: 8\n\nT902 is ground\nT904 is ground\nT908 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\nX833 is free\nX834 is free\nX835 is free\nX836 is free\nX837 is free\ndelete(s(T908), T2, tree(0, T902, T904)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T908), T2, tree(0, T902, T904)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))\ndelete(s(T908), T2, tree(0, T902, T904)) !=? delete(X833, tree(X834, X835, X836), tree(X834, X837, X836))", fontsize=16, style=filled, fillcolor=lightyellow];
532 [label="532: ','(less(T901, T900), delete(T900, T905, T904)), SCOPE: 13, CLAUSE: 8\n\nT900 is ground\nT901 is ground\nT902 is ground\nT904 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\nX833 is free\nX834 is free\nX835 is free\nX836 is free\nX837 is free\nX909 is free\ndelete(T900, T2, tree(T901, T902, T904)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T900, T2, tree(T901, T902, T904)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))\ndelete(T900, T2, tree(T901, T902, T904)) !=? delete(X833, tree(X834, X835, X836), tree(X834, X837, X836))\nless(T901, T900) !=? less(0, s(X909))", fontsize=16, style=filled, fillcolor=lightyellow];
533 [label="533: delete(s(T908), T905, T904)\n\nT902 is ground\nT904 is ground\nT908 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\nX833 is free\nX834 is free\nX835 is free\nX836 is free\nX837 is free\ndelete(s(T908), T2, tree(0, T902, T904)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T908), T2, tree(0, T902, T904)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))\ndelete(s(T908), T2, tree(0, T902, T904)) !=? delete(X833, tree(X834, X835, X836), tree(X834, X837, X836))", fontsize=16, style=filled, fillcolor=lightyellow];
534 [label="534: ','(less(0, s(T908)), delete(s(T908), T905, T904)), SCOPE: 13, CLAUSE: 8\n\nT902 is ground\nT904 is ground\nT908 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\nX833 is free\nX834 is free\nX835 is free\nX836 is free\nX837 is free\ndelete(s(T908), T2, tree(0, T902, T904)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T908), T2, tree(0, T902, T904)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))\ndelete(s(T908), T2, tree(0, T902, T904)) !=? delete(X833, tree(X834, X835, X836), tree(X834, X837, X836))", fontsize=16, style=filled, fillcolor=lightyellow];
535 [label="535: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
536 [label="536: ','(less(T921, T922), delete(s(T922), T905, T904))\n\nT902 is ground\nT904 is ground\nT921 is ground\nT922 is ground\nX6 is free\nX7 is free\nX661 is free\nX662 is free\nX663 is free\nX664 is free\nX665 is free\nX833 is free\nX834 is free\nX835 is free\nX836 is free\nX837 is free\ndelete(s(T922), T2, tree(s(T921), T902, T904)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T922), T2, tree(s(T921), T902, T904)) !=? delete(X661, tree(X661, X662, X663), tree(X664, X662, X665))\ndelete(s(T922), T2, tree(s(T921), T902, T904)) !=? delete(X833, tree(X834, X835, X836), tree(X834, X837, X836))", fontsize=16, style=filled, fillcolor=lightyellow];
537 [label="537: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
538 [label="538: delmin(T935, T933, T934) | delete(T930, T2, tree(T933, T931, T934)), SCOPE: 1, CLAUSE: 5 | delete(T930, T2, tree(T933, T931, T934)), SCOPE: 1, CLAUSE: 6\n\nT930 is ground\nT933 is ground\nT931 is ground\nT934 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X654, tree(X654, X655, void), X655)", fontsize=16, style=filled, fillcolor=lightyellow];
539 [label="539: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 5 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 6\n\nT1 is ground\nT3 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(T1, T2, T3) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))", fontsize=16, style=filled, fillcolor=lightyellow];
540 [label="540: delmin(T935, T933, T934), SCOPE: 14, CLAUSE: 2 | delmin(T935, T933, T934), SCOPE: 14, CLAUSE: 7 | ?_14 | delete(T930, T2, tree(T933, T931, T934)), SCOPE: 1, CLAUSE: 5 | delete(T930, T2, tree(T933, T931, T934)), SCOPE: 1, CLAUSE: 6\n\nT930 is ground\nT933 is ground\nT931 is ground\nT934 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X654, tree(X654, X655, void), X655)", fontsize=16, style=filled, fillcolor=lightyellow];
541 [label="541: true | delmin(T935, T940, T941), SCOPE: 14, CLAUSE: 7 | ?_14 | delete(T930, T2, tree(T940, T931, T941)), SCOPE: 1, CLAUSE: 5 | delete(T930, T2, tree(T940, T931, T941)), SCOPE: 1, CLAUSE: 6\n\nT930 is ground\nT931 is ground\nT940 is ground\nT941 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\ndelete(T930, T2, tree(T940, T931, T941)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T940, T931, T941)) !=? delete(X654, tree(X654, X655, void), X655)", fontsize=16, style=filled, fillcolor=lightyellow];
542 [label="542: delmin(T935, T933, T934), SCOPE: 14, CLAUSE: 7 | ?_14 | delete(T930, T2, tree(T933, T931, T934)), SCOPE: 1, CLAUSE: 5 | delete(T930, T2, tree(T933, T931, T934)), SCOPE: 1, CLAUSE: 6\n\nT930 is ground\nT933 is ground\nT931 is ground\nT934 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX942 is free\nX943 is free\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X654, tree(X654, X655, void), X655)\ndelmin(T935, T933, T934) !=? delmin(tree(X942, void, X943), X942, X943)", fontsize=16, style=filled, fillcolor=lightyellow];
543 [label="543: delmin(T935, T940, T941), SCOPE: 14, CLAUSE: 7 | ?_14 | delete(T930, T2, tree(T940, T931, T941)), SCOPE: 1, CLAUSE: 5 | delete(T930, T2, tree(T940, T931, T941)), SCOPE: 1, CLAUSE: 6\n\nT930 is ground\nT931 is ground\nT940 is ground\nT941 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\ndelete(T930, T2, tree(T940, T931, T941)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T940, T931, T941)) !=? delete(X654, tree(X654, X655, void), X655)", fontsize=16, style=filled, fillcolor=lightyellow];
574 [label="574: delmin(T935, T940, T941), SCOPE: 14, CLAUSE: 7\n\nT930 is ground\nT931 is ground\nT940 is ground\nT941 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\ndelete(T930, T2, tree(T940, T931, T941)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T940, T931, T941)) !=? delete(X654, tree(X654, X655, void), X655)", fontsize=16, style=filled, fillcolor=lightyellow];
575 [label="575: ?_14 | delete(T930, T2, tree(T940, T931, T941)), SCOPE: 1, CLAUSE: 5 | delete(T930, T2, tree(T940, T931, T941)), SCOPE: 1, CLAUSE: 6\n\nT930 is ground\nT931 is ground\nT940 is ground\nT941 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\ndelete(T930, T2, tree(T940, T931, T941)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T940, T931, T941)) !=? delete(X654, tree(X654, X655, void), X655)", fontsize=16, style=filled, fillcolor=lightyellow];
576 [label="576: delmin(T972, T969, T970)\n\nT930 is ground\nT931 is ground\nT969 is ground\nT966 is ground\nT970 is ground\nT971 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\ndelete(T930, T2, tree(T969, T931, tree(T966, T970, T971))) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T969, T931, tree(T966, T970, T971))) !=? delete(X654, tree(X654, X655, void), X655)", fontsize=16, style=filled, fillcolor=lightyellow];
577 [label="577: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
578 [label="578: delete(T930, T2, tree(T940, T931, T941)), SCOPE: 1, CLAUSE: 5 | delete(T930, T2, tree(T940, T931, T941)), SCOPE: 1, CLAUSE: 6\n\nT930 is ground\nT931 is ground\nT940 is ground\nT941 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\ndelete(T930, T2, tree(T940, T931, T941)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T940, T931, T941)) !=? delete(X654, tree(X654, X655, void), X655)", fontsize=16, style=filled, fillcolor=lightyellow];
579 [label="579: delete(T930, T2, tree(T940, T931, T941)), SCOPE: 1, CLAUSE: 5\n\nT930 is ground\nT931 is ground\nT940 is ground\nT941 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\ndelete(T930, T2, tree(T940, T931, T941)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T940, T931, T941)) !=? delete(X654, tree(X654, X655, void), X655)", fontsize=16, style=filled, fillcolor=lightyellow];
580 [label="580: delete(T930, T2, tree(T940, T931, T941)), SCOPE: 1, CLAUSE: 6\n\nT930 is ground\nT931 is ground\nT940 is ground\nT941 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\ndelete(T930, T2, tree(T940, T931, T941)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T940, T931, T941)) !=? delete(X654, tree(X654, X655, void), X655)", fontsize=16, style=filled, fillcolor=lightyellow];
581 [label="581: ','(less(T997, T998), delete(T997, T1002, T1001))\n\nT997 is ground\nT998 is ground\nT1001 is ground\nT1000 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\ndelete(T997, T2, tree(T998, T1001, T1000)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T997, T2, tree(T998, T1001, T1000)) !=? delete(X654, tree(X654, X655, void), X655)", fontsize=16, style=filled, fillcolor=lightyellow];
582 [label="582: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
583 [label="583: ','(less(T1016, T1015), delete(T1015, T1020, T1019))\n\nT1015 is ground\nT1016 is ground\nT1017 is ground\nT1019 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\ndelete(T1015, T2, tree(T1016, T1017, T1019)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1015, T2, tree(T1016, T1017, T1019)) !=? delete(X654, tree(X654, X655, void), X655)", fontsize=16, style=filled, fillcolor=lightyellow];
584 [label="584: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
585 [label="585: delmin(T935, T933, T934), SCOPE: 14, CLAUSE: 7\n\nT930 is ground\nT933 is ground\nT931 is ground\nT934 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX942 is free\nX943 is free\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X654, tree(X654, X655, void), X655)\ndelmin(T935, T933, T934) !=? delmin(tree(X942, void, X943), X942, X943)", fontsize=16, style=filled, fillcolor=lightyellow];
586 [label="586: ?_14 | delete(T930, T2, tree(T933, T931, T934)), SCOPE: 1, CLAUSE: 5 | delete(T930, T2, tree(T933, T931, T934)), SCOPE: 1, CLAUSE: 6\n\nT930 is ground\nT933 is ground\nT931 is ground\nT934 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX942 is free\nX943 is free\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X654, tree(X654, X655, void), X655)\ndelmin(T935, T933, T934) !=? delmin(tree(X942, void, X943), X942, X943)", fontsize=16, style=filled, fillcolor=lightyellow];
587 [label="587: delmin(T1053, T1050, T1051)\n\nT930 is ground\nT931 is ground\nT1050 is ground\nT1047 is ground\nT1051 is ground\nT1052 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX942 is free\nX943 is free\ndelete(T930, T2, tree(T1050, T931, tree(T1047, T1051, T1052))) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T1050, T931, tree(T1047, T1051, T1052))) !=? delete(X654, tree(X654, X655, void), X655)\ndelmin(T935, T1050, tree(T1047, T1051, T1052)) !=? delmin(tree(X942, void, X943), X942, X943)", fontsize=16, style=filled, fillcolor=lightyellow];
588 [label="588: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
589 [label="589: delete(T930, T2, tree(T933, T931, T934)), SCOPE: 1, CLAUSE: 5 | delete(T930, T2, tree(T933, T931, T934)), SCOPE: 1, CLAUSE: 6\n\nT930 is ground\nT933 is ground\nT931 is ground\nT934 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX942 is free\nX943 is free\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X654, tree(X654, X655, void), X655)\ndelmin(T935, T933, T934) !=? delmin(tree(X942, void, X943), X942, X943)", fontsize=16, style=filled, fillcolor=lightyellow];
590 [label="590: delete(T930, T2, tree(T933, T931, T934)), SCOPE: 1, CLAUSE: 5\n\nT930 is ground\nT933 is ground\nT931 is ground\nT934 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX942 is free\nX943 is free\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X654, tree(X654, X655, void), X655)\ndelmin(T935, T933, T934) !=? delmin(tree(X942, void, X943), X942, X943)", fontsize=16, style=filled, fillcolor=lightyellow];
591 [label="591: delete(T930, T2, tree(T933, T931, T934)), SCOPE: 1, CLAUSE: 6\n\nT930 is ground\nT933 is ground\nT931 is ground\nT934 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX942 is free\nX943 is free\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T930, T2, tree(T933, T931, T934)) !=? delete(X654, tree(X654, X655, void), X655)\ndelmin(T935, T933, T934) !=? delmin(tree(X942, void, X943), X942, X943)", fontsize=16, style=filled, fillcolor=lightyellow];
592 [label="592: ','(less(T1078, T1079), delete(T1078, T1083, T1082))\n\nT1078 is ground\nT1079 is ground\nT1082 is ground\nT1081 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX942 is free\nX943 is free\ndelete(T1078, T2, tree(T1079, T1082, T1081)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1078, T2, tree(T1079, T1082, T1081)) !=? delete(X654, tree(X654, X655, void), X655)\ndelmin(T935, T1079, T1081) !=? delmin(tree(X942, void, X943), X942, X943)", fontsize=16, style=filled, fillcolor=lightyellow];
593 [label="593: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
594 [label="594: ','(less(T1097, T1096), delete(T1096, T1101, T1100))\n\nT1096 is ground\nT1097 is ground\nT1098 is ground\nT1100 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX942 is free\nX943 is free\ndelete(T1096, T2, tree(T1097, T1098, T1100)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1096, T2, tree(T1097, T1098, T1100)) !=? delete(X654, tree(X654, X655, void), X655)\ndelmin(T935, T1097, T1100) !=? delmin(tree(X942, void, X943), X942, X943)", fontsize=16, style=filled, fillcolor=lightyellow];
595 [label="595: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
596 [label="596: ','(less(T1109, T1110), delete(T1109, T1114, T1113)) | delete(T1109, T2, tree(T1110, T1113, T1112)), SCOPE: 1, CLAUSE: 6\n\nT1109 is ground\nT1110 is ground\nT1113 is ground\nT1112 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))", fontsize=16, style=filled, fillcolor=lightyellow];
597 [label="597: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 6\n\nT1 is ground\nT3 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\nX1105 is free\nX1106 is free\nX1107 is free\nX1108 is free\nX1109 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(T1, T2, T3) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))\ndelete(T1, T2, T3) !=? delete(X1105, tree(X1106, X1107, X1108), tree(X1106, X1109, X1108))", fontsize=16, style=filled, fillcolor=lightyellow];
598 [label="598: ','(less(T1109, T1110), delete(T1109, T1114, T1113)), SCOPE: 15, CLAUSE: 3 | ','(less(T1109, T1110), delete(T1109, T1114, T1113)), SCOPE: 15, CLAUSE: 8 | ?_15 | delete(T1109, T2, tree(T1110, T1113, T1112)), SCOPE: 1, CLAUSE: 6\n\nT1109 is ground\nT1110 is ground\nT1113 is ground\nT1112 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))", fontsize=16, style=filled, fillcolor=lightyellow];
599 [label="599: delete(0, T1114, T1113) | ','(less(0, s(T1117)), delete(0, T1114, T1113)), SCOPE: 15, CLAUSE: 8 | ?_15 | delete(0, T2, tree(s(T1117), T1113, T1112)), SCOPE: 1, CLAUSE: 6\n\nT1113 is ground\nT1112 is ground\nT1117 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\ndelete(0, T2, tree(s(T1117), T1113, T1112)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(0, T2, tree(s(T1117), T1113, T1112)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(0, T2, tree(s(T1117), T1113, T1112)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))", fontsize=16, style=filled, fillcolor=lightyellow];
600 [label="600: ','(less(T1109, T1110), delete(T1109, T1114, T1113)), SCOPE: 15, CLAUSE: 8 | ?_15 | delete(T1109, T2, tree(T1110, T1113, T1112)), SCOPE: 1, CLAUSE: 6\n\nT1109 is ground\nT1110 is ground\nT1113 is ground\nT1112 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\nX1112 is free\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))\nless(T1109, T1110) !=? less(0, s(X1112))", fontsize=16, style=filled, fillcolor=lightyellow];
601 [label="601: delete(0, T1114, T1113)\n\nT1113 is ground\nT1112 is ground\nT1117 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\ndelete(0, T2, tree(s(T1117), T1113, T1112)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(0, T2, tree(s(T1117), T1113, T1112)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(0, T2, tree(s(T1117), T1113, T1112)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))", fontsize=16, style=filled, fillcolor=lightyellow];
602 [label="602: ','(less(0, s(T1117)), delete(0, T1114, T1113)), SCOPE: 15, CLAUSE: 8 | ?_15 | delete(0, T2, tree(s(T1117), T1113, T1112)), SCOPE: 1, CLAUSE: 6\n\nT1113 is ground\nT1112 is ground\nT1117 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\ndelete(0, T2, tree(s(T1117), T1113, T1112)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(0, T2, tree(s(T1117), T1113, T1112)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(0, T2, tree(s(T1117), T1113, T1112)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))", fontsize=16, style=filled, fillcolor=lightyellow];
603 [label="603: ?_15 | delete(0, T2, tree(s(T1117), T1113, T1112)), SCOPE: 1, CLAUSE: 6\n\nT1113 is ground\nT1112 is ground\nT1117 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\ndelete(0, T2, tree(s(T1117), T1113, T1112)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(0, T2, tree(s(T1117), T1113, T1112)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(0, T2, tree(s(T1117), T1113, T1112)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))", fontsize=16, style=filled, fillcolor=lightyellow];
604 [label="604: delete(0, T2, tree(s(T1117), T1113, T1112)), SCOPE: 1, CLAUSE: 6\n\nT1113 is ground\nT1112 is ground\nT1117 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\ndelete(0, T2, tree(s(T1117), T1113, T1112)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(0, T2, tree(s(T1117), T1113, T1112)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(0, T2, tree(s(T1117), T1113, T1112)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))", fontsize=16, style=filled, fillcolor=lightyellow];
605 [label="605: ','(less(s(T1135), 0), delete(0, T1137, T1136))\n\nT1135 is ground\nT1133 is ground\nT1136 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\ndelete(0, T2, tree(s(T1135), T1133, T1136)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(0, T2, tree(s(T1135), T1133, T1136)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(0, T2, tree(s(T1135), T1133, T1136)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))", fontsize=16, style=filled, fillcolor=lightyellow];
606 [label="606: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
607 [label="607: ','(less(T1109, T1110), delete(T1109, T1114, T1113)), SCOPE: 15, CLAUSE: 8\n\nT1109 is ground\nT1110 is ground\nT1113 is ground\nT1112 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\nX1112 is free\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))\nless(T1109, T1110) !=? less(0, s(X1112))", fontsize=16, style=filled, fillcolor=lightyellow];
608 [label="608: ?_15 | delete(T1109, T2, tree(T1110, T1113, T1112)), SCOPE: 1, CLAUSE: 6\n\nT1109 is ground\nT1110 is ground\nT1113 is ground\nT1112 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\nX1112 is free\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))\nless(T1109, T1110) !=? less(0, s(X1112))", fontsize=16, style=filled, fillcolor=lightyellow];
609 [label="609: ','(less(T1146, T1147), delete(s(T1146), T1114, T1113))\n\nT1113 is ground\nT1112 is ground\nT1146 is ground\nT1147 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\ndelete(s(T1146), T2, tree(s(T1147), T1113, T1112)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T1146), T2, tree(s(T1147), T1113, T1112)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(s(T1146), T2, tree(s(T1147), T1113, T1112)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))", fontsize=16, style=filled, fillcolor=lightyellow];
610 [label="610: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
611 [label="611: delete(T1109, T2, tree(T1110, T1113, T1112)), SCOPE: 1, CLAUSE: 6\n\nT1109 is ground\nT1110 is ground\nT1113 is ground\nT1112 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\nX1112 is free\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(T1109, T2, tree(T1110, T1113, T1112)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))\nless(T1109, T1110) !=? less(0, s(X1112))", fontsize=16, style=filled, fillcolor=lightyellow];
612 [label="612: ','(less(T1161, T1160), delete(T1160, T1165, T1164))\n\nT1160 is ground\nT1161 is ground\nT1162 is ground\nT1164 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\nX1112 is free\ndelete(T1160, T2, tree(T1161, T1162, T1164)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1160, T2, tree(T1161, T1162, T1164)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(T1160, T2, tree(T1161, T1162, T1164)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))\nless(T1160, T1161) !=? less(0, s(X1112))", fontsize=16, style=filled, fillcolor=lightyellow];
613 [label="613: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
697 [label="697: ','(less(T1174, T1173), delete(T1173, T1178, T1177))\n\nT1173 is ground\nT1174 is ground\nT1175 is ground\nT1177 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\nX1105 is free\nX1106 is free\nX1107 is free\nX1108 is free\nX1109 is free\ndelete(T1173, T2, tree(T1174, T1175, T1177)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1173, T2, tree(T1174, T1175, T1177)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(T1173, T2, tree(T1174, T1175, T1177)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))\ndelete(T1173, T2, tree(T1174, T1175, T1177)) !=? delete(X1105, tree(X1106, X1107, X1108), tree(X1106, X1109, X1108))", fontsize=16, style=filled, fillcolor=lightyellow];
698 [label="698: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
699 [label="699: ','(less(T1174, T1173), delete(T1173, T1178, T1177)), SCOPE: 16, CLAUSE: 3 | ','(less(T1174, T1173), delete(T1173, T1178, T1177)), SCOPE: 16, CLAUSE: 8\n\nT1173 is ground\nT1174 is ground\nT1175 is ground\nT1177 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\nX1105 is free\nX1106 is free\nX1107 is free\nX1108 is free\nX1109 is free\ndelete(T1173, T2, tree(T1174, T1175, T1177)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1173, T2, tree(T1174, T1175, T1177)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(T1173, T2, tree(T1174, T1175, T1177)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))\ndelete(T1173, T2, tree(T1174, T1175, T1177)) !=? delete(X1105, tree(X1106, X1107, X1108), tree(X1106, X1109, X1108))", fontsize=16, style=filled, fillcolor=lightyellow];
700 [label="700: delete(s(T1181), T1178, T1177) | ','(less(0, s(T1181)), delete(s(T1181), T1178, T1177)), SCOPE: 16, CLAUSE: 8\n\nT1175 is ground\nT1177 is ground\nT1181 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\nX1105 is free\nX1106 is free\nX1107 is free\nX1108 is free\nX1109 is free\ndelete(s(T1181), T2, tree(0, T1175, T1177)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T1181), T2, tree(0, T1175, T1177)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(s(T1181), T2, tree(0, T1175, T1177)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))\ndelete(s(T1181), T2, tree(0, T1175, T1177)) !=? delete(X1105, tree(X1106, X1107, X1108), tree(X1106, X1109, X1108))", fontsize=16, style=filled, fillcolor=lightyellow];
701 [label="701: ','(less(T1174, T1173), delete(T1173, T1178, T1177)), SCOPE: 16, CLAUSE: 8\n\nT1173 is ground\nT1174 is ground\nT1175 is ground\nT1177 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\nX1105 is free\nX1106 is free\nX1107 is free\nX1108 is free\nX1109 is free\nX1181 is free\ndelete(T1173, T2, tree(T1174, T1175, T1177)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1173, T2, tree(T1174, T1175, T1177)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(T1173, T2, tree(T1174, T1175, T1177)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))\ndelete(T1173, T2, tree(T1174, T1175, T1177)) !=? delete(X1105, tree(X1106, X1107, X1108), tree(X1106, X1109, X1108))\nless(T1174, T1173) !=? less(0, s(X1181))", fontsize=16, style=filled, fillcolor=lightyellow];
702 [label="702: delete(s(T1181), T1178, T1177)\n\nT1175 is ground\nT1177 is ground\nT1181 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\nX1105 is free\nX1106 is free\nX1107 is free\nX1108 is free\nX1109 is free\ndelete(s(T1181), T2, tree(0, T1175, T1177)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T1181), T2, tree(0, T1175, T1177)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(s(T1181), T2, tree(0, T1175, T1177)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))\ndelete(s(T1181), T2, tree(0, T1175, T1177)) !=? delete(X1105, tree(X1106, X1107, X1108), tree(X1106, X1109, X1108))", fontsize=16, style=filled, fillcolor=lightyellow];
703 [label="703: ','(less(0, s(T1181)), delete(s(T1181), T1178, T1177)), SCOPE: 16, CLAUSE: 8\n\nT1175 is ground\nT1177 is ground\nT1181 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\nX1105 is free\nX1106 is free\nX1107 is free\nX1108 is free\nX1109 is free\ndelete(s(T1181), T2, tree(0, T1175, T1177)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T1181), T2, tree(0, T1175, T1177)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(s(T1181), T2, tree(0, T1175, T1177)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))\ndelete(s(T1181), T2, tree(0, T1175, T1177)) !=? delete(X1105, tree(X1106, X1107, X1108), tree(X1106, X1109, X1108))", fontsize=16, style=filled, fillcolor=lightyellow];
706 [label="706: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
740 [label="740: ','(less(T1194, T1195), delete(s(T1195), T1178, T1177))\n\nT1175 is ground\nT1177 is ground\nT1194 is ground\nT1195 is ground\nX6 is free\nX7 is free\nX654 is free\nX655 is free\nX933 is free\nX934 is free\nX935 is free\nX936 is free\nX937 is free\nX1105 is free\nX1106 is free\nX1107 is free\nX1108 is free\nX1109 is free\ndelete(s(T1195), T2, tree(s(T1194), T1175, T1177)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(s(T1195), T2, tree(s(T1194), T1175, T1177)) !=? delete(X654, tree(X654, X655, void), X655)\ndelete(s(T1195), T2, tree(s(T1194), T1175, T1177)) !=? delete(X933, tree(X933, X934, X935), tree(X936, X934, X937))\ndelete(s(T1195), T2, tree(s(T1194), T1175, T1177)) !=? delete(X1105, tree(X1106, X1107, X1108), tree(X1106, X1109, X1108))", fontsize=16, style=filled, fillcolor=lightyellow];
741 [label="741: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
742 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2 -> 742 [arrowhead = none ];
742 -> 3;

743 [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];
3 -> 743 [arrowhead = none ];
743 -> 6;

744 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 744 [arrowhead = none ];
744 -> 8;

745 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 745 [arrowhead = none ];
745 -> 10;

746 [label="EVAL with clause\ndelete(X654, tree(X654, X655, void), X655).\nand substitutionT1 -> T650,\nX654 -> T650,\nX655 -> T651,\nT2 -> tree(T650, T651, void),\nT3 -> T651", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 746 [arrowhead = none ];
746 -> 318;

747 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 747 [arrowhead = none ];
747 -> 319;

748 [label="EVAL with clause\ndelete(X10, tree(X10, X11, void), X11).\nand substitutionT6 -> T10,\nX10 -> T10,\nX11 -> T11,\nT2 -> tree(T10, T11, void),\nT7 -> T11", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 748 [arrowhead = none ];
748 -> 12;

749 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
10 -> 749 [arrowhead = none ];
749 -> 15;

750 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 750 [arrowhead = none ];
750 -> 16;

751 [label="EVAL with clause\ndelete(X385, tree(X385, X386, X387), tree(X388, X386, X389)) :- delmin(X387, X388, X389).\nand substitutionT6 -> T380,\nX385 -> T380,\nX386 -> T381,\nX387 -> T385,\nT2 -> tree(T380, T381, T385),\nX388 -> T383,\nX389 -> T384,\nT7 -> tree(T383, T381, T384),\nT382 -> T385", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 751 [arrowhead = none ];
751 -> 163;

752 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
15 -> 752 [arrowhead = none ];
752 -> 164;

753 [label="EVAL with clause\ndelete(X17, tree(X17, X18, X19), tree(X20, X18, X21)) :- delmin(X19, X20, X21).\nand substitutionT10 -> T17,\nX17 -> T17,\nX18 -> T18,\nX19 -> T22,\nT2 -> tree(T17, T18, T22),\nX20 -> T20,\nX21 -> T21,\nT11 -> tree(T20, T18, T21),\nT19 -> T22", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 753 [arrowhead = none ];
753 -> 19;

754 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 754 [arrowhead = none ];
754 -> 20;

755 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
19 -> 755 [arrowhead = none ];
755 -> 21;

756 [label="EVAL with clause\ndelete(X264, tree(X265, X266, X267), tree(X265, X268, X267)) :- ','(less(X264, X265), delete(X264, X266, X268)).\nand substitutionT10 -> T271,\nX264 -> T271,\nX265 -> T272,\nX266 -> T276,\nX267 -> T274,\nT2 -> tree(T272, T276, T274),\nX268 -> T275,\nT11 -> tree(T272, T275, T274),\nT273 -> T276", fontsize=14, style = filled, fillcolor = lightblue];
20 -> 756 [arrowhead = none ];
756 -> 110;

757 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
20 -> 757 [arrowhead = none ];
757 -> 111;

758 [label="EVAL with clause\ndelmin(tree(X26, void, X27), X26, X27).\nand substitutionX26 -> T27,\nX27 -> T28,\nT22 -> tree(T27, void, T28),\nT20 -> T27,\nT21 -> T28", fontsize=14, style = filled, fillcolor = lightblue];
21 -> 758 [arrowhead = none ];
758 -> 22;

759 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
21 -> 759 [arrowhead = none ];
759 -> 23;

760 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
22 -> 760 [arrowhead = none ];
760 -> 25;

761 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
23 -> 761 [arrowhead = none ];
761 -> 86;

762 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
23 -> 762 [arrowhead = none ];
762 -> 87;

763 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
25 -> 763 [arrowhead = none ];
763 -> 27;

764 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
25 -> 764 [arrowhead = none ];
764 -> 28;

765 [label="EVAL with clause\ndelmin(tree(X52, X53, X54), X55, tree(X52, X56, X57)) :- delmin(X53, X55, X56).\nand substitutionX52 -> T53,\nX53 -> T59,\nX54 -> T55,\nT22 -> tree(T53, T59, T55),\nT27 -> T56,\nX55 -> T56,\nX56 -> T57,\nX57 -> T58,\nT28 -> tree(T53, T57, T58),\nT54 -> T59", fontsize=14, style = filled, fillcolor = lightblue];
27 -> 765 [arrowhead = none ];
765 -> 33;

766 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
27 -> 766 [arrowhead = none ];
766 -> 34;

767 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
28 -> 767 [arrowhead = none ];
767 -> 49;

768 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
33 -> 768 [arrowhead = none ];
768 -> 35;

769 [label="EVAL with clause\ndelmin(tree(X66, void, X67), X66, X67).\nand substitutionX66 -> T68,\nX67 -> T69,\nT59 -> tree(T68, void, T69),\nT56 -> T68,\nT57 -> T69", fontsize=14, style = filled, fillcolor = lightblue];
35 -> 769 [arrowhead = none ];
769 -> 36;

770 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
35 -> 770 [arrowhead = none ];
770 -> 37;

771 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
36 -> 771 [arrowhead = none ];
771 -> 38;

772 [label="EVAL with clause\ndelmin(tree(X102, X103, X104), X105, tree(X102, X106, X107)) :- delmin(X103, X105, X106).\nand substitutionX102 -> T105,\nX103 -> T111,\nX104 -> T107,\nT59 -> tree(T105, T111, T107),\nT56 -> T108,\nX105 -> T108,\nX106 -> T109,\nX107 -> T110,\nT57 -> tree(T105, T109, T110),\nT106 -> T111", fontsize=14, style = filled, fillcolor = lightblue];
37 -> 772 [arrowhead = none ];
772 -> 45;

773 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
37 -> 773 [arrowhead = none ];
773 -> 46;

774 [label="EVAL with clause\ndelmin(tree(X80, X81, X82), X83, tree(X80, X84, X85)) :- delmin(X81, X83, X84).\nand substitutionX80 -> T82,\nX81 -> T88,\nX82 -> T84,\nT59 -> tree(T82, T88, T84),\nT68 -> T85,\nX83 -> T85,\nX84 -> T86,\nX85 -> T87,\nT69 -> tree(T82, T86, T87),\nT83 -> T88", fontsize=14, style = filled, fillcolor = lightblue];
38 -> 774 [arrowhead = none ];
774 -> 41;

775 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
38 -> 775 [arrowhead = none ];
775 -> 42;

776 [label="INSTANCE with matching:\nT59 -> T88\nT56 -> T85\nT57 -> T86", fontsize=14, style = filled, fillcolor = lightgrey];
41 -> 776 [arrowhead = none , style=dashed];
776 -> 33[style=dashed];

777 [label="INSTANCE with matching:\nT59 -> T111\nT56 -> T108\nT57 -> T109", fontsize=14, style = filled, fillcolor = lightgrey];
45 -> 777 [arrowhead = none , style=dashed];
777 -> 33[style=dashed];

778 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
49 -> 778 [arrowhead = none ];
778 -> 52;

779 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
49 -> 779 [arrowhead = none ];
779 -> 53;

780 [label="EVAL with clause\ndelete(X132, tree(X133, X134, X135), tree(X133, X136, X135)) :- ','(less(X132, X133), delete(X132, X134, X136)).\nand substitutionT17 -> T136,\nX132 -> T136,\nX133 -> T137,\nX134 -> T141,\nX135 -> T139,\nT2 -> tree(T137, T141, T139),\nT27 -> T137,\nT18 -> T140,\nX136 -> T140,\nT28 -> T139,\nT138 -> T141", fontsize=14, style = filled, fillcolor = lightblue];
52 -> 780 [arrowhead = none ];
780 -> 61;

781 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
52 -> 781 [arrowhead = none ];
781 -> 62;

782 [label="EVAL with clause\ndelete(X168, tree(X169, X170, X171), tree(X169, X170, X172)) :- ','(less(X169, X168), delete(X168, X171, X172)).\nand substitutionT17 -> T171,\nX168 -> T171,\nX169 -> T172,\nX170 -> T173,\nX171 -> T176,\nT2 -> tree(T172, T173, T176),\nT27 -> T172,\nT18 -> T173,\nT28 -> T175,\nX172 -> T175,\nT174 -> T176", fontsize=14, style = filled, fillcolor = lightblue];
53 -> 782 [arrowhead = none ];
782 -> 78;

783 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
53 -> 783 [arrowhead = none ];
783 -> 79;

784 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
61 -> 784 [arrowhead = none ];
784 -> 63;

785 [label="SPLIT 2\nnew knowledge:\nT136 is ground\nT137 is ground", fontsize=14, style = filled, fillcolor = violet];
61 -> 785 [arrowhead = none ];
785 -> 64;

786 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
63 -> 786 [arrowhead = none ];
786 -> 67;

787 [label="INSTANCE with matching:\nT1 -> T136\nT2 -> T141\nT3 -> T140", fontsize=14, style = filled, fillcolor = lightgrey];
64 -> 787 [arrowhead = none , style=dashed];
787 -> 2[style=dashed];

788 [label="EVAL with clause\nless(0, s(X143)).\nand substitutionT136 -> 0,\nX143 -> T148,\nT137 -> s(T148)", fontsize=14, style = filled, fillcolor = lightblue];
67 -> 788 [arrowhead = none ];
788 -> 68;

789 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
67 -> 789 [arrowhead = none ];
789 -> 69;

790 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
68 -> 790 [arrowhead = none ];
790 -> 70;

791 [label="EVAL with clause\nless(s(X150), s(X151)) :- less(X150, X151).\nand substitutionX150 -> T153,\nT136 -> s(T153),\nX151 -> T154,\nT137 -> s(T154)", fontsize=14, style = filled, fillcolor = lightblue];
69 -> 791 [arrowhead = none ];
791 -> 72;

792 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
69 -> 792 [arrowhead = none ];
792 -> 73;

793 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
70 -> 793 [arrowhead = none ];
793 -> 71;

794 [label="INSTANCE with matching:\nT136 -> T153\nT137 -> T154", fontsize=14, style = filled, fillcolor = lightgrey];
72 -> 794 [arrowhead = none , style=dashed];
794 -> 63[style=dashed];

795 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
78 -> 795 [arrowhead = none ];
795 -> 80;

796 [label="SPLIT 2\nnew knowledge:\nT172 is ground\nT171 is ground", fontsize=14, style = filled, fillcolor = violet];
78 -> 796 [arrowhead = none ];
796 -> 81;

797 [label="INSTANCE with matching:\nT136 -> T172\nT137 -> T171", fontsize=14, style = filled, fillcolor = lightgrey];
80 -> 797 [arrowhead = none , style=dashed];
797 -> 63[style=dashed];

798 [label="INSTANCE with matching:\nT1 -> T171\nT2 -> T176\nT3 -> T175", fontsize=14, style = filled, fillcolor = lightgrey];
81 -> 798 [arrowhead = none , style=dashed];
798 -> 2[style=dashed];

799 [label="EVAL with clause\ndelmin(tree(X205, X206, X207), X208, tree(X205, X209, X210)) :- delmin(X206, X208, X209).\nand substitutionX205 -> T209,\nX206 -> T215,\nX207 -> T211,\nT22 -> tree(T209, T215, T211),\nT20 -> T212,\nX208 -> T212,\nX209 -> T213,\nX210 -> T214,\nT21 -> tree(T209, T213, T214),\nT210 -> T215", fontsize=14, style = filled, fillcolor = lightblue];
86 -> 799 [arrowhead = none ];
799 -> 90;

800 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
86 -> 800 [arrowhead = none ];
800 -> 91;

801 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
87 -> 801 [arrowhead = none ];
801 -> 92;

802 [label="INSTANCE with matching:\nT59 -> T215\nT56 -> T212\nT57 -> T213", fontsize=14, style = filled, fillcolor = lightgrey];
90 -> 802 [arrowhead = none , style=dashed];
802 -> 33[style=dashed];

803 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
92 -> 803 [arrowhead = none ];
803 -> 95;

804 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
92 -> 804 [arrowhead = none ];
804 -> 96;

805 [label="EVAL with clause\ndelete(X235, tree(X236, X237, X238), tree(X236, X239, X238)) :- ','(less(X235, X236), delete(X235, X237, X239)).\nand substitutionT17 -> T240,\nX235 -> T240,\nX236 -> T241,\nX237 -> T245,\nX238 -> T243,\nT2 -> tree(T241, T245, T243),\nT20 -> T241,\nT18 -> T244,\nX239 -> T244,\nT21 -> T243,\nT242 -> T245", fontsize=14, style = filled, fillcolor = lightblue];
95 -> 805 [arrowhead = none ];
805 -> 99;

806 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
95 -> 806 [arrowhead = none ];
806 -> 100;

807 [label="EVAL with clause\ndelete(X252, tree(X253, X254, X255), tree(X253, X254, X256)) :- ','(less(X253, X252), delete(X252, X255, X256)).\nand substitutionT17 -> T258,\nX252 -> T258,\nX253 -> T259,\nX254 -> T260,\nX255 -> T263,\nT2 -> tree(T259, T260, T263),\nT20 -> T259,\nT18 -> T260,\nT21 -> T262,\nX256 -> T262,\nT261 -> T263", fontsize=14, style = filled, fillcolor = lightblue];
96 -> 807 [arrowhead = none ];
807 -> 105;

808 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
96 -> 808 [arrowhead = none ];
808 -> 107;

809 [label="INSTANCE with matching:\nT136 -> T240\nT137 -> T241\nT141 -> T245\nT140 -> T244", fontsize=14, style = filled, fillcolor = lightgrey];
99 -> 809 [arrowhead = none , style=dashed];
809 -> 61[style=dashed];

810 [label="INSTANCE with matching:\nT172 -> T259\nT171 -> T258\nT176 -> T263\nT175 -> T262", fontsize=14, style = filled, fillcolor = lightgrey];
105 -> 810 [arrowhead = none , style=dashed];
810 -> 78[style=dashed];

811 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
110 -> 811 [arrowhead = none ];
811 -> 112;

812 [label="EVAL with clause\ndelete(X348, tree(X349, X350, X351), tree(X349, X350, X352)) :- ','(less(X349, X348), delete(X348, X351, X352)).\nand substitutionT10 -> T344,\nX348 -> T344,\nX349 -> T345,\nX350 -> T346,\nX351 -> T349,\nT2 -> tree(T345, T346, T349),\nX352 -> T348,\nT11 -> tree(T345, T346, T348),\nT347 -> T349", fontsize=14, style = filled, fillcolor = lightblue];
111 -> 812 [arrowhead = none ];
812 -> 151;

813 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
111 -> 813 [arrowhead = none ];
813 -> 152;

814 [label="EVAL with clause\nless(0, s(X271)).\nand substitutionT271 -> 0,\nX271 -> T279,\nT272 -> s(T279)", fontsize=14, style = filled, fillcolor = lightblue];
112 -> 814 [arrowhead = none ];
814 -> 113;

815 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
112 -> 815 [arrowhead = none ];
815 -> 114;

816 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
113 -> 816 [arrowhead = none ];
816 -> 117;

817 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
113 -> 817 [arrowhead = none ];
817 -> 118;

818 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
114 -> 818 [arrowhead = none ];
818 -> 134;

819 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
114 -> 819 [arrowhead = none ];
819 -> 135;

820 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T276\nT3 -> T275", fontsize=14, style = filled, fillcolor = lightgrey];
117 -> 820 [arrowhead = none , style=dashed];
820 -> 2[style=dashed];

821 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
118 -> 821 [arrowhead = none ];
821 -> 120;

822 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
120 -> 822 [arrowhead = none ];
822 -> 122;

823 [label="EVAL with clause\ndelete(X292, tree(X293, X294, X295), tree(X293, X294, X296)) :- ','(less(X293, X292), delete(X292, X295, X296)).\nand substitutionX292 -> 0,\nX293 -> s(T297),\nX294 -> T295,\nX295 -> T299,\nT2 -> tree(s(T297), T295, T299),\nT279 -> T297,\nT294 -> s(T297),\nT275 -> T295,\nT274 -> T298,\nX296 -> T298,\nT296 -> T299", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 823 [arrowhead = none ];
823 -> 123;

824 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
122 -> 824 [arrowhead = none ];
824 -> 125;

825 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
123 -> 825 [arrowhead = none ];
825 -> 127;

826 [label="SPLIT 2\nnew knowledge:\nT297 is ground", fontsize=14, style = filled, fillcolor = violet];
123 -> 826 [arrowhead = none ];
826 -> 128;

827 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
127 -> 827 [arrowhead = none ];
827 -> 129;

828 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T299\nT3 -> T298", fontsize=14, style = filled, fillcolor = lightgrey];
128 -> 828 [arrowhead = none , style=dashed];
828 -> 2[style=dashed];

829 [label="BACKTRACK\nfor clause: less(0, s(X3))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 829 [arrowhead = none ];
829 -> 131;

830 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
131 -> 830 [arrowhead = none ];
830 -> 133;

831 [label="EVAL with clause\nless(s(X316), s(X317)) :- less(X316, X317).\nand substitutionX316 -> T311,\nT271 -> s(T311),\nX317 -> T312,\nT272 -> s(T312)", fontsize=14, style = filled, fillcolor = lightblue];
134 -> 831 [arrowhead = none ];
831 -> 138;

832 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
134 -> 832 [arrowhead = none ];
832 -> 139;

833 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
135 -> 833 [arrowhead = none ];
833 -> 144;

834 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
138 -> 834 [arrowhead = none ];
834 -> 140;

835 [label="SPLIT 2\nnew knowledge:\nT311 is ground\nT312 is ground", fontsize=14, style = filled, fillcolor = violet];
138 -> 835 [arrowhead = none ];
835 -> 141;

836 [label="INSTANCE with matching:\nT136 -> T311\nT137 -> T312", fontsize=14, style = filled, fillcolor = lightgrey];
140 -> 836 [arrowhead = none , style=dashed];
836 -> 63[style=dashed];

837 [label="INSTANCE with matching:\nT1 -> s(T311)\nT2 -> T276\nT3 -> T275", fontsize=14, style = filled, fillcolor = lightgrey];
141 -> 837 [arrowhead = none , style=dashed];
837 -> 2[style=dashed];

838 [label="EVAL with clause\ndelete(X336, tree(X337, X338, X339), tree(X337, X338, X340)) :- ','(less(X337, X336), delete(X336, X339, X340)).\nand substitutionT271 -> T331,\nX336 -> T331,\nX337 -> T332,\nX338 -> T333,\nX339 -> T336,\nT2 -> tree(T332, T333, T336),\nT272 -> T332,\nT275 -> T333,\nT274 -> T335,\nX340 -> T335,\nT334 -> T336", fontsize=14, style = filled, fillcolor = lightblue];
144 -> 838 [arrowhead = none ];
838 -> 147;

839 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
144 -> 839 [arrowhead = none ];
839 -> 148;

840 [label="INSTANCE with matching:\nT172 -> T332\nT171 -> T331\nT176 -> T336\nT175 -> T335", fontsize=14, style = filled, fillcolor = lightgrey];
147 -> 840 [arrowhead = none , style=dashed];
840 -> 78[style=dashed];

841 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
151 -> 841 [arrowhead = none ];
841 -> 153;

842 [label="EVAL with clause\nless(0, s(X355)).\nand substitutionT345 -> 0,\nX355 -> T352,\nT344 -> s(T352)", fontsize=14, style = filled, fillcolor = lightblue];
153 -> 842 [arrowhead = none ];
842 -> 154;

843 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
153 -> 843 [arrowhead = none ];
843 -> 155;

844 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
154 -> 844 [arrowhead = none ];
844 -> 156;

845 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
154 -> 845 [arrowhead = none ];
845 -> 157;

846 [label="EVAL with clause\nless(s(X370), s(X371)) :- less(X370, X371).\nand substitutionX370 -> T365,\nT345 -> s(T365),\nX371 -> T366,\nT344 -> s(T366)", fontsize=14, style = filled, fillcolor = lightblue];
155 -> 846 [arrowhead = none ];
846 -> 159;

847 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
155 -> 847 [arrowhead = none ];
847 -> 160;

848 [label="INSTANCE with matching:\nT1 -> s(T352)\nT2 -> T349\nT3 -> T348", fontsize=14, style = filled, fillcolor = lightgrey];
156 -> 848 [arrowhead = none , style=dashed];
848 -> 2[style=dashed];

849 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
157 -> 849 [arrowhead = none ];
849 -> 158;

850 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
159 -> 850 [arrowhead = none ];
850 -> 161;

851 [label="SPLIT 2\nnew knowledge:\nT365 is ground\nT366 is ground", fontsize=14, style = filled, fillcolor = violet];
159 -> 851 [arrowhead = none ];
851 -> 162;

852 [label="INSTANCE with matching:\nT136 -> T365\nT137 -> T366", fontsize=14, style = filled, fillcolor = lightgrey];
161 -> 852 [arrowhead = none , style=dashed];
852 -> 63[style=dashed];

853 [label="INSTANCE with matching:\nT1 -> s(T366)\nT2 -> T349\nT3 -> T348", fontsize=14, style = filled, fillcolor = lightgrey];
162 -> 853 [arrowhead = none , style=dashed];
853 -> 2[style=dashed];

854 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
163 -> 854 [arrowhead = none ];
854 -> 165;

855 [label="EVAL with clause\ndelete(X557, tree(X558, X559, X560), tree(X558, X561, X560)) :- ','(less(X557, X558), delete(X557, X559, X561)).\nand substitutionT6 -> T559,\nX557 -> T559,\nX558 -> T560,\nX559 -> T564,\nX560 -> T562,\nT2 -> tree(T560, T564, T562),\nX561 -> T563,\nT7 -> tree(T560, T563, T562),\nT561 -> T564", fontsize=14, style = filled, fillcolor = lightblue];
164 -> 855 [arrowhead = none ];
855 -> 261;

856 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
164 -> 856 [arrowhead = none ];
856 -> 262;

857 [label="EVAL with clause\ndelmin(tree(X394, void, X395), X394, X395).\nand substitutionX394 -> T390,\nX395 -> T391,\nT385 -> tree(T390, void, T391),\nT383 -> T390,\nT384 -> T391", fontsize=14, style = filled, fillcolor = lightblue];
165 -> 857 [arrowhead = none ];
857 -> 166;

858 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
165 -> 858 [arrowhead = none ];
858 -> 167;

859 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
166 -> 859 [arrowhead = none ];
859 -> 168;

860 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
167 -> 860 [arrowhead = none ];
860 -> 211;

861 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
167 -> 861 [arrowhead = none ];
861 -> 212;

862 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
168 -> 862 [arrowhead = none ];
862 -> 169;

863 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
168 -> 863 [arrowhead = none ];
863 -> 170;

864 [label="EVAL with clause\ndelmin(tree(X420, X421, X422), X423, tree(X420, X424, X425)) :- delmin(X421, X423, X424).\nand substitutionX420 -> T416,\nX421 -> T422,\nX422 -> T418,\nT385 -> tree(T416, T422, T418),\nT390 -> T419,\nX423 -> T419,\nX424 -> T420,\nX425 -> T421,\nT391 -> tree(T416, T420, T421),\nT417 -> T422", fontsize=14, style = filled, fillcolor = lightblue];
169 -> 864 [arrowhead = none ];
864 -> 171;

865 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
169 -> 865 [arrowhead = none ];
865 -> 172;

866 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
170 -> 866 [arrowhead = none ];
866 -> 173;

867 [label="INSTANCE with matching:\nT59 -> T422\nT56 -> T419\nT57 -> T420", fontsize=14, style = filled, fillcolor = lightgrey];
171 -> 867 [arrowhead = none , style=dashed];
867 -> 33[style=dashed];

868 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
173 -> 868 [arrowhead = none ];
868 -> 174;

869 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
173 -> 869 [arrowhead = none ];
869 -> 175;

870 [label="EVAL with clause\ndelete(X450, tree(X451, X452, X453), tree(X451, X454, X453)) :- ','(less(X450, X451), delete(X450, X452, X454)).\nand substitutionT380 -> T447,\nX450 -> T447,\nX451 -> T448,\nX452 -> T452,\nX453 -> T450,\nT2 -> tree(T448, T452, T450),\nT390 -> T448,\nT381 -> T451,\nX454 -> T451,\nT391 -> T450,\nT449 -> T452", fontsize=14, style = filled, fillcolor = lightblue];
174 -> 870 [arrowhead = none ];
870 -> 176;

871 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
174 -> 871 [arrowhead = none ];
871 -> 177;

872 [label="EVAL with clause\ndelete(X467, tree(X468, X469, X470), tree(X468, X469, X471)) :- ','(less(X468, X467), delete(X467, X470, X471)).\nand substitutionT380 -> T465,\nX467 -> T465,\nX468 -> T466,\nX469 -> T467,\nX470 -> T470,\nT2 -> tree(T466, T467, T470),\nT390 -> T466,\nT381 -> T467,\nT391 -> T469,\nX471 -> T469,\nT468 -> T470", fontsize=14, style = filled, fillcolor = lightblue];
175 -> 872 [arrowhead = none ];
872 -> 178;

873 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
175 -> 873 [arrowhead = none ];
873 -> 179;

874 [label="INSTANCE with matching:\nT136 -> T447\nT137 -> T448\nT141 -> T452\nT140 -> T451", fontsize=14, style = filled, fillcolor = lightgrey];
176 -> 874 [arrowhead = none , style=dashed];
874 -> 61[style=dashed];

875 [label="INSTANCE with matching:\nT172 -> T466\nT171 -> T465\nT176 -> T470\nT175 -> T469", fontsize=14, style = filled, fillcolor = lightgrey];
178 -> 875 [arrowhead = none , style=dashed];
875 -> 78[style=dashed];

876 [label="EVAL with clause\ndelmin(tree(X498, X499, X500), X501, tree(X498, X502, X503)) :- delmin(X499, X501, X502).\nand substitutionX498 -> T497,\nX499 -> T503,\nX500 -> T499,\nT385 -> tree(T497, T503, T499),\nT383 -> T500,\nX501 -> T500,\nX502 -> T501,\nX503 -> T502,\nT384 -> tree(T497, T501, T502),\nT498 -> T503", fontsize=14, style = filled, fillcolor = lightblue];
211 -> 876 [arrowhead = none ];
876 -> 213;

877 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
211 -> 877 [arrowhead = none ];
877 -> 214;

878 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
212 -> 878 [arrowhead = none ];
878 -> 215;

879 [label="INSTANCE with matching:\nT59 -> T503\nT56 -> T500\nT57 -> T501", fontsize=14, style = filled, fillcolor = lightgrey];
213 -> 879 [arrowhead = none , style=dashed];
879 -> 33[style=dashed];

880 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
215 -> 880 [arrowhead = none ];
880 -> 216;

881 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
215 -> 881 [arrowhead = none ];
881 -> 217;

882 [label="EVAL with clause\ndelete(X528, tree(X529, X530, X531), tree(X529, X532, X531)) :- ','(less(X528, X529), delete(X528, X530, X532)).\nand substitutionT380 -> T528,\nX528 -> T528,\nX529 -> T529,\nX530 -> T533,\nX531 -> T531,\nT2 -> tree(T529, T533, T531),\nT383 -> T529,\nT381 -> T532,\nX532 -> T532,\nT384 -> T531,\nT530 -> T533", fontsize=14, style = filled, fillcolor = lightblue];
216 -> 882 [arrowhead = none ];
882 -> 218;

883 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
216 -> 883 [arrowhead = none ];
883 -> 219;

884 [label="EVAL with clause\ndelete(X545, tree(X546, X547, X548), tree(X546, X547, X549)) :- ','(less(X546, X545), delete(X545, X548, X549)).\nand substitutionT380 -> T546,\nX545 -> T546,\nX546 -> T547,\nX547 -> T548,\nX548 -> T551,\nT2 -> tree(T547, T548, T551),\nT383 -> T547,\nT381 -> T548,\nT384 -> T550,\nX549 -> T550,\nT549 -> T551", fontsize=14, style = filled, fillcolor = lightblue];
217 -> 884 [arrowhead = none ];
884 -> 220;

885 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
217 -> 885 [arrowhead = none ];
885 -> 221;

886 [label="INSTANCE with matching:\nT136 -> T528\nT137 -> T529\nT141 -> T533\nT140 -> T532", fontsize=14, style = filled, fillcolor = lightgrey];
218 -> 886 [arrowhead = none , style=dashed];
886 -> 61[style=dashed];

887 [label="INSTANCE with matching:\nT172 -> T547\nT171 -> T546\nT176 -> T551\nT175 -> T550", fontsize=14, style = filled, fillcolor = lightgrey];
220 -> 887 [arrowhead = none , style=dashed];
887 -> 78[style=dashed];

888 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
261 -> 888 [arrowhead = none ];
888 -> 263;

889 [label="EVAL with clause\ndelete(X626, tree(X627, X628, X629), tree(X627, X628, X630)) :- ','(less(X627, X626), delete(X626, X629, X630)).\nand substitutionT6 -> T623,\nX626 -> T623,\nX627 -> T624,\nX628 -> T625,\nX629 -> T628,\nT2 -> tree(T624, T625, T628),\nX630 -> T627,\nT7 -> tree(T624, T625, T627),\nT626 -> T628", fontsize=14, style = filled, fillcolor = lightblue];
262 -> 889 [arrowhead = none ];
889 -> 308;

890 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
262 -> 890 [arrowhead = none ];
890 -> 309;

891 [label="EVAL with clause\nless(0, s(X564)).\nand substitutionT559 -> 0,\nX564 -> T567,\nT560 -> s(T567)", fontsize=14, style = filled, fillcolor = lightblue];
263 -> 891 [arrowhead = none ];
891 -> 264;

892 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
263 -> 892 [arrowhead = none ];
892 -> 265;

893 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
264 -> 893 [arrowhead = none ];
893 -> 266;

894 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
264 -> 894 [arrowhead = none ];
894 -> 267;

895 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
265 -> 895 [arrowhead = none ];
895 -> 301;

896 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
265 -> 896 [arrowhead = none ];
896 -> 302;

897 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T564\nT3 -> T563", fontsize=14, style = filled, fillcolor = lightgrey];
266 -> 897 [arrowhead = none , style=dashed];
897 -> 2[style=dashed];

898 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
267 -> 898 [arrowhead = none ];
898 -> 274;

899 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
274 -> 899 [arrowhead = none ];
899 -> 275;

900 [label="EVAL with clause\ndelete(X585, tree(X586, X587, X588), tree(X586, X587, X589)) :- ','(less(X586, X585), delete(X585, X588, X589)).\nand substitutionX585 -> 0,\nX586 -> s(T585),\nX587 -> T583,\nX588 -> T587,\nT2 -> tree(s(T585), T583, T587),\nT567 -> T585,\nT582 -> s(T585),\nT563 -> T583,\nT562 -> T586,\nX589 -> T586,\nT584 -> T587", fontsize=14, style = filled, fillcolor = lightblue];
275 -> 900 [arrowhead = none ];
900 -> 293;

901 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
275 -> 901 [arrowhead = none ];
901 -> 294;

902 [label="INSTANCE with matching:\nT297 -> T585\nT299 -> T587\nT298 -> T586\nT295 -> T583\nX17 -> X385\nX18 -> X386\nX19 -> X387\nX20 -> X388\nX21 -> X389", fontsize=14, style = filled, fillcolor = lightgrey];
293 -> 902 [arrowhead = none , style=dashed];
902 -> 123[style=dashed];

903 [label="EVAL with clause\nless(s(X600), s(X601)) :- less(X600, X601).\nand substitutionX600 -> T596,\nT559 -> s(T596),\nX601 -> T597,\nT560 -> s(T597)", fontsize=14, style = filled, fillcolor = lightblue];
301 -> 903 [arrowhead = none ];
903 -> 303;

904 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
301 -> 904 [arrowhead = none ];
904 -> 304;

905 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
302 -> 905 [arrowhead = none ];
905 -> 305;

906 [label="INSTANCE with matching:\nT311 -> T596\nT312 -> T597\nT276 -> T564\nT275 -> T563\nT274 -> T562\nX17 -> X385\nX18 -> X386\nX19 -> X387\nX20 -> X388\nX21 -> X389", fontsize=14, style = filled, fillcolor = lightgrey];
303 -> 906 [arrowhead = none , style=dashed];
906 -> 138[style=dashed];

907 [label="EVAL with clause\ndelete(X614, tree(X615, X616, X617), tree(X615, X616, X618)) :- ','(less(X615, X614), delete(X614, X617, X618)).\nand substitutionT559 -> T610,\nX614 -> T610,\nX615 -> T611,\nX616 -> T612,\nX617 -> T615,\nT2 -> tree(T611, T612, T615),\nT560 -> T611,\nT563 -> T612,\nT562 -> T614,\nX618 -> T614,\nT613 -> T615", fontsize=14, style = filled, fillcolor = lightblue];
305 -> 907 [arrowhead = none ];
907 -> 306;

908 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
305 -> 908 [arrowhead = none ];
908 -> 307;

909 [label="INSTANCE with matching:\nT172 -> T611\nT171 -> T610\nT176 -> T615\nT175 -> T614", fontsize=14, style = filled, fillcolor = lightgrey];
306 -> 909 [arrowhead = none , style=dashed];
909 -> 78[style=dashed];

910 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
308 -> 910 [arrowhead = none ];
910 -> 310;

911 [label="EVAL with clause\nless(0, s(X633)).\nand substitutionT624 -> 0,\nX633 -> T631,\nT623 -> s(T631)", fontsize=14, style = filled, fillcolor = lightblue];
310 -> 911 [arrowhead = none ];
911 -> 311;

912 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
310 -> 912 [arrowhead = none ];
912 -> 312;

913 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
311 -> 913 [arrowhead = none ];
913 -> 313;

914 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
311 -> 914 [arrowhead = none ];
914 -> 314;

915 [label="EVAL with clause\nless(s(X648), s(X649)) :- less(X648, X649).\nand substitutionX648 -> T644,\nT624 -> s(T644),\nX649 -> T645,\nT623 -> s(T645)", fontsize=14, style = filled, fillcolor = lightblue];
312 -> 915 [arrowhead = none ];
915 -> 316;

916 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
312 -> 916 [arrowhead = none ];
916 -> 317;

917 [label="INSTANCE with matching:\nT1 -> s(T631)\nT2 -> T628\nT3 -> T627", fontsize=14, style = filled, fillcolor = lightgrey];
313 -> 917 [arrowhead = none , style=dashed];
917 -> 2[style=dashed];

918 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
314 -> 918 [arrowhead = none ];
918 -> 315;

919 [label="INSTANCE with matching:\nT365 -> T644\nT366 -> T645\nT349 -> T628\nT348 -> T627\nT346 -> T625\nX17 -> X385\nX18 -> X386\nX19 -> X387\nX20 -> X388\nX21 -> X389\nX264 -> X557\nX265 -> X558\nX266 -> X559\nX267 -> X560\nX268 -> X561", fontsize=14, style = filled, fillcolor = lightgrey];
316 -> 919 [arrowhead = none , style=dashed];
919 -> 159[style=dashed];

920 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
318 -> 920 [arrowhead = none ];
920 -> 320;

921 [label="EVAL with clause\ndelete(X933, tree(X933, X934, X935), tree(X936, X934, X937)) :- delmin(X935, X936, X937).\nand substitutionT1 -> T930,\nX933 -> T930,\nX934 -> T931,\nX935 -> T935,\nT2 -> tree(T930, T931, T935),\nX936 -> T933,\nX937 -> T934,\nT3 -> tree(T933, T931, T934),\nT932 -> T935", fontsize=14, style = filled, fillcolor = lightblue];
319 -> 921 [arrowhead = none ];
921 -> 538;

922 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
319 -> 922 [arrowhead = none ];
922 -> 539;

923 [label="EVAL with clause\ndelete(X661, tree(X661, X662, X663), tree(X664, X662, X665)) :- delmin(X663, X664, X665).\nand substitutionT650 -> T657,\nX661 -> T657,\nX662 -> T658,\nX663 -> T662,\nT2 -> tree(T657, T658, T662),\nX664 -> T660,\nX665 -> T661,\nT651 -> tree(T660, T658, T661),\nT659 -> T662", fontsize=14, style = filled, fillcolor = lightblue];
320 -> 923 [arrowhead = none ];
923 -> 321;

924 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
320 -> 924 [arrowhead = none ];
924 -> 322;

925 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
321 -> 925 [arrowhead = none ];
925 -> 323;

926 [label="EVAL with clause\ndelete(X833, tree(X834, X835, X836), tree(X834, X837, X836)) :- ','(less(X833, X834), delete(X833, X835, X837)).\nand substitutionT650 -> T836,\nX833 -> T836,\nX834 -> T837,\nX835 -> T841,\nX836 -> T839,\nT2 -> tree(T837, T841, T839),\nX837 -> T840,\nT651 -> tree(T837, T840, T839),\nT838 -> T841", fontsize=14, style = filled, fillcolor = lightblue];
322 -> 926 [arrowhead = none ];
926 -> 467;

927 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
322 -> 927 [arrowhead = none ];
927 -> 468;

928 [label="EVAL with clause\ndelmin(tree(X670, void, X671), X670, X671).\nand substitutionX670 -> T667,\nX671 -> T668,\nT662 -> tree(T667, void, T668),\nT660 -> T667,\nT661 -> T668", fontsize=14, style = filled, fillcolor = lightblue];
323 -> 928 [arrowhead = none ];
928 -> 324;

929 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
323 -> 929 [arrowhead = none ];
929 -> 325;

930 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
324 -> 930 [arrowhead = none ];
930 -> 326;

931 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
325 -> 931 [arrowhead = none ];
931 -> 422;

932 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
325 -> 932 [arrowhead = none ];
932 -> 424;

933 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
326 -> 933 [arrowhead = none ];
933 -> 327;

934 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
326 -> 934 [arrowhead = none ];
934 -> 328;

935 [label="EVAL with clause\ndelmin(tree(X696, X697, X698), X699, tree(X696, X700, X701)) :- delmin(X697, X699, X700).\nand substitutionX696 -> T693,\nX697 -> T699,\nX698 -> T695,\nT662 -> tree(T693, T699, T695),\nT667 -> T696,\nX699 -> T696,\nX700 -> T697,\nX701 -> T698,\nT668 -> tree(T693, T697, T698),\nT694 -> T699", fontsize=14, style = filled, fillcolor = lightblue];
327 -> 935 [arrowhead = none ];
935 -> 329;

936 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
327 -> 936 [arrowhead = none ];
936 -> 330;

937 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
328 -> 937 [arrowhead = none ];
937 -> 414;

938 [label="INSTANCE with matching:\nT59 -> T699\nT56 -> T696\nT57 -> T697", fontsize=14, style = filled, fillcolor = lightgrey];
329 -> 938 [arrowhead = none , style=dashed];
938 -> 33[style=dashed];

939 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
414 -> 939 [arrowhead = none ];
939 -> 415;

940 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
414 -> 940 [arrowhead = none ];
940 -> 416;

941 [label="EVAL with clause\ndelete(X726, tree(X727, X728, X729), tree(X727, X730, X729)) :- ','(less(X726, X727), delete(X726, X728, X730)).\nand substitutionT657 -> T724,\nX726 -> T724,\nX727 -> T725,\nX728 -> T729,\nX729 -> T727,\nT2 -> tree(T725, T729, T727),\nT667 -> T725,\nT658 -> T728,\nX730 -> T728,\nT668 -> T727,\nT726 -> T729", fontsize=14, style = filled, fillcolor = lightblue];
415 -> 941 [arrowhead = none ];
941 -> 417;

942 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
415 -> 942 [arrowhead = none ];
942 -> 418;

943 [label="EVAL with clause\ndelete(X743, tree(X744, X745, X746), tree(X744, X745, X747)) :- ','(less(X744, X743), delete(X743, X746, X747)).\nand substitutionT657 -> T742,\nX743 -> T742,\nX744 -> T743,\nX745 -> T744,\nX746 -> T747,\nT2 -> tree(T743, T744, T747),\nT667 -> T743,\nT658 -> T744,\nT668 -> T746,\nX747 -> T746,\nT745 -> T747", fontsize=14, style = filled, fillcolor = lightblue];
416 -> 943 [arrowhead = none ];
943 -> 419;

944 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
416 -> 944 [arrowhead = none ];
944 -> 420;

945 [label="INSTANCE with matching:\nT136 -> T724\nT137 -> T725\nT141 -> T729\nT140 -> T728", fontsize=14, style = filled, fillcolor = lightgrey];
417 -> 945 [arrowhead = none , style=dashed];
945 -> 61[style=dashed];

946 [label="INSTANCE with matching:\nT172 -> T743\nT171 -> T742\nT176 -> T747\nT175 -> T746", fontsize=14, style = filled, fillcolor = lightgrey];
419 -> 946 [arrowhead = none , style=dashed];
946 -> 78[style=dashed];

947 [label="EVAL with clause\ndelmin(tree(X774, X775, X776), X777, tree(X774, X778, X779)) :- delmin(X775, X777, X778).\nand substitutionX774 -> T774,\nX775 -> T780,\nX776 -> T776,\nT662 -> tree(T774, T780, T776),\nT660 -> T777,\nX777 -> T777,\nX778 -> T778,\nX779 -> T779,\nT661 -> tree(T774, T778, T779),\nT775 -> T780", fontsize=14, style = filled, fillcolor = lightblue];
422 -> 947 [arrowhead = none ];
947 -> 458;

948 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
422 -> 948 [arrowhead = none ];
948 -> 459;

949 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
424 -> 949 [arrowhead = none ];
949 -> 460;

950 [label="INSTANCE with matching:\nT59 -> T780\nT56 -> T777\nT57 -> T778", fontsize=14, style = filled, fillcolor = lightgrey];
458 -> 950 [arrowhead = none , style=dashed];
950 -> 33[style=dashed];

951 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
460 -> 951 [arrowhead = none ];
951 -> 461;

952 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
460 -> 952 [arrowhead = none ];
952 -> 462;

953 [label="EVAL with clause\ndelete(X804, tree(X805, X806, X807), tree(X805, X808, X807)) :- ','(less(X804, X805), delete(X804, X806, X808)).\nand substitutionT657 -> T805,\nX804 -> T805,\nX805 -> T806,\nX806 -> T810,\nX807 -> T808,\nT2 -> tree(T806, T810, T808),\nT660 -> T806,\nT658 -> T809,\nX808 -> T809,\nT661 -> T808,\nT807 -> T810", fontsize=14, style = filled, fillcolor = lightblue];
461 -> 953 [arrowhead = none ];
953 -> 463;

954 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
461 -> 954 [arrowhead = none ];
954 -> 464;

955 [label="EVAL with clause\ndelete(X821, tree(X822, X823, X824), tree(X822, X823, X825)) :- ','(less(X822, X821), delete(X821, X824, X825)).\nand substitutionT657 -> T823,\nX821 -> T823,\nX822 -> T824,\nX823 -> T825,\nX824 -> T828,\nT2 -> tree(T824, T825, T828),\nT660 -> T824,\nT658 -> T825,\nT661 -> T827,\nX825 -> T827,\nT826 -> T828", fontsize=14, style = filled, fillcolor = lightblue];
462 -> 955 [arrowhead = none ];
955 -> 465;

956 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
462 -> 956 [arrowhead = none ];
956 -> 466;

957 [label="INSTANCE with matching:\nT136 -> T805\nT137 -> T806\nT141 -> T810\nT140 -> T809", fontsize=14, style = filled, fillcolor = lightgrey];
463 -> 957 [arrowhead = none , style=dashed];
957 -> 61[style=dashed];

958 [label="INSTANCE with matching:\nT172 -> T824\nT171 -> T823\nT176 -> T828\nT175 -> T827", fontsize=14, style = filled, fillcolor = lightgrey];
465 -> 958 [arrowhead = none , style=dashed];
958 -> 78[style=dashed];

959 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
467 -> 959 [arrowhead = none ];
959 -> 469;

960 [label="EVAL with clause\ndelete(X902, tree(X903, X904, X905), tree(X903, X904, X906)) :- ','(less(X903, X902), delete(X902, X905, X906)).\nand substitutionT650 -> T900,\nX902 -> T900,\nX903 -> T901,\nX904 -> T902,\nX905 -> T905,\nT2 -> tree(T901, T902, T905),\nX906 -> T904,\nT651 -> tree(T901, T902, T904),\nT903 -> T905", fontsize=14, style = filled, fillcolor = lightblue];
468 -> 960 [arrowhead = none ];
960 -> 528;

961 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
468 -> 961 [arrowhead = none ];
961 -> 529;

962 [label="EVAL with clause\nless(0, s(X840)).\nand substitutionT836 -> 0,\nX840 -> T844,\nT837 -> s(T844)", fontsize=14, style = filled, fillcolor = lightblue];
469 -> 962 [arrowhead = none ];
962 -> 470;

963 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
469 -> 963 [arrowhead = none ];
963 -> 471;

964 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
470 -> 964 [arrowhead = none ];
964 -> 475;

965 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
470 -> 965 [arrowhead = none ];
965 -> 476;

966 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
471 -> 966 [arrowhead = none ];
966 -> 521;

967 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
471 -> 967 [arrowhead = none ];
967 -> 522;

968 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T841\nT3 -> T840", fontsize=14, style = filled, fillcolor = lightgrey];
475 -> 968 [arrowhead = none , style=dashed];
968 -> 2[style=dashed];

969 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
476 -> 969 [arrowhead = none ];
969 -> 478;

970 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
478 -> 970 [arrowhead = none ];
970 -> 479;

971 [label="EVAL with clause\ndelete(X861, tree(X862, X863, X864), tree(X862, X863, X865)) :- ','(less(X862, X861), delete(X861, X864, X865)).\nand substitutionX861 -> 0,\nX862 -> s(T862),\nX863 -> T860,\nX864 -> T864,\nT2 -> tree(s(T862), T860, T864),\nT844 -> T862,\nT859 -> s(T862),\nT840 -> T860,\nT839 -> T863,\nX865 -> T863,\nT861 -> T864", fontsize=14, style = filled, fillcolor = lightblue];
479 -> 971 [arrowhead = none ];
971 -> 519;

972 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
479 -> 972 [arrowhead = none ];
972 -> 520;

973 [label="INSTANCE with matching:\nT297 -> T862\nT299 -> T864\nT298 -> T863\nT295 -> T860\nX17 -> X661\nX18 -> X662\nX19 -> X663\nX20 -> X664\nX21 -> X665", fontsize=14, style = filled, fillcolor = lightgrey];
519 -> 973 [arrowhead = none , style=dashed];
973 -> 123[style=dashed];

974 [label="EVAL with clause\nless(s(X876), s(X877)) :- less(X876, X877).\nand substitutionX876 -> T873,\nT836 -> s(T873),\nX877 -> T874,\nT837 -> s(T874)", fontsize=14, style = filled, fillcolor = lightblue];
521 -> 974 [arrowhead = none ];
974 -> 523;

975 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
521 -> 975 [arrowhead = none ];
975 -> 524;

976 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
522 -> 976 [arrowhead = none ];
976 -> 525;

977 [label="INSTANCE with matching:\nT311 -> T873\nT312 -> T874\nT276 -> T841\nT275 -> T840\nT274 -> T839\nX17 -> X661\nX18 -> X662\nX19 -> X663\nX20 -> X664\nX21 -> X665", fontsize=14, style = filled, fillcolor = lightgrey];
523 -> 977 [arrowhead = none , style=dashed];
977 -> 138[style=dashed];

978 [label="EVAL with clause\ndelete(X890, tree(X891, X892, X893), tree(X891, X892, X894)) :- ','(less(X891, X890), delete(X890, X893, X894)).\nand substitutionT836 -> T887,\nX890 -> T887,\nX891 -> T888,\nX892 -> T889,\nX893 -> T892,\nT2 -> tree(T888, T889, T892),\nT837 -> T888,\nT840 -> T889,\nT839 -> T891,\nX894 -> T891,\nT890 -> T892", fontsize=14, style = filled, fillcolor = lightblue];
525 -> 978 [arrowhead = none ];
978 -> 526;

979 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
525 -> 979 [arrowhead = none ];
979 -> 527;

980 [label="INSTANCE with matching:\nT172 -> T888\nT171 -> T887\nT176 -> T892\nT175 -> T891", fontsize=14, style = filled, fillcolor = lightgrey];
526 -> 980 [arrowhead = none , style=dashed];
980 -> 78[style=dashed];

981 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
528 -> 981 [arrowhead = none ];
981 -> 530;

982 [label="EVAL with clause\nless(0, s(X909)).\nand substitutionT901 -> 0,\nX909 -> T908,\nT900 -> s(T908)", fontsize=14, style = filled, fillcolor = lightblue];
530 -> 982 [arrowhead = none ];
982 -> 531;

983 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
530 -> 983 [arrowhead = none ];
983 -> 532;

984 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
531 -> 984 [arrowhead = none ];
984 -> 533;

985 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
531 -> 985 [arrowhead = none ];
985 -> 534;

986 [label="EVAL with clause\nless(s(X924), s(X925)) :- less(X924, X925).\nand substitutionX924 -> T921,\nT901 -> s(T921),\nX925 -> T922,\nT900 -> s(T922)", fontsize=14, style = filled, fillcolor = lightblue];
532 -> 986 [arrowhead = none ];
986 -> 536;

987 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
532 -> 987 [arrowhead = none ];
987 -> 537;

988 [label="INSTANCE with matching:\nT1 -> s(T908)\nT2 -> T905\nT3 -> T904", fontsize=14, style = filled, fillcolor = lightgrey];
533 -> 988 [arrowhead = none , style=dashed];
988 -> 2[style=dashed];

989 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
534 -> 989 [arrowhead = none ];
989 -> 535;

990 [label="INSTANCE with matching:\nT365 -> T921\nT366 -> T922\nT349 -> T905\nT348 -> T904\nT346 -> T902\nX17 -> X661\nX18 -> X662\nX19 -> X663\nX20 -> X664\nX21 -> X665\nX264 -> X833\nX265 -> X834\nX266 -> X835\nX267 -> X836\nX268 -> X837", fontsize=14, style = filled, fillcolor = lightgrey];
536 -> 990 [arrowhead = none , style=dashed];
990 -> 159[style=dashed];

991 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
538 -> 991 [arrowhead = none ];
991 -> 540;

992 [label="EVAL with clause\ndelete(X1105, tree(X1106, X1107, X1108), tree(X1106, X1109, X1108)) :- ','(less(X1105, X1106), delete(X1105, X1107, X1109)).\nand substitutionT1 -> T1109,\nX1105 -> T1109,\nX1106 -> T1110,\nX1107 -> T1114,\nX1108 -> T1112,\nT2 -> tree(T1110, T1114, T1112),\nX1109 -> T1113,\nT3 -> tree(T1110, T1113, T1112),\nT1111 -> T1114", fontsize=14, style = filled, fillcolor = lightblue];
539 -> 992 [arrowhead = none ];
992 -> 596;

993 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
539 -> 993 [arrowhead = none ];
993 -> 597;

994 [label="EVAL with clause\ndelmin(tree(X942, void, X943), X942, X943).\nand substitutionX942 -> T940,\nX943 -> T941,\nT935 -> tree(T940, void, T941),\nT933 -> T940,\nT934 -> T941", fontsize=14, style = filled, fillcolor = lightblue];
540 -> 994 [arrowhead = none ];
994 -> 541;

995 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
540 -> 995 [arrowhead = none ];
995 -> 542;

996 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
541 -> 996 [arrowhead = none ];
996 -> 543;

997 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
542 -> 997 [arrowhead = none ];
997 -> 585;

998 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
542 -> 998 [arrowhead = none ];
998 -> 586;

999 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
543 -> 999 [arrowhead = none ];
999 -> 574;

1000 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
543 -> 1000 [arrowhead = none ];
1000 -> 575;

1001 [label="EVAL with clause\ndelmin(tree(X968, X969, X970), X971, tree(X968, X972, X973)) :- delmin(X969, X971, X972).\nand substitutionX968 -> T966,\nX969 -> T972,\nX970 -> T968,\nT935 -> tree(T966, T972, T968),\nT940 -> T969,\nX971 -> T969,\nX972 -> T970,\nX973 -> T971,\nT941 -> tree(T966, T970, T971),\nT967 -> T972", fontsize=14, style = filled, fillcolor = lightblue];
574 -> 1001 [arrowhead = none ];
1001 -> 576;

1002 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
574 -> 1002 [arrowhead = none ];
1002 -> 577;

1003 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
575 -> 1003 [arrowhead = none ];
1003 -> 578;

1004 [label="INSTANCE with matching:\nT59 -> T972\nT56 -> T969\nT57 -> T970", fontsize=14, style = filled, fillcolor = lightgrey];
576 -> 1004 [arrowhead = none , style=dashed];
1004 -> 33[style=dashed];

1005 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
578 -> 1005 [arrowhead = none ];
1005 -> 579;

1006 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
578 -> 1006 [arrowhead = none ];
1006 -> 580;

1007 [label="EVAL with clause\ndelete(X998, tree(X999, X1000, X1001), tree(X999, X1002, X1001)) :- ','(less(X998, X999), delete(X998, X1000, X1002)).\nand substitutionT930 -> T997,\nX998 -> T997,\nX999 -> T998,\nX1000 -> T1002,\nX1001 -> T1000,\nT2 -> tree(T998, T1002, T1000),\nT940 -> T998,\nT931 -> T1001,\nX1002 -> T1001,\nT941 -> T1000,\nT999 -> T1002", fontsize=14, style = filled, fillcolor = lightblue];
579 -> 1007 [arrowhead = none ];
1007 -> 581;

1008 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
579 -> 1008 [arrowhead = none ];
1008 -> 582;

1009 [label="EVAL with clause\ndelete(X1015, tree(X1016, X1017, X1018), tree(X1016, X1017, X1019)) :- ','(less(X1016, X1015), delete(X1015, X1018, X1019)).\nand substitutionT930 -> T1015,\nX1015 -> T1015,\nX1016 -> T1016,\nX1017 -> T1017,\nX1018 -> T1020,\nT2 -> tree(T1016, T1017, T1020),\nT940 -> T1016,\nT931 -> T1017,\nT941 -> T1019,\nX1019 -> T1019,\nT1018 -> T1020", fontsize=14, style = filled, fillcolor = lightblue];
580 -> 1009 [arrowhead = none ];
1009 -> 583;

1010 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
580 -> 1010 [arrowhead = none ];
1010 -> 584;

1011 [label="INSTANCE with matching:\nT136 -> T997\nT137 -> T998\nT141 -> T1002\nT140 -> T1001", fontsize=14, style = filled, fillcolor = lightgrey];
581 -> 1011 [arrowhead = none , style=dashed];
1011 -> 61[style=dashed];

1012 [label="INSTANCE with matching:\nT172 -> T1016\nT171 -> T1015\nT176 -> T1020\nT175 -> T1019", fontsize=14, style = filled, fillcolor = lightgrey];
583 -> 1012 [arrowhead = none , style=dashed];
1012 -> 78[style=dashed];

1013 [label="EVAL with clause\ndelmin(tree(X1046, X1047, X1048), X1049, tree(X1046, X1050, X1051)) :- delmin(X1047, X1049, X1050).\nand substitutionX1046 -> T1047,\nX1047 -> T1053,\nX1048 -> T1049,\nT935 -> tree(T1047, T1053, T1049),\nT933 -> T1050,\nX1049 -> T1050,\nX1050 -> T1051,\nX1051 -> T1052,\nT934 -> tree(T1047, T1051, T1052),\nT1048 -> T1053", fontsize=14, style = filled, fillcolor = lightblue];
585 -> 1013 [arrowhead = none ];
1013 -> 587;

1014 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
585 -> 1014 [arrowhead = none ];
1014 -> 588;

1015 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
586 -> 1015 [arrowhead = none ];
1015 -> 589;

1016 [label="INSTANCE with matching:\nT59 -> T1053\nT56 -> T1050\nT57 -> T1051", fontsize=14, style = filled, fillcolor = lightgrey];
587 -> 1016 [arrowhead = none , style=dashed];
1016 -> 33[style=dashed];

1017 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
589 -> 1017 [arrowhead = none ];
1017 -> 590;

1018 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
589 -> 1018 [arrowhead = none ];
1018 -> 591;

1019 [label="EVAL with clause\ndelete(X1076, tree(X1077, X1078, X1079), tree(X1077, X1080, X1079)) :- ','(less(X1076, X1077), delete(X1076, X1078, X1080)).\nand substitutionT930 -> T1078,\nX1076 -> T1078,\nX1077 -> T1079,\nX1078 -> T1083,\nX1079 -> T1081,\nT2 -> tree(T1079, T1083, T1081),\nT933 -> T1079,\nT931 -> T1082,\nX1080 -> T1082,\nT934 -> T1081,\nT1080 -> T1083", fontsize=14, style = filled, fillcolor = lightblue];
590 -> 1019 [arrowhead = none ];
1019 -> 592;

1020 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
590 -> 1020 [arrowhead = none ];
1020 -> 593;

1021 [label="EVAL with clause\ndelete(X1093, tree(X1094, X1095, X1096), tree(X1094, X1095, X1097)) :- ','(less(X1094, X1093), delete(X1093, X1096, X1097)).\nand substitutionT930 -> T1096,\nX1093 -> T1096,\nX1094 -> T1097,\nX1095 -> T1098,\nX1096 -> T1101,\nT2 -> tree(T1097, T1098, T1101),\nT933 -> T1097,\nT931 -> T1098,\nT934 -> T1100,\nX1097 -> T1100,\nT1099 -> T1101", fontsize=14, style = filled, fillcolor = lightblue];
591 -> 1021 [arrowhead = none ];
1021 -> 594;

1022 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
591 -> 1022 [arrowhead = none ];
1022 -> 595;

1023 [label="INSTANCE with matching:\nT136 -> T1078\nT137 -> T1079\nT141 -> T1083\nT140 -> T1082", fontsize=14, style = filled, fillcolor = lightgrey];
592 -> 1023 [arrowhead = none , style=dashed];
1023 -> 61[style=dashed];

1024 [label="INSTANCE with matching:\nT172 -> T1097\nT171 -> T1096\nT176 -> T1101\nT175 -> T1100", fontsize=14, style = filled, fillcolor = lightgrey];
594 -> 1024 [arrowhead = none , style=dashed];
1024 -> 78[style=dashed];

1025 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
596 -> 1025 [arrowhead = none ];
1025 -> 598;

1026 [label="EVAL with clause\ndelete(X1174, tree(X1175, X1176, X1177), tree(X1175, X1176, X1178)) :- ','(less(X1175, X1174), delete(X1174, X1177, X1178)).\nand substitutionT1 -> T1173,\nX1174 -> T1173,\nX1175 -> T1174,\nX1176 -> T1175,\nX1177 -> T1178,\nT2 -> tree(T1174, T1175, T1178),\nX1178 -> T1177,\nT3 -> tree(T1174, T1175, T1177),\nT1176 -> T1178", fontsize=14, style = filled, fillcolor = lightblue];
597 -> 1026 [arrowhead = none ];
1026 -> 697;

1027 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
597 -> 1027 [arrowhead = none ];
1027 -> 698;

1028 [label="EVAL with clause\nless(0, s(X1112)).\nand substitutionT1109 -> 0,\nX1112 -> T1117,\nT1110 -> s(T1117)", fontsize=14, style = filled, fillcolor = lightblue];
598 -> 1028 [arrowhead = none ];
1028 -> 599;

1029 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
598 -> 1029 [arrowhead = none ];
1029 -> 600;

1030 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
599 -> 1030 [arrowhead = none ];
1030 -> 601;

1031 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
599 -> 1031 [arrowhead = none ];
1031 -> 602;

1032 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
600 -> 1032 [arrowhead = none ];
1032 -> 607;

1033 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
600 -> 1033 [arrowhead = none ];
1033 -> 608;

1034 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T1114\nT3 -> T1113", fontsize=14, style = filled, fillcolor = lightgrey];
601 -> 1034 [arrowhead = none , style=dashed];
1034 -> 2[style=dashed];

1035 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
602 -> 1035 [arrowhead = none ];
1035 -> 603;

1036 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
603 -> 1036 [arrowhead = none ];
1036 -> 604;

1037 [label="EVAL with clause\ndelete(X1133, tree(X1134, X1135, X1136), tree(X1134, X1135, X1137)) :- ','(less(X1134, X1133), delete(X1133, X1136, X1137)).\nand substitutionX1133 -> 0,\nX1134 -> s(T1135),\nX1135 -> T1133,\nX1136 -> T1137,\nT2 -> tree(s(T1135), T1133, T1137),\nT1117 -> T1135,\nT1132 -> s(T1135),\nT1113 -> T1133,\nT1112 -> T1136,\nX1137 -> T1136,\nT1134 -> T1137", fontsize=14, style = filled, fillcolor = lightblue];
604 -> 1037 [arrowhead = none ];
1037 -> 605;

1038 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
604 -> 1038 [arrowhead = none ];
1038 -> 606;

1039 [label="INSTANCE with matching:\nT297 -> T1135\nT299 -> T1137\nT298 -> T1136\nT295 -> T1133\nX17 -> X933\nX18 -> X934\nX19 -> X935\nX20 -> X936\nX21 -> X937", fontsize=14, style = filled, fillcolor = lightgrey];
605 -> 1039 [arrowhead = none , style=dashed];
1039 -> 123[style=dashed];

1040 [label="EVAL with clause\nless(s(X1148), s(X1149)) :- less(X1148, X1149).\nand substitutionX1148 -> T1146,\nT1109 -> s(T1146),\nX1149 -> T1147,\nT1110 -> s(T1147)", fontsize=14, style = filled, fillcolor = lightblue];
607 -> 1040 [arrowhead = none ];
1040 -> 609;

1041 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
607 -> 1041 [arrowhead = none ];
1041 -> 610;

1042 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
608 -> 1042 [arrowhead = none ];
1042 -> 611;

1043 [label="INSTANCE with matching:\nT311 -> T1146\nT312 -> T1147\nT276 -> T1114\nT275 -> T1113\nT274 -> T1112\nX17 -> X933\nX18 -> X934\nX19 -> X935\nX20 -> X936\nX21 -> X937", fontsize=14, style = filled, fillcolor = lightgrey];
609 -> 1043 [arrowhead = none , style=dashed];
1043 -> 138[style=dashed];

1044 [label="EVAL with clause\ndelete(X1162, tree(X1163, X1164, X1165), tree(X1163, X1164, X1166)) :- ','(less(X1163, X1162), delete(X1162, X1165, X1166)).\nand substitutionT1109 -> T1160,\nX1162 -> T1160,\nX1163 -> T1161,\nX1164 -> T1162,\nX1165 -> T1165,\nT2 -> tree(T1161, T1162, T1165),\nT1110 -> T1161,\nT1113 -> T1162,\nT1112 -> T1164,\nX1166 -> T1164,\nT1163 -> T1165", fontsize=14, style = filled, fillcolor = lightblue];
611 -> 1044 [arrowhead = none ];
1044 -> 612;

1045 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
611 -> 1045 [arrowhead = none ];
1045 -> 613;

1046 [label="INSTANCE with matching:\nT172 -> T1161\nT171 -> T1160\nT176 -> T1165\nT175 -> T1164", fontsize=14, style = filled, fillcolor = lightgrey];
612 -> 1046 [arrowhead = none , style=dashed];
1046 -> 78[style=dashed];

1047 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
697 -> 1047 [arrowhead = none ];
1047 -> 699;

1048 [label="EVAL with clause\nless(0, s(X1181)).\nand substitutionT1174 -> 0,\nX1181 -> T1181,\nT1173 -> s(T1181)", fontsize=14, style = filled, fillcolor = lightblue];
699 -> 1048 [arrowhead = none ];
1048 -> 700;

1049 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
699 -> 1049 [arrowhead = none ];
1049 -> 701;

1050 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
700 -> 1050 [arrowhead = none ];
1050 -> 702;

1051 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
700 -> 1051 [arrowhead = none ];
1051 -> 703;

1052 [label="EVAL with clause\nless(s(X1196), s(X1197)) :- less(X1196, X1197).\nand substitutionX1196 -> T1194,\nT1174 -> s(T1194),\nX1197 -> T1195,\nT1173 -> s(T1195)", fontsize=14, style = filled, fillcolor = lightblue];
701 -> 1052 [arrowhead = none ];
1052 -> 740;

1053 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
701 -> 1053 [arrowhead = none ];
1053 -> 741;

1054 [label="INSTANCE with matching:\nT1 -> s(T1181)\nT2 -> T1178\nT3 -> T1177", fontsize=14, style = filled, fillcolor = lightgrey];
702 -> 1054 [arrowhead = none , style=dashed];
1054 -> 2[style=dashed];

1055 [label="BACKTRACK\nfor clause: less(s(X), s(Y)) :- less(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
703 -> 1055 [arrowhead = none ];
1055 -> 706;

1056 [label="INSTANCE with matching:\nT365 -> T1194\nT366 -> T1195\nT349 -> T1178\nT348 -> T1177\nT346 -> T1175\nX17 -> X933\nX18 -> X934\nX19 -> X935\nX20 -> X936\nX21 -> X937\nX264 -> X1105\nX265 -> X1106\nX266 -> X1107\nX267 -> X1108\nX268 -> X1109", fontsize=14, style = filled, fillcolor = lightgrey];
740 -> 1056 [arrowhead = none , style=dashed];
1056 -> 159[style=dashed];

}

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → U1(f25_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U2(f23_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U3(f113_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f114_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f154_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U7(f168_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U8(f167_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U9(f264_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U10(f265_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U11(f311_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U12(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U13(f326_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U14(f325_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U15(f470_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U16(f471_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U17(f531_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U18(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U19(f543_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U20(f542_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U21(f599_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U22(f600_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U23(f700_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U24(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f25_out1, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out3, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out4, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out1, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out3, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out4, z0, tree(z1, z2, z3)) → f2_out1
U3(f113_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U4(f114_out1, z0, tree(z1, z2, z3)) → f2_out1
U4(f114_out3, z0, tree(z1, z2, z3)) → f2_out1
U5(f154_out1, s(z0), tree(0, z1, z2)) → f2_out1
U5(f154_out2, s(z0), tree(0, z1, z2)) → f2_out1
U6(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U7(f168_out1, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out3, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out4, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out1, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out3, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out4, z0, tree(z1, z2, z3)) → f2_out1
U9(f264_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U10(f265_out1, z0, tree(z1, z2, z3)) → f2_out1
U10(f265_out3, z0, tree(z1, z2, z3)) → f2_out1
U11(f311_out1, s(z0), tree(0, z1, z2)) → f2_out1
U11(f311_out2, s(z0), tree(0, z1, z2)) → f2_out1
U12(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U13(f326_out1, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out3, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out4, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out3, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out4, z0, tree(z1, z2, z3)) → f2_out1
U15(f470_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U16(f471_out1, z0, tree(z1, z2, z3)) → f2_out1
U16(f471_out3, z0, tree(z1, z2, z3)) → f2_out1
U17(f531_out1, s(z0), tree(0, z1, z2)) → f2_out1
U17(f531_out2, s(z0), tree(0, z1, z2)) → f2_out1
U18(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U19(f543_out1, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out3, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out4, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out1, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out3, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out4, z0, tree(z1, z2, z3)) → f2_out1
U21(f599_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U22(f600_out1, z0, tree(z1, z2, z3)) → f2_out1
U22(f600_out3, z0, tree(z1, z2, z3)) → f2_out1
U23(f700_out1, s(z0), tree(0, z1, z2)) → f2_out1
U23(f700_out2, s(z0), tree(0, z1, z2)) → f2_out1
U24(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f33_in(z0, z1) → f33_out1
f33_in(z0, tree(z1, z2, z3)) → U25(f33_in(z0, z2), z0, tree(z1, z2, z3))
f33_in(z0, tree(z1, z2, z3)) → U26(f33_in(z0, z2), z0, tree(z1, z2, z3))
U25(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
U26(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
f63_in(0, s(z0)) → f63_out1
f63_in(s(z0), s(z1)) → U27(f63_in(z0, z1), s(z0), s(z1))
U27(f63_out1, s(z0), s(z1)) → f63_out1
f585_in(z0, tree(z1, z2, z3)) → U28(f33_in(z0, z2), z0, tree(z1, z2, z3))
U28(f33_out1, z0, tree(z1, z2, z3)) → f585_out1
f586_in(z0, z1, z2, z3) → U29(f589_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f589_out1, z0, z1, z2, z3) → f586_out2
U29(f589_out2, z0, z1, z2, z3) → f586_out3
f211_in(z0, tree(z1, z2, z3)) → U30(f33_in(z0, z2), z0, tree(z1, z2, z3))
U30(f33_out1, z0, tree(z1, z2, z3)) → f211_out1
f212_in(z0, z1, z2, z3) → U31(f215_in(z0, z1, z2, z3), z0, z1, z2, z3)
U31(f215_out1, z0, z1, z2, z3) → f212_out2
U31(f215_out2, z0, z1, z2, z3) → f212_out3
f422_in(z0, tree(z1, z2, z3)) → U32(f33_in(z0, z2), z0, tree(z1, z2, z3))
U32(f33_out1, z0, tree(z1, z2, z3)) → f422_out1
f424_in(z0, z1, z2, z3) → U33(f460_in(z0, z1, z2, z3), z0, z1, z2, z3)
U33(f460_out1, z0, z1, z2, z3) → f424_out2
U33(f460_out2, z0, z1, z2, z3) → f424_out3
f574_in(z0, tree(z1, z2, z3)) → U34(f33_in(z0, z2), z0, tree(z1, z2, z3))
U34(f33_out1, z0, tree(z1, z2, z3)) → f574_out1
f575_in(z0, z1, z2, z3) → U35(f578_in(z0, z1, z2, z3), z0, z1, z2, z3)
U35(f578_out1, z0, z1, z2, z3) → f575_out2
U35(f578_out2, z0, z1, z2, z3) → f575_out3
f602_in(z0, z1, z2) → U36(f123_in(z0, z2), z0, z1, z2)
U36(f123_out1, z0, z1, z2) → f602_out3
f607_in(s(z0), s(z1), z2) → U37(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U37(f138_out1, s(z0), s(z1), z2) → f607_out1
f608_in(z0, z1, z2, z3) → U38(f78_in(z1, z0, z3), z0, z1, z2, z3)
U38(f78_out1, z0, z1, z2, z3) → f608_out2
f86_in(z0, tree(z1, z2, z3)) → U39(f33_in(z0, z2), z0, tree(z1, z2, z3))
U39(f33_out1, z0, tree(z1, z2, z3)) → f86_out1
f87_in(z0, z1, z2, z3) → U40(f92_in(z0, z1, z2, z3), z0, z1, z2, z3)
U40(f92_out1, z0, z1, z2, z3) → f87_out2
U40(f92_out2, z0, z1, z2, z3) → f87_out3
f169_in(z0, tree(z1, z2, z3)) → U41(f33_in(z0, z2), z0, tree(z1, z2, z3))
U41(f33_out1, z0, tree(z1, z2, z3)) → f169_out1
f170_in(z0, z1, z2, z3) → U42(f173_in(z0, z1, z2, z3), z0, z1, z2, z3)
U42(f173_out1, z0, z1, z2, z3) → f170_out2
U42(f173_out2, z0, z1, z2, z3) → f170_out3
f267_in(z0, z1, z2) → U43(f123_in(z0, z2), z0, z1, z2)
U43(f123_out1, z0, z1, z2) → f267_out3
f301_in(s(z0), s(z1), z2) → U44(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U44(f138_out1, s(z0), s(z1), z2) → f301_out1
f302_in(z0, z1, z2, z3) → U45(f78_in(z1, z0, z3), z0, z1, z2, z3)
U45(f78_out1, z0, z1, z2, z3) → f302_out2
f327_in(z0, tree(z1, z2, z3)) → U46(f33_in(z0, z2), z0, tree(z1, z2, z3))
U46(f33_out1, z0, tree(z1, z2, z3)) → f327_out1
f328_in(z0, z1, z2, z3) → U47(f414_in(z0, z1, z2, z3), z0, z1, z2, z3)
U47(f414_out1, z0, z1, z2, z3) → f328_out2
U47(f414_out2, z0, z1, z2, z3) → f328_out3
f476_in(z0, z1, z2) → U48(f123_in(z0, z2), z0, z1, z2)
U48(f123_out1, z0, z1, z2) → f476_out3
f521_in(s(z0), s(z1), z2) → U49(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U49(f138_out1, s(z0), s(z1), z2) → f521_out1
f522_in(z0, z1, z2, z3) → U50(f78_in(z1, z0, z3), z0, z1, z2, z3)
U50(f78_out1, z0, z1, z2, z3) → f522_out2
f590_in(z0, z1, z2, z3) → U51(f61_in(z0, z1, z2), z0, z1, z2, z3)
U51(f61_out1, z0, z1, z2, z3) → f590_out1
f591_in(z0, z1, z2, z3) → U52(f78_in(z1, z0, z3), z0, z1, z2, z3)
U52(f78_out1, z0, z1, z2, z3) → f591_out1
f27_in(z0, tree(z1, z2, z3)) → U53(f33_in(z0, z2), z0, tree(z1, z2, z3))
U53(f33_out1, z0, tree(z1, z2, z3)) → f27_out1
f28_in(z0, z1, z2, z3) → U54(f49_in(z0, z1, z2, z3), z0, z1, z2, z3)
U54(f49_out1, z0, z1, z2, z3) → f28_out2
U54(f49_out2, z0, z1, z2, z3) → f28_out3
f118_in(z0, z1, z2) → U55(f123_in(z0, z2), z0, z1, z2)
U55(f123_out1, z0, z1, z2) → f118_out3
f134_in(s(z0), s(z1), z2) → U56(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U56(f138_out1, s(z0), s(z1), z2) → f134_out1
f135_in(z0, z1, z2, z3) → U57(f78_in(z1, z0, z3), z0, z1, z2, z3)
U57(f78_out1, z0, z1, z2, z3) → f135_out2
f216_in(z0, z1, z2, z3) → U58(f61_in(z0, z1, z2), z0, z1, z2, z3)
U58(f61_out1, z0, z1, z2, z3) → f216_out1
f217_in(z0, z1, z2, z3) → U59(f78_in(z1, z0, z3), z0, z1, z2, z3)
U59(f78_out1, z0, z1, z2, z3) → f217_out1
f461_in(z0, z1, z2, z3) → U60(f61_in(z0, z1, z2), z0, z1, z2, z3)
U60(f61_out1, z0, z1, z2, z3) → f461_out1
f462_in(z0, z1, z2, z3) → U61(f78_in(z1, z0, z3), z0, z1, z2, z3)
U61(f78_out1, z0, z1, z2, z3) → f462_out1
f579_in(z0, z1, z2, z3) → U62(f61_in(z0, z1, z2), z0, z1, z2, z3)
U62(f61_out1, z0, z1, z2, z3) → f579_out1
f580_in(z0, z1, z2, z3) → U63(f78_in(z1, z0, z3), z0, z1, z2, z3)
U63(f78_out1, z0, z1, z2, z3) → f580_out1
f95_in(z0, z1, z2, z3) → U64(f61_in(z0, z1, z2), z0, z1, z2, z3)
U64(f61_out1, z0, z1, z2, z3) → f95_out1
f96_in(z0, z1, z2, z3) → U65(f78_in(z1, z0, z3), z0, z1, z2, z3)
U65(f78_out1, z0, z1, z2, z3) → f96_out1
f174_in(z0, z1, z2, z3) → U66(f61_in(z0, z1, z2), z0, z1, z2, z3)
U66(f61_out1, z0, z1, z2, z3) → f174_out1
f175_in(z0, z1, z2, z3) → U67(f78_in(z1, z0, z3), z0, z1, z2, z3)
U67(f78_out1, z0, z1, z2, z3) → f175_out1
f415_in(z0, z1, z2, z3) → U68(f61_in(z0, z1, z2), z0, z1, z2, z3)
U68(f61_out1, z0, z1, z2, z3) → f415_out1
f416_in(z0, z1, z2, z3) → U69(f78_in(z1, z0, z3), z0, z1, z2, z3)
U69(f78_out1, z0, z1, z2, z3) → f416_out1
f52_in(z0, z1, z2, z3) → U70(f61_in(z0, z1, z2), z0, z1, z2, z3)
U70(f61_out1, z0, z1, z2, z3) → f52_out1
f53_in(z0, z1, z2, z3) → U71(f78_in(z1, z0, z3), z0, z1, z2, z3)
U71(f78_out1, z0, z1, z2, z3) → f53_out1
f61_in(z0, z1, z2) → U72(f63_in(z0, z1), z0, z1, z2)
U72(f63_out1, z0, z1, z2) → U73(f2_in(z0, z2), z0, z1, z2)
U73(f2_out1, z0, z1, z2) → f61_out1
f78_in(z0, z1, z2) → U74(f63_in(z0, z1), z0, z1, z2)
U74(f63_out1, z0, z1, z2) → U75(f2_in(z1, z2), z0, z1, z2)
U75(f2_out1, z0, z1, z2) → f78_out1
f123_in(z0, z1) → U76(f127_in(z0), z0, z1)
U76(f127_out1, z0, z1) → U77(f2_in(0, z1), z0, z1)
U77(f2_out1, z0, z1) → f123_out1
f138_in(z0, z1, z2) → U78(f63_in(z0, z1), z0, z1, z2)
U78(f63_out1, z0, z1, z2) → U79(f2_in(s(z0), z2), z0, z1, z2)
U79(f2_out1, z0, z1, z2) → f138_out1
f159_in(z0, z1, z2) → U80(f63_in(z0, z1), z0, z1, z2)
U80(f63_out1, z0, z1, z2) → U81(f2_in(s(z1), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f159_out1
f23_in(z0, z1, z2, z3) → U82(f86_in(z0, z1), f87_in(z2, z0, z3, z1), z0, z1, z2, z3)
U82(f86_out1, z0, z1, z2, z3, z4) → f23_out1
U82(z0, f87_out2, z1, z2, z3, z4) → f23_out3
U82(z0, f87_out3, z1, z2, z3, z4) → f23_out4
f25_in(z0, z1, z2, z3) → U83(f27_in(z0, z1), f28_in(z2, z0, z3, z1), z0, z1, z2, z3)
U83(f27_out1, z0, z1, z2, z3, z4) → f25_out1
U83(z0, f28_out2, z1, z2, z3, z4) → f25_out3
U83(z0, f28_out3, z1, z2, z3, z4) → f25_out4
f49_in(z0, z1, z2, z3) → U84(f52_in(z0, z1, z2, z3), f53_in(z0, z1, z2, z3), z0, z1, z2, z3)
U84(f52_out1, z0, z1, z2, z3, z4) → f49_out1
U84(z0, f53_out1, z1, z2, z3, z4) → f49_out2
f92_in(z0, z1, z2, z3) → U85(f95_in(z0, z1, z2, z3), f96_in(z0, z1, z2, z3), z0, z1, z2, z3)
U85(f95_out1, z0, z1, z2, z3, z4) → f92_out1
U85(z0, f96_out1, z1, z2, z3, z4) → f92_out2
f113_in(z0, z1, z2) → U86(f2_in(0, z0), f118_in(z1, z0, z2), z0, z1, z2)
U86(f2_out1, z0, z1, z2, z3) → f113_out1
U86(z0, f118_out1, z1, z2, z3) → f113_out2
U86(z0, f118_out3, z1, z2, z3) → f113_out4
f114_in(z0, z1, z2, z3) → U87(f134_in(z0, z1, z2), f135_in(z0, z1, z2, z3), z0, z1, z2, z3)
U87(f134_out1, z0, z1, z2, z3, z4) → f114_out1
U87(z0, f135_out2, z1, z2, z3, z4) → f114_out3
f154_in(z0, z1) → U88(f2_in(s(z0), z1), f157_in(z0, z1), z0, z1)
U88(f2_out1, z0, z1, z2) → f154_out1
U88(z0, f157_out1, z1, z2) → f154_out2
f167_in(z0, z1, z2, z3) → U89(f211_in(z0, z1), f212_in(z2, z0, z3, z1), z0, z1, z2, z3)
U89(f211_out1, z0, z1, z2, z3, z4) → f167_out1
U89(z0, f212_out2, z1, z2, z3, z4) → f167_out3
U89(z0, f212_out3, z1, z2, z3, z4) → f167_out4
f168_in(z0, z1, z2, z3) → U90(f169_in(z0, z1), f170_in(z2, z0, z3, z1), z0, z1, z2, z3)
U90(f169_out1, z0, z1, z2, z3, z4) → f168_out1
U90(z0, f170_out2, z1, z2, z3, z4) → f168_out3
U90(z0, f170_out3, z1, z2, z3, z4) → f168_out4
f173_in(z0, z1, z2, z3) → U91(f174_in(z0, z1, z2, z3), f175_in(z0, z1, z2, z3), z0, z1, z2, z3)
U91(f174_out1, z0, z1, z2, z3, z4) → f173_out1
U91(z0, f175_out1, z1, z2, z3, z4) → f173_out2
f215_in(z0, z1, z2, z3) → U92(f216_in(z0, z1, z2, z3), f217_in(z0, z1, z2, z3), z0, z1, z2, z3)
U92(f216_out1, z0, z1, z2, z3, z4) → f215_out1
U92(z0, f217_out1, z1, z2, z3, z4) → f215_out2
f264_in(z0, z1, z2) → U93(f2_in(0, z0), f267_in(z1, z0, z2), z0, z1, z2)
U93(f2_out1, z0, z1, z2, z3) → f264_out1
U93(z0, f267_out1, z1, z2, z3) → f264_out2
U93(z0, f267_out3, z1, z2, z3) → f264_out4
f265_in(z0, z1, z2, z3) → U94(f301_in(z0, z1, z2), f302_in(z0, z1, z2, z3), z0, z1, z2, z3)
U94(f301_out1, z0, z1, z2, z3, z4) → f265_out1
U94(z0, f302_out2, z1, z2, z3, z4) → f265_out3
f311_in(z0, z1) → U95(f2_in(s(z0), z1), f314_in(z0, z1), z0, z1)
U95(f2_out1, z0, z1, z2) → f311_out1
U95(z0, f314_out1, z1, z2) → f311_out2
f325_in(z0, z1, z2, z3) → U96(f422_in(z0, z1), f424_in(z2, z0, z3, z1), z0, z1, z2, z3)
U96(f422_out1, z0, z1, z2, z3, z4) → f325_out1
U96(z0, f424_out2, z1, z2, z3, z4) → f325_out3
U96(z0, f424_out3, z1, z2, z3, z4) → f325_out4
f326_in(z0, z1, z2, z3) → U97(f327_in(z0, z1), f328_in(z2, z0, z3, z1), z0, z1, z2, z3)
U97(f327_out1, z0, z1, z2, z3, z4) → f326_out1
U97(z0, f328_out2, z1, z2, z3, z4) → f326_out3
U97(z0, f328_out3, z1, z2, z3, z4) → f326_out4
f414_in(z0, z1, z2, z3) → U98(f415_in(z0, z1, z2, z3), f416_in(z0, z1, z2, z3), z0, z1, z2, z3)
U98(f415_out1, z0, z1, z2, z3, z4) → f414_out1
U98(z0, f416_out1, z1, z2, z3, z4) → f414_out2
f460_in(z0, z1, z2, z3) → U99(f461_in(z0, z1, z2, z3), f462_in(z0, z1, z2, z3), z0, z1, z2, z3)
U99(f461_out1, z0, z1, z2, z3, z4) → f460_out1
U99(z0, f462_out1, z1, z2, z3, z4) → f460_out2
f470_in(z0, z1, z2) → U100(f2_in(0, z0), f476_in(z1, z0, z2), z0, z1, z2)
U100(f2_out1, z0, z1, z2, z3) → f470_out1
U100(z0, f476_out1, z1, z2, z3) → f470_out2
U100(z0, f476_out3, z1, z2, z3) → f470_out4
f471_in(z0, z1, z2, z3) → U101(f521_in(z0, z1, z2), f522_in(z0, z1, z2, z3), z0, z1, z2, z3)
U101(f521_out1, z0, z1, z2, z3, z4) → f471_out1
U101(z0, f522_out2, z1, z2, z3, z4) → f471_out3
f531_in(z0, z1) → U102(f2_in(s(z0), z1), f534_in(z0, z1), z0, z1)
U102(f2_out1, z0, z1, z2) → f531_out1
U102(z0, f534_out1, z1, z2) → f531_out2
f542_in(z0, z1, z2, z3) → U103(f585_in(z0, z1), f586_in(z2, z0, z3, z1), z0, z1, z2, z3)
U103(f585_out1, z0, z1, z2, z3, z4) → f542_out1
U103(z0, f586_out2, z1, z2, z3, z4) → f542_out3
U103(z0, f586_out3, z1, z2, z3, z4) → f542_out4
f543_in(z0, z1, z2, z3) → U104(f574_in(z0, z1), f575_in(z2, z0, z3, z1), z0, z1, z2, z3)
U104(f574_out1, z0, z1, z2, z3, z4) → f543_out1
U104(z0, f575_out2, z1, z2, z3, z4) → f543_out3
U104(z0, f575_out3, z1, z2, z3, z4) → f543_out4
f578_in(z0, z1, z2, z3) → U105(f579_in(z0, z1, z2, z3), f580_in(z0, z1, z2, z3), z0, z1, z2, z3)
U105(f579_out1, z0, z1, z2, z3, z4) → f578_out1
U105(z0, f580_out1, z1, z2, z3, z4) → f578_out2
f589_in(z0, z1, z2, z3) → U106(f590_in(z0, z1, z2, z3), f591_in(z0, z1, z2, z3), z0, z1, z2, z3)
U106(f590_out1, z0, z1, z2, z3, z4) → f589_out1
U106(z0, f591_out1, z1, z2, z3, z4) → f589_out2
f599_in(z0, z1, z2) → U107(f2_in(0, z0), f602_in(z1, z0, z2), z0, z1, z2)
U107(f2_out1, z0, z1, z2, z3) → f599_out1
U107(z0, f602_out1, z1, z2, z3) → f599_out2
U107(z0, f602_out3, z1, z2, z3) → f599_out4
f600_in(z0, z1, z2, z3) → U108(f607_in(z0, z1, z2), f608_in(z0, z1, z2, z3), z0, z1, z2, z3)
U108(f607_out1, z0, z1, z2, z3, z4) → f600_out1
U108(z0, f608_out2, z1, z2, z3, z4) → f600_out3
f700_in(z0, z1) → U109(f2_in(s(z0), z1), f703_in(z0, z1), z0, z1)
U109(f2_out1, z0, z1, z2) → f700_out1
U109(z0, f703_out1, z1, z2) → f700_out2

Tuples:

F2_IN(z0, tree(z1, z2, z3)) → c2(U1'(f25_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(U2'(f23_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(U3'(f113_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(U4'(f114_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(U5'(f154_in(z0, z2), s(z0), tree(0, z1, z2)), F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(U6'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(U7'(f168_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(U8'(f167_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(U9'(f264_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(U10'(f265_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(U11'(f311_in(z0, z2), s(z0), tree(0, z1, z2)), F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(U12'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(U13'(f326_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(U14'(f325_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(U15'(f470_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(U16'(f471_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(U17'(f531_in(z0, z2), s(z0), tree(0, z1, z2)), F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(U18'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(U19'(f543_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(U20'(f542_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(U21'(f599_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(U22'(f600_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(U23'(f700_in(z0, z2), s(z0), tree(0, z1, z2)), F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(U24'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(U25'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(U26'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(U27'(f63_in(z0, z1), s(z0), s(z1)), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c90(U28'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F586_IN(z0, z1, z2, z3) → c92(U29'(f589_in(z0, z1, z2, z3), z0, z1, z2, z3), F589_IN(z0, z1, z2, z3))
F211_IN(z0, tree(z1, z2, z3)) → c95(U30'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F212_IN(z0, z1, z2, z3) → c97(U31'(f215_in(z0, z1, z2, z3), z0, z1, z2, z3), F215_IN(z0, z1, z2, z3))
F422_IN(z0, tree(z1, z2, z3)) → c100(U32'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F424_IN(z0, z1, z2, z3) → c102(U33'(f460_in(z0, z1, z2, z3), z0, z1, z2, z3), F460_IN(z0, z1, z2, z3))
F574_IN(z0, tree(z1, z2, z3)) → c105(U34'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F575_IN(z0, z1, z2, z3) → c107(U35'(f578_in(z0, z1, z2, z3), z0, z1, z2, z3), F578_IN(z0, z1, z2, z3))
F602_IN(z0, z1, z2) → c110(U36'(f123_in(z0, z2), z0, z1, z2), F123_IN(z0, z2))
F607_IN(s(z0), s(z1), z2) → c112(U37'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(U38'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F86_IN(z0, tree(z1, z2, z3)) → c116(U39'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F87_IN(z0, z1, z2, z3) → c118(U40'(f92_in(z0, z1, z2, z3), z0, z1, z2, z3), F92_IN(z0, z1, z2, z3))
F169_IN(z0, tree(z1, z2, z3)) → c121(U41'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F170_IN(z0, z1, z2, z3) → c123(U42'(f173_in(z0, z1, z2, z3), z0, z1, z2, z3), F173_IN(z0, z1, z2, z3))
F267_IN(z0, z1, z2) → c126(U43'(f123_in(z0, z2), z0, z1, z2), F123_IN(z0, z2))
F301_IN(s(z0), s(z1), z2) → c128(U44'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(U45'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F327_IN(z0, tree(z1, z2, z3)) → c132(U46'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F328_IN(z0, z1, z2, z3) → c134(U47'(f414_in(z0, z1, z2, z3), z0, z1, z2, z3), F414_IN(z0, z1, z2, z3))
F476_IN(z0, z1, z2) → c137(U48'(f123_in(z0, z2), z0, z1, z2), F123_IN(z0, z2))
F521_IN(s(z0), s(z1), z2) → c139(U49'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(U50'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(U51'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(U52'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F27_IN(z0, tree(z1, z2, z3)) → c147(U53'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F28_IN(z0, z1, z2, z3) → c149(U54'(f49_in(z0, z1, z2, z3), z0, z1, z2, z3), F49_IN(z0, z1, z2, z3))
F118_IN(z0, z1, z2) → c152(U55'(f123_in(z0, z2), z0, z1, z2), F123_IN(z0, z2))
F134_IN(s(z0), s(z1), z2) → c154(U56'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(U57'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(U58'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(U59'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(U60'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(U61'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(U62'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(U63'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(U64'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(U65'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(U66'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(U67'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(U68'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(U69'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(U70'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(U71'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U72'(f63_out1, z0, z1, z2) → c187(U73'(f2_in(z0, z2), z0, z1, z2), F2_IN(z0, z2))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U74'(f63_out1, z0, z1, z2) → c190(U75'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F123_IN(z0, z1) → c192(U76'(f127_in(z0), z0, z1))
U76'(f127_out1, z0, z1) → c193(U77'(f2_in(0, z1), z0, z1), F2_IN(0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U78'(f63_out1, z0, z1, z2) → c196(U79'(f2_in(s(z0), z2), z0, z1, z2), F2_IN(s(z0), z2))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U80'(f63_out1, z0, z1, z2) → c199(U81'(f2_in(s(z1), z2), z0, z1, z2), F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(U82'(f86_in(z0, z1), f87_in(z2, z0, z3, z1), z0, z1, z2, z3), F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(U83'(f27_in(z0, z1), f28_in(z2, z0, z3, z1), z0, z1, z2, z3), F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(U84'(f52_in(z0, z1, z2, z3), f53_in(z0, z1, z2, z3), z0, z1, z2, z3), F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(U85'(f95_in(z0, z1, z2, z3), f96_in(z0, z1, z2, z3), z0, z1, z2, z3), F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F113_IN(z0, z1, z2) → c215(U86'(f2_in(0, z0), f118_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(U87'(f134_in(z0, z1, z2), f135_in(z0, z1, z2, z3), z0, z1, z2, z3), F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(U88'(f2_in(s(z0), z1), f157_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(U89'(f211_in(z0, z1), f212_in(z2, z0, z3, z1), z0, z1, z2, z3), F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(U90'(f169_in(z0, z1), f170_in(z2, z0, z3, z1), z0, z1, z2, z3), F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(U91'(f174_in(z0, z1, z2, z3), f175_in(z0, z1, z2, z3), z0, z1, z2, z3), F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(U92'(f216_in(z0, z1, z2, z3), f217_in(z0, z1, z2, z3), z0, z1, z2, z3), F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F264_IN(z0, z1, z2) → c239(U93'(f2_in(0, z0), f267_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(U94'(f301_in(z0, z1, z2), f302_in(z0, z1, z2, z3), z0, z1, z2, z3), F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(U95'(f2_in(s(z0), z1), f314_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(U96'(f422_in(z0, z1), f424_in(z2, z0, z3, z1), z0, z1, z2, z3), F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(U97'(f327_in(z0, z1), f328_in(z2, z0, z3, z1), z0, z1, z2, z3), F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(U98'(f415_in(z0, z1, z2, z3), f416_in(z0, z1, z2, z3), z0, z1, z2, z3), F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(U99'(f461_in(z0, z1, z2, z3), f462_in(z0, z1, z2, z3), z0, z1, z2, z3), F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(U100'(f2_in(0, z0), f476_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(U101'(f521_in(z0, z1, z2), f522_in(z0, z1, z2, z3), z0, z1, z2, z3), F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(U102'(f2_in(s(z0), z1), f534_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(U103'(f585_in(z0, z1), f586_in(z2, z0, z3, z1), z0, z1, z2, z3), F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(U104'(f574_in(z0, z1), f575_in(z2, z0, z3, z1), z0, z1, z2, z3), F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(U105'(f579_in(z0, z1, z2, z3), f580_in(z0, z1, z2, z3), z0, z1, z2, z3), F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(U106'(f590_in(z0, z1, z2, z3), f591_in(z0, z1, z2, z3), z0, z1, z2, z3), F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(U107'(f2_in(0, z0), f602_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F602_IN(z1, z0, z2))
F600_IN(z0, z1, z2, z3) → c291(U108'(f607_in(z0, z1, z2), f608_in(z0, z1, z2, z3), z0, z1, z2, z3), F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(U109'(f2_in(s(z0), z1), f703_in(z0, z1), z0, z1), F2_IN(s(z0), z1))

S tuples:

F2_IN(z0, tree(z1, z2, z3)) → c2(U1'(f25_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(U2'(f23_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(U3'(f113_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(U4'(f114_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(U5'(f154_in(z0, z2), s(z0), tree(0, z1, z2)), F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(U6'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(U7'(f168_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(U8'(f167_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(U9'(f264_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(U10'(f265_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(U11'(f311_in(z0, z2), s(z0), tree(0, z1, z2)), F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(U12'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(U13'(f326_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(U14'(f325_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(U15'(f470_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(U16'(f471_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(U17'(f531_in(z0, z2), s(z0), tree(0, z1, z2)), F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(U18'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(U19'(f543_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(U20'(f542_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(U21'(f599_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(U22'(f600_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(U23'(f700_in(z0, z2), s(z0), tree(0, z1, z2)), F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(U24'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(U25'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(U26'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(U27'(f63_in(z0, z1), s(z0), s(z1)), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c90(U28'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F586_IN(z0, z1, z2, z3) → c92(U29'(f589_in(z0, z1, z2, z3), z0, z1, z2, z3), F589_IN(z0, z1, z2, z3))
F211_IN(z0, tree(z1, z2, z3)) → c95(U30'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F212_IN(z0, z1, z2, z3) → c97(U31'(f215_in(z0, z1, z2, z3), z0, z1, z2, z3), F215_IN(z0, z1, z2, z3))
F422_IN(z0, tree(z1, z2, z3)) → c100(U32'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F424_IN(z0, z1, z2, z3) → c102(U33'(f460_in(z0, z1, z2, z3), z0, z1, z2, z3), F460_IN(z0, z1, z2, z3))
F574_IN(z0, tree(z1, z2, z3)) → c105(U34'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F575_IN(z0, z1, z2, z3) → c107(U35'(f578_in(z0, z1, z2, z3), z0, z1, z2, z3), F578_IN(z0, z1, z2, z3))
F602_IN(z0, z1, z2) → c110(U36'(f123_in(z0, z2), z0, z1, z2), F123_IN(z0, z2))
F607_IN(s(z0), s(z1), z2) → c112(U37'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(U38'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F86_IN(z0, tree(z1, z2, z3)) → c116(U39'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F87_IN(z0, z1, z2, z3) → c118(U40'(f92_in(z0, z1, z2, z3), z0, z1, z2, z3), F92_IN(z0, z1, z2, z3))
F169_IN(z0, tree(z1, z2, z3)) → c121(U41'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F170_IN(z0, z1, z2, z3) → c123(U42'(f173_in(z0, z1, z2, z3), z0, z1, z2, z3), F173_IN(z0, z1, z2, z3))
F267_IN(z0, z1, z2) → c126(U43'(f123_in(z0, z2), z0, z1, z2), F123_IN(z0, z2))
F301_IN(s(z0), s(z1), z2) → c128(U44'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(U45'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F327_IN(z0, tree(z1, z2, z3)) → c132(U46'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F328_IN(z0, z1, z2, z3) → c134(U47'(f414_in(z0, z1, z2, z3), z0, z1, z2, z3), F414_IN(z0, z1, z2, z3))
F476_IN(z0, z1, z2) → c137(U48'(f123_in(z0, z2), z0, z1, z2), F123_IN(z0, z2))
F521_IN(s(z0), s(z1), z2) → c139(U49'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(U50'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(U51'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(U52'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F27_IN(z0, tree(z1, z2, z3)) → c147(U53'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F28_IN(z0, z1, z2, z3) → c149(U54'(f49_in(z0, z1, z2, z3), z0, z1, z2, z3), F49_IN(z0, z1, z2, z3))
F118_IN(z0, z1, z2) → c152(U55'(f123_in(z0, z2), z0, z1, z2), F123_IN(z0, z2))
F134_IN(s(z0), s(z1), z2) → c154(U56'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(U57'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(U58'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(U59'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(U60'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(U61'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(U62'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(U63'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(U64'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(U65'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(U66'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(U67'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(U68'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(U69'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(U70'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(U71'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U72'(f63_out1, z0, z1, z2) → c187(U73'(f2_in(z0, z2), z0, z1, z2), F2_IN(z0, z2))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U74'(f63_out1, z0, z1, z2) → c190(U75'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F123_IN(z0, z1) → c192(U76'(f127_in(z0), z0, z1))
U76'(f127_out1, z0, z1) → c193(U77'(f2_in(0, z1), z0, z1), F2_IN(0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U78'(f63_out1, z0, z1, z2) → c196(U79'(f2_in(s(z0), z2), z0, z1, z2), F2_IN(s(z0), z2))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U80'(f63_out1, z0, z1, z2) → c199(U81'(f2_in(s(z1), z2), z0, z1, z2), F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(U82'(f86_in(z0, z1), f87_in(z2, z0, z3, z1), z0, z1, z2, z3), F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(U83'(f27_in(z0, z1), f28_in(z2, z0, z3, z1), z0, z1, z2, z3), F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(U84'(f52_in(z0, z1, z2, z3), f53_in(z0, z1, z2, z3), z0, z1, z2, z3), F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(U85'(f95_in(z0, z1, z2, z3), f96_in(z0, z1, z2, z3), z0, z1, z2, z3), F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F113_IN(z0, z1, z2) → c215(U86'(f2_in(0, z0), f118_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(U87'(f134_in(z0, z1, z2), f135_in(z0, z1, z2, z3), z0, z1, z2, z3), F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(U88'(f2_in(s(z0), z1), f157_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(U89'(f211_in(z0, z1), f212_in(z2, z0, z3, z1), z0, z1, z2, z3), F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(U90'(f169_in(z0, z1), f170_in(z2, z0, z3, z1), z0, z1, z2, z3), F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(U91'(f174_in(z0, z1, z2, z3), f175_in(z0, z1, z2, z3), z0, z1, z2, z3), F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(U92'(f216_in(z0, z1, z2, z3), f217_in(z0, z1, z2, z3), z0, z1, z2, z3), F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F264_IN(z0, z1, z2) → c239(U93'(f2_in(0, z0), f267_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(U94'(f301_in(z0, z1, z2), f302_in(z0, z1, z2, z3), z0, z1, z2, z3), F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(U95'(f2_in(s(z0), z1), f314_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(U96'(f422_in(z0, z1), f424_in(z2, z0, z3, z1), z0, z1, z2, z3), F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(U97'(f327_in(z0, z1), f328_in(z2, z0, z3, z1), z0, z1, z2, z3), F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(U98'(f415_in(z0, z1, z2, z3), f416_in(z0, z1, z2, z3), z0, z1, z2, z3), F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(U99'(f461_in(z0, z1, z2, z3), f462_in(z0, z1, z2, z3), z0, z1, z2, z3), F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(U100'(f2_in(0, z0), f476_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(U101'(f521_in(z0, z1, z2), f522_in(z0, z1, z2, z3), z0, z1, z2, z3), F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(U102'(f2_in(s(z0), z1), f534_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(U103'(f585_in(z0, z1), f586_in(z2, z0, z3, z1), z0, z1, z2, z3), F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(U104'(f574_in(z0, z1), f575_in(z2, z0, z3, z1), z0, z1, z2, z3), F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(U105'(f579_in(z0, z1, z2, z3), f580_in(z0, z1, z2, z3), z0, z1, z2, z3), F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(U106'(f590_in(z0, z1, z2, z3), f591_in(z0, z1, z2, z3), z0, z1, z2, z3), F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(U107'(f2_in(0, z0), f602_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F602_IN(z1, z0, z2))
F600_IN(z0, z1, z2, z3) → c291(U108'(f607_in(z0, z1, z2), f608_in(z0, z1, z2, z3), z0, z1, z2, z3), F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(U109'(f2_in(s(z0), z1), f703_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, U17, U18, U19, U20, U21, U22, U23, U24, f33_in, U25, U26, f63_in, U27, f585_in, U28, f586_in, U29, f211_in, U30, f212_in, U31, f422_in, U32, f424_in, U33, f574_in, U34, f575_in, U35, f602_in, U36, f607_in, U37, f608_in, U38, f86_in, U39, f87_in, U40, f169_in, U41, f170_in, U42, f267_in, U43, f301_in, U44, f302_in, U45, f327_in, U46, f328_in, U47, f476_in, U48, f521_in, U49, f522_in, U50, f590_in, U51, f591_in, U52, f27_in, U53, f28_in, U54, f118_in, U55, f134_in, U56, f135_in, U57, f216_in, U58, f217_in, U59, f461_in, U60, f462_in, U61, f579_in, U62, f580_in, U63, f95_in, U64, f96_in, U65, f174_in, U66, f175_in, U67, f415_in, U68, f416_in, U69, f52_in, U70, f53_in, U71, f61_in, U72, U73, f78_in, U74, U75, f123_in, U76, U77, f138_in, U78, U79, f159_in, U80, U81, f23_in, U82, f25_in, U83, f49_in, U84, f92_in, U85, f113_in, U86, f114_in, U87, f154_in, U88, f167_in, U89, f168_in, U90, f173_in, U91, f215_in, U92, f264_in, U93, f265_in, U94, f311_in, U95, f325_in, U96, f326_in, U97, f414_in, U98, f460_in, U99, f470_in, U100, f471_in, U101, f531_in, U102, f542_in, U103, f543_in, U104, f578_in, U105, f589_in, U106, f599_in, U107, f600_in, U108, f700_in, U109

Defined Pair Symbols:

F2_IN, F33_IN, F63_IN, F585_IN, F586_IN, F211_IN, F212_IN, F422_IN, F424_IN, F574_IN, F575_IN, F602_IN, F607_IN, F608_IN, F86_IN, F87_IN, F169_IN, F170_IN, F267_IN, F301_IN, F302_IN, F327_IN, F328_IN, F476_IN, F521_IN, F522_IN, F590_IN, F591_IN, F27_IN, F28_IN, F118_IN, F134_IN, F135_IN, F216_IN, F217_IN, F461_IN, F462_IN, F579_IN, F580_IN, F95_IN, F96_IN, F174_IN, F175_IN, F415_IN, F416_IN, F52_IN, F53_IN, F61_IN, U72', F78_IN, U74', F123_IN, U76', F138_IN, U78', F159_IN, U80', F23_IN, F25_IN, F49_IN, F92_IN, F113_IN, F114_IN, F154_IN, F167_IN, F168_IN, F173_IN, F215_IN, F264_IN, F265_IN, F311_IN, F325_IN, F326_IN, F414_IN, F460_IN, F470_IN, F471_IN, F531_IN, F542_IN, F543_IN, F578_IN, F589_IN, F599_IN, F600_IN, F700_IN

Compound Symbols:

c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c83, c84, c88, c90, c92, c95, c97, c100, c102, c105, c107, c110, c112, c114, c116, c118, c121, c123, c126, c128, c130, c132, c134, c137, c139, c141, c143, c145, c147, c149, c152, c154, c156, c158, c160, c162, c164, c166, c168, c170, c172, c174, c176, c178, c180, c182, c184, c186, c187, c189, c190, c192, c193, c195, c196, c198, c199, c201, c205, c209, c212, c215, c219, c222, c225, c229, c233, c236, c239, c243, c246, c249, c253, c257, c260, c263, c267, c270, c273, c277, c281, c284, c287, c291, c294

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

Split RHS of tuples not part of any SCC

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → U1(f25_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U2(f23_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U3(f113_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f114_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f154_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U7(f168_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U8(f167_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U9(f264_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U10(f265_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U11(f311_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U12(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U13(f326_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U14(f325_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U15(f470_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U16(f471_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U17(f531_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U18(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U19(f543_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U20(f542_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U21(f599_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U22(f600_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U23(f700_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U24(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f25_out1, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out3, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out4, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out1, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out3, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out4, z0, tree(z1, z2, z3)) → f2_out1
U3(f113_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U4(f114_out1, z0, tree(z1, z2, z3)) → f2_out1
U4(f114_out3, z0, tree(z1, z2, z3)) → f2_out1
U5(f154_out1, s(z0), tree(0, z1, z2)) → f2_out1
U5(f154_out2, s(z0), tree(0, z1, z2)) → f2_out1
U6(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U7(f168_out1, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out3, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out4, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out1, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out3, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out4, z0, tree(z1, z2, z3)) → f2_out1
U9(f264_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U10(f265_out1, z0, tree(z1, z2, z3)) → f2_out1
U10(f265_out3, z0, tree(z1, z2, z3)) → f2_out1
U11(f311_out1, s(z0), tree(0, z1, z2)) → f2_out1
U11(f311_out2, s(z0), tree(0, z1, z2)) → f2_out1
U12(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U13(f326_out1, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out3, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out4, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out3, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out4, z0, tree(z1, z2, z3)) → f2_out1
U15(f470_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U16(f471_out1, z0, tree(z1, z2, z3)) → f2_out1
U16(f471_out3, z0, tree(z1, z2, z3)) → f2_out1
U17(f531_out1, s(z0), tree(0, z1, z2)) → f2_out1
U17(f531_out2, s(z0), tree(0, z1, z2)) → f2_out1
U18(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U19(f543_out1, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out3, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out4, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out1, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out3, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out4, z0, tree(z1, z2, z3)) → f2_out1
U21(f599_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U22(f600_out1, z0, tree(z1, z2, z3)) → f2_out1
U22(f600_out3, z0, tree(z1, z2, z3)) → f2_out1
U23(f700_out1, s(z0), tree(0, z1, z2)) → f2_out1
U23(f700_out2, s(z0), tree(0, z1, z2)) → f2_out1
U24(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f33_in(z0, z1) → f33_out1
f33_in(z0, tree(z1, z2, z3)) → U25(f33_in(z0, z2), z0, tree(z1, z2, z3))
f33_in(z0, tree(z1, z2, z3)) → U26(f33_in(z0, z2), z0, tree(z1, z2, z3))
U25(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
U26(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
f63_in(0, s(z0)) → f63_out1
f63_in(s(z0), s(z1)) → U27(f63_in(z0, z1), s(z0), s(z1))
U27(f63_out1, s(z0), s(z1)) → f63_out1
f585_in(z0, tree(z1, z2, z3)) → U28(f33_in(z0, z2), z0, tree(z1, z2, z3))
U28(f33_out1, z0, tree(z1, z2, z3)) → f585_out1
f586_in(z0, z1, z2, z3) → U29(f589_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f589_out1, z0, z1, z2, z3) → f586_out2
U29(f589_out2, z0, z1, z2, z3) → f586_out3
f211_in(z0, tree(z1, z2, z3)) → U30(f33_in(z0, z2), z0, tree(z1, z2, z3))
U30(f33_out1, z0, tree(z1, z2, z3)) → f211_out1
f212_in(z0, z1, z2, z3) → U31(f215_in(z0, z1, z2, z3), z0, z1, z2, z3)
U31(f215_out1, z0, z1, z2, z3) → f212_out2
U31(f215_out2, z0, z1, z2, z3) → f212_out3
f422_in(z0, tree(z1, z2, z3)) → U32(f33_in(z0, z2), z0, tree(z1, z2, z3))
U32(f33_out1, z0, tree(z1, z2, z3)) → f422_out1
f424_in(z0, z1, z2, z3) → U33(f460_in(z0, z1, z2, z3), z0, z1, z2, z3)
U33(f460_out1, z0, z1, z2, z3) → f424_out2
U33(f460_out2, z0, z1, z2, z3) → f424_out3
f574_in(z0, tree(z1, z2, z3)) → U34(f33_in(z0, z2), z0, tree(z1, z2, z3))
U34(f33_out1, z0, tree(z1, z2, z3)) → f574_out1
f575_in(z0, z1, z2, z3) → U35(f578_in(z0, z1, z2, z3), z0, z1, z2, z3)
U35(f578_out1, z0, z1, z2, z3) → f575_out2
U35(f578_out2, z0, z1, z2, z3) → f575_out3
f602_in(z0, z1, z2) → U36(f123_in(z0, z2), z0, z1, z2)
U36(f123_out1, z0, z1, z2) → f602_out3
f607_in(s(z0), s(z1), z2) → U37(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U37(f138_out1, s(z0), s(z1), z2) → f607_out1
f608_in(z0, z1, z2, z3) → U38(f78_in(z1, z0, z3), z0, z1, z2, z3)
U38(f78_out1, z0, z1, z2, z3) → f608_out2
f86_in(z0, tree(z1, z2, z3)) → U39(f33_in(z0, z2), z0, tree(z1, z2, z3))
U39(f33_out1, z0, tree(z1, z2, z3)) → f86_out1
f87_in(z0, z1, z2, z3) → U40(f92_in(z0, z1, z2, z3), z0, z1, z2, z3)
U40(f92_out1, z0, z1, z2, z3) → f87_out2
U40(f92_out2, z0, z1, z2, z3) → f87_out3
f169_in(z0, tree(z1, z2, z3)) → U41(f33_in(z0, z2), z0, tree(z1, z2, z3))
U41(f33_out1, z0, tree(z1, z2, z3)) → f169_out1
f170_in(z0, z1, z2, z3) → U42(f173_in(z0, z1, z2, z3), z0, z1, z2, z3)
U42(f173_out1, z0, z1, z2, z3) → f170_out2
U42(f173_out2, z0, z1, z2, z3) → f170_out3
f267_in(z0, z1, z2) → U43(f123_in(z0, z2), z0, z1, z2)
U43(f123_out1, z0, z1, z2) → f267_out3
f301_in(s(z0), s(z1), z2) → U44(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U44(f138_out1, s(z0), s(z1), z2) → f301_out1
f302_in(z0, z1, z2, z3) → U45(f78_in(z1, z0, z3), z0, z1, z2, z3)
U45(f78_out1, z0, z1, z2, z3) → f302_out2
f327_in(z0, tree(z1, z2, z3)) → U46(f33_in(z0, z2), z0, tree(z1, z2, z3))
U46(f33_out1, z0, tree(z1, z2, z3)) → f327_out1
f328_in(z0, z1, z2, z3) → U47(f414_in(z0, z1, z2, z3), z0, z1, z2, z3)
U47(f414_out1, z0, z1, z2, z3) → f328_out2
U47(f414_out2, z0, z1, z2, z3) → f328_out3
f476_in(z0, z1, z2) → U48(f123_in(z0, z2), z0, z1, z2)
U48(f123_out1, z0, z1, z2) → f476_out3
f521_in(s(z0), s(z1), z2) → U49(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U49(f138_out1, s(z0), s(z1), z2) → f521_out1
f522_in(z0, z1, z2, z3) → U50(f78_in(z1, z0, z3), z0, z1, z2, z3)
U50(f78_out1, z0, z1, z2, z3) → f522_out2
f590_in(z0, z1, z2, z3) → U51(f61_in(z0, z1, z2), z0, z1, z2, z3)
U51(f61_out1, z0, z1, z2, z3) → f590_out1
f591_in(z0, z1, z2, z3) → U52(f78_in(z1, z0, z3), z0, z1, z2, z3)
U52(f78_out1, z0, z1, z2, z3) → f591_out1
f27_in(z0, tree(z1, z2, z3)) → U53(f33_in(z0, z2), z0, tree(z1, z2, z3))
U53(f33_out1, z0, tree(z1, z2, z3)) → f27_out1
f28_in(z0, z1, z2, z3) → U54(f49_in(z0, z1, z2, z3), z0, z1, z2, z3)
U54(f49_out1, z0, z1, z2, z3) → f28_out2
U54(f49_out2, z0, z1, z2, z3) → f28_out3
f118_in(z0, z1, z2) → U55(f123_in(z0, z2), z0, z1, z2)
U55(f123_out1, z0, z1, z2) → f118_out3
f134_in(s(z0), s(z1), z2) → U56(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U56(f138_out1, s(z0), s(z1), z2) → f134_out1
f135_in(z0, z1, z2, z3) → U57(f78_in(z1, z0, z3), z0, z1, z2, z3)
U57(f78_out1, z0, z1, z2, z3) → f135_out2
f216_in(z0, z1, z2, z3) → U58(f61_in(z0, z1, z2), z0, z1, z2, z3)
U58(f61_out1, z0, z1, z2, z3) → f216_out1
f217_in(z0, z1, z2, z3) → U59(f78_in(z1, z0, z3), z0, z1, z2, z3)
U59(f78_out1, z0, z1, z2, z3) → f217_out1
f461_in(z0, z1, z2, z3) → U60(f61_in(z0, z1, z2), z0, z1, z2, z3)
U60(f61_out1, z0, z1, z2, z3) → f461_out1
f462_in(z0, z1, z2, z3) → U61(f78_in(z1, z0, z3), z0, z1, z2, z3)
U61(f78_out1, z0, z1, z2, z3) → f462_out1
f579_in(z0, z1, z2, z3) → U62(f61_in(z0, z1, z2), z0, z1, z2, z3)
U62(f61_out1, z0, z1, z2, z3) → f579_out1
f580_in(z0, z1, z2, z3) → U63(f78_in(z1, z0, z3), z0, z1, z2, z3)
U63(f78_out1, z0, z1, z2, z3) → f580_out1
f95_in(z0, z1, z2, z3) → U64(f61_in(z0, z1, z2), z0, z1, z2, z3)
U64(f61_out1, z0, z1, z2, z3) → f95_out1
f96_in(z0, z1, z2, z3) → U65(f78_in(z1, z0, z3), z0, z1, z2, z3)
U65(f78_out1, z0, z1, z2, z3) → f96_out1
f174_in(z0, z1, z2, z3) → U66(f61_in(z0, z1, z2), z0, z1, z2, z3)
U66(f61_out1, z0, z1, z2, z3) → f174_out1
f175_in(z0, z1, z2, z3) → U67(f78_in(z1, z0, z3), z0, z1, z2, z3)
U67(f78_out1, z0, z1, z2, z3) → f175_out1
f415_in(z0, z1, z2, z3) → U68(f61_in(z0, z1, z2), z0, z1, z2, z3)
U68(f61_out1, z0, z1, z2, z3) → f415_out1
f416_in(z0, z1, z2, z3) → U69(f78_in(z1, z0, z3), z0, z1, z2, z3)
U69(f78_out1, z0, z1, z2, z3) → f416_out1
f52_in(z0, z1, z2, z3) → U70(f61_in(z0, z1, z2), z0, z1, z2, z3)
U70(f61_out1, z0, z1, z2, z3) → f52_out1
f53_in(z0, z1, z2, z3) → U71(f78_in(z1, z0, z3), z0, z1, z2, z3)
U71(f78_out1, z0, z1, z2, z3) → f53_out1
f61_in(z0, z1, z2) → U72(f63_in(z0, z1), z0, z1, z2)
U72(f63_out1, z0, z1, z2) → U73(f2_in(z0, z2), z0, z1, z2)
U73(f2_out1, z0, z1, z2) → f61_out1
f78_in(z0, z1, z2) → U74(f63_in(z0, z1), z0, z1, z2)
U74(f63_out1, z0, z1, z2) → U75(f2_in(z1, z2), z0, z1, z2)
U75(f2_out1, z0, z1, z2) → f78_out1
f123_in(z0, z1) → U76(f127_in(z0), z0, z1)
U76(f127_out1, z0, z1) → U77(f2_in(0, z1), z0, z1)
U77(f2_out1, z0, z1) → f123_out1
f138_in(z0, z1, z2) → U78(f63_in(z0, z1), z0, z1, z2)
U78(f63_out1, z0, z1, z2) → U79(f2_in(s(z0), z2), z0, z1, z2)
U79(f2_out1, z0, z1, z2) → f138_out1
f159_in(z0, z1, z2) → U80(f63_in(z0, z1), z0, z1, z2)
U80(f63_out1, z0, z1, z2) → U81(f2_in(s(z1), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f159_out1
f23_in(z0, z1, z2, z3) → U82(f86_in(z0, z1), f87_in(z2, z0, z3, z1), z0, z1, z2, z3)
U82(f86_out1, z0, z1, z2, z3, z4) → f23_out1
U82(z0, f87_out2, z1, z2, z3, z4) → f23_out3
U82(z0, f87_out3, z1, z2, z3, z4) → f23_out4
f25_in(z0, z1, z2, z3) → U83(f27_in(z0, z1), f28_in(z2, z0, z3, z1), z0, z1, z2, z3)
U83(f27_out1, z0, z1, z2, z3, z4) → f25_out1
U83(z0, f28_out2, z1, z2, z3, z4) → f25_out3
U83(z0, f28_out3, z1, z2, z3, z4) → f25_out4
f49_in(z0, z1, z2, z3) → U84(f52_in(z0, z1, z2, z3), f53_in(z0, z1, z2, z3), z0, z1, z2, z3)
U84(f52_out1, z0, z1, z2, z3, z4) → f49_out1
U84(z0, f53_out1, z1, z2, z3, z4) → f49_out2
f92_in(z0, z1, z2, z3) → U85(f95_in(z0, z1, z2, z3), f96_in(z0, z1, z2, z3), z0, z1, z2, z3)
U85(f95_out1, z0, z1, z2, z3, z4) → f92_out1
U85(z0, f96_out1, z1, z2, z3, z4) → f92_out2
f113_in(z0, z1, z2) → U86(f2_in(0, z0), f118_in(z1, z0, z2), z0, z1, z2)
U86(f2_out1, z0, z1, z2, z3) → f113_out1
U86(z0, f118_out1, z1, z2, z3) → f113_out2
U86(z0, f118_out3, z1, z2, z3) → f113_out4
f114_in(z0, z1, z2, z3) → U87(f134_in(z0, z1, z2), f135_in(z0, z1, z2, z3), z0, z1, z2, z3)
U87(f134_out1, z0, z1, z2, z3, z4) → f114_out1
U87(z0, f135_out2, z1, z2, z3, z4) → f114_out3
f154_in(z0, z1) → U88(f2_in(s(z0), z1), f157_in(z0, z1), z0, z1)
U88(f2_out1, z0, z1, z2) → f154_out1
U88(z0, f157_out1, z1, z2) → f154_out2
f167_in(z0, z1, z2, z3) → U89(f211_in(z0, z1), f212_in(z2, z0, z3, z1), z0, z1, z2, z3)
U89(f211_out1, z0, z1, z2, z3, z4) → f167_out1
U89(z0, f212_out2, z1, z2, z3, z4) → f167_out3
U89(z0, f212_out3, z1, z2, z3, z4) → f167_out4
f168_in(z0, z1, z2, z3) → U90(f169_in(z0, z1), f170_in(z2, z0, z3, z1), z0, z1, z2, z3)
U90(f169_out1, z0, z1, z2, z3, z4) → f168_out1
U90(z0, f170_out2, z1, z2, z3, z4) → f168_out3
U90(z0, f170_out3, z1, z2, z3, z4) → f168_out4
f173_in(z0, z1, z2, z3) → U91(f174_in(z0, z1, z2, z3), f175_in(z0, z1, z2, z3), z0, z1, z2, z3)
U91(f174_out1, z0, z1, z2, z3, z4) → f173_out1
U91(z0, f175_out1, z1, z2, z3, z4) → f173_out2
f215_in(z0, z1, z2, z3) → U92(f216_in(z0, z1, z2, z3), f217_in(z0, z1, z2, z3), z0, z1, z2, z3)
U92(f216_out1, z0, z1, z2, z3, z4) → f215_out1
U92(z0, f217_out1, z1, z2, z3, z4) → f215_out2
f264_in(z0, z1, z2) → U93(f2_in(0, z0), f267_in(z1, z0, z2), z0, z1, z2)
U93(f2_out1, z0, z1, z2, z3) → f264_out1
U93(z0, f267_out1, z1, z2, z3) → f264_out2
U93(z0, f267_out3, z1, z2, z3) → f264_out4
f265_in(z0, z1, z2, z3) → U94(f301_in(z0, z1, z2), f302_in(z0, z1, z2, z3), z0, z1, z2, z3)
U94(f301_out1, z0, z1, z2, z3, z4) → f265_out1
U94(z0, f302_out2, z1, z2, z3, z4) → f265_out3
f311_in(z0, z1) → U95(f2_in(s(z0), z1), f314_in(z0, z1), z0, z1)
U95(f2_out1, z0, z1, z2) → f311_out1
U95(z0, f314_out1, z1, z2) → f311_out2
f325_in(z0, z1, z2, z3) → U96(f422_in(z0, z1), f424_in(z2, z0, z3, z1), z0, z1, z2, z3)
U96(f422_out1, z0, z1, z2, z3, z4) → f325_out1
U96(z0, f424_out2, z1, z2, z3, z4) → f325_out3
U96(z0, f424_out3, z1, z2, z3, z4) → f325_out4
f326_in(z0, z1, z2, z3) → U97(f327_in(z0, z1), f328_in(z2, z0, z3, z1), z0, z1, z2, z3)
U97(f327_out1, z0, z1, z2, z3, z4) → f326_out1
U97(z0, f328_out2, z1, z2, z3, z4) → f326_out3
U97(z0, f328_out3, z1, z2, z3, z4) → f326_out4
f414_in(z0, z1, z2, z3) → U98(f415_in(z0, z1, z2, z3), f416_in(z0, z1, z2, z3), z0, z1, z2, z3)
U98(f415_out1, z0, z1, z2, z3, z4) → f414_out1
U98(z0, f416_out1, z1, z2, z3, z4) → f414_out2
f460_in(z0, z1, z2, z3) → U99(f461_in(z0, z1, z2, z3), f462_in(z0, z1, z2, z3), z0, z1, z2, z3)
U99(f461_out1, z0, z1, z2, z3, z4) → f460_out1
U99(z0, f462_out1, z1, z2, z3, z4) → f460_out2
f470_in(z0, z1, z2) → U100(f2_in(0, z0), f476_in(z1, z0, z2), z0, z1, z2)
U100(f2_out1, z0, z1, z2, z3) → f470_out1
U100(z0, f476_out1, z1, z2, z3) → f470_out2
U100(z0, f476_out3, z1, z2, z3) → f470_out4
f471_in(z0, z1, z2, z3) → U101(f521_in(z0, z1, z2), f522_in(z0, z1, z2, z3), z0, z1, z2, z3)
U101(f521_out1, z0, z1, z2, z3, z4) → f471_out1
U101(z0, f522_out2, z1, z2, z3, z4) → f471_out3
f531_in(z0, z1) → U102(f2_in(s(z0), z1), f534_in(z0, z1), z0, z1)
U102(f2_out1, z0, z1, z2) → f531_out1
U102(z0, f534_out1, z1, z2) → f531_out2
f542_in(z0, z1, z2, z3) → U103(f585_in(z0, z1), f586_in(z2, z0, z3, z1), z0, z1, z2, z3)
U103(f585_out1, z0, z1, z2, z3, z4) → f542_out1
U103(z0, f586_out2, z1, z2, z3, z4) → f542_out3
U103(z0, f586_out3, z1, z2, z3, z4) → f542_out4
f543_in(z0, z1, z2, z3) → U104(f574_in(z0, z1), f575_in(z2, z0, z3, z1), z0, z1, z2, z3)
U104(f574_out1, z0, z1, z2, z3, z4) → f543_out1
U104(z0, f575_out2, z1, z2, z3, z4) → f543_out3
U104(z0, f575_out3, z1, z2, z3, z4) → f543_out4
f578_in(z0, z1, z2, z3) → U105(f579_in(z0, z1, z2, z3), f580_in(z0, z1, z2, z3), z0, z1, z2, z3)
U105(f579_out1, z0, z1, z2, z3, z4) → f578_out1
U105(z0, f580_out1, z1, z2, z3, z4) → f578_out2
f589_in(z0, z1, z2, z3) → U106(f590_in(z0, z1, z2, z3), f591_in(z0, z1, z2, z3), z0, z1, z2, z3)
U106(f590_out1, z0, z1, z2, z3, z4) → f589_out1
U106(z0, f591_out1, z1, z2, z3, z4) → f589_out2
f599_in(z0, z1, z2) → U107(f2_in(0, z0), f602_in(z1, z0, z2), z0, z1, z2)
U107(f2_out1, z0, z1, z2, z3) → f599_out1
U107(z0, f602_out1, z1, z2, z3) → f599_out2
U107(z0, f602_out3, z1, z2, z3) → f599_out4
f600_in(z0, z1, z2, z3) → U108(f607_in(z0, z1, z2), f608_in(z0, z1, z2, z3), z0, z1, z2, z3)
U108(f607_out1, z0, z1, z2, z3, z4) → f600_out1
U108(z0, f608_out2, z1, z2, z3, z4) → f600_out3
f700_in(z0, z1) → U109(f2_in(s(z0), z1), f703_in(z0, z1), z0, z1)
U109(f2_out1, z0, z1, z2) → f700_out1
U109(z0, f703_out1, z1, z2) → f700_out2

Tuples:

F2_IN(z0, tree(z1, z2, z3)) → c2(U1'(f25_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(U2'(f23_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(U3'(f113_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(U4'(f114_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(U5'(f154_in(z0, z2), s(z0), tree(0, z1, z2)), F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(U6'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(U7'(f168_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(U8'(f167_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(U9'(f264_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(U10'(f265_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(U11'(f311_in(z0, z2), s(z0), tree(0, z1, z2)), F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(U12'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(U13'(f326_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(U14'(f325_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(U15'(f470_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(U16'(f471_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(U17'(f531_in(z0, z2), s(z0), tree(0, z1, z2)), F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(U18'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(U19'(f543_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(U20'(f542_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(U21'(f599_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(U22'(f600_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(U23'(f700_in(z0, z2), s(z0), tree(0, z1, z2)), F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(U24'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(U25'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(U26'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(U27'(f63_in(z0, z1), s(z0), s(z1)), F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(U29'(f589_in(z0, z1, z2, z3), z0, z1, z2, z3), F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(U31'(f215_in(z0, z1, z2, z3), z0, z1, z2, z3), F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(U33'(f460_in(z0, z1, z2, z3), z0, z1, z2, z3), F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(U35'(f578_in(z0, z1, z2, z3), z0, z1, z2, z3), F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(U37'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(U38'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(U40'(f92_in(z0, z1, z2, z3), z0, z1, z2, z3), F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(U42'(f173_in(z0, z1, z2, z3), z0, z1, z2, z3), F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(U44'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(U45'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(U47'(f414_in(z0, z1, z2, z3), z0, z1, z2, z3), F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(U49'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(U50'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(U51'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(U52'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(U54'(f49_in(z0, z1, z2, z3), z0, z1, z2, z3), F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(U56'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(U57'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(U58'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(U59'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(U60'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(U61'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(U62'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(U63'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(U64'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(U65'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(U66'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(U67'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(U68'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(U69'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(U70'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(U71'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U72'(f63_out1, z0, z1, z2) → c187(U73'(f2_in(z0, z2), z0, z1, z2), F2_IN(z0, z2))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U74'(f63_out1, z0, z1, z2) → c190(U75'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F123_IN(z0, z1) → c192(U76'(f127_in(z0), z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U78'(f63_out1, z0, z1, z2) → c196(U79'(f2_in(s(z0), z2), z0, z1, z2), F2_IN(s(z0), z2))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U80'(f63_out1, z0, z1, z2) → c199(U81'(f2_in(s(z1), z2), z0, z1, z2), F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(U82'(f86_in(z0, z1), f87_in(z2, z0, z3, z1), z0, z1, z2, z3), F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(U83'(f27_in(z0, z1), f28_in(z2, z0, z3, z1), z0, z1, z2, z3), F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(U84'(f52_in(z0, z1, z2, z3), f53_in(z0, z1, z2, z3), z0, z1, z2, z3), F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(U85'(f95_in(z0, z1, z2, z3), f96_in(z0, z1, z2, z3), z0, z1, z2, z3), F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F113_IN(z0, z1, z2) → c215(U86'(f2_in(0, z0), f118_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(U87'(f134_in(z0, z1, z2), f135_in(z0, z1, z2, z3), z0, z1, z2, z3), F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(U88'(f2_in(s(z0), z1), f157_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(U89'(f211_in(z0, z1), f212_in(z2, z0, z3, z1), z0, z1, z2, z3), F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(U90'(f169_in(z0, z1), f170_in(z2, z0, z3, z1), z0, z1, z2, z3), F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(U91'(f174_in(z0, z1, z2, z3), f175_in(z0, z1, z2, z3), z0, z1, z2, z3), F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(U92'(f216_in(z0, z1, z2, z3), f217_in(z0, z1, z2, z3), z0, z1, z2, z3), F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F264_IN(z0, z1, z2) → c239(U93'(f2_in(0, z0), f267_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(U94'(f301_in(z0, z1, z2), f302_in(z0, z1, z2, z3), z0, z1, z2, z3), F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(U95'(f2_in(s(z0), z1), f314_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(U96'(f422_in(z0, z1), f424_in(z2, z0, z3, z1), z0, z1, z2, z3), F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(U97'(f327_in(z0, z1), f328_in(z2, z0, z3, z1), z0, z1, z2, z3), F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(U98'(f415_in(z0, z1, z2, z3), f416_in(z0, z1, z2, z3), z0, z1, z2, z3), F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(U99'(f461_in(z0, z1, z2, z3), f462_in(z0, z1, z2, z3), z0, z1, z2, z3), F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(U100'(f2_in(0, z0), f476_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(U101'(f521_in(z0, z1, z2), f522_in(z0, z1, z2, z3), z0, z1, z2, z3), F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(U102'(f2_in(s(z0), z1), f534_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(U103'(f585_in(z0, z1), f586_in(z2, z0, z3, z1), z0, z1, z2, z3), F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(U104'(f574_in(z0, z1), f575_in(z2, z0, z3, z1), z0, z1, z2, z3), F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(U105'(f579_in(z0, z1, z2, z3), f580_in(z0, z1, z2, z3), z0, z1, z2, z3), F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(U106'(f590_in(z0, z1, z2, z3), f591_in(z0, z1, z2, z3), z0, z1, z2, z3), F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(U107'(f2_in(0, z0), f602_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F602_IN(z1, z0, z2))
F600_IN(z0, z1, z2, z3) → c291(U108'(f607_in(z0, z1, z2), f608_in(z0, z1, z2, z3), z0, z1, z2, z3), F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(U109'(f2_in(s(z0), z1), f703_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c(U28'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(U30'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(U32'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(U34'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F602_IN(z0, z1, z2) → c(U36'(f123_in(z0, z2), z0, z1, z2))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(U39'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(U41'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(U43'(f123_in(z0, z2), z0, z1, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(U46'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F476_IN(z0, z1, z2) → c(U48'(f123_in(z0, z2), z0, z1, z2))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(U53'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(U55'(f123_in(z0, z2), z0, z1, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
U76'(f127_out1, z0, z1) → c(U77'(f2_in(0, z1), z0, z1))
U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))

S tuples:

F2_IN(z0, tree(z1, z2, z3)) → c2(U1'(f25_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(U2'(f23_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(U3'(f113_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(U4'(f114_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(U5'(f154_in(z0, z2), s(z0), tree(0, z1, z2)), F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(U6'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(U7'(f168_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(U8'(f167_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(U9'(f264_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(U10'(f265_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(U11'(f311_in(z0, z2), s(z0), tree(0, z1, z2)), F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(U12'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(U13'(f326_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(U14'(f325_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(U15'(f470_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(U16'(f471_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(U17'(f531_in(z0, z2), s(z0), tree(0, z1, z2)), F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(U18'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(U19'(f543_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(U20'(f542_in(z1, z3, z0, z2), z0, tree(z1, z2, z3)), F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(U21'(f599_in(z1, z0, z2), 0, tree(s(z0), z1, z2)), F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(U22'(f600_in(z0, z1, z2, z3), z0, tree(z1, z2, z3)), F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(U23'(f700_in(z0, z2), s(z0), tree(0, z1, z2)), F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(U24'(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3)), F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(U25'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(U26'(f33_in(z0, z2), z0, tree(z1, z2, z3)), F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(U27'(f63_in(z0, z1), s(z0), s(z1)), F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(U29'(f589_in(z0, z1, z2, z3), z0, z1, z2, z3), F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(U31'(f215_in(z0, z1, z2, z3), z0, z1, z2, z3), F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(U33'(f460_in(z0, z1, z2, z3), z0, z1, z2, z3), F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(U35'(f578_in(z0, z1, z2, z3), z0, z1, z2, z3), F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(U37'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(U38'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(U40'(f92_in(z0, z1, z2, z3), z0, z1, z2, z3), F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(U42'(f173_in(z0, z1, z2, z3), z0, z1, z2, z3), F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(U44'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(U45'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(U47'(f414_in(z0, z1, z2, z3), z0, z1, z2, z3), F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(U49'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(U50'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(U51'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(U52'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(U54'(f49_in(z0, z1, z2, z3), z0, z1, z2, z3), F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(U56'(f138_in(z0, z1, z2), s(z0), s(z1), z2), F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(U57'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(U58'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(U59'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(U60'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(U61'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(U62'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(U63'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(U64'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(U65'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(U66'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(U67'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(U68'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(U69'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(U70'(f61_in(z0, z1, z2), z0, z1, z2, z3), F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(U71'(f78_in(z1, z0, z3), z0, z1, z2, z3), F78_IN(z1, z0, z3))
F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U72'(f63_out1, z0, z1, z2) → c187(U73'(f2_in(z0, z2), z0, z1, z2), F2_IN(z0, z2))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U74'(f63_out1, z0, z1, z2) → c190(U75'(f2_in(z1, z2), z0, z1, z2), F2_IN(z1, z2))
F123_IN(z0, z1) → c192(U76'(f127_in(z0), z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U78'(f63_out1, z0, z1, z2) → c196(U79'(f2_in(s(z0), z2), z0, z1, z2), F2_IN(s(z0), z2))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U80'(f63_out1, z0, z1, z2) → c199(U81'(f2_in(s(z1), z2), z0, z1, z2), F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(U82'(f86_in(z0, z1), f87_in(z2, z0, z3, z1), z0, z1, z2, z3), F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(U83'(f27_in(z0, z1), f28_in(z2, z0, z3, z1), z0, z1, z2, z3), F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(U84'(f52_in(z0, z1, z2, z3), f53_in(z0, z1, z2, z3), z0, z1, z2, z3), F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(U85'(f95_in(z0, z1, z2, z3), f96_in(z0, z1, z2, z3), z0, z1, z2, z3), F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F113_IN(z0, z1, z2) → c215(U86'(f2_in(0, z0), f118_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(U87'(f134_in(z0, z1, z2), f135_in(z0, z1, z2, z3), z0, z1, z2, z3), F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(U88'(f2_in(s(z0), z1), f157_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(U89'(f211_in(z0, z1), f212_in(z2, z0, z3, z1), z0, z1, z2, z3), F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(U90'(f169_in(z0, z1), f170_in(z2, z0, z3, z1), z0, z1, z2, z3), F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(U91'(f174_in(z0, z1, z2, z3), f175_in(z0, z1, z2, z3), z0, z1, z2, z3), F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(U92'(f216_in(z0, z1, z2, z3), f217_in(z0, z1, z2, z3), z0, z1, z2, z3), F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F264_IN(z0, z1, z2) → c239(U93'(f2_in(0, z0), f267_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(U94'(f301_in(z0, z1, z2), f302_in(z0, z1, z2, z3), z0, z1, z2, z3), F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(U95'(f2_in(s(z0), z1), f314_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(U96'(f422_in(z0, z1), f424_in(z2, z0, z3, z1), z0, z1, z2, z3), F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(U97'(f327_in(z0, z1), f328_in(z2, z0, z3, z1), z0, z1, z2, z3), F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(U98'(f415_in(z0, z1, z2, z3), f416_in(z0, z1, z2, z3), z0, z1, z2, z3), F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(U99'(f461_in(z0, z1, z2, z3), f462_in(z0, z1, z2, z3), z0, z1, z2, z3), F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(U100'(f2_in(0, z0), f476_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(U101'(f521_in(z0, z1, z2), f522_in(z0, z1, z2, z3), z0, z1, z2, z3), F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(U102'(f2_in(s(z0), z1), f534_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(U103'(f585_in(z0, z1), f586_in(z2, z0, z3, z1), z0, z1, z2, z3), F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(U104'(f574_in(z0, z1), f575_in(z2, z0, z3, z1), z0, z1, z2, z3), F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(U105'(f579_in(z0, z1, z2, z3), f580_in(z0, z1, z2, z3), z0, z1, z2, z3), F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(U106'(f590_in(z0, z1, z2, z3), f591_in(z0, z1, z2, z3), z0, z1, z2, z3), F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(U107'(f2_in(0, z0), f602_in(z1, z0, z2), z0, z1, z2), F2_IN(0, z0), F602_IN(z1, z0, z2))
F600_IN(z0, z1, z2, z3) → c291(U108'(f607_in(z0, z1, z2), f608_in(z0, z1, z2, z3), z0, z1, z2, z3), F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(U109'(f2_in(s(z0), z1), f703_in(z0, z1), z0, z1), F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c(U28'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(U30'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(U32'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(U34'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F602_IN(z0, z1, z2) → c(U36'(f123_in(z0, z2), z0, z1, z2))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(U39'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(U41'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(U43'(f123_in(z0, z2), z0, z1, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(U46'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F476_IN(z0, z1, z2) → c(U48'(f123_in(z0, z2), z0, z1, z2))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(U53'(f33_in(z0, z2), z0, tree(z1, z2, z3)))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(U55'(f123_in(z0, z2), z0, z1, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
U76'(f127_out1, z0, z1) → c(U77'(f2_in(0, z1), z0, z1))
U76'(f127_out1, z0, z1) → c(F2_IN(0, 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, U17, U18, U19, U20, U21, U22, U23, U24, f33_in, U25, U26, f63_in, U27, f585_in, U28, f586_in, U29, f211_in, U30, f212_in, U31, f422_in, U32, f424_in, U33, f574_in, U34, f575_in, U35, f602_in, U36, f607_in, U37, f608_in, U38, f86_in, U39, f87_in, U40, f169_in, U41, f170_in, U42, f267_in, U43, f301_in, U44, f302_in, U45, f327_in, U46, f328_in, U47, f476_in, U48, f521_in, U49, f522_in, U50, f590_in, U51, f591_in, U52, f27_in, U53, f28_in, U54, f118_in, U55, f134_in, U56, f135_in, U57, f216_in, U58, f217_in, U59, f461_in, U60, f462_in, U61, f579_in, U62, f580_in, U63, f95_in, U64, f96_in, U65, f174_in, U66, f175_in, U67, f415_in, U68, f416_in, U69, f52_in, U70, f53_in, U71, f61_in, U72, U73, f78_in, U74, U75, f123_in, U76, U77, f138_in, U78, U79, f159_in, U80, U81, f23_in, U82, f25_in, U83, f49_in, U84, f92_in, U85, f113_in, U86, f114_in, U87, f154_in, U88, f167_in, U89, f168_in, U90, f173_in, U91, f215_in, U92, f264_in, U93, f265_in, U94, f311_in, U95, f325_in, U96, f326_in, U97, f414_in, U98, f460_in, U99, f470_in, U100, f471_in, U101, f531_in, U102, f542_in, U103, f543_in, U104, f578_in, U105, f589_in, U106, f599_in, U107, f600_in, U108, f700_in, U109

Defined Pair Symbols:

F2_IN, F33_IN, F63_IN, F586_IN, F212_IN, F424_IN, F575_IN, F607_IN, F608_IN, F87_IN, F170_IN, F301_IN, F302_IN, F328_IN, F521_IN, F522_IN, F590_IN, F591_IN, F28_IN, F134_IN, F135_IN, F216_IN, F217_IN, F461_IN, F462_IN, F579_IN, F580_IN, F95_IN, F96_IN, F174_IN, F175_IN, F415_IN, F416_IN, F52_IN, F53_IN, F61_IN, U72', F78_IN, U74', F123_IN, F138_IN, U78', F159_IN, U80', F23_IN, F25_IN, F49_IN, F92_IN, F113_IN, F114_IN, F154_IN, F167_IN, F168_IN, F173_IN, F215_IN, F264_IN, F265_IN, F311_IN, F325_IN, F326_IN, F414_IN, F460_IN, F470_IN, F471_IN, F531_IN, F542_IN, F543_IN, F578_IN, F589_IN, F599_IN, F600_IN, F700_IN, F585_IN, F211_IN, F422_IN, F574_IN, F602_IN, F86_IN, F169_IN, F267_IN, F327_IN, F476_IN, F27_IN, F118_IN, U76'

Compound Symbols:

c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c83, c84, c88, c92, c97, c102, c107, c112, c114, c118, c123, c128, c130, c134, c139, c141, c143, c145, c149, c154, c156, c158, c160, c162, c164, c166, c168, c170, c172, c174, c176, c178, c180, c182, c184, c186, c187, c189, c190, c192, c195, c196, c198, c199, c201, c205, c209, c212, c215, c219, c222, c225, c229, c233, c236, c239, c243, c246, c249, c253, c257, c260, c263, c267, c270, c273, c277, c281, c284, c287, c291, c294, c

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

Removed 105 trailing tuple parts

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → U1(f25_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U2(f23_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U3(f113_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f114_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f154_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U7(f168_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U8(f167_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U9(f264_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U10(f265_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U11(f311_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U12(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U13(f326_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U14(f325_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U15(f470_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U16(f471_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U17(f531_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U18(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U19(f543_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U20(f542_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U21(f599_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U22(f600_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U23(f700_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U24(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f25_out1, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out3, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out4, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out1, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out3, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out4, z0, tree(z1, z2, z3)) → f2_out1
U3(f113_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U4(f114_out1, z0, tree(z1, z2, z3)) → f2_out1
U4(f114_out3, z0, tree(z1, z2, z3)) → f2_out1
U5(f154_out1, s(z0), tree(0, z1, z2)) → f2_out1
U5(f154_out2, s(z0), tree(0, z1, z2)) → f2_out1
U6(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U7(f168_out1, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out3, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out4, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out1, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out3, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out4, z0, tree(z1, z2, z3)) → f2_out1
U9(f264_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U10(f265_out1, z0, tree(z1, z2, z3)) → f2_out1
U10(f265_out3, z0, tree(z1, z2, z3)) → f2_out1
U11(f311_out1, s(z0), tree(0, z1, z2)) → f2_out1
U11(f311_out2, s(z0), tree(0, z1, z2)) → f2_out1
U12(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U13(f326_out1, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out3, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out4, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out3, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out4, z0, tree(z1, z2, z3)) → f2_out1
U15(f470_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U16(f471_out1, z0, tree(z1, z2, z3)) → f2_out1
U16(f471_out3, z0, tree(z1, z2, z3)) → f2_out1
U17(f531_out1, s(z0), tree(0, z1, z2)) → f2_out1
U17(f531_out2, s(z0), tree(0, z1, z2)) → f2_out1
U18(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U19(f543_out1, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out3, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out4, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out1, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out3, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out4, z0, tree(z1, z2, z3)) → f2_out1
U21(f599_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U22(f600_out1, z0, tree(z1, z2, z3)) → f2_out1
U22(f600_out3, z0, tree(z1, z2, z3)) → f2_out1
U23(f700_out1, s(z0), tree(0, z1, z2)) → f2_out1
U23(f700_out2, s(z0), tree(0, z1, z2)) → f2_out1
U24(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f33_in(z0, z1) → f33_out1
f33_in(z0, tree(z1, z2, z3)) → U25(f33_in(z0, z2), z0, tree(z1, z2, z3))
f33_in(z0, tree(z1, z2, z3)) → U26(f33_in(z0, z2), z0, tree(z1, z2, z3))
U25(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
U26(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
f63_in(0, s(z0)) → f63_out1
f63_in(s(z0), s(z1)) → U27(f63_in(z0, z1), s(z0), s(z1))
U27(f63_out1, s(z0), s(z1)) → f63_out1
f585_in(z0, tree(z1, z2, z3)) → U28(f33_in(z0, z2), z0, tree(z1, z2, z3))
U28(f33_out1, z0, tree(z1, z2, z3)) → f585_out1
f586_in(z0, z1, z2, z3) → U29(f589_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f589_out1, z0, z1, z2, z3) → f586_out2
U29(f589_out2, z0, z1, z2, z3) → f586_out3
f211_in(z0, tree(z1, z2, z3)) → U30(f33_in(z0, z2), z0, tree(z1, z2, z3))
U30(f33_out1, z0, tree(z1, z2, z3)) → f211_out1
f212_in(z0, z1, z2, z3) → U31(f215_in(z0, z1, z2, z3), z0, z1, z2, z3)
U31(f215_out1, z0, z1, z2, z3) → f212_out2
U31(f215_out2, z0, z1, z2, z3) → f212_out3
f422_in(z0, tree(z1, z2, z3)) → U32(f33_in(z0, z2), z0, tree(z1, z2, z3))
U32(f33_out1, z0, tree(z1, z2, z3)) → f422_out1
f424_in(z0, z1, z2, z3) → U33(f460_in(z0, z1, z2, z3), z0, z1, z2, z3)
U33(f460_out1, z0, z1, z2, z3) → f424_out2
U33(f460_out2, z0, z1, z2, z3) → f424_out3
f574_in(z0, tree(z1, z2, z3)) → U34(f33_in(z0, z2), z0, tree(z1, z2, z3))
U34(f33_out1, z0, tree(z1, z2, z3)) → f574_out1
f575_in(z0, z1, z2, z3) → U35(f578_in(z0, z1, z2, z3), z0, z1, z2, z3)
U35(f578_out1, z0, z1, z2, z3) → f575_out2
U35(f578_out2, z0, z1, z2, z3) → f575_out3
f602_in(z0, z1, z2) → U36(f123_in(z0, z2), z0, z1, z2)
U36(f123_out1, z0, z1, z2) → f602_out3
f607_in(s(z0), s(z1), z2) → U37(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U37(f138_out1, s(z0), s(z1), z2) → f607_out1
f608_in(z0, z1, z2, z3) → U38(f78_in(z1, z0, z3), z0, z1, z2, z3)
U38(f78_out1, z0, z1, z2, z3) → f608_out2
f86_in(z0, tree(z1, z2, z3)) → U39(f33_in(z0, z2), z0, tree(z1, z2, z3))
U39(f33_out1, z0, tree(z1, z2, z3)) → f86_out1
f87_in(z0, z1, z2, z3) → U40(f92_in(z0, z1, z2, z3), z0, z1, z2, z3)
U40(f92_out1, z0, z1, z2, z3) → f87_out2
U40(f92_out2, z0, z1, z2, z3) → f87_out3
f169_in(z0, tree(z1, z2, z3)) → U41(f33_in(z0, z2), z0, tree(z1, z2, z3))
U41(f33_out1, z0, tree(z1, z2, z3)) → f169_out1
f170_in(z0, z1, z2, z3) → U42(f173_in(z0, z1, z2, z3), z0, z1, z2, z3)
U42(f173_out1, z0, z1, z2, z3) → f170_out2
U42(f173_out2, z0, z1, z2, z3) → f170_out3
f267_in(z0, z1, z2) → U43(f123_in(z0, z2), z0, z1, z2)
U43(f123_out1, z0, z1, z2) → f267_out3
f301_in(s(z0), s(z1), z2) → U44(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U44(f138_out1, s(z0), s(z1), z2) → f301_out1
f302_in(z0, z1, z2, z3) → U45(f78_in(z1, z0, z3), z0, z1, z2, z3)
U45(f78_out1, z0, z1, z2, z3) → f302_out2
f327_in(z0, tree(z1, z2, z3)) → U46(f33_in(z0, z2), z0, tree(z1, z2, z3))
U46(f33_out1, z0, tree(z1, z2, z3)) → f327_out1
f328_in(z0, z1, z2, z3) → U47(f414_in(z0, z1, z2, z3), z0, z1, z2, z3)
U47(f414_out1, z0, z1, z2, z3) → f328_out2
U47(f414_out2, z0, z1, z2, z3) → f328_out3
f476_in(z0, z1, z2) → U48(f123_in(z0, z2), z0, z1, z2)
U48(f123_out1, z0, z1, z2) → f476_out3
f521_in(s(z0), s(z1), z2) → U49(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U49(f138_out1, s(z0), s(z1), z2) → f521_out1
f522_in(z0, z1, z2, z3) → U50(f78_in(z1, z0, z3), z0, z1, z2, z3)
U50(f78_out1, z0, z1, z2, z3) → f522_out2
f590_in(z0, z1, z2, z3) → U51(f61_in(z0, z1, z2), z0, z1, z2, z3)
U51(f61_out1, z0, z1, z2, z3) → f590_out1
f591_in(z0, z1, z2, z3) → U52(f78_in(z1, z0, z3), z0, z1, z2, z3)
U52(f78_out1, z0, z1, z2, z3) → f591_out1
f27_in(z0, tree(z1, z2, z3)) → U53(f33_in(z0, z2), z0, tree(z1, z2, z3))
U53(f33_out1, z0, tree(z1, z2, z3)) → f27_out1
f28_in(z0, z1, z2, z3) → U54(f49_in(z0, z1, z2, z3), z0, z1, z2, z3)
U54(f49_out1, z0, z1, z2, z3) → f28_out2
U54(f49_out2, z0, z1, z2, z3) → f28_out3
f118_in(z0, z1, z2) → U55(f123_in(z0, z2), z0, z1, z2)
U55(f123_out1, z0, z1, z2) → f118_out3
f134_in(s(z0), s(z1), z2) → U56(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U56(f138_out1, s(z0), s(z1), z2) → f134_out1
f135_in(z0, z1, z2, z3) → U57(f78_in(z1, z0, z3), z0, z1, z2, z3)
U57(f78_out1, z0, z1, z2, z3) → f135_out2
f216_in(z0, z1, z2, z3) → U58(f61_in(z0, z1, z2), z0, z1, z2, z3)
U58(f61_out1, z0, z1, z2, z3) → f216_out1
f217_in(z0, z1, z2, z3) → U59(f78_in(z1, z0, z3), z0, z1, z2, z3)
U59(f78_out1, z0, z1, z2, z3) → f217_out1
f461_in(z0, z1, z2, z3) → U60(f61_in(z0, z1, z2), z0, z1, z2, z3)
U60(f61_out1, z0, z1, z2, z3) → f461_out1
f462_in(z0, z1, z2, z3) → U61(f78_in(z1, z0, z3), z0, z1, z2, z3)
U61(f78_out1, z0, z1, z2, z3) → f462_out1
f579_in(z0, z1, z2, z3) → U62(f61_in(z0, z1, z2), z0, z1, z2, z3)
U62(f61_out1, z0, z1, z2, z3) → f579_out1
f580_in(z0, z1, z2, z3) → U63(f78_in(z1, z0, z3), z0, z1, z2, z3)
U63(f78_out1, z0, z1, z2, z3) → f580_out1
f95_in(z0, z1, z2, z3) → U64(f61_in(z0, z1, z2), z0, z1, z2, z3)
U64(f61_out1, z0, z1, z2, z3) → f95_out1
f96_in(z0, z1, z2, z3) → U65(f78_in(z1, z0, z3), z0, z1, z2, z3)
U65(f78_out1, z0, z1, z2, z3) → f96_out1
f174_in(z0, z1, z2, z3) → U66(f61_in(z0, z1, z2), z0, z1, z2, z3)
U66(f61_out1, z0, z1, z2, z3) → f174_out1
f175_in(z0, z1, z2, z3) → U67(f78_in(z1, z0, z3), z0, z1, z2, z3)
U67(f78_out1, z0, z1, z2, z3) → f175_out1
f415_in(z0, z1, z2, z3) → U68(f61_in(z0, z1, z2), z0, z1, z2, z3)
U68(f61_out1, z0, z1, z2, z3) → f415_out1
f416_in(z0, z1, z2, z3) → U69(f78_in(z1, z0, z3), z0, z1, z2, z3)
U69(f78_out1, z0, z1, z2, z3) → f416_out1
f52_in(z0, z1, z2, z3) → U70(f61_in(z0, z1, z2), z0, z1, z2, z3)
U70(f61_out1, z0, z1, z2, z3) → f52_out1
f53_in(z0, z1, z2, z3) → U71(f78_in(z1, z0, z3), z0, z1, z2, z3)
U71(f78_out1, z0, z1, z2, z3) → f53_out1
f61_in(z0, z1, z2) → U72(f63_in(z0, z1), z0, z1, z2)
U72(f63_out1, z0, z1, z2) → U73(f2_in(z0, z2), z0, z1, z2)
U73(f2_out1, z0, z1, z2) → f61_out1
f78_in(z0, z1, z2) → U74(f63_in(z0, z1), z0, z1, z2)
U74(f63_out1, z0, z1, z2) → U75(f2_in(z1, z2), z0, z1, z2)
U75(f2_out1, z0, z1, z2) → f78_out1
f123_in(z0, z1) → U76(f127_in(z0), z0, z1)
U76(f127_out1, z0, z1) → U77(f2_in(0, z1), z0, z1)
U77(f2_out1, z0, z1) → f123_out1
f138_in(z0, z1, z2) → U78(f63_in(z0, z1), z0, z1, z2)
U78(f63_out1, z0, z1, z2) → U79(f2_in(s(z0), z2), z0, z1, z2)
U79(f2_out1, z0, z1, z2) → f138_out1
f159_in(z0, z1, z2) → U80(f63_in(z0, z1), z0, z1, z2)
U80(f63_out1, z0, z1, z2) → U81(f2_in(s(z1), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f159_out1
f23_in(z0, z1, z2, z3) → U82(f86_in(z0, z1), f87_in(z2, z0, z3, z1), z0, z1, z2, z3)
U82(f86_out1, z0, z1, z2, z3, z4) → f23_out1
U82(z0, f87_out2, z1, z2, z3, z4) → f23_out3
U82(z0, f87_out3, z1, z2, z3, z4) → f23_out4
f25_in(z0, z1, z2, z3) → U83(f27_in(z0, z1), f28_in(z2, z0, z3, z1), z0, z1, z2, z3)
U83(f27_out1, z0, z1, z2, z3, z4) → f25_out1
U83(z0, f28_out2, z1, z2, z3, z4) → f25_out3
U83(z0, f28_out3, z1, z2, z3, z4) → f25_out4
f49_in(z0, z1, z2, z3) → U84(f52_in(z0, z1, z2, z3), f53_in(z0, z1, z2, z3), z0, z1, z2, z3)
U84(f52_out1, z0, z1, z2, z3, z4) → f49_out1
U84(z0, f53_out1, z1, z2, z3, z4) → f49_out2
f92_in(z0, z1, z2, z3) → U85(f95_in(z0, z1, z2, z3), f96_in(z0, z1, z2, z3), z0, z1, z2, z3)
U85(f95_out1, z0, z1, z2, z3, z4) → f92_out1
U85(z0, f96_out1, z1, z2, z3, z4) → f92_out2
f113_in(z0, z1, z2) → U86(f2_in(0, z0), f118_in(z1, z0, z2), z0, z1, z2)
U86(f2_out1, z0, z1, z2, z3) → f113_out1
U86(z0, f118_out1, z1, z2, z3) → f113_out2
U86(z0, f118_out3, z1, z2, z3) → f113_out4
f114_in(z0, z1, z2, z3) → U87(f134_in(z0, z1, z2), f135_in(z0, z1, z2, z3), z0, z1, z2, z3)
U87(f134_out1, z0, z1, z2, z3, z4) → f114_out1
U87(z0, f135_out2, z1, z2, z3, z4) → f114_out3
f154_in(z0, z1) → U88(f2_in(s(z0), z1), f157_in(z0, z1), z0, z1)
U88(f2_out1, z0, z1, z2) → f154_out1
U88(z0, f157_out1, z1, z2) → f154_out2
f167_in(z0, z1, z2, z3) → U89(f211_in(z0, z1), f212_in(z2, z0, z3, z1), z0, z1, z2, z3)
U89(f211_out1, z0, z1, z2, z3, z4) → f167_out1
U89(z0, f212_out2, z1, z2, z3, z4) → f167_out3
U89(z0, f212_out3, z1, z2, z3, z4) → f167_out4
f168_in(z0, z1, z2, z3) → U90(f169_in(z0, z1), f170_in(z2, z0, z3, z1), z0, z1, z2, z3)
U90(f169_out1, z0, z1, z2, z3, z4) → f168_out1
U90(z0, f170_out2, z1, z2, z3, z4) → f168_out3
U90(z0, f170_out3, z1, z2, z3, z4) → f168_out4
f173_in(z0, z1, z2, z3) → U91(f174_in(z0, z1, z2, z3), f175_in(z0, z1, z2, z3), z0, z1, z2, z3)
U91(f174_out1, z0, z1, z2, z3, z4) → f173_out1
U91(z0, f175_out1, z1, z2, z3, z4) → f173_out2
f215_in(z0, z1, z2, z3) → U92(f216_in(z0, z1, z2, z3), f217_in(z0, z1, z2, z3), z0, z1, z2, z3)
U92(f216_out1, z0, z1, z2, z3, z4) → f215_out1
U92(z0, f217_out1, z1, z2, z3, z4) → f215_out2
f264_in(z0, z1, z2) → U93(f2_in(0, z0), f267_in(z1, z0, z2), z0, z1, z2)
U93(f2_out1, z0, z1, z2, z3) → f264_out1
U93(z0, f267_out1, z1, z2, z3) → f264_out2
U93(z0, f267_out3, z1, z2, z3) → f264_out4
f265_in(z0, z1, z2, z3) → U94(f301_in(z0, z1, z2), f302_in(z0, z1, z2, z3), z0, z1, z2, z3)
U94(f301_out1, z0, z1, z2, z3, z4) → f265_out1
U94(z0, f302_out2, z1, z2, z3, z4) → f265_out3
f311_in(z0, z1) → U95(f2_in(s(z0), z1), f314_in(z0, z1), z0, z1)
U95(f2_out1, z0, z1, z2) → f311_out1
U95(z0, f314_out1, z1, z2) → f311_out2
f325_in(z0, z1, z2, z3) → U96(f422_in(z0, z1), f424_in(z2, z0, z3, z1), z0, z1, z2, z3)
U96(f422_out1, z0, z1, z2, z3, z4) → f325_out1
U96(z0, f424_out2, z1, z2, z3, z4) → f325_out3
U96(z0, f424_out3, z1, z2, z3, z4) → f325_out4
f326_in(z0, z1, z2, z3) → U97(f327_in(z0, z1), f328_in(z2, z0, z3, z1), z0, z1, z2, z3)
U97(f327_out1, z0, z1, z2, z3, z4) → f326_out1
U97(z0, f328_out2, z1, z2, z3, z4) → f326_out3
U97(z0, f328_out3, z1, z2, z3, z4) → f326_out4
f414_in(z0, z1, z2, z3) → U98(f415_in(z0, z1, z2, z3), f416_in(z0, z1, z2, z3), z0, z1, z2, z3)
U98(f415_out1, z0, z1, z2, z3, z4) → f414_out1
U98(z0, f416_out1, z1, z2, z3, z4) → f414_out2
f460_in(z0, z1, z2, z3) → U99(f461_in(z0, z1, z2, z3), f462_in(z0, z1, z2, z3), z0, z1, z2, z3)
U99(f461_out1, z0, z1, z2, z3, z4) → f460_out1
U99(z0, f462_out1, z1, z2, z3, z4) → f460_out2
f470_in(z0, z1, z2) → U100(f2_in(0, z0), f476_in(z1, z0, z2), z0, z1, z2)
U100(f2_out1, z0, z1, z2, z3) → f470_out1
U100(z0, f476_out1, z1, z2, z3) → f470_out2
U100(z0, f476_out3, z1, z2, z3) → f470_out4
f471_in(z0, z1, z2, z3) → U101(f521_in(z0, z1, z2), f522_in(z0, z1, z2, z3), z0, z1, z2, z3)
U101(f521_out1, z0, z1, z2, z3, z4) → f471_out1
U101(z0, f522_out2, z1, z2, z3, z4) → f471_out3
f531_in(z0, z1) → U102(f2_in(s(z0), z1), f534_in(z0, z1), z0, z1)
U102(f2_out1, z0, z1, z2) → f531_out1
U102(z0, f534_out1, z1, z2) → f531_out2
f542_in(z0, z1, z2, z3) → U103(f585_in(z0, z1), f586_in(z2, z0, z3, z1), z0, z1, z2, z3)
U103(f585_out1, z0, z1, z2, z3, z4) → f542_out1
U103(z0, f586_out2, z1, z2, z3, z4) → f542_out3
U103(z0, f586_out3, z1, z2, z3, z4) → f542_out4
f543_in(z0, z1, z2, z3) → U104(f574_in(z0, z1), f575_in(z2, z0, z3, z1), z0, z1, z2, z3)
U104(f574_out1, z0, z1, z2, z3, z4) → f543_out1
U104(z0, f575_out2, z1, z2, z3, z4) → f543_out3
U104(z0, f575_out3, z1, z2, z3, z4) → f543_out4
f578_in(z0, z1, z2, z3) → U105(f579_in(z0, z1, z2, z3), f580_in(z0, z1, z2, z3), z0, z1, z2, z3)
U105(f579_out1, z0, z1, z2, z3, z4) → f578_out1
U105(z0, f580_out1, z1, z2, z3, z4) → f578_out2
f589_in(z0, z1, z2, z3) → U106(f590_in(z0, z1, z2, z3), f591_in(z0, z1, z2, z3), z0, z1, z2, z3)
U106(f590_out1, z0, z1, z2, z3, z4) → f589_out1
U106(z0, f591_out1, z1, z2, z3, z4) → f589_out2
f599_in(z0, z1, z2) → U107(f2_in(0, z0), f602_in(z1, z0, z2), z0, z1, z2)
U107(f2_out1, z0, z1, z2, z3) → f599_out1
U107(z0, f602_out1, z1, z2, z3) → f599_out2
U107(z0, f602_out3, z1, z2, z3) → f599_out4
f600_in(z0, z1, z2, z3) → U108(f607_in(z0, z1, z2), f608_in(z0, z1, z2, z3), z0, z1, z2, z3)
U108(f607_out1, z0, z1, z2, z3, z4) → f600_out1
U108(z0, f608_out2, z1, z2, z3, z4) → f600_out3
f700_in(z0, z1) → U109(f2_in(s(z0), z1), f703_in(z0, z1), z0, z1)
U109(f2_out1, z0, z1, z2) → f700_out1
U109(z0, f703_out1, z1, z2) → f700_out2

Tuples:

F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F123_IN(z0, z1) → c192
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c
F211_IN(z0, tree(z1, z2, z3)) → c
F422_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F602_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c
U76'(f127_out1, z0, z1) → c

S tuples:

F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F123_IN(z0, z1) → c192
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c
F211_IN(z0, tree(z1, z2, z3)) → c
F422_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F602_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c
U76'(f127_out1, z0, z1) → 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, U17, U18, U19, U20, U21, U22, U23, U24, f33_in, U25, U26, f63_in, U27, f585_in, U28, f586_in, U29, f211_in, U30, f212_in, U31, f422_in, U32, f424_in, U33, f574_in, U34, f575_in, U35, f602_in, U36, f607_in, U37, f608_in, U38, f86_in, U39, f87_in, U40, f169_in, U41, f170_in, U42, f267_in, U43, f301_in, U44, f302_in, U45, f327_in, U46, f328_in, U47, f476_in, U48, f521_in, U49, f522_in, U50, f590_in, U51, f591_in, U52, f27_in, U53, f28_in, U54, f118_in, U55, f134_in, U56, f135_in, U57, f216_in, U58, f217_in, U59, f461_in, U60, f462_in, U61, f579_in, U62, f580_in, U63, f95_in, U64, f96_in, U65, f174_in, U66, f175_in, U67, f415_in, U68, f416_in, U69, f52_in, U70, f53_in, U71, f61_in, U72, U73, f78_in, U74, U75, f123_in, U76, U77, f138_in, U78, U79, f159_in, U80, U81, f23_in, U82, f25_in, U83, f49_in, U84, f92_in, U85, f113_in, U86, f114_in, U87, f154_in, U88, f167_in, U89, f168_in, U90, f173_in, U91, f215_in, U92, f264_in, U93, f265_in, U94, f311_in, U95, f325_in, U96, f326_in, U97, f414_in, U98, f460_in, U99, f470_in, U100, f471_in, U101, f531_in, U102, f542_in, U103, f543_in, U104, f578_in, U105, f589_in, U106, f599_in, U107, f600_in, U108, f700_in, U109

Defined Pair Symbols:

F61_IN, F78_IN, F138_IN, F159_IN, F585_IN, F211_IN, F422_IN, F574_IN, F602_IN, F86_IN, F169_IN, F267_IN, F327_IN, F476_IN, F27_IN, F118_IN, U76', F2_IN, F33_IN, F63_IN, F586_IN, F212_IN, F424_IN, F575_IN, F607_IN, F608_IN, F87_IN, F170_IN, F301_IN, F302_IN, F328_IN, F521_IN, F522_IN, F590_IN, F591_IN, F28_IN, F134_IN, F135_IN, F216_IN, F217_IN, F461_IN, F462_IN, F579_IN, F580_IN, F95_IN, F96_IN, F174_IN, F175_IN, F415_IN, F416_IN, F52_IN, F53_IN, U72', U74', F123_IN, U78', U80', F23_IN, F25_IN, F49_IN, F92_IN, F113_IN, F114_IN, F154_IN, F167_IN, F168_IN, F173_IN, F215_IN, F264_IN, F265_IN, F311_IN, F325_IN, F326_IN, F414_IN, F460_IN, F470_IN, F471_IN, F531_IN, F542_IN, F543_IN, F578_IN, F589_IN, F599_IN, F600_IN, F700_IN

Compound Symbols:

c186, c189, c195, c198, c, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c83, c84, c88, c92, c97, c102, c107, c112, c114, c118, c123, c128, c130, c134, c139, c141, c143, c145, c149, c154, c156, c158, c160, c162, c164, c166, c168, c170, c172, c174, c176, c178, c180, c182, c184, c187, c190, c192, c196, c199, c201, c205, c209, c212, c215, c219, c222, c225, c229, c233, c236, c239, c243, c246, c249, c253, c257, c260, c263, c267, c270, c273, c277, c281, c284, c287, c291, c294, c

(31) CdtKnowledgeProof (EQUIVALENT transformation)

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

U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
U76'(f127_out1, z0, z1) → c

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → U1(f25_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U2(f23_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U3(f113_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f114_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f154_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U7(f168_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U8(f167_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U9(f264_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U10(f265_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U11(f311_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U12(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U13(f326_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U14(f325_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U15(f470_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U16(f471_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U17(f531_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U18(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U19(f543_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U20(f542_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U21(f599_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U22(f600_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U23(f700_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U24(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f25_out1, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out3, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out4, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out1, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out3, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out4, z0, tree(z1, z2, z3)) → f2_out1
U3(f113_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U4(f114_out1, z0, tree(z1, z2, z3)) → f2_out1
U4(f114_out3, z0, tree(z1, z2, z3)) → f2_out1
U5(f154_out1, s(z0), tree(0, z1, z2)) → f2_out1
U5(f154_out2, s(z0), tree(0, z1, z2)) → f2_out1
U6(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U7(f168_out1, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out3, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out4, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out1, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out3, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out4, z0, tree(z1, z2, z3)) → f2_out1
U9(f264_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U10(f265_out1, z0, tree(z1, z2, z3)) → f2_out1
U10(f265_out3, z0, tree(z1, z2, z3)) → f2_out1
U11(f311_out1, s(z0), tree(0, z1, z2)) → f2_out1
U11(f311_out2, s(z0), tree(0, z1, z2)) → f2_out1
U12(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U13(f326_out1, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out3, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out4, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out3, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out4, z0, tree(z1, z2, z3)) → f2_out1
U15(f470_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U16(f471_out1, z0, tree(z1, z2, z3)) → f2_out1
U16(f471_out3, z0, tree(z1, z2, z3)) → f2_out1
U17(f531_out1, s(z0), tree(0, z1, z2)) → f2_out1
U17(f531_out2, s(z0), tree(0, z1, z2)) → f2_out1
U18(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U19(f543_out1, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out3, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out4, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out1, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out3, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out4, z0, tree(z1, z2, z3)) → f2_out1
U21(f599_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U22(f600_out1, z0, tree(z1, z2, z3)) → f2_out1
U22(f600_out3, z0, tree(z1, z2, z3)) → f2_out1
U23(f700_out1, s(z0), tree(0, z1, z2)) → f2_out1
U23(f700_out2, s(z0), tree(0, z1, z2)) → f2_out1
U24(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f33_in(z0, z1) → f33_out1
f33_in(z0, tree(z1, z2, z3)) → U25(f33_in(z0, z2), z0, tree(z1, z2, z3))
f33_in(z0, tree(z1, z2, z3)) → U26(f33_in(z0, z2), z0, tree(z1, z2, z3))
U25(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
U26(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
f63_in(0, s(z0)) → f63_out1
f63_in(s(z0), s(z1)) → U27(f63_in(z0, z1), s(z0), s(z1))
U27(f63_out1, s(z0), s(z1)) → f63_out1
f585_in(z0, tree(z1, z2, z3)) → U28(f33_in(z0, z2), z0, tree(z1, z2, z3))
U28(f33_out1, z0, tree(z1, z2, z3)) → f585_out1
f586_in(z0, z1, z2, z3) → U29(f589_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f589_out1, z0, z1, z2, z3) → f586_out2
U29(f589_out2, z0, z1, z2, z3) → f586_out3
f211_in(z0, tree(z1, z2, z3)) → U30(f33_in(z0, z2), z0, tree(z1, z2, z3))
U30(f33_out1, z0, tree(z1, z2, z3)) → f211_out1
f212_in(z0, z1, z2, z3) → U31(f215_in(z0, z1, z2, z3), z0, z1, z2, z3)
U31(f215_out1, z0, z1, z2, z3) → f212_out2
U31(f215_out2, z0, z1, z2, z3) → f212_out3
f422_in(z0, tree(z1, z2, z3)) → U32(f33_in(z0, z2), z0, tree(z1, z2, z3))
U32(f33_out1, z0, tree(z1, z2, z3)) → f422_out1
f424_in(z0, z1, z2, z3) → U33(f460_in(z0, z1, z2, z3), z0, z1, z2, z3)
U33(f460_out1, z0, z1, z2, z3) → f424_out2
U33(f460_out2, z0, z1, z2, z3) → f424_out3
f574_in(z0, tree(z1, z2, z3)) → U34(f33_in(z0, z2), z0, tree(z1, z2, z3))
U34(f33_out1, z0, tree(z1, z2, z3)) → f574_out1
f575_in(z0, z1, z2, z3) → U35(f578_in(z0, z1, z2, z3), z0, z1, z2, z3)
U35(f578_out1, z0, z1, z2, z3) → f575_out2
U35(f578_out2, z0, z1, z2, z3) → f575_out3
f602_in(z0, z1, z2) → U36(f123_in(z0, z2), z0, z1, z2)
U36(f123_out1, z0, z1, z2) → f602_out3
f607_in(s(z0), s(z1), z2) → U37(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U37(f138_out1, s(z0), s(z1), z2) → f607_out1
f608_in(z0, z1, z2, z3) → U38(f78_in(z1, z0, z3), z0, z1, z2, z3)
U38(f78_out1, z0, z1, z2, z3) → f608_out2
f86_in(z0, tree(z1, z2, z3)) → U39(f33_in(z0, z2), z0, tree(z1, z2, z3))
U39(f33_out1, z0, tree(z1, z2, z3)) → f86_out1
f87_in(z0, z1, z2, z3) → U40(f92_in(z0, z1, z2, z3), z0, z1, z2, z3)
U40(f92_out1, z0, z1, z2, z3) → f87_out2
U40(f92_out2, z0, z1, z2, z3) → f87_out3
f169_in(z0, tree(z1, z2, z3)) → U41(f33_in(z0, z2), z0, tree(z1, z2, z3))
U41(f33_out1, z0, tree(z1, z2, z3)) → f169_out1
f170_in(z0, z1, z2, z3) → U42(f173_in(z0, z1, z2, z3), z0, z1, z2, z3)
U42(f173_out1, z0, z1, z2, z3) → f170_out2
U42(f173_out2, z0, z1, z2, z3) → f170_out3
f267_in(z0, z1, z2) → U43(f123_in(z0, z2), z0, z1, z2)
U43(f123_out1, z0, z1, z2) → f267_out3
f301_in(s(z0), s(z1), z2) → U44(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U44(f138_out1, s(z0), s(z1), z2) → f301_out1
f302_in(z0, z1, z2, z3) → U45(f78_in(z1, z0, z3), z0, z1, z2, z3)
U45(f78_out1, z0, z1, z2, z3) → f302_out2
f327_in(z0, tree(z1, z2, z3)) → U46(f33_in(z0, z2), z0, tree(z1, z2, z3))
U46(f33_out1, z0, tree(z1, z2, z3)) → f327_out1
f328_in(z0, z1, z2, z3) → U47(f414_in(z0, z1, z2, z3), z0, z1, z2, z3)
U47(f414_out1, z0, z1, z2, z3) → f328_out2
U47(f414_out2, z0, z1, z2, z3) → f328_out3
f476_in(z0, z1, z2) → U48(f123_in(z0, z2), z0, z1, z2)
U48(f123_out1, z0, z1, z2) → f476_out3
f521_in(s(z0), s(z1), z2) → U49(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U49(f138_out1, s(z0), s(z1), z2) → f521_out1
f522_in(z0, z1, z2, z3) → U50(f78_in(z1, z0, z3), z0, z1, z2, z3)
U50(f78_out1, z0, z1, z2, z3) → f522_out2
f590_in(z0, z1, z2, z3) → U51(f61_in(z0, z1, z2), z0, z1, z2, z3)
U51(f61_out1, z0, z1, z2, z3) → f590_out1
f591_in(z0, z1, z2, z3) → U52(f78_in(z1, z0, z3), z0, z1, z2, z3)
U52(f78_out1, z0, z1, z2, z3) → f591_out1
f27_in(z0, tree(z1, z2, z3)) → U53(f33_in(z0, z2), z0, tree(z1, z2, z3))
U53(f33_out1, z0, tree(z1, z2, z3)) → f27_out1
f28_in(z0, z1, z2, z3) → U54(f49_in(z0, z1, z2, z3), z0, z1, z2, z3)
U54(f49_out1, z0, z1, z2, z3) → f28_out2
U54(f49_out2, z0, z1, z2, z3) → f28_out3
f118_in(z0, z1, z2) → U55(f123_in(z0, z2), z0, z1, z2)
U55(f123_out1, z0, z1, z2) → f118_out3
f134_in(s(z0), s(z1), z2) → U56(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U56(f138_out1, s(z0), s(z1), z2) → f134_out1
f135_in(z0, z1, z2, z3) → U57(f78_in(z1, z0, z3), z0, z1, z2, z3)
U57(f78_out1, z0, z1, z2, z3) → f135_out2
f216_in(z0, z1, z2, z3) → U58(f61_in(z0, z1, z2), z0, z1, z2, z3)
U58(f61_out1, z0, z1, z2, z3) → f216_out1
f217_in(z0, z1, z2, z3) → U59(f78_in(z1, z0, z3), z0, z1, z2, z3)
U59(f78_out1, z0, z1, z2, z3) → f217_out1
f461_in(z0, z1, z2, z3) → U60(f61_in(z0, z1, z2), z0, z1, z2, z3)
U60(f61_out1, z0, z1, z2, z3) → f461_out1
f462_in(z0, z1, z2, z3) → U61(f78_in(z1, z0, z3), z0, z1, z2, z3)
U61(f78_out1, z0, z1, z2, z3) → f462_out1
f579_in(z0, z1, z2, z3) → U62(f61_in(z0, z1, z2), z0, z1, z2, z3)
U62(f61_out1, z0, z1, z2, z3) → f579_out1
f580_in(z0, z1, z2, z3) → U63(f78_in(z1, z0, z3), z0, z1, z2, z3)
U63(f78_out1, z0, z1, z2, z3) → f580_out1
f95_in(z0, z1, z2, z3) → U64(f61_in(z0, z1, z2), z0, z1, z2, z3)
U64(f61_out1, z0, z1, z2, z3) → f95_out1
f96_in(z0, z1, z2, z3) → U65(f78_in(z1, z0, z3), z0, z1, z2, z3)
U65(f78_out1, z0, z1, z2, z3) → f96_out1
f174_in(z0, z1, z2, z3) → U66(f61_in(z0, z1, z2), z0, z1, z2, z3)
U66(f61_out1, z0, z1, z2, z3) → f174_out1
f175_in(z0, z1, z2, z3) → U67(f78_in(z1, z0, z3), z0, z1, z2, z3)
U67(f78_out1, z0, z1, z2, z3) → f175_out1
f415_in(z0, z1, z2, z3) → U68(f61_in(z0, z1, z2), z0, z1, z2, z3)
U68(f61_out1, z0, z1, z2, z3) → f415_out1
f416_in(z0, z1, z2, z3) → U69(f78_in(z1, z0, z3), z0, z1, z2, z3)
U69(f78_out1, z0, z1, z2, z3) → f416_out1
f52_in(z0, z1, z2, z3) → U70(f61_in(z0, z1, z2), z0, z1, z2, z3)
U70(f61_out1, z0, z1, z2, z3) → f52_out1
f53_in(z0, z1, z2, z3) → U71(f78_in(z1, z0, z3), z0, z1, z2, z3)
U71(f78_out1, z0, z1, z2, z3) → f53_out1
f61_in(z0, z1, z2) → U72(f63_in(z0, z1), z0, z1, z2)
U72(f63_out1, z0, z1, z2) → U73(f2_in(z0, z2), z0, z1, z2)
U73(f2_out1, z0, z1, z2) → f61_out1
f78_in(z0, z1, z2) → U74(f63_in(z0, z1), z0, z1, z2)
U74(f63_out1, z0, z1, z2) → U75(f2_in(z1, z2), z0, z1, z2)
U75(f2_out1, z0, z1, z2) → f78_out1
f123_in(z0, z1) → U76(f127_in(z0), z0, z1)
U76(f127_out1, z0, z1) → U77(f2_in(0, z1), z0, z1)
U77(f2_out1, z0, z1) → f123_out1
f138_in(z0, z1, z2) → U78(f63_in(z0, z1), z0, z1, z2)
U78(f63_out1, z0, z1, z2) → U79(f2_in(s(z0), z2), z0, z1, z2)
U79(f2_out1, z0, z1, z2) → f138_out1
f159_in(z0, z1, z2) → U80(f63_in(z0, z1), z0, z1, z2)
U80(f63_out1, z0, z1, z2) → U81(f2_in(s(z1), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f159_out1
f23_in(z0, z1, z2, z3) → U82(f86_in(z0, z1), f87_in(z2, z0, z3, z1), z0, z1, z2, z3)
U82(f86_out1, z0, z1, z2, z3, z4) → f23_out1
U82(z0, f87_out2, z1, z2, z3, z4) → f23_out3
U82(z0, f87_out3, z1, z2, z3, z4) → f23_out4
f25_in(z0, z1, z2, z3) → U83(f27_in(z0, z1), f28_in(z2, z0, z3, z1), z0, z1, z2, z3)
U83(f27_out1, z0, z1, z2, z3, z4) → f25_out1
U83(z0, f28_out2, z1, z2, z3, z4) → f25_out3
U83(z0, f28_out3, z1, z2, z3, z4) → f25_out4
f49_in(z0, z1, z2, z3) → U84(f52_in(z0, z1, z2, z3), f53_in(z0, z1, z2, z3), z0, z1, z2, z3)
U84(f52_out1, z0, z1, z2, z3, z4) → f49_out1
U84(z0, f53_out1, z1, z2, z3, z4) → f49_out2
f92_in(z0, z1, z2, z3) → U85(f95_in(z0, z1, z2, z3), f96_in(z0, z1, z2, z3), z0, z1, z2, z3)
U85(f95_out1, z0, z1, z2, z3, z4) → f92_out1
U85(z0, f96_out1, z1, z2, z3, z4) → f92_out2
f113_in(z0, z1, z2) → U86(f2_in(0, z0), f118_in(z1, z0, z2), z0, z1, z2)
U86(f2_out1, z0, z1, z2, z3) → f113_out1
U86(z0, f118_out1, z1, z2, z3) → f113_out2
U86(z0, f118_out3, z1, z2, z3) → f113_out4
f114_in(z0, z1, z2, z3) → U87(f134_in(z0, z1, z2), f135_in(z0, z1, z2, z3), z0, z1, z2, z3)
U87(f134_out1, z0, z1, z2, z3, z4) → f114_out1
U87(z0, f135_out2, z1, z2, z3, z4) → f114_out3
f154_in(z0, z1) → U88(f2_in(s(z0), z1), f157_in(z0, z1), z0, z1)
U88(f2_out1, z0, z1, z2) → f154_out1
U88(z0, f157_out1, z1, z2) → f154_out2
f167_in(z0, z1, z2, z3) → U89(f211_in(z0, z1), f212_in(z2, z0, z3, z1), z0, z1, z2, z3)
U89(f211_out1, z0, z1, z2, z3, z4) → f167_out1
U89(z0, f212_out2, z1, z2, z3, z4) → f167_out3
U89(z0, f212_out3, z1, z2, z3, z4) → f167_out4
f168_in(z0, z1, z2, z3) → U90(f169_in(z0, z1), f170_in(z2, z0, z3, z1), z0, z1, z2, z3)
U90(f169_out1, z0, z1, z2, z3, z4) → f168_out1
U90(z0, f170_out2, z1, z2, z3, z4) → f168_out3
U90(z0, f170_out3, z1, z2, z3, z4) → f168_out4
f173_in(z0, z1, z2, z3) → U91(f174_in(z0, z1, z2, z3), f175_in(z0, z1, z2, z3), z0, z1, z2, z3)
U91(f174_out1, z0, z1, z2, z3, z4) → f173_out1
U91(z0, f175_out1, z1, z2, z3, z4) → f173_out2
f215_in(z0, z1, z2, z3) → U92(f216_in(z0, z1, z2, z3), f217_in(z0, z1, z2, z3), z0, z1, z2, z3)
U92(f216_out1, z0, z1, z2, z3, z4) → f215_out1
U92(z0, f217_out1, z1, z2, z3, z4) → f215_out2
f264_in(z0, z1, z2) → U93(f2_in(0, z0), f267_in(z1, z0, z2), z0, z1, z2)
U93(f2_out1, z0, z1, z2, z3) → f264_out1
U93(z0, f267_out1, z1, z2, z3) → f264_out2
U93(z0, f267_out3, z1, z2, z3) → f264_out4
f265_in(z0, z1, z2, z3) → U94(f301_in(z0, z1, z2), f302_in(z0, z1, z2, z3), z0, z1, z2, z3)
U94(f301_out1, z0, z1, z2, z3, z4) → f265_out1
U94(z0, f302_out2, z1, z2, z3, z4) → f265_out3
f311_in(z0, z1) → U95(f2_in(s(z0), z1), f314_in(z0, z1), z0, z1)
U95(f2_out1, z0, z1, z2) → f311_out1
U95(z0, f314_out1, z1, z2) → f311_out2
f325_in(z0, z1, z2, z3) → U96(f422_in(z0, z1), f424_in(z2, z0, z3, z1), z0, z1, z2, z3)
U96(f422_out1, z0, z1, z2, z3, z4) → f325_out1
U96(z0, f424_out2, z1, z2, z3, z4) → f325_out3
U96(z0, f424_out3, z1, z2, z3, z4) → f325_out4
f326_in(z0, z1, z2, z3) → U97(f327_in(z0, z1), f328_in(z2, z0, z3, z1), z0, z1, z2, z3)
U97(f327_out1, z0, z1, z2, z3, z4) → f326_out1
U97(z0, f328_out2, z1, z2, z3, z4) → f326_out3
U97(z0, f328_out3, z1, z2, z3, z4) → f326_out4
f414_in(z0, z1, z2, z3) → U98(f415_in(z0, z1, z2, z3), f416_in(z0, z1, z2, z3), z0, z1, z2, z3)
U98(f415_out1, z0, z1, z2, z3, z4) → f414_out1
U98(z0, f416_out1, z1, z2, z3, z4) → f414_out2
f460_in(z0, z1, z2, z3) → U99(f461_in(z0, z1, z2, z3), f462_in(z0, z1, z2, z3), z0, z1, z2, z3)
U99(f461_out1, z0, z1, z2, z3, z4) → f460_out1
U99(z0, f462_out1, z1, z2, z3, z4) → f460_out2
f470_in(z0, z1, z2) → U100(f2_in(0, z0), f476_in(z1, z0, z2), z0, z1, z2)
U100(f2_out1, z0, z1, z2, z3) → f470_out1
U100(z0, f476_out1, z1, z2, z3) → f470_out2
U100(z0, f476_out3, z1, z2, z3) → f470_out4
f471_in(z0, z1, z2, z3) → U101(f521_in(z0, z1, z2), f522_in(z0, z1, z2, z3), z0, z1, z2, z3)
U101(f521_out1, z0, z1, z2, z3, z4) → f471_out1
U101(z0, f522_out2, z1, z2, z3, z4) → f471_out3
f531_in(z0, z1) → U102(f2_in(s(z0), z1), f534_in(z0, z1), z0, z1)
U102(f2_out1, z0, z1, z2) → f531_out1
U102(z0, f534_out1, z1, z2) → f531_out2
f542_in(z0, z1, z2, z3) → U103(f585_in(z0, z1), f586_in(z2, z0, z3, z1), z0, z1, z2, z3)
U103(f585_out1, z0, z1, z2, z3, z4) → f542_out1
U103(z0, f586_out2, z1, z2, z3, z4) → f542_out3
U103(z0, f586_out3, z1, z2, z3, z4) → f542_out4
f543_in(z0, z1, z2, z3) → U104(f574_in(z0, z1), f575_in(z2, z0, z3, z1), z0, z1, z2, z3)
U104(f574_out1, z0, z1, z2, z3, z4) → f543_out1
U104(z0, f575_out2, z1, z2, z3, z4) → f543_out3
U104(z0, f575_out3, z1, z2, z3, z4) → f543_out4
f578_in(z0, z1, z2, z3) → U105(f579_in(z0, z1, z2, z3), f580_in(z0, z1, z2, z3), z0, z1, z2, z3)
U105(f579_out1, z0, z1, z2, z3, z4) → f578_out1
U105(z0, f580_out1, z1, z2, z3, z4) → f578_out2
f589_in(z0, z1, z2, z3) → U106(f590_in(z0, z1, z2, z3), f591_in(z0, z1, z2, z3), z0, z1, z2, z3)
U106(f590_out1, z0, z1, z2, z3, z4) → f589_out1
U106(z0, f591_out1, z1, z2, z3, z4) → f589_out2
f599_in(z0, z1, z2) → U107(f2_in(0, z0), f602_in(z1, z0, z2), z0, z1, z2)
U107(f2_out1, z0, z1, z2, z3) → f599_out1
U107(z0, f602_out1, z1, z2, z3) → f599_out2
U107(z0, f602_out3, z1, z2, z3) → f599_out4
f600_in(z0, z1, z2, z3) → U108(f607_in(z0, z1, z2), f608_in(z0, z1, z2, z3), z0, z1, z2, z3)
U108(f607_out1, z0, z1, z2, z3, z4) → f600_out1
U108(z0, f608_out2, z1, z2, z3, z4) → f600_out3
f700_in(z0, z1) → U109(f2_in(s(z0), z1), f703_in(z0, z1), z0, z1)
U109(f2_out1, z0, z1, z2) → f700_out1
U109(z0, f703_out1, z1, z2) → f700_out2

Tuples:

F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F123_IN(z0, z1) → c192
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c
F211_IN(z0, tree(z1, z2, z3)) → c
F422_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F602_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c
U76'(f127_out1, z0, z1) → c

S tuples:

F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F123_IN(z0, z1) → c192
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c
F211_IN(z0, tree(z1, z2, z3)) → c
F422_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F602_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c

K tuples:

U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
U76'(f127_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, U17, U18, U19, U20, U21, U22, U23, U24, f33_in, U25, U26, f63_in, U27, f585_in, U28, f586_in, U29, f211_in, U30, f212_in, U31, f422_in, U32, f424_in, U33, f574_in, U34, f575_in, U35, f602_in, U36, f607_in, U37, f608_in, U38, f86_in, U39, f87_in, U40, f169_in, U41, f170_in, U42, f267_in, U43, f301_in, U44, f302_in, U45, f327_in, U46, f328_in, U47, f476_in, U48, f521_in, U49, f522_in, U50, f590_in, U51, f591_in, U52, f27_in, U53, f28_in, U54, f118_in, U55, f134_in, U56, f135_in, U57, f216_in, U58, f217_in, U59, f461_in, U60, f462_in, U61, f579_in, U62, f580_in, U63, f95_in, U64, f96_in, U65, f174_in, U66, f175_in, U67, f415_in, U68, f416_in, U69, f52_in, U70, f53_in, U71, f61_in, U72, U73, f78_in, U74, U75, f123_in, U76, U77, f138_in, U78, U79, f159_in, U80, U81, f23_in, U82, f25_in, U83, f49_in, U84, f92_in, U85, f113_in, U86, f114_in, U87, f154_in, U88, f167_in, U89, f168_in, U90, f173_in, U91, f215_in, U92, f264_in, U93, f265_in, U94, f311_in, U95, f325_in, U96, f326_in, U97, f414_in, U98, f460_in, U99, f470_in, U100, f471_in, U101, f531_in, U102, f542_in, U103, f543_in, U104, f578_in, U105, f589_in, U106, f599_in, U107, f600_in, U108, f700_in, U109

Defined Pair Symbols:

F61_IN, F78_IN, F138_IN, F159_IN, F585_IN, F211_IN, F422_IN, F574_IN, F602_IN, F86_IN, F169_IN, F267_IN, F327_IN, F476_IN, F27_IN, F118_IN, U76', F2_IN, F33_IN, F63_IN, F586_IN, F212_IN, F424_IN, F575_IN, F607_IN, F608_IN, F87_IN, F170_IN, F301_IN, F302_IN, F328_IN, F521_IN, F522_IN, F590_IN, F591_IN, F28_IN, F134_IN, F135_IN, F216_IN, F217_IN, F461_IN, F462_IN, F579_IN, F580_IN, F95_IN, F96_IN, F174_IN, F175_IN, F415_IN, F416_IN, F52_IN, F53_IN, U72', U74', F123_IN, U78', U80', F23_IN, F25_IN, F49_IN, F92_IN, F113_IN, F114_IN, F154_IN, F167_IN, F168_IN, F173_IN, F215_IN, F264_IN, F265_IN, F311_IN, F325_IN, F326_IN, F414_IN, F460_IN, F470_IN, F471_IN, F531_IN, F542_IN, F543_IN, F578_IN, F589_IN, F599_IN, F600_IN, F700_IN

Compound Symbols:

c186, c189, c195, c198, c, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c83, c84, c88, c92, c97, c102, c107, c112, c114, c118, c123, c128, c130, c134, c139, c141, c143, c145, c149, c154, c156, c158, c160, c162, c164, c166, c168, c170, c172, c174, c176, c178, c180, c182, c184, c187, c190, c192, c196, c199, c201, c205, c209, c212, c215, c219, c222, c225, c229, c233, c236, c239, c243, c246, c249, c253, c257, c260, c263, c267, c270, c273, c277, c281, c284, c287, c291, c294, c

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

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

F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))

We considered the (Usable) Rules:

f63_in(0, s(z0)) → f63_out1
f63_in(s(z0), s(z1)) → U27(f63_in(z0, z1), s(z0), s(z1))
U27(f63_out1, s(z0), s(z1)) → f63_out1

And the Tuples:

F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F123_IN(z0, z1) → c192
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c
F211_IN(z0, tree(z1, z2, z3)) → c
F422_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F602_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c
U76'(f127_out1, z0, z1) → c

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

POL(0) = 0   
POL(F113_IN(x₁, x₂, x₃)) = [1] + [2]x₁ + [2]x₃   
POL(F114_IN(x₁, x₂, x₃, x₄)) = [2] + [2]x₃ + [2]x₄   
POL(F118_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F123_IN(x₁, x₂)) = 0   
POL(F134_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F135_IN(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(F138_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F154_IN(x₁, x₂)) = [2] + [2]x₂   
POL(F159_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F167_IN(x₁, x₂, x₃, x₄)) = [2]x₂ + [2]x₄   
POL(F168_IN(x₁, x₂, x₃, x₄)) = [2]x₂ + [2]x₄   
POL(F169_IN(x₁, x₂)) = 0   
POL(F170_IN(x₁, x₂, x₃, x₄)) = [2]x₃ + [2]x₄   
POL(F173_IN(x₁, x₂, x₃, x₄)) = [2]x₃ + [2]x₄   
POL(F174_IN(x₁, x₂, x₃, x₄)) = [2]x₃   
POL(F175_IN(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(F211_IN(x₁, x₂)) = 0   
POL(F212_IN(x₁, x₂, x₃, x₄)) = [2]x₃ + [2]x₄   
POL(F215_IN(x₁, x₂, x₃, x₄)) = [2]x₃ + [2]x₄   
POL(F216_IN(x₁, x₂, x₃, x₄)) = [2]x₃   
POL(F217_IN(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(F23_IN(x₁, x₂, x₃, x₄)) = [2]x₂ + [2]x₄   
POL(F25_IN(x₁, x₂, x₃, x₄)) = [2] + [2]x₂ + [2]x₄   
POL(F264_IN(x₁, x₂, x₃)) = [1] + [2]x₁ + x₃   
POL(F265_IN(x₁, x₂, x₃, x₄)) = [1] + [2]x₃ + [2]x₄   
POL(F267_IN(x₁, x₂, x₃)) = 0   
POL(F27_IN(x₁, x₂)) = 0   
POL(F28_IN(x₁, x₂, x₃, x₄)) = [2]x₃ + [2]x₄   
POL(F2_IN(x₁, x₂)) = [2]x₂   
POL(F301_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F302_IN(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(F311_IN(x₁, x₂)) = [2] + [2]x₂   
POL(F325_IN(x₁, x₂, x₃, x₄)) = [2] + [2]x₂ + [2]x₄   
POL(F326_IN(x₁, x₂, x₃, x₄)) = [1] + [2]x₂ + [2]x₄   
POL(F327_IN(x₁, x₂)) = 0   
POL(F328_IN(x₁, x₂, x₃, x₄)) = [2]x₃ + [2]x₄   
POL(F33_IN(x₁, x₂)) = 0   
POL(F414_IN(x₁, x₂, x₃, x₄)) = [2]x₃ + [2]x₄   
POL(F415_IN(x₁, x₂, x₃, x₄)) = [2]x₃   
POL(F416_IN(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(F422_IN(x₁, x₂)) = 0   
POL(F424_IN(x₁, x₂, x₃, x₄)) = [2] + [2]x₃ + [2]x₄   
POL(F460_IN(x₁, x₂, x₃, x₄)) = [2] + [2]x₃ + [2]x₄   
POL(F461_IN(x₁, x₂, x₃, x₄)) = [2]x₃   
POL(F462_IN(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(F470_IN(x₁, x₂, x₃)) = [2]x₁ + [2]x₃   
POL(F471_IN(x₁, x₂, x₃, x₄)) = [2]x₃ + [2]x₄   
POL(F476_IN(x₁, x₂, x₃)) = x₃   
POL(F49_IN(x₁, x₂, x₃, x₄)) = [2]x₃ + [2]x₄   
POL(F521_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F522_IN(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(F52_IN(x₁, x₂, x₃, x₄)) = [2]x₃   
POL(F531_IN(x₁, x₂)) = [2]x₂   
POL(F53_IN(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(F542_IN(x₁, x₂, x₃, x₄)) = [2] + [2]x₂ + [2]x₄   
POL(F543_IN(x₁, x₂, x₃, x₄)) = [2] + [2]x₂ + [2]x₄   
POL(F574_IN(x₁, x₂)) = 0   
POL(F575_IN(x₁, x₂, x₃, x₄)) = [1] + [2]x₃ + [2]x₄   
POL(F578_IN(x₁, x₂, x₃, x₄)) = [2]x₃ + [2]x₄   
POL(F579_IN(x₁, x₂, x₃, x₄)) = [2]x₃   
POL(F580_IN(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(F585_IN(x₁, x₂)) = 0   
POL(F586_IN(x₁, x₂, x₃, x₄)) = [2]x₃ + [2]x₄   
POL(F589_IN(x₁, x₂, x₃, x₄)) = [2]x₃ + [2]x₄   
POL(F590_IN(x₁, x₂, x₃, x₄)) = [2]x₃   
POL(F591_IN(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(F599_IN(x₁, x₂, x₃)) = [2]x₁ + [2]x₃   
POL(F600_IN(x₁, x₂, x₃, x₄)) = [2] + [2]x₃ + [2]x₄   
POL(F602_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F607_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F608_IN(x₁, x₂, x₃, x₄)) = [1] + [2]x₄   
POL(F61_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F63_IN(x₁, x₂)) = 0   
POL(F700_IN(x₁, x₂)) = [2]x₂   
POL(F78_IN(x₁, x₂, x₃)) = [2]x₃   
POL(F86_IN(x₁, x₂)) = 0   
POL(F87_IN(x₁, x₂, x₃, x₄)) = [2]x₃ + [2]x₄   
POL(F92_IN(x₁, x₂, x₃, x₄)) = [2]x₃ + [2]x₄   
POL(F95_IN(x₁, x₂, x₃, x₄)) = [2]x₃   
POL(F96_IN(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(U27(x₁, x₂, x₃)) = 0   
POL(U72'(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(U74'(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(U76'(x₁, x₂, x₃)) = [3]x₃   
POL(U78'(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(U80'(x₁, x₂, x₃, x₄)) = [2]x₄   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c10(x₁)) = x₁   
POL(c102(x₁)) = x₁   
POL(c107(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c112(x₁)) = x₁   
POL(c114(x₁)) = x₁   
POL(c118(x₁)) = x₁   
POL(c12(x₁)) = x₁   
POL(c123(x₁)) = x₁   
POL(c128(x₁)) = x₁   
POL(c13(x₁)) = x₁   
POL(c130(x₁)) = x₁   
POL(c134(x₁)) = x₁   
POL(c139(x₁)) = x₁   
POL(c14(x₁)) = x₁   
POL(c141(x₁)) = x₁   
POL(c143(x₁)) = x₁   
POL(c145(x₁)) = x₁   
POL(c149(x₁)) = x₁   
POL(c15(x₁)) = x₁   
POL(c154(x₁)) = x₁   
POL(c156(x₁)) = x₁   
POL(c158(x₁)) = x₁   
POL(c16(x₁)) = x₁   
POL(c160(x₁)) = x₁   
POL(c162(x₁)) = x₁   
POL(c164(x₁)) = x₁   
POL(c166(x₁)) = x₁   
POL(c168(x₁)) = x₁   
POL(c17(x₁)) = x₁   
POL(c170(x₁)) = x₁   
POL(c172(x₁)) = x₁   
POL(c174(x₁)) = x₁   
POL(c176(x₁)) = x₁   
POL(c178(x₁)) = x₁   
POL(c18(x₁)) = x₁   
POL(c180(x₁)) = x₁   
POL(c182(x₁)) = x₁   
POL(c184(x₁)) = x₁   
POL(c186(x₁, x₂)) = x₁ + x₂   
POL(c187(x₁)) = x₁   
POL(c189(x₁, x₂)) = x₁ + x₂   
POL(c19(x₁)) = x₁   
POL(c190(x₁)) = x₁   
POL(c192) = 0   
POL(c195(x₁, x₂)) = x₁ + x₂   
POL(c196(x₁)) = x₁   
POL(c198(x₁, x₂)) = x₁ + x₂   
POL(c199(x₁)) = x₁   
POL(c2(x₁)) = x₁   
POL(c20(x₁)) = x₁   
POL(c201(x₁, x₂)) = x₁ + x₂   
POL(c205(x₁, x₂)) = x₁ + x₂   
POL(c209(x₁, x₂)) = x₁ + x₂   
POL(c21(x₁)) = x₁   
POL(c212(x₁, x₂)) = x₁ + x₂   
POL(c215(x₁, x₂)) = x₁ + x₂   
POL(c219(x₁, x₂)) = x₁ + x₂   
POL(c22(x₁)) = x₁   
POL(c222(x₁)) = x₁   
POL(c225(x₁, x₂)) = x₁ + x₂   
POL(c229(x₁, x₂)) = x₁ + x₂   
POL(c23(x₁)) = x₁   
POL(c233(x₁, x₂)) = x₁ + x₂   
POL(c236(x₁, x₂)) = x₁ + x₂   
POL(c239(x₁, x₂)) = x₁ + x₂   
POL(c24(x₁)) = x₁   
POL(c243(x₁, x₂)) = x₁ + x₂   
POL(c246(x₁)) = x₁   
POL(c249(x₁, x₂)) = x₁ + x₂   
POL(c25(x₁)) = x₁   
POL(c253(x₁, x₂)) = x₁ + x₂   
POL(c257(x₁, x₂)) = x₁ + x₂   
POL(c260(x₁, x₂)) = x₁ + x₂   
POL(c263(x₁, x₂)) = x₁ + x₂   
POL(c267(x₁, x₂)) = x₁ + x₂   
POL(c270(x₁)) = x₁   
POL(c273(x₁, x₂)) = x₁ + x₂   
POL(c277(x₁, x₂)) = x₁ + x₂   
POL(c281(x₁, x₂)) = x₁ + x₂   
POL(c284(x₁, x₂)) = x₁ + x₂   
POL(c287(x₁, x₂)) = x₁ + x₂   
POL(c291(x₁, x₂)) = x₁ + x₂   
POL(c294(x₁)) = x₁   
POL(c3(x₁)) = x₁   
POL(c4(x₁)) = x₁   
POL(c5(x₁)) = x₁   
POL(c6(x₁)) = x₁   
POL(c7(x₁)) = x₁   
POL(c8(x₁)) = x₁   
POL(c83(x₁)) = x₁   
POL(c84(x₁)) = x₁   
POL(c88(x₁)) = x₁   
POL(c9(x₁)) = x₁   
POL(c92(x₁)) = x₁   
POL(c97(x₁)) = x₁   
POL(f127_out1) = 0   
POL(f63_in(x₁, x₂)) = 0   
POL(f63_out1) = 0   
POL(s(x₁)) = 0   
POL(tree(x₁, x₂, x₃)) = [1] + x₂ + x₃   

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → U1(f25_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U2(f23_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U3(f113_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f114_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f154_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U7(f168_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U8(f167_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U9(f264_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U10(f265_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U11(f311_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U12(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U13(f326_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U14(f325_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U15(f470_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U16(f471_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U17(f531_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U18(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U19(f543_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U20(f542_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U21(f599_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U22(f600_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U23(f700_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U24(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f25_out1, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out3, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out4, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out1, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out3, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out4, z0, tree(z1, z2, z3)) → f2_out1
U3(f113_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U4(f114_out1, z0, tree(z1, z2, z3)) → f2_out1
U4(f114_out3, z0, tree(z1, z2, z3)) → f2_out1
U5(f154_out1, s(z0), tree(0, z1, z2)) → f2_out1
U5(f154_out2, s(z0), tree(0, z1, z2)) → f2_out1
U6(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U7(f168_out1, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out3, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out4, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out1, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out3, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out4, z0, tree(z1, z2, z3)) → f2_out1
U9(f264_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U10(f265_out1, z0, tree(z1, z2, z3)) → f2_out1
U10(f265_out3, z0, tree(z1, z2, z3)) → f2_out1
U11(f311_out1, s(z0), tree(0, z1, z2)) → f2_out1
U11(f311_out2, s(z0), tree(0, z1, z2)) → f2_out1
U12(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U13(f326_out1, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out3, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out4, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out3, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out4, z0, tree(z1, z2, z3)) → f2_out1
U15(f470_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U16(f471_out1, z0, tree(z1, z2, z3)) → f2_out1
U16(f471_out3, z0, tree(z1, z2, z3)) → f2_out1
U17(f531_out1, s(z0), tree(0, z1, z2)) → f2_out1
U17(f531_out2, s(z0), tree(0, z1, z2)) → f2_out1
U18(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U19(f543_out1, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out3, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out4, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out1, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out3, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out4, z0, tree(z1, z2, z3)) → f2_out1
U21(f599_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U22(f600_out1, z0, tree(z1, z2, z3)) → f2_out1
U22(f600_out3, z0, tree(z1, z2, z3)) → f2_out1
U23(f700_out1, s(z0), tree(0, z1, z2)) → f2_out1
U23(f700_out2, s(z0), tree(0, z1, z2)) → f2_out1
U24(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f33_in(z0, z1) → f33_out1
f33_in(z0, tree(z1, z2, z3)) → U25(f33_in(z0, z2), z0, tree(z1, z2, z3))
f33_in(z0, tree(z1, z2, z3)) → U26(f33_in(z0, z2), z0, tree(z1, z2, z3))
U25(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
U26(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
f63_in(0, s(z0)) → f63_out1
f63_in(s(z0), s(z1)) → U27(f63_in(z0, z1), s(z0), s(z1))
U27(f63_out1, s(z0), s(z1)) → f63_out1
f585_in(z0, tree(z1, z2, z3)) → U28(f33_in(z0, z2), z0, tree(z1, z2, z3))
U28(f33_out1, z0, tree(z1, z2, z3)) → f585_out1
f586_in(z0, z1, z2, z3) → U29(f589_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f589_out1, z0, z1, z2, z3) → f586_out2
U29(f589_out2, z0, z1, z2, z3) → f586_out3
f211_in(z0, tree(z1, z2, z3)) → U30(f33_in(z0, z2), z0, tree(z1, z2, z3))
U30(f33_out1, z0, tree(z1, z2, z3)) → f211_out1
f212_in(z0, z1, z2, z3) → U31(f215_in(z0, z1, z2, z3), z0, z1, z2, z3)
U31(f215_out1, z0, z1, z2, z3) → f212_out2
U31(f215_out2, z0, z1, z2, z3) → f212_out3
f422_in(z0, tree(z1, z2, z3)) → U32(f33_in(z0, z2), z0, tree(z1, z2, z3))
U32(f33_out1, z0, tree(z1, z2, z3)) → f422_out1
f424_in(z0, z1, z2, z3) → U33(f460_in(z0, z1, z2, z3), z0, z1, z2, z3)
U33(f460_out1, z0, z1, z2, z3) → f424_out2
U33(f460_out2, z0, z1, z2, z3) → f424_out3
f574_in(z0, tree(z1, z2, z3)) → U34(f33_in(z0, z2), z0, tree(z1, z2, z3))
U34(f33_out1, z0, tree(z1, z2, z3)) → f574_out1
f575_in(z0, z1, z2, z3) → U35(f578_in(z0, z1, z2, z3), z0, z1, z2, z3)
U35(f578_out1, z0, z1, z2, z3) → f575_out2
U35(f578_out2, z0, z1, z2, z3) → f575_out3
f602_in(z0, z1, z2) → U36(f123_in(z0, z2), z0, z1, z2)
U36(f123_out1, z0, z1, z2) → f602_out3
f607_in(s(z0), s(z1), z2) → U37(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U37(f138_out1, s(z0), s(z1), z2) → f607_out1
f608_in(z0, z1, z2, z3) → U38(f78_in(z1, z0, z3), z0, z1, z2, z3)
U38(f78_out1, z0, z1, z2, z3) → f608_out2
f86_in(z0, tree(z1, z2, z3)) → U39(f33_in(z0, z2), z0, tree(z1, z2, z3))
U39(f33_out1, z0, tree(z1, z2, z3)) → f86_out1
f87_in(z0, z1, z2, z3) → U40(f92_in(z0, z1, z2, z3), z0, z1, z2, z3)
U40(f92_out1, z0, z1, z2, z3) → f87_out2
U40(f92_out2, z0, z1, z2, z3) → f87_out3
f169_in(z0, tree(z1, z2, z3)) → U41(f33_in(z0, z2), z0, tree(z1, z2, z3))
U41(f33_out1, z0, tree(z1, z2, z3)) → f169_out1
f170_in(z0, z1, z2, z3) → U42(f173_in(z0, z1, z2, z3), z0, z1, z2, z3)
U42(f173_out1, z0, z1, z2, z3) → f170_out2
U42(f173_out2, z0, z1, z2, z3) → f170_out3
f267_in(z0, z1, z2) → U43(f123_in(z0, z2), z0, z1, z2)
U43(f123_out1, z0, z1, z2) → f267_out3
f301_in(s(z0), s(z1), z2) → U44(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U44(f138_out1, s(z0), s(z1), z2) → f301_out1
f302_in(z0, z1, z2, z3) → U45(f78_in(z1, z0, z3), z0, z1, z2, z3)
U45(f78_out1, z0, z1, z2, z3) → f302_out2
f327_in(z0, tree(z1, z2, z3)) → U46(f33_in(z0, z2), z0, tree(z1, z2, z3))
U46(f33_out1, z0, tree(z1, z2, z3)) → f327_out1
f328_in(z0, z1, z2, z3) → U47(f414_in(z0, z1, z2, z3), z0, z1, z2, z3)
U47(f414_out1, z0, z1, z2, z3) → f328_out2
U47(f414_out2, z0, z1, z2, z3) → f328_out3
f476_in(z0, z1, z2) → U48(f123_in(z0, z2), z0, z1, z2)
U48(f123_out1, z0, z1, z2) → f476_out3
f521_in(s(z0), s(z1), z2) → U49(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U49(f138_out1, s(z0), s(z1), z2) → f521_out1
f522_in(z0, z1, z2, z3) → U50(f78_in(z1, z0, z3), z0, z1, z2, z3)
U50(f78_out1, z0, z1, z2, z3) → f522_out2
f590_in(z0, z1, z2, z3) → U51(f61_in(z0, z1, z2), z0, z1, z2, z3)
U51(f61_out1, z0, z1, z2, z3) → f590_out1
f591_in(z0, z1, z2, z3) → U52(f78_in(z1, z0, z3), z0, z1, z2, z3)
U52(f78_out1, z0, z1, z2, z3) → f591_out1
f27_in(z0, tree(z1, z2, z3)) → U53(f33_in(z0, z2), z0, tree(z1, z2, z3))
U53(f33_out1, z0, tree(z1, z2, z3)) → f27_out1
f28_in(z0, z1, z2, z3) → U54(f49_in(z0, z1, z2, z3), z0, z1, z2, z3)
U54(f49_out1, z0, z1, z2, z3) → f28_out2
U54(f49_out2, z0, z1, z2, z3) → f28_out3
f118_in(z0, z1, z2) → U55(f123_in(z0, z2), z0, z1, z2)
U55(f123_out1, z0, z1, z2) → f118_out3
f134_in(s(z0), s(z1), z2) → U56(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U56(f138_out1, s(z0), s(z1), z2) → f134_out1
f135_in(z0, z1, z2, z3) → U57(f78_in(z1, z0, z3), z0, z1, z2, z3)
U57(f78_out1, z0, z1, z2, z3) → f135_out2
f216_in(z0, z1, z2, z3) → U58(f61_in(z0, z1, z2), z0, z1, z2, z3)
U58(f61_out1, z0, z1, z2, z3) → f216_out1
f217_in(z0, z1, z2, z3) → U59(f78_in(z1, z0, z3), z0, z1, z2, z3)
U59(f78_out1, z0, z1, z2, z3) → f217_out1
f461_in(z0, z1, z2, z3) → U60(f61_in(z0, z1, z2), z0, z1, z2, z3)
U60(f61_out1, z0, z1, z2, z3) → f461_out1
f462_in(z0, z1, z2, z3) → U61(f78_in(z1, z0, z3), z0, z1, z2, z3)
U61(f78_out1, z0, z1, z2, z3) → f462_out1
f579_in(z0, z1, z2, z3) → U62(f61_in(z0, z1, z2), z0, z1, z2, z3)
U62(f61_out1, z0, z1, z2, z3) → f579_out1
f580_in(z0, z1, z2, z3) → U63(f78_in(z1, z0, z3), z0, z1, z2, z3)
U63(f78_out1, z0, z1, z2, z3) → f580_out1
f95_in(z0, z1, z2, z3) → U64(f61_in(z0, z1, z2), z0, z1, z2, z3)
U64(f61_out1, z0, z1, z2, z3) → f95_out1
f96_in(z0, z1, z2, z3) → U65(f78_in(z1, z0, z3), z0, z1, z2, z3)
U65(f78_out1, z0, z1, z2, z3) → f96_out1
f174_in(z0, z1, z2, z3) → U66(f61_in(z0, z1, z2), z0, z1, z2, z3)
U66(f61_out1, z0, z1, z2, z3) → f174_out1
f175_in(z0, z1, z2, z3) → U67(f78_in(z1, z0, z3), z0, z1, z2, z3)
U67(f78_out1, z0, z1, z2, z3) → f175_out1
f415_in(z0, z1, z2, z3) → U68(f61_in(z0, z1, z2), z0, z1, z2, z3)
U68(f61_out1, z0, z1, z2, z3) → f415_out1
f416_in(z0, z1, z2, z3) → U69(f78_in(z1, z0, z3), z0, z1, z2, z3)
U69(f78_out1, z0, z1, z2, z3) → f416_out1
f52_in(z0, z1, z2, z3) → U70(f61_in(z0, z1, z2), z0, z1, z2, z3)
U70(f61_out1, z0, z1, z2, z3) → f52_out1
f53_in(z0, z1, z2, z3) → U71(f78_in(z1, z0, z3), z0, z1, z2, z3)
U71(f78_out1, z0, z1, z2, z3) → f53_out1
f61_in(z0, z1, z2) → U72(f63_in(z0, z1), z0, z1, z2)
U72(f63_out1, z0, z1, z2) → U73(f2_in(z0, z2), z0, z1, z2)
U73(f2_out1, z0, z1, z2) → f61_out1
f78_in(z0, z1, z2) → U74(f63_in(z0, z1), z0, z1, z2)
U74(f63_out1, z0, z1, z2) → U75(f2_in(z1, z2), z0, z1, z2)
U75(f2_out1, z0, z1, z2) → f78_out1
f123_in(z0, z1) → U76(f127_in(z0), z0, z1)
U76(f127_out1, z0, z1) → U77(f2_in(0, z1), z0, z1)
U77(f2_out1, z0, z1) → f123_out1
f138_in(z0, z1, z2) → U78(f63_in(z0, z1), z0, z1, z2)
U78(f63_out1, z0, z1, z2) → U79(f2_in(s(z0), z2), z0, z1, z2)
U79(f2_out1, z0, z1, z2) → f138_out1
f159_in(z0, z1, z2) → U80(f63_in(z0, z1), z0, z1, z2)
U80(f63_out1, z0, z1, z2) → U81(f2_in(s(z1), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f159_out1
f23_in(z0, z1, z2, z3) → U82(f86_in(z0, z1), f87_in(z2, z0, z3, z1), z0, z1, z2, z3)
U82(f86_out1, z0, z1, z2, z3, z4) → f23_out1
U82(z0, f87_out2, z1, z2, z3, z4) → f23_out3
U82(z0, f87_out3, z1, z2, z3, z4) → f23_out4
f25_in(z0, z1, z2, z3) → U83(f27_in(z0, z1), f28_in(z2, z0, z3, z1), z0, z1, z2, z3)
U83(f27_out1, z0, z1, z2, z3, z4) → f25_out1
U83(z0, f28_out2, z1, z2, z3, z4) → f25_out3
U83(z0, f28_out3, z1, z2, z3, z4) → f25_out4
f49_in(z0, z1, z2, z3) → U84(f52_in(z0, z1, z2, z3), f53_in(z0, z1, z2, z3), z0, z1, z2, z3)
U84(f52_out1, z0, z1, z2, z3, z4) → f49_out1
U84(z0, f53_out1, z1, z2, z3, z4) → f49_out2
f92_in(z0, z1, z2, z3) → U85(f95_in(z0, z1, z2, z3), f96_in(z0, z1, z2, z3), z0, z1, z2, z3)
U85(f95_out1, z0, z1, z2, z3, z4) → f92_out1
U85(z0, f96_out1, z1, z2, z3, z4) → f92_out2
f113_in(z0, z1, z2) → U86(f2_in(0, z0), f118_in(z1, z0, z2), z0, z1, z2)
U86(f2_out1, z0, z1, z2, z3) → f113_out1
U86(z0, f118_out1, z1, z2, z3) → f113_out2
U86(z0, f118_out3, z1, z2, z3) → f113_out4
f114_in(z0, z1, z2, z3) → U87(f134_in(z0, z1, z2), f135_in(z0, z1, z2, z3), z0, z1, z2, z3)
U87(f134_out1, z0, z1, z2, z3, z4) → f114_out1
U87(z0, f135_out2, z1, z2, z3, z4) → f114_out3
f154_in(z0, z1) → U88(f2_in(s(z0), z1), f157_in(z0, z1), z0, z1)
U88(f2_out1, z0, z1, z2) → f154_out1
U88(z0, f157_out1, z1, z2) → f154_out2
f167_in(z0, z1, z2, z3) → U89(f211_in(z0, z1), f212_in(z2, z0, z3, z1), z0, z1, z2, z3)
U89(f211_out1, z0, z1, z2, z3, z4) → f167_out1
U89(z0, f212_out2, z1, z2, z3, z4) → f167_out3
U89(z0, f212_out3, z1, z2, z3, z4) → f167_out4
f168_in(z0, z1, z2, z3) → U90(f169_in(z0, z1), f170_in(z2, z0, z3, z1), z0, z1, z2, z3)
U90(f169_out1, z0, z1, z2, z3, z4) → f168_out1
U90(z0, f170_out2, z1, z2, z3, z4) → f168_out3
U90(z0, f170_out3, z1, z2, z3, z4) → f168_out4
f173_in(z0, z1, z2, z3) → U91(f174_in(z0, z1, z2, z3), f175_in(z0, z1, z2, z3), z0, z1, z2, z3)
U91(f174_out1, z0, z1, z2, z3, z4) → f173_out1
U91(z0, f175_out1, z1, z2, z3, z4) → f173_out2
f215_in(z0, z1, z2, z3) → U92(f216_in(z0, z1, z2, z3), f217_in(z0, z1, z2, z3), z0, z1, z2, z3)
U92(f216_out1, z0, z1, z2, z3, z4) → f215_out1
U92(z0, f217_out1, z1, z2, z3, z4) → f215_out2
f264_in(z0, z1, z2) → U93(f2_in(0, z0), f267_in(z1, z0, z2), z0, z1, z2)
U93(f2_out1, z0, z1, z2, z3) → f264_out1
U93(z0, f267_out1, z1, z2, z3) → f264_out2
U93(z0, f267_out3, z1, z2, z3) → f264_out4
f265_in(z0, z1, z2, z3) → U94(f301_in(z0, z1, z2), f302_in(z0, z1, z2, z3), z0, z1, z2, z3)
U94(f301_out1, z0, z1, z2, z3, z4) → f265_out1
U94(z0, f302_out2, z1, z2, z3, z4) → f265_out3
f311_in(z0, z1) → U95(f2_in(s(z0), z1), f314_in(z0, z1), z0, z1)
U95(f2_out1, z0, z1, z2) → f311_out1
U95(z0, f314_out1, z1, z2) → f311_out2
f325_in(z0, z1, z2, z3) → U96(f422_in(z0, z1), f424_in(z2, z0, z3, z1), z0, z1, z2, z3)
U96(f422_out1, z0, z1, z2, z3, z4) → f325_out1
U96(z0, f424_out2, z1, z2, z3, z4) → f325_out3
U96(z0, f424_out3, z1, z2, z3, z4) → f325_out4
f326_in(z0, z1, z2, z3) → U97(f327_in(z0, z1), f328_in(z2, z0, z3, z1), z0, z1, z2, z3)
U97(f327_out1, z0, z1, z2, z3, z4) → f326_out1
U97(z0, f328_out2, z1, z2, z3, z4) → f326_out3
U97(z0, f328_out3, z1, z2, z3, z4) → f326_out4
f414_in(z0, z1, z2, z3) → U98(f415_in(z0, z1, z2, z3), f416_in(z0, z1, z2, z3), z0, z1, z2, z3)
U98(f415_out1, z0, z1, z2, z3, z4) → f414_out1
U98(z0, f416_out1, z1, z2, z3, z4) → f414_out2
f460_in(z0, z1, z2, z3) → U99(f461_in(z0, z1, z2, z3), f462_in(z0, z1, z2, z3), z0, z1, z2, z3)
U99(f461_out1, z0, z1, z2, z3, z4) → f460_out1
U99(z0, f462_out1, z1, z2, z3, z4) → f460_out2
f470_in(z0, z1, z2) → U100(f2_in(0, z0), f476_in(z1, z0, z2), z0, z1, z2)
U100(f2_out1, z0, z1, z2, z3) → f470_out1
U100(z0, f476_out1, z1, z2, z3) → f470_out2
U100(z0, f476_out3, z1, z2, z3) → f470_out4
f471_in(z0, z1, z2, z3) → U101(f521_in(z0, z1, z2), f522_in(z0, z1, z2, z3), z0, z1, z2, z3)
U101(f521_out1, z0, z1, z2, z3, z4) → f471_out1
U101(z0, f522_out2, z1, z2, z3, z4) → f471_out3
f531_in(z0, z1) → U102(f2_in(s(z0), z1), f534_in(z0, z1), z0, z1)
U102(f2_out1, z0, z1, z2) → f531_out1
U102(z0, f534_out1, z1, z2) → f531_out2
f542_in(z0, z1, z2, z3) → U103(f585_in(z0, z1), f586_in(z2, z0, z3, z1), z0, z1, z2, z3)
U103(f585_out1, z0, z1, z2, z3, z4) → f542_out1
U103(z0, f586_out2, z1, z2, z3, z4) → f542_out3
U103(z0, f586_out3, z1, z2, z3, z4) → f542_out4
f543_in(z0, z1, z2, z3) → U104(f574_in(z0, z1), f575_in(z2, z0, z3, z1), z0, z1, z2, z3)
U104(f574_out1, z0, z1, z2, z3, z4) → f543_out1
U104(z0, f575_out2, z1, z2, z3, z4) → f543_out3
U104(z0, f575_out3, z1, z2, z3, z4) → f543_out4
f578_in(z0, z1, z2, z3) → U105(f579_in(z0, z1, z2, z3), f580_in(z0, z1, z2, z3), z0, z1, z2, z3)
U105(f579_out1, z0, z1, z2, z3, z4) → f578_out1
U105(z0, f580_out1, z1, z2, z3, z4) → f578_out2
f589_in(z0, z1, z2, z3) → U106(f590_in(z0, z1, z2, z3), f591_in(z0, z1, z2, z3), z0, z1, z2, z3)
U106(f590_out1, z0, z1, z2, z3, z4) → f589_out1
U106(z0, f591_out1, z1, z2, z3, z4) → f589_out2
f599_in(z0, z1, z2) → U107(f2_in(0, z0), f602_in(z1, z0, z2), z0, z1, z2)
U107(f2_out1, z0, z1, z2, z3) → f599_out1
U107(z0, f602_out1, z1, z2, z3) → f599_out2
U107(z0, f602_out3, z1, z2, z3) → f599_out4
f600_in(z0, z1, z2, z3) → U108(f607_in(z0, z1, z2), f608_in(z0, z1, z2, z3), z0, z1, z2, z3)
U108(f607_out1, z0, z1, z2, z3, z4) → f600_out1
U108(z0, f608_out2, z1, z2, z3, z4) → f600_out3
f700_in(z0, z1) → U109(f2_in(s(z0), z1), f703_in(z0, z1), z0, z1)
U109(f2_out1, z0, z1, z2) → f700_out1
U109(z0, f703_out1, z1, z2) → f700_out2

Tuples:

F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F123_IN(z0, z1) → c192
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c
F211_IN(z0, tree(z1, z2, z3)) → c
F422_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F602_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c
U76'(f127_out1, z0, z1) → c

S tuples:

F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F123_IN(z0, z1) → c192
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c
F211_IN(z0, tree(z1, z2, z3)) → c
F422_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F602_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c

K tuples:

U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
U76'(f127_out1, z0, z1) → c
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, U17, U18, U19, U20, U21, U22, U23, U24, f33_in, U25, U26, f63_in, U27, f585_in, U28, f586_in, U29, f211_in, U30, f212_in, U31, f422_in, U32, f424_in, U33, f574_in, U34, f575_in, U35, f602_in, U36, f607_in, U37, f608_in, U38, f86_in, U39, f87_in, U40, f169_in, U41, f170_in, U42, f267_in, U43, f301_in, U44, f302_in, U45, f327_in, U46, f328_in, U47, f476_in, U48, f521_in, U49, f522_in, U50, f590_in, U51, f591_in, U52, f27_in, U53, f28_in, U54, f118_in, U55, f134_in, U56, f135_in, U57, f216_in, U58, f217_in, U59, f461_in, U60, f462_in, U61, f579_in, U62, f580_in, U63, f95_in, U64, f96_in, U65, f174_in, U66, f175_in, U67, f415_in, U68, f416_in, U69, f52_in, U70, f53_in, U71, f61_in, U72, U73, f78_in, U74, U75, f123_in, U76, U77, f138_in, U78, U79, f159_in, U80, U81, f23_in, U82, f25_in, U83, f49_in, U84, f92_in, U85, f113_in, U86, f114_in, U87, f154_in, U88, f167_in, U89, f168_in, U90, f173_in, U91, f215_in, U92, f264_in, U93, f265_in, U94, f311_in, U95, f325_in, U96, f326_in, U97, f414_in, U98, f460_in, U99, f470_in, U100, f471_in, U101, f531_in, U102, f542_in, U103, f543_in, U104, f578_in, U105, f589_in, U106, f599_in, U107, f600_in, U108, f700_in, U109

Defined Pair Symbols:

F61_IN, F78_IN, F138_IN, F159_IN, F585_IN, F211_IN, F422_IN, F574_IN, F602_IN, F86_IN, F169_IN, F267_IN, F327_IN, F476_IN, F27_IN, F118_IN, U76', F2_IN, F33_IN, F63_IN, F586_IN, F212_IN, F424_IN, F575_IN, F607_IN, F608_IN, F87_IN, F170_IN, F301_IN, F302_IN, F328_IN, F521_IN, F522_IN, F590_IN, F591_IN, F28_IN, F134_IN, F135_IN, F216_IN, F217_IN, F461_IN, F462_IN, F579_IN, F580_IN, F95_IN, F96_IN, F174_IN, F175_IN, F415_IN, F416_IN, F52_IN, F53_IN, U72', U74', F123_IN, U78', U80', F23_IN, F25_IN, F49_IN, F92_IN, F113_IN, F114_IN, F154_IN, F167_IN, F168_IN, F173_IN, F215_IN, F264_IN, F265_IN, F311_IN, F325_IN, F326_IN, F414_IN, F460_IN, F470_IN, F471_IN, F531_IN, F542_IN, F543_IN, F578_IN, F589_IN, F599_IN, F600_IN, F700_IN

Compound Symbols:

c186, c189, c195, c198, c, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c83, c84, c88, c92, c97, c102, c107, c112, c114, c118, c123, c128, c130, c134, c139, c141, c143, c145, c149, c154, c156, c158, c160, c162, c164, c166, c168, c170, c172, c174, c176, c178, c180, c182, c184, c187, c190, c192, c196, c199, c201, c205, c209, c212, c215, c219, c222, c225, c229, c233, c236, c239, c243, c246, c249, c253, c257, c260, c263, c267, c270, c273, c277, c281, c284, c287, c291, c294, c

(35) CdtKnowledgeProof (EQUIVALENT transformation)

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

F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c
F211_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F602_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F86_IN(z0, tree(z1, z2, z3)) → c
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F211_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F169_IN(z0, tree(z1, z2, z3)) → c
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F476_IN(z0, z1, z2) → c
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F602_IN(z0, z1, z2) → c
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F123_IN(z0, z1) → c192
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F123_IN(z0, z1) → c192
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F422_IN(z0, tree(z1, z2, z3)) → c
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → U1(f25_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U2(f23_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U3(f113_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f114_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f154_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U7(f168_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U8(f167_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U9(f264_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U10(f265_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U11(f311_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U12(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U13(f326_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U14(f325_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U15(f470_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U16(f471_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U17(f531_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U18(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U19(f543_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U20(f542_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U21(f599_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U22(f600_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U23(f700_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U24(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f25_out1, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out3, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out4, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out1, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out3, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out4, z0, tree(z1, z2, z3)) → f2_out1
U3(f113_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U4(f114_out1, z0, tree(z1, z2, z3)) → f2_out1
U4(f114_out3, z0, tree(z1, z2, z3)) → f2_out1
U5(f154_out1, s(z0), tree(0, z1, z2)) → f2_out1
U5(f154_out2, s(z0), tree(0, z1, z2)) → f2_out1
U6(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U7(f168_out1, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out3, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out4, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out1, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out3, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out4, z0, tree(z1, z2, z3)) → f2_out1
U9(f264_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U10(f265_out1, z0, tree(z1, z2, z3)) → f2_out1
U10(f265_out3, z0, tree(z1, z2, z3)) → f2_out1
U11(f311_out1, s(z0), tree(0, z1, z2)) → f2_out1
U11(f311_out2, s(z0), tree(0, z1, z2)) → f2_out1
U12(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U13(f326_out1, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out3, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out4, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out3, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out4, z0, tree(z1, z2, z3)) → f2_out1
U15(f470_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U16(f471_out1, z0, tree(z1, z2, z3)) → f2_out1
U16(f471_out3, z0, tree(z1, z2, z3)) → f2_out1
U17(f531_out1, s(z0), tree(0, z1, z2)) → f2_out1
U17(f531_out2, s(z0), tree(0, z1, z2)) → f2_out1
U18(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U19(f543_out1, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out3, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out4, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out1, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out3, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out4, z0, tree(z1, z2, z3)) → f2_out1
U21(f599_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U22(f600_out1, z0, tree(z1, z2, z3)) → f2_out1
U22(f600_out3, z0, tree(z1, z2, z3)) → f2_out1
U23(f700_out1, s(z0), tree(0, z1, z2)) → f2_out1
U23(f700_out2, s(z0), tree(0, z1, z2)) → f2_out1
U24(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f33_in(z0, z1) → f33_out1
f33_in(z0, tree(z1, z2, z3)) → U25(f33_in(z0, z2), z0, tree(z1, z2, z3))
f33_in(z0, tree(z1, z2, z3)) → U26(f33_in(z0, z2), z0, tree(z1, z2, z3))
U25(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
U26(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
f63_in(0, s(z0)) → f63_out1
f63_in(s(z0), s(z1)) → U27(f63_in(z0, z1), s(z0), s(z1))
U27(f63_out1, s(z0), s(z1)) → f63_out1
f585_in(z0, tree(z1, z2, z3)) → U28(f33_in(z0, z2), z0, tree(z1, z2, z3))
U28(f33_out1, z0, tree(z1, z2, z3)) → f585_out1
f586_in(z0, z1, z2, z3) → U29(f589_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f589_out1, z0, z1, z2, z3) → f586_out2
U29(f589_out2, z0, z1, z2, z3) → f586_out3
f211_in(z0, tree(z1, z2, z3)) → U30(f33_in(z0, z2), z0, tree(z1, z2, z3))
U30(f33_out1, z0, tree(z1, z2, z3)) → f211_out1
f212_in(z0, z1, z2, z3) → U31(f215_in(z0, z1, z2, z3), z0, z1, z2, z3)
U31(f215_out1, z0, z1, z2, z3) → f212_out2
U31(f215_out2, z0, z1, z2, z3) → f212_out3
f422_in(z0, tree(z1, z2, z3)) → U32(f33_in(z0, z2), z0, tree(z1, z2, z3))
U32(f33_out1, z0, tree(z1, z2, z3)) → f422_out1
f424_in(z0, z1, z2, z3) → U33(f460_in(z0, z1, z2, z3), z0, z1, z2, z3)
U33(f460_out1, z0, z1, z2, z3) → f424_out2
U33(f460_out2, z0, z1, z2, z3) → f424_out3
f574_in(z0, tree(z1, z2, z3)) → U34(f33_in(z0, z2), z0, tree(z1, z2, z3))
U34(f33_out1, z0, tree(z1, z2, z3)) → f574_out1
f575_in(z0, z1, z2, z3) → U35(f578_in(z0, z1, z2, z3), z0, z1, z2, z3)
U35(f578_out1, z0, z1, z2, z3) → f575_out2
U35(f578_out2, z0, z1, z2, z3) → f575_out3
f602_in(z0, z1, z2) → U36(f123_in(z0, z2), z0, z1, z2)
U36(f123_out1, z0, z1, z2) → f602_out3
f607_in(s(z0), s(z1), z2) → U37(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U37(f138_out1, s(z0), s(z1), z2) → f607_out1
f608_in(z0, z1, z2, z3) → U38(f78_in(z1, z0, z3), z0, z1, z2, z3)
U38(f78_out1, z0, z1, z2, z3) → f608_out2
f86_in(z0, tree(z1, z2, z3)) → U39(f33_in(z0, z2), z0, tree(z1, z2, z3))
U39(f33_out1, z0, tree(z1, z2, z3)) → f86_out1
f87_in(z0, z1, z2, z3) → U40(f92_in(z0, z1, z2, z3), z0, z1, z2, z3)
U40(f92_out1, z0, z1, z2, z3) → f87_out2
U40(f92_out2, z0, z1, z2, z3) → f87_out3
f169_in(z0, tree(z1, z2, z3)) → U41(f33_in(z0, z2), z0, tree(z1, z2, z3))
U41(f33_out1, z0, tree(z1, z2, z3)) → f169_out1
f170_in(z0, z1, z2, z3) → U42(f173_in(z0, z1, z2, z3), z0, z1, z2, z3)
U42(f173_out1, z0, z1, z2, z3) → f170_out2
U42(f173_out2, z0, z1, z2, z3) → f170_out3
f267_in(z0, z1, z2) → U43(f123_in(z0, z2), z0, z1, z2)
U43(f123_out1, z0, z1, z2) → f267_out3
f301_in(s(z0), s(z1), z2) → U44(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U44(f138_out1, s(z0), s(z1), z2) → f301_out1
f302_in(z0, z1, z2, z3) → U45(f78_in(z1, z0, z3), z0, z1, z2, z3)
U45(f78_out1, z0, z1, z2, z3) → f302_out2
f327_in(z0, tree(z1, z2, z3)) → U46(f33_in(z0, z2), z0, tree(z1, z2, z3))
U46(f33_out1, z0, tree(z1, z2, z3)) → f327_out1
f328_in(z0, z1, z2, z3) → U47(f414_in(z0, z1, z2, z3), z0, z1, z2, z3)
U47(f414_out1, z0, z1, z2, z3) → f328_out2
U47(f414_out2, z0, z1, z2, z3) → f328_out3
f476_in(z0, z1, z2) → U48(f123_in(z0, z2), z0, z1, z2)
U48(f123_out1, z0, z1, z2) → f476_out3
f521_in(s(z0), s(z1), z2) → U49(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U49(f138_out1, s(z0), s(z1), z2) → f521_out1
f522_in(z0, z1, z2, z3) → U50(f78_in(z1, z0, z3), z0, z1, z2, z3)
U50(f78_out1, z0, z1, z2, z3) → f522_out2
f590_in(z0, z1, z2, z3) → U51(f61_in(z0, z1, z2), z0, z1, z2, z3)
U51(f61_out1, z0, z1, z2, z3) → f590_out1
f591_in(z0, z1, z2, z3) → U52(f78_in(z1, z0, z3), z0, z1, z2, z3)
U52(f78_out1, z0, z1, z2, z3) → f591_out1
f27_in(z0, tree(z1, z2, z3)) → U53(f33_in(z0, z2), z0, tree(z1, z2, z3))
U53(f33_out1, z0, tree(z1, z2, z3)) → f27_out1
f28_in(z0, z1, z2, z3) → U54(f49_in(z0, z1, z2, z3), z0, z1, z2, z3)
U54(f49_out1, z0, z1, z2, z3) → f28_out2
U54(f49_out2, z0, z1, z2, z3) → f28_out3
f118_in(z0, z1, z2) → U55(f123_in(z0, z2), z0, z1, z2)
U55(f123_out1, z0, z1, z2) → f118_out3
f134_in(s(z0), s(z1), z2) → U56(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U56(f138_out1, s(z0), s(z1), z2) → f134_out1
f135_in(z0, z1, z2, z3) → U57(f78_in(z1, z0, z3), z0, z1, z2, z3)
U57(f78_out1, z0, z1, z2, z3) → f135_out2
f216_in(z0, z1, z2, z3) → U58(f61_in(z0, z1, z2), z0, z1, z2, z3)
U58(f61_out1, z0, z1, z2, z3) → f216_out1
f217_in(z0, z1, z2, z3) → U59(f78_in(z1, z0, z3), z0, z1, z2, z3)
U59(f78_out1, z0, z1, z2, z3) → f217_out1
f461_in(z0, z1, z2, z3) → U60(f61_in(z0, z1, z2), z0, z1, z2, z3)
U60(f61_out1, z0, z1, z2, z3) → f461_out1
f462_in(z0, z1, z2, z3) → U61(f78_in(z1, z0, z3), z0, z1, z2, z3)
U61(f78_out1, z0, z1, z2, z3) → f462_out1
f579_in(z0, z1, z2, z3) → U62(f61_in(z0, z1, z2), z0, z1, z2, z3)
U62(f61_out1, z0, z1, z2, z3) → f579_out1
f580_in(z0, z1, z2, z3) → U63(f78_in(z1, z0, z3), z0, z1, z2, z3)
U63(f78_out1, z0, z1, z2, z3) → f580_out1
f95_in(z0, z1, z2, z3) → U64(f61_in(z0, z1, z2), z0, z1, z2, z3)
U64(f61_out1, z0, z1, z2, z3) → f95_out1
f96_in(z0, z1, z2, z3) → U65(f78_in(z1, z0, z3), z0, z1, z2, z3)
U65(f78_out1, z0, z1, z2, z3) → f96_out1
f174_in(z0, z1, z2, z3) → U66(f61_in(z0, z1, z2), z0, z1, z2, z3)
U66(f61_out1, z0, z1, z2, z3) → f174_out1
f175_in(z0, z1, z2, z3) → U67(f78_in(z1, z0, z3), z0, z1, z2, z3)
U67(f78_out1, z0, z1, z2, z3) → f175_out1
f415_in(z0, z1, z2, z3) → U68(f61_in(z0, z1, z2), z0, z1, z2, z3)
U68(f61_out1, z0, z1, z2, z3) → f415_out1
f416_in(z0, z1, z2, z3) → U69(f78_in(z1, z0, z3), z0, z1, z2, z3)
U69(f78_out1, z0, z1, z2, z3) → f416_out1
f52_in(z0, z1, z2, z3) → U70(f61_in(z0, z1, z2), z0, z1, z2, z3)
U70(f61_out1, z0, z1, z2, z3) → f52_out1
f53_in(z0, z1, z2, z3) → U71(f78_in(z1, z0, z3), z0, z1, z2, z3)
U71(f78_out1, z0, z1, z2, z3) → f53_out1
f61_in(z0, z1, z2) → U72(f63_in(z0, z1), z0, z1, z2)
U72(f63_out1, z0, z1, z2) → U73(f2_in(z0, z2), z0, z1, z2)
U73(f2_out1, z0, z1, z2) → f61_out1
f78_in(z0, z1, z2) → U74(f63_in(z0, z1), z0, z1, z2)
U74(f63_out1, z0, z1, z2) → U75(f2_in(z1, z2), z0, z1, z2)
U75(f2_out1, z0, z1, z2) → f78_out1
f123_in(z0, z1) → U76(f127_in(z0), z0, z1)
U76(f127_out1, z0, z1) → U77(f2_in(0, z1), z0, z1)
U77(f2_out1, z0, z1) → f123_out1
f138_in(z0, z1, z2) → U78(f63_in(z0, z1), z0, z1, z2)
U78(f63_out1, z0, z1, z2) → U79(f2_in(s(z0), z2), z0, z1, z2)
U79(f2_out1, z0, z1, z2) → f138_out1
f159_in(z0, z1, z2) → U80(f63_in(z0, z1), z0, z1, z2)
U80(f63_out1, z0, z1, z2) → U81(f2_in(s(z1), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f159_out1
f23_in(z0, z1, z2, z3) → U82(f86_in(z0, z1), f87_in(z2, z0, z3, z1), z0, z1, z2, z3)
U82(f86_out1, z0, z1, z2, z3, z4) → f23_out1
U82(z0, f87_out2, z1, z2, z3, z4) → f23_out3
U82(z0, f87_out3, z1, z2, z3, z4) → f23_out4
f25_in(z0, z1, z2, z3) → U83(f27_in(z0, z1), f28_in(z2, z0, z3, z1), z0, z1, z2, z3)
U83(f27_out1, z0, z1, z2, z3, z4) → f25_out1
U83(z0, f28_out2, z1, z2, z3, z4) → f25_out3
U83(z0, f28_out3, z1, z2, z3, z4) → f25_out4
f49_in(z0, z1, z2, z3) → U84(f52_in(z0, z1, z2, z3), f53_in(z0, z1, z2, z3), z0, z1, z2, z3)
U84(f52_out1, z0, z1, z2, z3, z4) → f49_out1
U84(z0, f53_out1, z1, z2, z3, z4) → f49_out2
f92_in(z0, z1, z2, z3) → U85(f95_in(z0, z1, z2, z3), f96_in(z0, z1, z2, z3), z0, z1, z2, z3)
U85(f95_out1, z0, z1, z2, z3, z4) → f92_out1
U85(z0, f96_out1, z1, z2, z3, z4) → f92_out2
f113_in(z0, z1, z2) → U86(f2_in(0, z0), f118_in(z1, z0, z2), z0, z1, z2)
U86(f2_out1, z0, z1, z2, z3) → f113_out1
U86(z0, f118_out1, z1, z2, z3) → f113_out2
U86(z0, f118_out3, z1, z2, z3) → f113_out4
f114_in(z0, z1, z2, z3) → U87(f134_in(z0, z1, z2), f135_in(z0, z1, z2, z3), z0, z1, z2, z3)
U87(f134_out1, z0, z1, z2, z3, z4) → f114_out1
U87(z0, f135_out2, z1, z2, z3, z4) → f114_out3
f154_in(z0, z1) → U88(f2_in(s(z0), z1), f157_in(z0, z1), z0, z1)
U88(f2_out1, z0, z1, z2) → f154_out1
U88(z0, f157_out1, z1, z2) → f154_out2
f167_in(z0, z1, z2, z3) → U89(f211_in(z0, z1), f212_in(z2, z0, z3, z1), z0, z1, z2, z3)
U89(f211_out1, z0, z1, z2, z3, z4) → f167_out1
U89(z0, f212_out2, z1, z2, z3, z4) → f167_out3
U89(z0, f212_out3, z1, z2, z3, z4) → f167_out4
f168_in(z0, z1, z2, z3) → U90(f169_in(z0, z1), f170_in(z2, z0, z3, z1), z0, z1, z2, z3)
U90(f169_out1, z0, z1, z2, z3, z4) → f168_out1
U90(z0, f170_out2, z1, z2, z3, z4) → f168_out3
U90(z0, f170_out3, z1, z2, z3, z4) → f168_out4
f173_in(z0, z1, z2, z3) → U91(f174_in(z0, z1, z2, z3), f175_in(z0, z1, z2, z3), z0, z1, z2, z3)
U91(f174_out1, z0, z1, z2, z3, z4) → f173_out1
U91(z0, f175_out1, z1, z2, z3, z4) → f173_out2
f215_in(z0, z1, z2, z3) → U92(f216_in(z0, z1, z2, z3), f217_in(z0, z1, z2, z3), z0, z1, z2, z3)
U92(f216_out1, z0, z1, z2, z3, z4) → f215_out1
U92(z0, f217_out1, z1, z2, z3, z4) → f215_out2
f264_in(z0, z1, z2) → U93(f2_in(0, z0), f267_in(z1, z0, z2), z0, z1, z2)
U93(f2_out1, z0, z1, z2, z3) → f264_out1
U93(z0, f267_out1, z1, z2, z3) → f264_out2
U93(z0, f267_out3, z1, z2, z3) → f264_out4
f265_in(z0, z1, z2, z3) → U94(f301_in(z0, z1, z2), f302_in(z0, z1, z2, z3), z0, z1, z2, z3)
U94(f301_out1, z0, z1, z2, z3, z4) → f265_out1
U94(z0, f302_out2, z1, z2, z3, z4) → f265_out3
f311_in(z0, z1) → U95(f2_in(s(z0), z1), f314_in(z0, z1), z0, z1)
U95(f2_out1, z0, z1, z2) → f311_out1
U95(z0, f314_out1, z1, z2) → f311_out2
f325_in(z0, z1, z2, z3) → U96(f422_in(z0, z1), f424_in(z2, z0, z3, z1), z0, z1, z2, z3)
U96(f422_out1, z0, z1, z2, z3, z4) → f325_out1
U96(z0, f424_out2, z1, z2, z3, z4) → f325_out3
U96(z0, f424_out3, z1, z2, z3, z4) → f325_out4
f326_in(z0, z1, z2, z3) → U97(f327_in(z0, z1), f328_in(z2, z0, z3, z1), z0, z1, z2, z3)
U97(f327_out1, z0, z1, z2, z3, z4) → f326_out1
U97(z0, f328_out2, z1, z2, z3, z4) → f326_out3
U97(z0, f328_out3, z1, z2, z3, z4) → f326_out4
f414_in(z0, z1, z2, z3) → U98(f415_in(z0, z1, z2, z3), f416_in(z0, z1, z2, z3), z0, z1, z2, z3)
U98(f415_out1, z0, z1, z2, z3, z4) → f414_out1
U98(z0, f416_out1, z1, z2, z3, z4) → f414_out2
f460_in(z0, z1, z2, z3) → U99(f461_in(z0, z1, z2, z3), f462_in(z0, z1, z2, z3), z0, z1, z2, z3)
U99(f461_out1, z0, z1, z2, z3, z4) → f460_out1
U99(z0, f462_out1, z1, z2, z3, z4) → f460_out2
f470_in(z0, z1, z2) → U100(f2_in(0, z0), f476_in(z1, z0, z2), z0, z1, z2)
U100(f2_out1, z0, z1, z2, z3) → f470_out1
U100(z0, f476_out1, z1, z2, z3) → f470_out2
U100(z0, f476_out3, z1, z2, z3) → f470_out4
f471_in(z0, z1, z2, z3) → U101(f521_in(z0, z1, z2), f522_in(z0, z1, z2, z3), z0, z1, z2, z3)
U101(f521_out1, z0, z1, z2, z3, z4) → f471_out1
U101(z0, f522_out2, z1, z2, z3, z4) → f471_out3
f531_in(z0, z1) → U102(f2_in(s(z0), z1), f534_in(z0, z1), z0, z1)
U102(f2_out1, z0, z1, z2) → f531_out1
U102(z0, f534_out1, z1, z2) → f531_out2
f542_in(z0, z1, z2, z3) → U103(f585_in(z0, z1), f586_in(z2, z0, z3, z1), z0, z1, z2, z3)
U103(f585_out1, z0, z1, z2, z3, z4) → f542_out1
U103(z0, f586_out2, z1, z2, z3, z4) → f542_out3
U103(z0, f586_out3, z1, z2, z3, z4) → f542_out4
f543_in(z0, z1, z2, z3) → U104(f574_in(z0, z1), f575_in(z2, z0, z3, z1), z0, z1, z2, z3)
U104(f574_out1, z0, z1, z2, z3, z4) → f543_out1
U104(z0, f575_out2, z1, z2, z3, z4) → f543_out3
U104(z0, f575_out3, z1, z2, z3, z4) → f543_out4
f578_in(z0, z1, z2, z3) → U105(f579_in(z0, z1, z2, z3), f580_in(z0, z1, z2, z3), z0, z1, z2, z3)
U105(f579_out1, z0, z1, z2, z3, z4) → f578_out1
U105(z0, f580_out1, z1, z2, z3, z4) → f578_out2
f589_in(z0, z1, z2, z3) → U106(f590_in(z0, z1, z2, z3), f591_in(z0, z1, z2, z3), z0, z1, z2, z3)
U106(f590_out1, z0, z1, z2, z3, z4) → f589_out1
U106(z0, f591_out1, z1, z2, z3, z4) → f589_out2
f599_in(z0, z1, z2) → U107(f2_in(0, z0), f602_in(z1, z0, z2), z0, z1, z2)
U107(f2_out1, z0, z1, z2, z3) → f599_out1
U107(z0, f602_out1, z1, z2, z3) → f599_out2
U107(z0, f602_out3, z1, z2, z3) → f599_out4
f600_in(z0, z1, z2, z3) → U108(f607_in(z0, z1, z2), f608_in(z0, z1, z2, z3), z0, z1, z2, z3)
U108(f607_out1, z0, z1, z2, z3, z4) → f600_out1
U108(z0, f608_out2, z1, z2, z3, z4) → f600_out3
f700_in(z0, z1) → U109(f2_in(s(z0), z1), f703_in(z0, z1), z0, z1)
U109(f2_out1, z0, z1, z2) → f700_out1
U109(z0, f703_out1, z1, z2) → f700_out2

Tuples:

F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F123_IN(z0, z1) → c192
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c
F211_IN(z0, tree(z1, z2, z3)) → c
F422_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F602_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c
U76'(f127_out1, z0, z1) → c

S tuples:

F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))

K tuples:

U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
U76'(f127_out1, z0, z1) → c
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c
F211_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F602_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F123_IN(z0, z1) → c192
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F422_IN(z0, tree(z1, z2, z3)) → c

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, U17, U18, U19, U20, U21, U22, U23, U24, f33_in, U25, U26, f63_in, U27, f585_in, U28, f586_in, U29, f211_in, U30, f212_in, U31, f422_in, U32, f424_in, U33, f574_in, U34, f575_in, U35, f602_in, U36, f607_in, U37, f608_in, U38, f86_in, U39, f87_in, U40, f169_in, U41, f170_in, U42, f267_in, U43, f301_in, U44, f302_in, U45, f327_in, U46, f328_in, U47, f476_in, U48, f521_in, U49, f522_in, U50, f590_in, U51, f591_in, U52, f27_in, U53, f28_in, U54, f118_in, U55, f134_in, U56, f135_in, U57, f216_in, U58, f217_in, U59, f461_in, U60, f462_in, U61, f579_in, U62, f580_in, U63, f95_in, U64, f96_in, U65, f174_in, U66, f175_in, U67, f415_in, U68, f416_in, U69, f52_in, U70, f53_in, U71, f61_in, U72, U73, f78_in, U74, U75, f123_in, U76, U77, f138_in, U78, U79, f159_in, U80, U81, f23_in, U82, f25_in, U83, f49_in, U84, f92_in, U85, f113_in, U86, f114_in, U87, f154_in, U88, f167_in, U89, f168_in, U90, f173_in, U91, f215_in, U92, f264_in, U93, f265_in, U94, f311_in, U95, f325_in, U96, f326_in, U97, f414_in, U98, f460_in, U99, f470_in, U100, f471_in, U101, f531_in, U102, f542_in, U103, f543_in, U104, f578_in, U105, f589_in, U106, f599_in, U107, f600_in, U108, f700_in, U109

Defined Pair Symbols:

F61_IN, F78_IN, F138_IN, F159_IN, F585_IN, F211_IN, F422_IN, F574_IN, F602_IN, F86_IN, F169_IN, F267_IN, F327_IN, F476_IN, F27_IN, F118_IN, U76', F2_IN, F33_IN, F63_IN, F586_IN, F212_IN, F424_IN, F575_IN, F607_IN, F608_IN, F87_IN, F170_IN, F301_IN, F302_IN, F328_IN, F521_IN, F522_IN, F590_IN, F591_IN, F28_IN, F134_IN, F135_IN, F216_IN, F217_IN, F461_IN, F462_IN, F579_IN, F580_IN, F95_IN, F96_IN, F174_IN, F175_IN, F415_IN, F416_IN, F52_IN, F53_IN, U72', U74', F123_IN, U78', U80', F23_IN, F25_IN, F49_IN, F92_IN, F113_IN, F114_IN, F154_IN, F167_IN, F168_IN, F173_IN, F215_IN, F264_IN, F265_IN, F311_IN, F325_IN, F326_IN, F414_IN, F460_IN, F470_IN, F471_IN, F531_IN, F542_IN, F543_IN, F578_IN, F589_IN, F599_IN, F600_IN, F700_IN

Compound Symbols:

c186, c189, c195, c198, c, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c83, c84, c88, c92, c97, c102, c107, c112, c114, c118, c123, c128, c130, c134, c139, c141, c143, c145, c149, c154, c156, c158, c160, c162, c164, c166, c168, c170, c172, c174, c176, c178, c180, c182, c184, c187, c190, c192, c196, c199, c201, c205, c209, c212, c215, c219, c222, c225, c229, c233, c236, c239, c243, c246, c249, c253, c257, c260, c263, c267, c270, c273, c277, c281, c284, c287, c291, c294, c

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

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

F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))

We considered the (Usable) Rules:

f63_in(0, s(z0)) → f63_out1
f63_in(s(z0), s(z1)) → U27(f63_in(z0, z1), s(z0), s(z1))
U27(f63_out1, s(z0), s(z1)) → f63_out1

And the Tuples:

F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F123_IN(z0, z1) → c192
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c
F211_IN(z0, tree(z1, z2, z3)) → c
F422_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F602_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c
U76'(f127_out1, z0, z1) → c

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

POL(0) = 0   
POL(F113_IN(x₁, x₂, x₃)) = x₃ + x₁²   
POL(F114_IN(x₁, x₂, x₃, x₄)) = x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F118_IN(x₁, x₂, x₃)) = 0   
POL(F123_IN(x₁, x₂)) = 0   
POL(F134_IN(x₁, x₂, x₃)) = x₃² + x₁·x₃   
POL(F135_IN(x₁, x₂, x₃, x₄)) = x₄² + x₁·x₄   
POL(F138_IN(x₁, x₂, x₃)) = x₃ + x₃² + x₁·x₃   
POL(F154_IN(x₁, x₂)) = x₂ + x₂² + x₁·x₂   
POL(F159_IN(x₁, x₂, x₃)) = x₂ + x₃ + x₃² + x₂·x₃   
POL(F167_IN(x₁, x₂, x₃, x₄)) = [1] + x₂ + x₃ + x₄² + x₃·x₄ + x₂·x₃ + x₂²   
POL(F168_IN(x₁, x₂, x₃, x₄)) = [1] + x₂ + x₃ + x₄² + x₃·x₄ + x₂·x₄ + x₂·x₃ + x₂²   
POL(F169_IN(x₁, x₂)) = x₂   
POL(F170_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F173_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F174_IN(x₁, x₂, x₃, x₄)) = x₁ + x₁·x₃ + x₃²   
POL(F175_IN(x₁, x₂, x₃, x₄)) = x₄² + x₁·x₄   
POL(F211_IN(x₁, x₂)) = x₂   
POL(F212_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F215_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F216_IN(x₁, x₂, x₃, x₄)) = x₁ + x₁·x₃ + x₃²   
POL(F217_IN(x₁, x₂, x₃, x₄)) = x₄² + x₁·x₄   
POL(F23_IN(x₁, x₂, x₃, x₄)) = [1] + x₂ + x₃ + x₄² + x₃·x₄ + x₂·x₃ + x₂²   
POL(F25_IN(x₁, x₂, x₃, x₄)) = [1] + x₂ + x₃ + x₄² + x₃·x₄ + x₂·x₃ + x₂²   
POL(F264_IN(x₁, x₂, x₃)) = [1] + x₃ + x₁²   
POL(F265_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₃·x₄ + x₁·x₄ + x₁·x₃ + x₃²   
POL(F267_IN(x₁, x₂, x₃)) = x₃   
POL(F27_IN(x₁, x₂)) = x₂   
POL(F28_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F2_IN(x₁, x₂)) = x₂² + x₁·x₂   
POL(F301_IN(x₁, x₂, x₃)) = x₃² + x₁·x₃   
POL(F302_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₃·x₄ + x₁·x₄   
POL(F311_IN(x₁, x₂)) = x₂ + x₂² + x₁·x₂   
POL(F325_IN(x₁, x₂, x₃, x₄)) = [1] + x₂ + x₃ + x₄ + x₄² + x₃·x₄ + x₂·x₄ + x₂·x₃ + x₂²   
POL(F326_IN(x₁, x₂, x₃, x₄)) = [1] + x₂ + x₃ + x₄² + x₃·x₄ + x₂·x₄ + x₂·x₃ + x₂²   
POL(F327_IN(x₁, x₂)) = x₂   
POL(F328_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F33_IN(x₁, x₂)) = x₂   
POL(F414_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F415_IN(x₁, x₂, x₃, x₄)) = x₁ + x₁·x₃ + x₃²   
POL(F416_IN(x₁, x₂, x₃, x₄)) = x₄² + x₁·x₄   
POL(F422_IN(x₁, x₂)) = x₂   
POL(F424_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F460_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F461_IN(x₁, x₂, x₃, x₄)) = x₁ + x₁·x₃ + x₃²   
POL(F462_IN(x₁, x₂, x₃, x₄)) = x₄² + x₁·x₄   
POL(F470_IN(x₁, x₂, x₃)) = [1] + x₁·x₃ + x₁²   
POL(F471_IN(x₁, x₂, x₃, x₄)) = x₄² + x₃·x₄ + x₁·x₄ + x₁·x₃ + x₃²   
POL(F476_IN(x₁, x₂, x₃)) = x₂·x₃   
POL(F49_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F521_IN(x₁, x₂, x₃)) = x₃² + x₁·x₃   
POL(F522_IN(x₁, x₂, x₃, x₄)) = x₄² + x₃·x₄ + x₁·x₄   
POL(F52_IN(x₁, x₂, x₃, x₄)) = x₁ + x₁·x₃ + x₃²   
POL(F531_IN(x₁, x₂)) = [1] + x₂ + x₂² + x₁·x₂   
POL(F53_IN(x₁, x₂, x₃, x₄)) = x₄² + x₁·x₄   
POL(F542_IN(x₁, x₂, x₃, x₄)) = [1] + x₂ + x₃ + x₄² + x₃·x₄ + x₂·x₄ + x₂·x₃ + x₂²   
POL(F543_IN(x₁, x₂, x₃, x₄)) = [1] + x₂ + x₃ + x₄² + x₃·x₄ + x₂·x₄ + x₂·x₃ + x₂²   
POL(F574_IN(x₁, x₂)) = x₂   
POL(F575_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F578_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F579_IN(x₁, x₂, x₃, x₄)) = x₁ + x₁·x₃ + x₃²   
POL(F580_IN(x₁, x₂, x₃, x₄)) = x₄² + x₁·x₄   
POL(F585_IN(x₁, x₂)) = x₂   
POL(F586_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F589_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F590_IN(x₁, x₂, x₃, x₄)) = x₁ + x₁·x₃ + x₃²   
POL(F591_IN(x₁, x₂, x₃, x₄)) = x₄² + x₁·x₄   
POL(F599_IN(x₁, x₂, x₃)) = [1] + x₃ + x₁·x₃ + x₁²   
POL(F600_IN(x₁, x₂, x₃, x₄)) = x₄² + x₃·x₄ + x₁·x₄ + x₁·x₃ + x₃²   
POL(F602_IN(x₁, x₂, x₃)) = x₂·x₃   
POL(F607_IN(x₁, x₂, x₃)) = x₃² + x₁·x₃   
POL(F608_IN(x₁, x₂, x₃, x₄)) = x₄² + x₃·x₄ + x₁·x₄   
POL(F61_IN(x₁, x₂, x₃)) = x₁ + x₃² + x₁·x₃   
POL(F63_IN(x₁, x₂)) = 0   
POL(F700_IN(x₁, x₂)) = x₂ + x₂² + x₁·x₂   
POL(F78_IN(x₁, x₂, x₃)) = x₃² + x₂·x₃   
POL(F86_IN(x₁, x₂)) = x₂   
POL(F87_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F92_IN(x₁, x₂, x₃, x₄)) = x₁ + x₄² + x₁·x₄ + x₁·x₃ + x₃²   
POL(F95_IN(x₁, x₂, x₃, x₄)) = x₁ + x₁·x₃ + x₃²   
POL(F96_IN(x₁, x₂, x₃, x₄)) = x₄² + x₁·x₄   
POL(U27(x₁, x₂, x₃)) = 0   
POL(U72'(x₁, x₂, x₃, x₄)) = x₂ + x₄² + x₂·x₄   
POL(U74'(x₁, x₂, x₃, x₄)) = x₄² + x₃·x₄   
POL(U76'(x₁, x₂, x₃)) = [1] + x₁ + x₃ + x₃² + x₁·x₃ + x₁²   
POL(U78'(x₁, x₂, x₃, x₄)) = x₄ + x₄² + x₂·x₄   
POL(U80'(x₁, x₂, x₃, x₄)) = x₃ + x₄ + x₄² + x₃·x₄   
POL(c) = 0   
POL(c(x₁)) = x₁   
POL(c10(x₁)) = x₁   
POL(c102(x₁)) = x₁   
POL(c107(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c112(x₁)) = x₁   
POL(c114(x₁)) = x₁   
POL(c118(x₁)) = x₁   
POL(c12(x₁)) = x₁   
POL(c123(x₁)) = x₁   
POL(c128(x₁)) = x₁   
POL(c13(x₁)) = x₁   
POL(c130(x₁)) = x₁   
POL(c134(x₁)) = x₁   
POL(c139(x₁)) = x₁   
POL(c14(x₁)) = x₁   
POL(c141(x₁)) = x₁   
POL(c143(x₁)) = x₁   
POL(c145(x₁)) = x₁   
POL(c149(x₁)) = x₁   
POL(c15(x₁)) = x₁   
POL(c154(x₁)) = x₁   
POL(c156(x₁)) = x₁   
POL(c158(x₁)) = x₁   
POL(c16(x₁)) = x₁   
POL(c160(x₁)) = x₁   
POL(c162(x₁)) = x₁   
POL(c164(x₁)) = x₁   
POL(c166(x₁)) = x₁   
POL(c168(x₁)) = x₁   
POL(c17(x₁)) = x₁   
POL(c170(x₁)) = x₁   
POL(c172(x₁)) = x₁   
POL(c174(x₁)) = x₁   
POL(c176(x₁)) = x₁   
POL(c178(x₁)) = x₁   
POL(c18(x₁)) = x₁   
POL(c180(x₁)) = x₁   
POL(c182(x₁)) = x₁   
POL(c184(x₁)) = x₁   
POL(c186(x₁, x₂)) = x₁ + x₂   
POL(c187(x₁)) = x₁   
POL(c189(x₁, x₂)) = x₁ + x₂   
POL(c19(x₁)) = x₁   
POL(c190(x₁)) = x₁   
POL(c192) = 0   
POL(c195(x₁, x₂)) = x₁ + x₂   
POL(c196(x₁)) = x₁   
POL(c198(x₁, x₂)) = x₁ + x₂   
POL(c199(x₁)) = x₁   
POL(c2(x₁)) = x₁   
POL(c20(x₁)) = x₁   
POL(c201(x₁, x₂)) = x₁ + x₂   
POL(c205(x₁, x₂)) = x₁ + x₂   
POL(c209(x₁, x₂)) = x₁ + x₂   
POL(c21(x₁)) = x₁   
POL(c212(x₁, x₂)) = x₁ + x₂   
POL(c215(x₁, x₂)) = x₁ + x₂   
POL(c219(x₁, x₂)) = x₁ + x₂   
POL(c22(x₁)) = x₁   
POL(c222(x₁)) = x₁   
POL(c225(x₁, x₂)) = x₁ + x₂   
POL(c229(x₁, x₂)) = x₁ + x₂   
POL(c23(x₁)) = x₁   
POL(c233(x₁, x₂)) = x₁ + x₂   
POL(c236(x₁, x₂)) = x₁ + x₂   
POL(c239(x₁, x₂)) = x₁ + x₂   
POL(c24(x₁)) = x₁   
POL(c243(x₁, x₂)) = x₁ + x₂   
POL(c246(x₁)) = x₁   
POL(c249(x₁, x₂)) = x₁ + x₂   
POL(c25(x₁)) = x₁   
POL(c253(x₁, x₂)) = x₁ + x₂   
POL(c257(x₁, x₂)) = x₁ + x₂   
POL(c260(x₁, x₂)) = x₁ + x₂   
POL(c263(x₁, x₂)) = x₁ + x₂   
POL(c267(x₁, x₂)) = x₁ + x₂   
POL(c270(x₁)) = x₁   
POL(c273(x₁, x₂)) = x₁ + x₂   
POL(c277(x₁, x₂)) = x₁ + x₂   
POL(c281(x₁, x₂)) = x₁ + x₂   
POL(c284(x₁, x₂)) = x₁ + x₂   
POL(c287(x₁, x₂)) = x₁ + x₂   
POL(c291(x₁, x₂)) = x₁ + x₂   
POL(c294(x₁)) = x₁   
POL(c3(x₁)) = x₁   
POL(c4(x₁)) = x₁   
POL(c5(x₁)) = x₁   
POL(c6(x₁)) = x₁   
POL(c7(x₁)) = x₁   
POL(c8(x₁)) = x₁   
POL(c83(x₁)) = x₁   
POL(c84(x₁)) = x₁   
POL(c88(x₁)) = x₁   
POL(c9(x₁)) = x₁   
POL(c92(x₁)) = x₁   
POL(c97(x₁)) = x₁   
POL(f127_out1) = [1]   
POL(f63_in(x₁, x₂)) = x₁·x₂ + x₁²   
POL(f63_out1) = 0   
POL(s(x₁)) = [1] + x₁   
POL(tree(x₁, x₂, x₃)) = [1] + x₂ + x₃   

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → U1(f25_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U2(f23_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U3(f113_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f114_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f154_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U7(f168_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U8(f167_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U9(f264_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U10(f265_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U11(f311_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U12(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U13(f326_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U14(f325_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U15(f470_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U16(f471_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U17(f531_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U18(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U19(f543_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U20(f542_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U21(f599_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U22(f600_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U23(f700_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U24(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f25_out1, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out3, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out4, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out1, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out3, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out4, z0, tree(z1, z2, z3)) → f2_out1
U3(f113_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U4(f114_out1, z0, tree(z1, z2, z3)) → f2_out1
U4(f114_out3, z0, tree(z1, z2, z3)) → f2_out1
U5(f154_out1, s(z0), tree(0, z1, z2)) → f2_out1
U5(f154_out2, s(z0), tree(0, z1, z2)) → f2_out1
U6(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U7(f168_out1, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out3, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out4, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out1, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out3, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out4, z0, tree(z1, z2, z3)) → f2_out1
U9(f264_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U10(f265_out1, z0, tree(z1, z2, z3)) → f2_out1
U10(f265_out3, z0, tree(z1, z2, z3)) → f2_out1
U11(f311_out1, s(z0), tree(0, z1, z2)) → f2_out1
U11(f311_out2, s(z0), tree(0, z1, z2)) → f2_out1
U12(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U13(f326_out1, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out3, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out4, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out3, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out4, z0, tree(z1, z2, z3)) → f2_out1
U15(f470_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U16(f471_out1, z0, tree(z1, z2, z3)) → f2_out1
U16(f471_out3, z0, tree(z1, z2, z3)) → f2_out1
U17(f531_out1, s(z0), tree(0, z1, z2)) → f2_out1
U17(f531_out2, s(z0), tree(0, z1, z2)) → f2_out1
U18(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U19(f543_out1, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out3, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out4, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out1, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out3, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out4, z0, tree(z1, z2, z3)) → f2_out1
U21(f599_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U22(f600_out1, z0, tree(z1, z2, z3)) → f2_out1
U22(f600_out3, z0, tree(z1, z2, z3)) → f2_out1
U23(f700_out1, s(z0), tree(0, z1, z2)) → f2_out1
U23(f700_out2, s(z0), tree(0, z1, z2)) → f2_out1
U24(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f33_in(z0, z1) → f33_out1
f33_in(z0, tree(z1, z2, z3)) → U25(f33_in(z0, z2), z0, tree(z1, z2, z3))
f33_in(z0, tree(z1, z2, z3)) → U26(f33_in(z0, z2), z0, tree(z1, z2, z3))
U25(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
U26(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
f63_in(0, s(z0)) → f63_out1
f63_in(s(z0), s(z1)) → U27(f63_in(z0, z1), s(z0), s(z1))
U27(f63_out1, s(z0), s(z1)) → f63_out1
f585_in(z0, tree(z1, z2, z3)) → U28(f33_in(z0, z2), z0, tree(z1, z2, z3))
U28(f33_out1, z0, tree(z1, z2, z3)) → f585_out1
f586_in(z0, z1, z2, z3) → U29(f589_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f589_out1, z0, z1, z2, z3) → f586_out2
U29(f589_out2, z0, z1, z2, z3) → f586_out3
f211_in(z0, tree(z1, z2, z3)) → U30(f33_in(z0, z2), z0, tree(z1, z2, z3))
U30(f33_out1, z0, tree(z1, z2, z3)) → f211_out1
f212_in(z0, z1, z2, z3) → U31(f215_in(z0, z1, z2, z3), z0, z1, z2, z3)
U31(f215_out1, z0, z1, z2, z3) → f212_out2
U31(f215_out2, z0, z1, z2, z3) → f212_out3
f422_in(z0, tree(z1, z2, z3)) → U32(f33_in(z0, z2), z0, tree(z1, z2, z3))
U32(f33_out1, z0, tree(z1, z2, z3)) → f422_out1
f424_in(z0, z1, z2, z3) → U33(f460_in(z0, z1, z2, z3), z0, z1, z2, z3)
U33(f460_out1, z0, z1, z2, z3) → f424_out2
U33(f460_out2, z0, z1, z2, z3) → f424_out3
f574_in(z0, tree(z1, z2, z3)) → U34(f33_in(z0, z2), z0, tree(z1, z2, z3))
U34(f33_out1, z0, tree(z1, z2, z3)) → f574_out1
f575_in(z0, z1, z2, z3) → U35(f578_in(z0, z1, z2, z3), z0, z1, z2, z3)
U35(f578_out1, z0, z1, z2, z3) → f575_out2
U35(f578_out2, z0, z1, z2, z3) → f575_out3
f602_in(z0, z1, z2) → U36(f123_in(z0, z2), z0, z1, z2)
U36(f123_out1, z0, z1, z2) → f602_out3
f607_in(s(z0), s(z1), z2) → U37(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U37(f138_out1, s(z0), s(z1), z2) → f607_out1
f608_in(z0, z1, z2, z3) → U38(f78_in(z1, z0, z3), z0, z1, z2, z3)
U38(f78_out1, z0, z1, z2, z3) → f608_out2
f86_in(z0, tree(z1, z2, z3)) → U39(f33_in(z0, z2), z0, tree(z1, z2, z3))
U39(f33_out1, z0, tree(z1, z2, z3)) → f86_out1
f87_in(z0, z1, z2, z3) → U40(f92_in(z0, z1, z2, z3), z0, z1, z2, z3)
U40(f92_out1, z0, z1, z2, z3) → f87_out2
U40(f92_out2, z0, z1, z2, z3) → f87_out3
f169_in(z0, tree(z1, z2, z3)) → U41(f33_in(z0, z2), z0, tree(z1, z2, z3))
U41(f33_out1, z0, tree(z1, z2, z3)) → f169_out1
f170_in(z0, z1, z2, z3) → U42(f173_in(z0, z1, z2, z3), z0, z1, z2, z3)
U42(f173_out1, z0, z1, z2, z3) → f170_out2
U42(f173_out2, z0, z1, z2, z3) → f170_out3
f267_in(z0, z1, z2) → U43(f123_in(z0, z2), z0, z1, z2)
U43(f123_out1, z0, z1, z2) → f267_out3
f301_in(s(z0), s(z1), z2) → U44(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U44(f138_out1, s(z0), s(z1), z2) → f301_out1
f302_in(z0, z1, z2, z3) → U45(f78_in(z1, z0, z3), z0, z1, z2, z3)
U45(f78_out1, z0, z1, z2, z3) → f302_out2
f327_in(z0, tree(z1, z2, z3)) → U46(f33_in(z0, z2), z0, tree(z1, z2, z3))
U46(f33_out1, z0, tree(z1, z2, z3)) → f327_out1
f328_in(z0, z1, z2, z3) → U47(f414_in(z0, z1, z2, z3), z0, z1, z2, z3)
U47(f414_out1, z0, z1, z2, z3) → f328_out2
U47(f414_out2, z0, z1, z2, z3) → f328_out3
f476_in(z0, z1, z2) → U48(f123_in(z0, z2), z0, z1, z2)
U48(f123_out1, z0, z1, z2) → f476_out3
f521_in(s(z0), s(z1), z2) → U49(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U49(f138_out1, s(z0), s(z1), z2) → f521_out1
f522_in(z0, z1, z2, z3) → U50(f78_in(z1, z0, z3), z0, z1, z2, z3)
U50(f78_out1, z0, z1, z2, z3) → f522_out2
f590_in(z0, z1, z2, z3) → U51(f61_in(z0, z1, z2), z0, z1, z2, z3)
U51(f61_out1, z0, z1, z2, z3) → f590_out1
f591_in(z0, z1, z2, z3) → U52(f78_in(z1, z0, z3), z0, z1, z2, z3)
U52(f78_out1, z0, z1, z2, z3) → f591_out1
f27_in(z0, tree(z1, z2, z3)) → U53(f33_in(z0, z2), z0, tree(z1, z2, z3))
U53(f33_out1, z0, tree(z1, z2, z3)) → f27_out1
f28_in(z0, z1, z2, z3) → U54(f49_in(z0, z1, z2, z3), z0, z1, z2, z3)
U54(f49_out1, z0, z1, z2, z3) → f28_out2
U54(f49_out2, z0, z1, z2, z3) → f28_out3
f118_in(z0, z1, z2) → U55(f123_in(z0, z2), z0, z1, z2)
U55(f123_out1, z0, z1, z2) → f118_out3
f134_in(s(z0), s(z1), z2) → U56(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U56(f138_out1, s(z0), s(z1), z2) → f134_out1
f135_in(z0, z1, z2, z3) → U57(f78_in(z1, z0, z3), z0, z1, z2, z3)
U57(f78_out1, z0, z1, z2, z3) → f135_out2
f216_in(z0, z1, z2, z3) → U58(f61_in(z0, z1, z2), z0, z1, z2, z3)
U58(f61_out1, z0, z1, z2, z3) → f216_out1
f217_in(z0, z1, z2, z3) → U59(f78_in(z1, z0, z3), z0, z1, z2, z3)
U59(f78_out1, z0, z1, z2, z3) → f217_out1
f461_in(z0, z1, z2, z3) → U60(f61_in(z0, z1, z2), z0, z1, z2, z3)
U60(f61_out1, z0, z1, z2, z3) → f461_out1
f462_in(z0, z1, z2, z3) → U61(f78_in(z1, z0, z3), z0, z1, z2, z3)
U61(f78_out1, z0, z1, z2, z3) → f462_out1
f579_in(z0, z1, z2, z3) → U62(f61_in(z0, z1, z2), z0, z1, z2, z3)
U62(f61_out1, z0, z1, z2, z3) → f579_out1
f580_in(z0, z1, z2, z3) → U63(f78_in(z1, z0, z3), z0, z1, z2, z3)
U63(f78_out1, z0, z1, z2, z3) → f580_out1
f95_in(z0, z1, z2, z3) → U64(f61_in(z0, z1, z2), z0, z1, z2, z3)
U64(f61_out1, z0, z1, z2, z3) → f95_out1
f96_in(z0, z1, z2, z3) → U65(f78_in(z1, z0, z3), z0, z1, z2, z3)
U65(f78_out1, z0, z1, z2, z3) → f96_out1
f174_in(z0, z1, z2, z3) → U66(f61_in(z0, z1, z2), z0, z1, z2, z3)
U66(f61_out1, z0, z1, z2, z3) → f174_out1
f175_in(z0, z1, z2, z3) → U67(f78_in(z1, z0, z3), z0, z1, z2, z3)
U67(f78_out1, z0, z1, z2, z3) → f175_out1
f415_in(z0, z1, z2, z3) → U68(f61_in(z0, z1, z2), z0, z1, z2, z3)
U68(f61_out1, z0, z1, z2, z3) → f415_out1
f416_in(z0, z1, z2, z3) → U69(f78_in(z1, z0, z3), z0, z1, z2, z3)
U69(f78_out1, z0, z1, z2, z3) → f416_out1
f52_in(z0, z1, z2, z3) → U70(f61_in(z0, z1, z2), z0, z1, z2, z3)
U70(f61_out1, z0, z1, z2, z3) → f52_out1
f53_in(z0, z1, z2, z3) → U71(f78_in(z1, z0, z3), z0, z1, z2, z3)
U71(f78_out1, z0, z1, z2, z3) → f53_out1
f61_in(z0, z1, z2) → U72(f63_in(z0, z1), z0, z1, z2)
U72(f63_out1, z0, z1, z2) → U73(f2_in(z0, z2), z0, z1, z2)
U73(f2_out1, z0, z1, z2) → f61_out1
f78_in(z0, z1, z2) → U74(f63_in(z0, z1), z0, z1, z2)
U74(f63_out1, z0, z1, z2) → U75(f2_in(z1, z2), z0, z1, z2)
U75(f2_out1, z0, z1, z2) → f78_out1
f123_in(z0, z1) → U76(f127_in(z0), z0, z1)
U76(f127_out1, z0, z1) → U77(f2_in(0, z1), z0, z1)
U77(f2_out1, z0, z1) → f123_out1
f138_in(z0, z1, z2) → U78(f63_in(z0, z1), z0, z1, z2)
U78(f63_out1, z0, z1, z2) → U79(f2_in(s(z0), z2), z0, z1, z2)
U79(f2_out1, z0, z1, z2) → f138_out1
f159_in(z0, z1, z2) → U80(f63_in(z0, z1), z0, z1, z2)
U80(f63_out1, z0, z1, z2) → U81(f2_in(s(z1), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f159_out1
f23_in(z0, z1, z2, z3) → U82(f86_in(z0, z1), f87_in(z2, z0, z3, z1), z0, z1, z2, z3)
U82(f86_out1, z0, z1, z2, z3, z4) → f23_out1
U82(z0, f87_out2, z1, z2, z3, z4) → f23_out3
U82(z0, f87_out3, z1, z2, z3, z4) → f23_out4
f25_in(z0, z1, z2, z3) → U83(f27_in(z0, z1), f28_in(z2, z0, z3, z1), z0, z1, z2, z3)
U83(f27_out1, z0, z1, z2, z3, z4) → f25_out1
U83(z0, f28_out2, z1, z2, z3, z4) → f25_out3
U83(z0, f28_out3, z1, z2, z3, z4) → f25_out4
f49_in(z0, z1, z2, z3) → U84(f52_in(z0, z1, z2, z3), f53_in(z0, z1, z2, z3), z0, z1, z2, z3)
U84(f52_out1, z0, z1, z2, z3, z4) → f49_out1
U84(z0, f53_out1, z1, z2, z3, z4) → f49_out2
f92_in(z0, z1, z2, z3) → U85(f95_in(z0, z1, z2, z3), f96_in(z0, z1, z2, z3), z0, z1, z2, z3)
U85(f95_out1, z0, z1, z2, z3, z4) → f92_out1
U85(z0, f96_out1, z1, z2, z3, z4) → f92_out2
f113_in(z0, z1, z2) → U86(f2_in(0, z0), f118_in(z1, z0, z2), z0, z1, z2)
U86(f2_out1, z0, z1, z2, z3) → f113_out1
U86(z0, f118_out1, z1, z2, z3) → f113_out2
U86(z0, f118_out3, z1, z2, z3) → f113_out4
f114_in(z0, z1, z2, z3) → U87(f134_in(z0, z1, z2), f135_in(z0, z1, z2, z3), z0, z1, z2, z3)
U87(f134_out1, z0, z1, z2, z3, z4) → f114_out1
U87(z0, f135_out2, z1, z2, z3, z4) → f114_out3
f154_in(z0, z1) → U88(f2_in(s(z0), z1), f157_in(z0, z1), z0, z1)
U88(f2_out1, z0, z1, z2) → f154_out1
U88(z0, f157_out1, z1, z2) → f154_out2
f167_in(z0, z1, z2, z3) → U89(f211_in(z0, z1), f212_in(z2, z0, z3, z1), z0, z1, z2, z3)
U89(f211_out1, z0, z1, z2, z3, z4) → f167_out1
U89(z0, f212_out2, z1, z2, z3, z4) → f167_out3
U89(z0, f212_out3, z1, z2, z3, z4) → f167_out4
f168_in(z0, z1, z2, z3) → U90(f169_in(z0, z1), f170_in(z2, z0, z3, z1), z0, z1, z2, z3)
U90(f169_out1, z0, z1, z2, z3, z4) → f168_out1
U90(z0, f170_out2, z1, z2, z3, z4) → f168_out3
U90(z0, f170_out3, z1, z2, z3, z4) → f168_out4
f173_in(z0, z1, z2, z3) → U91(f174_in(z0, z1, z2, z3), f175_in(z0, z1, z2, z3), z0, z1, z2, z3)
U91(f174_out1, z0, z1, z2, z3, z4) → f173_out1
U91(z0, f175_out1, z1, z2, z3, z4) → f173_out2
f215_in(z0, z1, z2, z3) → U92(f216_in(z0, z1, z2, z3), f217_in(z0, z1, z2, z3), z0, z1, z2, z3)
U92(f216_out1, z0, z1, z2, z3, z4) → f215_out1
U92(z0, f217_out1, z1, z2, z3, z4) → f215_out2
f264_in(z0, z1, z2) → U93(f2_in(0, z0), f267_in(z1, z0, z2), z0, z1, z2)
U93(f2_out1, z0, z1, z2, z3) → f264_out1
U93(z0, f267_out1, z1, z2, z3) → f264_out2
U93(z0, f267_out3, z1, z2, z3) → f264_out4
f265_in(z0, z1, z2, z3) → U94(f301_in(z0, z1, z2), f302_in(z0, z1, z2, z3), z0, z1, z2, z3)
U94(f301_out1, z0, z1, z2, z3, z4) → f265_out1
U94(z0, f302_out2, z1, z2, z3, z4) → f265_out3
f311_in(z0, z1) → U95(f2_in(s(z0), z1), f314_in(z0, z1), z0, z1)
U95(f2_out1, z0, z1, z2) → f311_out1
U95(z0, f314_out1, z1, z2) → f311_out2
f325_in(z0, z1, z2, z3) → U96(f422_in(z0, z1), f424_in(z2, z0, z3, z1), z0, z1, z2, z3)
U96(f422_out1, z0, z1, z2, z3, z4) → f325_out1
U96(z0, f424_out2, z1, z2, z3, z4) → f325_out3
U96(z0, f424_out3, z1, z2, z3, z4) → f325_out4
f326_in(z0, z1, z2, z3) → U97(f327_in(z0, z1), f328_in(z2, z0, z3, z1), z0, z1, z2, z3)
U97(f327_out1, z0, z1, z2, z3, z4) → f326_out1
U97(z0, f328_out2, z1, z2, z3, z4) → f326_out3
U97(z0, f328_out3, z1, z2, z3, z4) → f326_out4
f414_in(z0, z1, z2, z3) → U98(f415_in(z0, z1, z2, z3), f416_in(z0, z1, z2, z3), z0, z1, z2, z3)
U98(f415_out1, z0, z1, z2, z3, z4) → f414_out1
U98(z0, f416_out1, z1, z2, z3, z4) → f414_out2
f460_in(z0, z1, z2, z3) → U99(f461_in(z0, z1, z2, z3), f462_in(z0, z1, z2, z3), z0, z1, z2, z3)
U99(f461_out1, z0, z1, z2, z3, z4) → f460_out1
U99(z0, f462_out1, z1, z2, z3, z4) → f460_out2
f470_in(z0, z1, z2) → U100(f2_in(0, z0), f476_in(z1, z0, z2), z0, z1, z2)
U100(f2_out1, z0, z1, z2, z3) → f470_out1
U100(z0, f476_out1, z1, z2, z3) → f470_out2
U100(z0, f476_out3, z1, z2, z3) → f470_out4
f471_in(z0, z1, z2, z3) → U101(f521_in(z0, z1, z2), f522_in(z0, z1, z2, z3), z0, z1, z2, z3)
U101(f521_out1, z0, z1, z2, z3, z4) → f471_out1
U101(z0, f522_out2, z1, z2, z3, z4) → f471_out3
f531_in(z0, z1) → U102(f2_in(s(z0), z1), f534_in(z0, z1), z0, z1)
U102(f2_out1, z0, z1, z2) → f531_out1
U102(z0, f534_out1, z1, z2) → f531_out2
f542_in(z0, z1, z2, z3) → U103(f585_in(z0, z1), f586_in(z2, z0, z3, z1), z0, z1, z2, z3)
U103(f585_out1, z0, z1, z2, z3, z4) → f542_out1
U103(z0, f586_out2, z1, z2, z3, z4) → f542_out3
U103(z0, f586_out3, z1, z2, z3, z4) → f542_out4
f543_in(z0, z1, z2, z3) → U104(f574_in(z0, z1), f575_in(z2, z0, z3, z1), z0, z1, z2, z3)
U104(f574_out1, z0, z1, z2, z3, z4) → f543_out1
U104(z0, f575_out2, z1, z2, z3, z4) → f543_out3
U104(z0, f575_out3, z1, z2, z3, z4) → f543_out4
f578_in(z0, z1, z2, z3) → U105(f579_in(z0, z1, z2, z3), f580_in(z0, z1, z2, z3), z0, z1, z2, z3)
U105(f579_out1, z0, z1, z2, z3, z4) → f578_out1
U105(z0, f580_out1, z1, z2, z3, z4) → f578_out2
f589_in(z0, z1, z2, z3) → U106(f590_in(z0, z1, z2, z3), f591_in(z0, z1, z2, z3), z0, z1, z2, z3)
U106(f590_out1, z0, z1, z2, z3, z4) → f589_out1
U106(z0, f591_out1, z1, z2, z3, z4) → f589_out2
f599_in(z0, z1, z2) → U107(f2_in(0, z0), f602_in(z1, z0, z2), z0, z1, z2)
U107(f2_out1, z0, z1, z2, z3) → f599_out1
U107(z0, f602_out1, z1, z2, z3) → f599_out2
U107(z0, f602_out3, z1, z2, z3) → f599_out4
f600_in(z0, z1, z2, z3) → U108(f607_in(z0, z1, z2), f608_in(z0, z1, z2, z3), z0, z1, z2, z3)
U108(f607_out1, z0, z1, z2, z3, z4) → f600_out1
U108(z0, f608_out2, z1, z2, z3, z4) → f600_out3
f700_in(z0, z1) → U109(f2_in(s(z0), z1), f703_in(z0, z1), z0, z1)
U109(f2_out1, z0, z1, z2) → f700_out1
U109(z0, f703_out1, z1, z2) → f700_out2

Tuples:

F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F123_IN(z0, z1) → c192
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c
F211_IN(z0, tree(z1, z2, z3)) → c
F422_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F602_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c
U76'(f127_out1, z0, z1) → c

S tuples:

F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))

K tuples:

U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
U76'(f127_out1, z0, z1) → c
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c
F211_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F602_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F123_IN(z0, z1) → c192
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F422_IN(z0, tree(z1, z2, z3)) → c
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, U17, U18, U19, U20, U21, U22, U23, U24, f33_in, U25, U26, f63_in, U27, f585_in, U28, f586_in, U29, f211_in, U30, f212_in, U31, f422_in, U32, f424_in, U33, f574_in, U34, f575_in, U35, f602_in, U36, f607_in, U37, f608_in, U38, f86_in, U39, f87_in, U40, f169_in, U41, f170_in, U42, f267_in, U43, f301_in, U44, f302_in, U45, f327_in, U46, f328_in, U47, f476_in, U48, f521_in, U49, f522_in, U50, f590_in, U51, f591_in, U52, f27_in, U53, f28_in, U54, f118_in, U55, f134_in, U56, f135_in, U57, f216_in, U58, f217_in, U59, f461_in, U60, f462_in, U61, f579_in, U62, f580_in, U63, f95_in, U64, f96_in, U65, f174_in, U66, f175_in, U67, f415_in, U68, f416_in, U69, f52_in, U70, f53_in, U71, f61_in, U72, U73, f78_in, U74, U75, f123_in, U76, U77, f138_in, U78, U79, f159_in, U80, U81, f23_in, U82, f25_in, U83, f49_in, U84, f92_in, U85, f113_in, U86, f114_in, U87, f154_in, U88, f167_in, U89, f168_in, U90, f173_in, U91, f215_in, U92, f264_in, U93, f265_in, U94, f311_in, U95, f325_in, U96, f326_in, U97, f414_in, U98, f460_in, U99, f470_in, U100, f471_in, U101, f531_in, U102, f542_in, U103, f543_in, U104, f578_in, U105, f589_in, U106, f599_in, U107, f600_in, U108, f700_in, U109

Defined Pair Symbols:

F61_IN, F78_IN, F138_IN, F159_IN, F585_IN, F211_IN, F422_IN, F574_IN, F602_IN, F86_IN, F169_IN, F267_IN, F327_IN, F476_IN, F27_IN, F118_IN, U76', F2_IN, F33_IN, F63_IN, F586_IN, F212_IN, F424_IN, F575_IN, F607_IN, F608_IN, F87_IN, F170_IN, F301_IN, F302_IN, F328_IN, F521_IN, F522_IN, F590_IN, F591_IN, F28_IN, F134_IN, F135_IN, F216_IN, F217_IN, F461_IN, F462_IN, F579_IN, F580_IN, F95_IN, F96_IN, F174_IN, F175_IN, F415_IN, F416_IN, F52_IN, F53_IN, U72', U74', F123_IN, U78', U80', F23_IN, F25_IN, F49_IN, F92_IN, F113_IN, F114_IN, F154_IN, F167_IN, F168_IN, F173_IN, F215_IN, F264_IN, F265_IN, F311_IN, F325_IN, F326_IN, F414_IN, F460_IN, F470_IN, F471_IN, F531_IN, F542_IN, F543_IN, F578_IN, F589_IN, F599_IN, F600_IN, F700_IN

Compound Symbols:

c186, c189, c195, c198, c, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c83, c84, c88, c92, c97, c102, c107, c112, c114, c118, c123, c128, c130, c134, c139, c141, c143, c145, c149, c154, c156, c158, c160, c162, c164, c166, c168, c170, c172, c174, c176, c178, c180, c182, c184, c187, c190, c192, c196, c199, c201, c205, c209, c212, c215, c219, c222, c225, c229, c233, c236, c239, c243, c246, c249, c253, c257, c260, c263, c267, c270, c273, c277, c281, c284, c287, c291, c294, c

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

Use narrowing to replace F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1)) by

F61_IN(0, s(z0), x2) → c186(U72'(f63_out1, 0, s(z0), x2), F63_IN(0, s(z0)))
F61_IN(s(z0), s(z1), x2) → c186(U72'(U27(f63_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F63_IN(s(z0), s(z1)))

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → U1(f25_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U2(f23_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U3(f113_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f114_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f154_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U7(f168_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U8(f167_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U9(f264_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U10(f265_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U11(f311_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U12(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U13(f326_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U14(f325_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U15(f470_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U16(f471_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U17(f531_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U18(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U19(f543_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U20(f542_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U21(f599_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U22(f600_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U23(f700_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U24(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f25_out1, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out3, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out4, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out1, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out3, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out4, z0, tree(z1, z2, z3)) → f2_out1
U3(f113_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U4(f114_out1, z0, tree(z1, z2, z3)) → f2_out1
U4(f114_out3, z0, tree(z1, z2, z3)) → f2_out1
U5(f154_out1, s(z0), tree(0, z1, z2)) → f2_out1
U5(f154_out2, s(z0), tree(0, z1, z2)) → f2_out1
U6(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U7(f168_out1, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out3, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out4, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out1, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out3, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out4, z0, tree(z1, z2, z3)) → f2_out1
U9(f264_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U10(f265_out1, z0, tree(z1, z2, z3)) → f2_out1
U10(f265_out3, z0, tree(z1, z2, z3)) → f2_out1
U11(f311_out1, s(z0), tree(0, z1, z2)) → f2_out1
U11(f311_out2, s(z0), tree(0, z1, z2)) → f2_out1
U12(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U13(f326_out1, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out3, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out4, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out3, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out4, z0, tree(z1, z2, z3)) → f2_out1
U15(f470_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U16(f471_out1, z0, tree(z1, z2, z3)) → f2_out1
U16(f471_out3, z0, tree(z1, z2, z3)) → f2_out1
U17(f531_out1, s(z0), tree(0, z1, z2)) → f2_out1
U17(f531_out2, s(z0), tree(0, z1, z2)) → f2_out1
U18(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U19(f543_out1, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out3, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out4, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out1, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out3, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out4, z0, tree(z1, z2, z3)) → f2_out1
U21(f599_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U22(f600_out1, z0, tree(z1, z2, z3)) → f2_out1
U22(f600_out3, z0, tree(z1, z2, z3)) → f2_out1
U23(f700_out1, s(z0), tree(0, z1, z2)) → f2_out1
U23(f700_out2, s(z0), tree(0, z1, z2)) → f2_out1
U24(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f33_in(z0, z1) → f33_out1
f33_in(z0, tree(z1, z2, z3)) → U25(f33_in(z0, z2), z0, tree(z1, z2, z3))
f33_in(z0, tree(z1, z2, z3)) → U26(f33_in(z0, z2), z0, tree(z1, z2, z3))
U25(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
U26(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
f63_in(0, s(z0)) → f63_out1
f63_in(s(z0), s(z1)) → U27(f63_in(z0, z1), s(z0), s(z1))
U27(f63_out1, s(z0), s(z1)) → f63_out1
f585_in(z0, tree(z1, z2, z3)) → U28(f33_in(z0, z2), z0, tree(z1, z2, z3))
U28(f33_out1, z0, tree(z1, z2, z3)) → f585_out1
f586_in(z0, z1, z2, z3) → U29(f589_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f589_out1, z0, z1, z2, z3) → f586_out2
U29(f589_out2, z0, z1, z2, z3) → f586_out3
f211_in(z0, tree(z1, z2, z3)) → U30(f33_in(z0, z2), z0, tree(z1, z2, z3))
U30(f33_out1, z0, tree(z1, z2, z3)) → f211_out1
f212_in(z0, z1, z2, z3) → U31(f215_in(z0, z1, z2, z3), z0, z1, z2, z3)
U31(f215_out1, z0, z1, z2, z3) → f212_out2
U31(f215_out2, z0, z1, z2, z3) → f212_out3
f422_in(z0, tree(z1, z2, z3)) → U32(f33_in(z0, z2), z0, tree(z1, z2, z3))
U32(f33_out1, z0, tree(z1, z2, z3)) → f422_out1
f424_in(z0, z1, z2, z3) → U33(f460_in(z0, z1, z2, z3), z0, z1, z2, z3)
U33(f460_out1, z0, z1, z2, z3) → f424_out2
U33(f460_out2, z0, z1, z2, z3) → f424_out3
f574_in(z0, tree(z1, z2, z3)) → U34(f33_in(z0, z2), z0, tree(z1, z2, z3))
U34(f33_out1, z0, tree(z1, z2, z3)) → f574_out1
f575_in(z0, z1, z2, z3) → U35(f578_in(z0, z1, z2, z3), z0, z1, z2, z3)
U35(f578_out1, z0, z1, z2, z3) → f575_out2
U35(f578_out2, z0, z1, z2, z3) → f575_out3
f602_in(z0, z1, z2) → U36(f123_in(z0, z2), z0, z1, z2)
U36(f123_out1, z0, z1, z2) → f602_out3
f607_in(s(z0), s(z1), z2) → U37(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U37(f138_out1, s(z0), s(z1), z2) → f607_out1
f608_in(z0, z1, z2, z3) → U38(f78_in(z1, z0, z3), z0, z1, z2, z3)
U38(f78_out1, z0, z1, z2, z3) → f608_out2
f86_in(z0, tree(z1, z2, z3)) → U39(f33_in(z0, z2), z0, tree(z1, z2, z3))
U39(f33_out1, z0, tree(z1, z2, z3)) → f86_out1
f87_in(z0, z1, z2, z3) → U40(f92_in(z0, z1, z2, z3), z0, z1, z2, z3)
U40(f92_out1, z0, z1, z2, z3) → f87_out2
U40(f92_out2, z0, z1, z2, z3) → f87_out3
f169_in(z0, tree(z1, z2, z3)) → U41(f33_in(z0, z2), z0, tree(z1, z2, z3))
U41(f33_out1, z0, tree(z1, z2, z3)) → f169_out1
f170_in(z0, z1, z2, z3) → U42(f173_in(z0, z1, z2, z3), z0, z1, z2, z3)
U42(f173_out1, z0, z1, z2, z3) → f170_out2
U42(f173_out2, z0, z1, z2, z3) → f170_out3
f267_in(z0, z1, z2) → U43(f123_in(z0, z2), z0, z1, z2)
U43(f123_out1, z0, z1, z2) → f267_out3
f301_in(s(z0), s(z1), z2) → U44(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U44(f138_out1, s(z0), s(z1), z2) → f301_out1
f302_in(z0, z1, z2, z3) → U45(f78_in(z1, z0, z3), z0, z1, z2, z3)
U45(f78_out1, z0, z1, z2, z3) → f302_out2
f327_in(z0, tree(z1, z2, z3)) → U46(f33_in(z0, z2), z0, tree(z1, z2, z3))
U46(f33_out1, z0, tree(z1, z2, z3)) → f327_out1
f328_in(z0, z1, z2, z3) → U47(f414_in(z0, z1, z2, z3), z0, z1, z2, z3)
U47(f414_out1, z0, z1, z2, z3) → f328_out2
U47(f414_out2, z0, z1, z2, z3) → f328_out3
f476_in(z0, z1, z2) → U48(f123_in(z0, z2), z0, z1, z2)
U48(f123_out1, z0, z1, z2) → f476_out3
f521_in(s(z0), s(z1), z2) → U49(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U49(f138_out1, s(z0), s(z1), z2) → f521_out1
f522_in(z0, z1, z2, z3) → U50(f78_in(z1, z0, z3), z0, z1, z2, z3)
U50(f78_out1, z0, z1, z2, z3) → f522_out2
f590_in(z0, z1, z2, z3) → U51(f61_in(z0, z1, z2), z0, z1, z2, z3)
U51(f61_out1, z0, z1, z2, z3) → f590_out1
f591_in(z0, z1, z2, z3) → U52(f78_in(z1, z0, z3), z0, z1, z2, z3)
U52(f78_out1, z0, z1, z2, z3) → f591_out1
f27_in(z0, tree(z1, z2, z3)) → U53(f33_in(z0, z2), z0, tree(z1, z2, z3))
U53(f33_out1, z0, tree(z1, z2, z3)) → f27_out1
f28_in(z0, z1, z2, z3) → U54(f49_in(z0, z1, z2, z3), z0, z1, z2, z3)
U54(f49_out1, z0, z1, z2, z3) → f28_out2
U54(f49_out2, z0, z1, z2, z3) → f28_out3
f118_in(z0, z1, z2) → U55(f123_in(z0, z2), z0, z1, z2)
U55(f123_out1, z0, z1, z2) → f118_out3
f134_in(s(z0), s(z1), z2) → U56(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U56(f138_out1, s(z0), s(z1), z2) → f134_out1
f135_in(z0, z1, z2, z3) → U57(f78_in(z1, z0, z3), z0, z1, z2, z3)
U57(f78_out1, z0, z1, z2, z3) → f135_out2
f216_in(z0, z1, z2, z3) → U58(f61_in(z0, z1, z2), z0, z1, z2, z3)
U58(f61_out1, z0, z1, z2, z3) → f216_out1
f217_in(z0, z1, z2, z3) → U59(f78_in(z1, z0, z3), z0, z1, z2, z3)
U59(f78_out1, z0, z1, z2, z3) → f217_out1
f461_in(z0, z1, z2, z3) → U60(f61_in(z0, z1, z2), z0, z1, z2, z3)
U60(f61_out1, z0, z1, z2, z3) → f461_out1
f462_in(z0, z1, z2, z3) → U61(f78_in(z1, z0, z3), z0, z1, z2, z3)
U61(f78_out1, z0, z1, z2, z3) → f462_out1
f579_in(z0, z1, z2, z3) → U62(f61_in(z0, z1, z2), z0, z1, z2, z3)
U62(f61_out1, z0, z1, z2, z3) → f579_out1
f580_in(z0, z1, z2, z3) → U63(f78_in(z1, z0, z3), z0, z1, z2, z3)
U63(f78_out1, z0, z1, z2, z3) → f580_out1
f95_in(z0, z1, z2, z3) → U64(f61_in(z0, z1, z2), z0, z1, z2, z3)
U64(f61_out1, z0, z1, z2, z3) → f95_out1
f96_in(z0, z1, z2, z3) → U65(f78_in(z1, z0, z3), z0, z1, z2, z3)
U65(f78_out1, z0, z1, z2, z3) → f96_out1
f174_in(z0, z1, z2, z3) → U66(f61_in(z0, z1, z2), z0, z1, z2, z3)
U66(f61_out1, z0, z1, z2, z3) → f174_out1
f175_in(z0, z1, z2, z3) → U67(f78_in(z1, z0, z3), z0, z1, z2, z3)
U67(f78_out1, z0, z1, z2, z3) → f175_out1
f415_in(z0, z1, z2, z3) → U68(f61_in(z0, z1, z2), z0, z1, z2, z3)
U68(f61_out1, z0, z1, z2, z3) → f415_out1
f416_in(z0, z1, z2, z3) → U69(f78_in(z1, z0, z3), z0, z1, z2, z3)
U69(f78_out1, z0, z1, z2, z3) → f416_out1
f52_in(z0, z1, z2, z3) → U70(f61_in(z0, z1, z2), z0, z1, z2, z3)
U70(f61_out1, z0, z1, z2, z3) → f52_out1
f53_in(z0, z1, z2, z3) → U71(f78_in(z1, z0, z3), z0, z1, z2, z3)
U71(f78_out1, z0, z1, z2, z3) → f53_out1
f61_in(z0, z1, z2) → U72(f63_in(z0, z1), z0, z1, z2)
U72(f63_out1, z0, z1, z2) → U73(f2_in(z0, z2), z0, z1, z2)
U73(f2_out1, z0, z1, z2) → f61_out1
f78_in(z0, z1, z2) → U74(f63_in(z0, z1), z0, z1, z2)
U74(f63_out1, z0, z1, z2) → U75(f2_in(z1, z2), z0, z1, z2)
U75(f2_out1, z0, z1, z2) → f78_out1
f123_in(z0, z1) → U76(f127_in(z0), z0, z1)
U76(f127_out1, z0, z1) → U77(f2_in(0, z1), z0, z1)
U77(f2_out1, z0, z1) → f123_out1
f138_in(z0, z1, z2) → U78(f63_in(z0, z1), z0, z1, z2)
U78(f63_out1, z0, z1, z2) → U79(f2_in(s(z0), z2), z0, z1, z2)
U79(f2_out1, z0, z1, z2) → f138_out1
f159_in(z0, z1, z2) → U80(f63_in(z0, z1), z0, z1, z2)
U80(f63_out1, z0, z1, z2) → U81(f2_in(s(z1), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f159_out1
f23_in(z0, z1, z2, z3) → U82(f86_in(z0, z1), f87_in(z2, z0, z3, z1), z0, z1, z2, z3)
U82(f86_out1, z0, z1, z2, z3, z4) → f23_out1
U82(z0, f87_out2, z1, z2, z3, z4) → f23_out3
U82(z0, f87_out3, z1, z2, z3, z4) → f23_out4
f25_in(z0, z1, z2, z3) → U83(f27_in(z0, z1), f28_in(z2, z0, z3, z1), z0, z1, z2, z3)
U83(f27_out1, z0, z1, z2, z3, z4) → f25_out1
U83(z0, f28_out2, z1, z2, z3, z4) → f25_out3
U83(z0, f28_out3, z1, z2, z3, z4) → f25_out4
f49_in(z0, z1, z2, z3) → U84(f52_in(z0, z1, z2, z3), f53_in(z0, z1, z2, z3), z0, z1, z2, z3)
U84(f52_out1, z0, z1, z2, z3, z4) → f49_out1
U84(z0, f53_out1, z1, z2, z3, z4) → f49_out2
f92_in(z0, z1, z2, z3) → U85(f95_in(z0, z1, z2, z3), f96_in(z0, z1, z2, z3), z0, z1, z2, z3)
U85(f95_out1, z0, z1, z2, z3, z4) → f92_out1
U85(z0, f96_out1, z1, z2, z3, z4) → f92_out2
f113_in(z0, z1, z2) → U86(f2_in(0, z0), f118_in(z1, z0, z2), z0, z1, z2)
U86(f2_out1, z0, z1, z2, z3) → f113_out1
U86(z0, f118_out1, z1, z2, z3) → f113_out2
U86(z0, f118_out3, z1, z2, z3) → f113_out4
f114_in(z0, z1, z2, z3) → U87(f134_in(z0, z1, z2), f135_in(z0, z1, z2, z3), z0, z1, z2, z3)
U87(f134_out1, z0, z1, z2, z3, z4) → f114_out1
U87(z0, f135_out2, z1, z2, z3, z4) → f114_out3
f154_in(z0, z1) → U88(f2_in(s(z0), z1), f157_in(z0, z1), z0, z1)
U88(f2_out1, z0, z1, z2) → f154_out1
U88(z0, f157_out1, z1, z2) → f154_out2
f167_in(z0, z1, z2, z3) → U89(f211_in(z0, z1), f212_in(z2, z0, z3, z1), z0, z1, z2, z3)
U89(f211_out1, z0, z1, z2, z3, z4) → f167_out1
U89(z0, f212_out2, z1, z2, z3, z4) → f167_out3
U89(z0, f212_out3, z1, z2, z3, z4) → f167_out4
f168_in(z0, z1, z2, z3) → U90(f169_in(z0, z1), f170_in(z2, z0, z3, z1), z0, z1, z2, z3)
U90(f169_out1, z0, z1, z2, z3, z4) → f168_out1
U90(z0, f170_out2, z1, z2, z3, z4) → f168_out3
U90(z0, f170_out3, z1, z2, z3, z4) → f168_out4
f173_in(z0, z1, z2, z3) → U91(f174_in(z0, z1, z2, z3), f175_in(z0, z1, z2, z3), z0, z1, z2, z3)
U91(f174_out1, z0, z1, z2, z3, z4) → f173_out1
U91(z0, f175_out1, z1, z2, z3, z4) → f173_out2
f215_in(z0, z1, z2, z3) → U92(f216_in(z0, z1, z2, z3), f217_in(z0, z1, z2, z3), z0, z1, z2, z3)
U92(f216_out1, z0, z1, z2, z3, z4) → f215_out1
U92(z0, f217_out1, z1, z2, z3, z4) → f215_out2
f264_in(z0, z1, z2) → U93(f2_in(0, z0), f267_in(z1, z0, z2), z0, z1, z2)
U93(f2_out1, z0, z1, z2, z3) → f264_out1
U93(z0, f267_out1, z1, z2, z3) → f264_out2
U93(z0, f267_out3, z1, z2, z3) → f264_out4
f265_in(z0, z1, z2, z3) → U94(f301_in(z0, z1, z2), f302_in(z0, z1, z2, z3), z0, z1, z2, z3)
U94(f301_out1, z0, z1, z2, z3, z4) → f265_out1
U94(z0, f302_out2, z1, z2, z3, z4) → f265_out3
f311_in(z0, z1) → U95(f2_in(s(z0), z1), f314_in(z0, z1), z0, z1)
U95(f2_out1, z0, z1, z2) → f311_out1
U95(z0, f314_out1, z1, z2) → f311_out2
f325_in(z0, z1, z2, z3) → U96(f422_in(z0, z1), f424_in(z2, z0, z3, z1), z0, z1, z2, z3)
U96(f422_out1, z0, z1, z2, z3, z4) → f325_out1
U96(z0, f424_out2, z1, z2, z3, z4) → f325_out3
U96(z0, f424_out3, z1, z2, z3, z4) → f325_out4
f326_in(z0, z1, z2, z3) → U97(f327_in(z0, z1), f328_in(z2, z0, z3, z1), z0, z1, z2, z3)
U97(f327_out1, z0, z1, z2, z3, z4) → f326_out1
U97(z0, f328_out2, z1, z2, z3, z4) → f326_out3
U97(z0, f328_out3, z1, z2, z3, z4) → f326_out4
f414_in(z0, z1, z2, z3) → U98(f415_in(z0, z1, z2, z3), f416_in(z0, z1, z2, z3), z0, z1, z2, z3)
U98(f415_out1, z0, z1, z2, z3, z4) → f414_out1
U98(z0, f416_out1, z1, z2, z3, z4) → f414_out2
f460_in(z0, z1, z2, z3) → U99(f461_in(z0, z1, z2, z3), f462_in(z0, z1, z2, z3), z0, z1, z2, z3)
U99(f461_out1, z0, z1, z2, z3, z4) → f460_out1
U99(z0, f462_out1, z1, z2, z3, z4) → f460_out2
f470_in(z0, z1, z2) → U100(f2_in(0, z0), f476_in(z1, z0, z2), z0, z1, z2)
U100(f2_out1, z0, z1, z2, z3) → f470_out1
U100(z0, f476_out1, z1, z2, z3) → f470_out2
U100(z0, f476_out3, z1, z2, z3) → f470_out4
f471_in(z0, z1, z2, z3) → U101(f521_in(z0, z1, z2), f522_in(z0, z1, z2, z3), z0, z1, z2, z3)
U101(f521_out1, z0, z1, z2, z3, z4) → f471_out1
U101(z0, f522_out2, z1, z2, z3, z4) → f471_out3
f531_in(z0, z1) → U102(f2_in(s(z0), z1), f534_in(z0, z1), z0, z1)
U102(f2_out1, z0, z1, z2) → f531_out1
U102(z0, f534_out1, z1, z2) → f531_out2
f542_in(z0, z1, z2, z3) → U103(f585_in(z0, z1), f586_in(z2, z0, z3, z1), z0, z1, z2, z3)
U103(f585_out1, z0, z1, z2, z3, z4) → f542_out1
U103(z0, f586_out2, z1, z2, z3, z4) → f542_out3
U103(z0, f586_out3, z1, z2, z3, z4) → f542_out4
f543_in(z0, z1, z2, z3) → U104(f574_in(z0, z1), f575_in(z2, z0, z3, z1), z0, z1, z2, z3)
U104(f574_out1, z0, z1, z2, z3, z4) → f543_out1
U104(z0, f575_out2, z1, z2, z3, z4) → f543_out3
U104(z0, f575_out3, z1, z2, z3, z4) → f543_out4
f578_in(z0, z1, z2, z3) → U105(f579_in(z0, z1, z2, z3), f580_in(z0, z1, z2, z3), z0, z1, z2, z3)
U105(f579_out1, z0, z1, z2, z3, z4) → f578_out1
U105(z0, f580_out1, z1, z2, z3, z4) → f578_out2
f589_in(z0, z1, z2, z3) → U106(f590_in(z0, z1, z2, z3), f591_in(z0, z1, z2, z3), z0, z1, z2, z3)
U106(f590_out1, z0, z1, z2, z3, z4) → f589_out1
U106(z0, f591_out1, z1, z2, z3, z4) → f589_out2
f599_in(z0, z1, z2) → U107(f2_in(0, z0), f602_in(z1, z0, z2), z0, z1, z2)
U107(f2_out1, z0, z1, z2, z3) → f599_out1
U107(z0, f602_out1, z1, z2, z3) → f599_out2
U107(z0, f602_out3, z1, z2, z3) → f599_out4
f600_in(z0, z1, z2, z3) → U108(f607_in(z0, z1, z2), f608_in(z0, z1, z2, z3), z0, z1, z2, z3)
U108(f607_out1, z0, z1, z2, z3, z4) → f600_out1
U108(z0, f608_out2, z1, z2, z3, z4) → f600_out3
f700_in(z0, z1) → U109(f2_in(s(z0), z1), f703_in(z0, z1), z0, z1)
U109(f2_out1, z0, z1, z2) → f700_out1
U109(z0, f703_out1, z1, z2) → f700_out2

Tuples:

F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F123_IN(z0, z1) → c192
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c
F211_IN(z0, tree(z1, z2, z3)) → c
F422_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F602_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c
U76'(f127_out1, z0, z1) → c
F61_IN(0, s(z0), x2) → c186(U72'(f63_out1, 0, s(z0), x2), F63_IN(0, s(z0)))
F61_IN(s(z0), s(z1), x2) → c186(U72'(U27(f63_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F63_IN(s(z0), s(z1)))

S tuples:

F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))

K tuples:

U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
U76'(f127_out1, z0, z1) → c
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F585_IN(z0, tree(z1, z2, z3)) → c
F211_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F602_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F169_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F123_IN(z0, z1) → c192
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
F61_IN(z0, z1, z2) → c186(U72'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F422_IN(z0, tree(z1, z2, z3)) → c
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, U17, U18, U19, U20, U21, U22, U23, U24, f33_in, U25, U26, f63_in, U27, f585_in, U28, f586_in, U29, f211_in, U30, f212_in, U31, f422_in, U32, f424_in, U33, f574_in, U34, f575_in, U35, f602_in, U36, f607_in, U37, f608_in, U38, f86_in, U39, f87_in, U40, f169_in, U41, f170_in, U42, f267_in, U43, f301_in, U44, f302_in, U45, f327_in, U46, f328_in, U47, f476_in, U48, f521_in, U49, f522_in, U50, f590_in, U51, f591_in, U52, f27_in, U53, f28_in, U54, f118_in, U55, f134_in, U56, f135_in, U57, f216_in, U58, f217_in, U59, f461_in, U60, f462_in, U61, f579_in, U62, f580_in, U63, f95_in, U64, f96_in, U65, f174_in, U66, f175_in, U67, f415_in, U68, f416_in, U69, f52_in, U70, f53_in, U71, f61_in, U72, U73, f78_in, U74, U75, f123_in, U76, U77, f138_in, U78, U79, f159_in, U80, U81, f23_in, U82, f25_in, U83, f49_in, U84, f92_in, U85, f113_in, U86, f114_in, U87, f154_in, U88, f167_in, U89, f168_in, U90, f173_in, U91, f215_in, U92, f264_in, U93, f265_in, U94, f311_in, U95, f325_in, U96, f326_in, U97, f414_in, U98, f460_in, U99, f470_in, U100, f471_in, U101, f531_in, U102, f542_in, U103, f543_in, U104, f578_in, U105, f589_in, U106, f599_in, U107, f600_in, U108, f700_in, U109

Defined Pair Symbols:

F78_IN, F138_IN, F159_IN, F585_IN, F211_IN, F422_IN, F574_IN, F602_IN, F86_IN, F169_IN, F267_IN, F327_IN, F476_IN, F27_IN, F118_IN, U76', F2_IN, F33_IN, F63_IN, F586_IN, F212_IN, F424_IN, F575_IN, F607_IN, F608_IN, F87_IN, F170_IN, F301_IN, F302_IN, F328_IN, F521_IN, F522_IN, F590_IN, F591_IN, F28_IN, F134_IN, F135_IN, F216_IN, F217_IN, F461_IN, F462_IN, F579_IN, F580_IN, F95_IN, F96_IN, F174_IN, F175_IN, F415_IN, F416_IN, F52_IN, F53_IN, U72', U74', F123_IN, U78', U80', F23_IN, F25_IN, F49_IN, F92_IN, F113_IN, F114_IN, F154_IN, F167_IN, F168_IN, F173_IN, F215_IN, F264_IN, F265_IN, F311_IN, F325_IN, F326_IN, F414_IN, F460_IN, F470_IN, F471_IN, F531_IN, F542_IN, F543_IN, F578_IN, F589_IN, F599_IN, F600_IN, F700_IN, F61_IN

Compound Symbols:

c189, c195, c198, c, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c83, c84, c88, c92, c97, c102, c107, c112, c114, c118, c123, c128, c130, c134, c139, c141, c143, c145, c149, c154, c156, c158, c160, c162, c164, c166, c168, c170, c172, c174, c176, c178, c180, c182, c184, c187, c190, c192, c196, c199, c201, c205, c209, c212, c215, c219, c222, c225, c229, c233, c236, c239, c243, c246, c249, c253, c257, c260, c263, c267, c270, c273, c277, c281, c284, c287, c291, c294, c, c186

(41) CdtGraphRemoveDanglingProof (ComplexityIfPolyImplication transformation)

Removed 19 of 123 dangling nodes:

U76'(f127_out1, z0, z1) → c(F2_IN(0, z1))
F602_IN(z0, z1, z2) → c
F602_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F476_IN(z0, z1, z2) → c
U76'(f127_out1, z0, z1) → c
F86_IN(z0, tree(z1, z2, z3)) → c
F476_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c
F574_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c
F422_IN(z0, tree(z1, z2, z3)) → c
F327_IN(z0, tree(z1, z2, z3)) → c
F118_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c
F267_IN(z0, z1, z2) → c(F123_IN(z0, z2))
F585_IN(z0, tree(z1, z2, z3)) → c
F123_IN(z0, z1) → c192
F118_IN(z0, z1, z2) → c
F27_IN(z0, tree(z1, z2, z3)) → c

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → U1(f25_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U2(f23_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U3(f113_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f114_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f154_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U7(f168_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U8(f167_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U9(f264_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U10(f265_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U11(f311_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U12(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U13(f326_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U14(f325_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U15(f470_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U16(f471_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U17(f531_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U18(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U19(f543_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U20(f542_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U21(f599_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U22(f600_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U23(f700_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U24(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f25_out1, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out3, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out4, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out1, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out3, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out4, z0, tree(z1, z2, z3)) → f2_out1
U3(f113_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U4(f114_out1, z0, tree(z1, z2, z3)) → f2_out1
U4(f114_out3, z0, tree(z1, z2, z3)) → f2_out1
U5(f154_out1, s(z0), tree(0, z1, z2)) → f2_out1
U5(f154_out2, s(z0), tree(0, z1, z2)) → f2_out1
U6(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U7(f168_out1, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out3, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out4, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out1, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out3, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out4, z0, tree(z1, z2, z3)) → f2_out1
U9(f264_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U10(f265_out1, z0, tree(z1, z2, z3)) → f2_out1
U10(f265_out3, z0, tree(z1, z2, z3)) → f2_out1
U11(f311_out1, s(z0), tree(0, z1, z2)) → f2_out1
U11(f311_out2, s(z0), tree(0, z1, z2)) → f2_out1
U12(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U13(f326_out1, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out3, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out4, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out3, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out4, z0, tree(z1, z2, z3)) → f2_out1
U15(f470_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U16(f471_out1, z0, tree(z1, z2, z3)) → f2_out1
U16(f471_out3, z0, tree(z1, z2, z3)) → f2_out1
U17(f531_out1, s(z0), tree(0, z1, z2)) → f2_out1
U17(f531_out2, s(z0), tree(0, z1, z2)) → f2_out1
U18(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U19(f543_out1, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out3, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out4, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out1, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out3, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out4, z0, tree(z1, z2, z3)) → f2_out1
U21(f599_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U22(f600_out1, z0, tree(z1, z2, z3)) → f2_out1
U22(f600_out3, z0, tree(z1, z2, z3)) → f2_out1
U23(f700_out1, s(z0), tree(0, z1, z2)) → f2_out1
U23(f700_out2, s(z0), tree(0, z1, z2)) → f2_out1
U24(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f33_in(z0, z1) → f33_out1
f33_in(z0, tree(z1, z2, z3)) → U25(f33_in(z0, z2), z0, tree(z1, z2, z3))
f33_in(z0, tree(z1, z2, z3)) → U26(f33_in(z0, z2), z0, tree(z1, z2, z3))
U25(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
U26(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
f63_in(0, s(z0)) → f63_out1
f63_in(s(z0), s(z1)) → U27(f63_in(z0, z1), s(z0), s(z1))
U27(f63_out1, s(z0), s(z1)) → f63_out1
f585_in(z0, tree(z1, z2, z3)) → U28(f33_in(z0, z2), z0, tree(z1, z2, z3))
U28(f33_out1, z0, tree(z1, z2, z3)) → f585_out1
f586_in(z0, z1, z2, z3) → U29(f589_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f589_out1, z0, z1, z2, z3) → f586_out2
U29(f589_out2, z0, z1, z2, z3) → f586_out3
f211_in(z0, tree(z1, z2, z3)) → U30(f33_in(z0, z2), z0, tree(z1, z2, z3))
U30(f33_out1, z0, tree(z1, z2, z3)) → f211_out1
f212_in(z0, z1, z2, z3) → U31(f215_in(z0, z1, z2, z3), z0, z1, z2, z3)
U31(f215_out1, z0, z1, z2, z3) → f212_out2
U31(f215_out2, z0, z1, z2, z3) → f212_out3
f422_in(z0, tree(z1, z2, z3)) → U32(f33_in(z0, z2), z0, tree(z1, z2, z3))
U32(f33_out1, z0, tree(z1, z2, z3)) → f422_out1
f424_in(z0, z1, z2, z3) → U33(f460_in(z0, z1, z2, z3), z0, z1, z2, z3)
U33(f460_out1, z0, z1, z2, z3) → f424_out2
U33(f460_out2, z0, z1, z2, z3) → f424_out3
f574_in(z0, tree(z1, z2, z3)) → U34(f33_in(z0, z2), z0, tree(z1, z2, z3))
U34(f33_out1, z0, tree(z1, z2, z3)) → f574_out1
f575_in(z0, z1, z2, z3) → U35(f578_in(z0, z1, z2, z3), z0, z1, z2, z3)
U35(f578_out1, z0, z1, z2, z3) → f575_out2
U35(f578_out2, z0, z1, z2, z3) → f575_out3
f602_in(z0, z1, z2) → U36(f123_in(z0, z2), z0, z1, z2)
U36(f123_out1, z0, z1, z2) → f602_out3
f607_in(s(z0), s(z1), z2) → U37(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U37(f138_out1, s(z0), s(z1), z2) → f607_out1
f608_in(z0, z1, z2, z3) → U38(f78_in(z1, z0, z3), z0, z1, z2, z3)
U38(f78_out1, z0, z1, z2, z3) → f608_out2
f86_in(z0, tree(z1, z2, z3)) → U39(f33_in(z0, z2), z0, tree(z1, z2, z3))
U39(f33_out1, z0, tree(z1, z2, z3)) → f86_out1
f87_in(z0, z1, z2, z3) → U40(f92_in(z0, z1, z2, z3), z0, z1, z2, z3)
U40(f92_out1, z0, z1, z2, z3) → f87_out2
U40(f92_out2, z0, z1, z2, z3) → f87_out3
f169_in(z0, tree(z1, z2, z3)) → U41(f33_in(z0, z2), z0, tree(z1, z2, z3))
U41(f33_out1, z0, tree(z1, z2, z3)) → f169_out1
f170_in(z0, z1, z2, z3) → U42(f173_in(z0, z1, z2, z3), z0, z1, z2, z3)
U42(f173_out1, z0, z1, z2, z3) → f170_out2
U42(f173_out2, z0, z1, z2, z3) → f170_out3
f267_in(z0, z1, z2) → U43(f123_in(z0, z2), z0, z1, z2)
U43(f123_out1, z0, z1, z2) → f267_out3
f301_in(s(z0), s(z1), z2) → U44(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U44(f138_out1, s(z0), s(z1), z2) → f301_out1
f302_in(z0, z1, z2, z3) → U45(f78_in(z1, z0, z3), z0, z1, z2, z3)
U45(f78_out1, z0, z1, z2, z3) → f302_out2
f327_in(z0, tree(z1, z2, z3)) → U46(f33_in(z0, z2), z0, tree(z1, z2, z3))
U46(f33_out1, z0, tree(z1, z2, z3)) → f327_out1
f328_in(z0, z1, z2, z3) → U47(f414_in(z0, z1, z2, z3), z0, z1, z2, z3)
U47(f414_out1, z0, z1, z2, z3) → f328_out2
U47(f414_out2, z0, z1, z2, z3) → f328_out3
f476_in(z0, z1, z2) → U48(f123_in(z0, z2), z0, z1, z2)
U48(f123_out1, z0, z1, z2) → f476_out3
f521_in(s(z0), s(z1), z2) → U49(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U49(f138_out1, s(z0), s(z1), z2) → f521_out1
f522_in(z0, z1, z2, z3) → U50(f78_in(z1, z0, z3), z0, z1, z2, z3)
U50(f78_out1, z0, z1, z2, z3) → f522_out2
f590_in(z0, z1, z2, z3) → U51(f61_in(z0, z1, z2), z0, z1, z2, z3)
U51(f61_out1, z0, z1, z2, z3) → f590_out1
f591_in(z0, z1, z2, z3) → U52(f78_in(z1, z0, z3), z0, z1, z2, z3)
U52(f78_out1, z0, z1, z2, z3) → f591_out1
f27_in(z0, tree(z1, z2, z3)) → U53(f33_in(z0, z2), z0, tree(z1, z2, z3))
U53(f33_out1, z0, tree(z1, z2, z3)) → f27_out1
f28_in(z0, z1, z2, z3) → U54(f49_in(z0, z1, z2, z3), z0, z1, z2, z3)
U54(f49_out1, z0, z1, z2, z3) → f28_out2
U54(f49_out2, z0, z1, z2, z3) → f28_out3
f118_in(z0, z1, z2) → U55(f123_in(z0, z2), z0, z1, z2)
U55(f123_out1, z0, z1, z2) → f118_out3
f134_in(s(z0), s(z1), z2) → U56(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U56(f138_out1, s(z0), s(z1), z2) → f134_out1
f135_in(z0, z1, z2, z3) → U57(f78_in(z1, z0, z3), z0, z1, z2, z3)
U57(f78_out1, z0, z1, z2, z3) → f135_out2
f216_in(z0, z1, z2, z3) → U58(f61_in(z0, z1, z2), z0, z1, z2, z3)
U58(f61_out1, z0, z1, z2, z3) → f216_out1
f217_in(z0, z1, z2, z3) → U59(f78_in(z1, z0, z3), z0, z1, z2, z3)
U59(f78_out1, z0, z1, z2, z3) → f217_out1
f461_in(z0, z1, z2, z3) → U60(f61_in(z0, z1, z2), z0, z1, z2, z3)
U60(f61_out1, z0, z1, z2, z3) → f461_out1
f462_in(z0, z1, z2, z3) → U61(f78_in(z1, z0, z3), z0, z1, z2, z3)
U61(f78_out1, z0, z1, z2, z3) → f462_out1
f579_in(z0, z1, z2, z3) → U62(f61_in(z0, z1, z2), z0, z1, z2, z3)
U62(f61_out1, z0, z1, z2, z3) → f579_out1
f580_in(z0, z1, z2, z3) → U63(f78_in(z1, z0, z3), z0, z1, z2, z3)
U63(f78_out1, z0, z1, z2, z3) → f580_out1
f95_in(z0, z1, z2, z3) → U64(f61_in(z0, z1, z2), z0, z1, z2, z3)
U64(f61_out1, z0, z1, z2, z3) → f95_out1
f96_in(z0, z1, z2, z3) → U65(f78_in(z1, z0, z3), z0, z1, z2, z3)
U65(f78_out1, z0, z1, z2, z3) → f96_out1
f174_in(z0, z1, z2, z3) → U66(f61_in(z0, z1, z2), z0, z1, z2, z3)
U66(f61_out1, z0, z1, z2, z3) → f174_out1
f175_in(z0, z1, z2, z3) → U67(f78_in(z1, z0, z3), z0, z1, z2, z3)
U67(f78_out1, z0, z1, z2, z3) → f175_out1
f415_in(z0, z1, z2, z3) → U68(f61_in(z0, z1, z2), z0, z1, z2, z3)
U68(f61_out1, z0, z1, z2, z3) → f415_out1
f416_in(z0, z1, z2, z3) → U69(f78_in(z1, z0, z3), z0, z1, z2, z3)
U69(f78_out1, z0, z1, z2, z3) → f416_out1
f52_in(z0, z1, z2, z3) → U70(f61_in(z0, z1, z2), z0, z1, z2, z3)
U70(f61_out1, z0, z1, z2, z3) → f52_out1
f53_in(z0, z1, z2, z3) → U71(f78_in(z1, z0, z3), z0, z1, z2, z3)
U71(f78_out1, z0, z1, z2, z3) → f53_out1
f61_in(z0, z1, z2) → U72(f63_in(z0, z1), z0, z1, z2)
U72(f63_out1, z0, z1, z2) → U73(f2_in(z0, z2), z0, z1, z2)
U73(f2_out1, z0, z1, z2) → f61_out1
f78_in(z0, z1, z2) → U74(f63_in(z0, z1), z0, z1, z2)
U74(f63_out1, z0, z1, z2) → U75(f2_in(z1, z2), z0, z1, z2)
U75(f2_out1, z0, z1, z2) → f78_out1
f123_in(z0, z1) → U76(f127_in(z0), z0, z1)
U76(f127_out1, z0, z1) → U77(f2_in(0, z1), z0, z1)
U77(f2_out1, z0, z1) → f123_out1
f138_in(z0, z1, z2) → U78(f63_in(z0, z1), z0, z1, z2)
U78(f63_out1, z0, z1, z2) → U79(f2_in(s(z0), z2), z0, z1, z2)
U79(f2_out1, z0, z1, z2) → f138_out1
f159_in(z0, z1, z2) → U80(f63_in(z0, z1), z0, z1, z2)
U80(f63_out1, z0, z1, z2) → U81(f2_in(s(z1), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f159_out1
f23_in(z0, z1, z2, z3) → U82(f86_in(z0, z1), f87_in(z2, z0, z3, z1), z0, z1, z2, z3)
U82(f86_out1, z0, z1, z2, z3, z4) → f23_out1
U82(z0, f87_out2, z1, z2, z3, z4) → f23_out3
U82(z0, f87_out3, z1, z2, z3, z4) → f23_out4
f25_in(z0, z1, z2, z3) → U83(f27_in(z0, z1), f28_in(z2, z0, z3, z1), z0, z1, z2, z3)
U83(f27_out1, z0, z1, z2, z3, z4) → f25_out1
U83(z0, f28_out2, z1, z2, z3, z4) → f25_out3
U83(z0, f28_out3, z1, z2, z3, z4) → f25_out4
f49_in(z0, z1, z2, z3) → U84(f52_in(z0, z1, z2, z3), f53_in(z0, z1, z2, z3), z0, z1, z2, z3)
U84(f52_out1, z0, z1, z2, z3, z4) → f49_out1
U84(z0, f53_out1, z1, z2, z3, z4) → f49_out2
f92_in(z0, z1, z2, z3) → U85(f95_in(z0, z1, z2, z3), f96_in(z0, z1, z2, z3), z0, z1, z2, z3)
U85(f95_out1, z0, z1, z2, z3, z4) → f92_out1
U85(z0, f96_out1, z1, z2, z3, z4) → f92_out2
f113_in(z0, z1, z2) → U86(f2_in(0, z0), f118_in(z1, z0, z2), z0, z1, z2)
U86(f2_out1, z0, z1, z2, z3) → f113_out1
U86(z0, f118_out1, z1, z2, z3) → f113_out2
U86(z0, f118_out3, z1, z2, z3) → f113_out4
f114_in(z0, z1, z2, z3) → U87(f134_in(z0, z1, z2), f135_in(z0, z1, z2, z3), z0, z1, z2, z3)
U87(f134_out1, z0, z1, z2, z3, z4) → f114_out1
U87(z0, f135_out2, z1, z2, z3, z4) → f114_out3
f154_in(z0, z1) → U88(f2_in(s(z0), z1), f157_in(z0, z1), z0, z1)
U88(f2_out1, z0, z1, z2) → f154_out1
U88(z0, f157_out1, z1, z2) → f154_out2
f167_in(z0, z1, z2, z3) → U89(f211_in(z0, z1), f212_in(z2, z0, z3, z1), z0, z1, z2, z3)
U89(f211_out1, z0, z1, z2, z3, z4) → f167_out1
U89(z0, f212_out2, z1, z2, z3, z4) → f167_out3
U89(z0, f212_out3, z1, z2, z3, z4) → f167_out4
f168_in(z0, z1, z2, z3) → U90(f169_in(z0, z1), f170_in(z2, z0, z3, z1), z0, z1, z2, z3)
U90(f169_out1, z0, z1, z2, z3, z4) → f168_out1
U90(z0, f170_out2, z1, z2, z3, z4) → f168_out3
U90(z0, f170_out3, z1, z2, z3, z4) → f168_out4
f173_in(z0, z1, z2, z3) → U91(f174_in(z0, z1, z2, z3), f175_in(z0, z1, z2, z3), z0, z1, z2, z3)
U91(f174_out1, z0, z1, z2, z3, z4) → f173_out1
U91(z0, f175_out1, z1, z2, z3, z4) → f173_out2
f215_in(z0, z1, z2, z3) → U92(f216_in(z0, z1, z2, z3), f217_in(z0, z1, z2, z3), z0, z1, z2, z3)
U92(f216_out1, z0, z1, z2, z3, z4) → f215_out1
U92(z0, f217_out1, z1, z2, z3, z4) → f215_out2
f264_in(z0, z1, z2) → U93(f2_in(0, z0), f267_in(z1, z0, z2), z0, z1, z2)
U93(f2_out1, z0, z1, z2, z3) → f264_out1
U93(z0, f267_out1, z1, z2, z3) → f264_out2
U93(z0, f267_out3, z1, z2, z3) → f264_out4
f265_in(z0, z1, z2, z3) → U94(f301_in(z0, z1, z2), f302_in(z0, z1, z2, z3), z0, z1, z2, z3)
U94(f301_out1, z0, z1, z2, z3, z4) → f265_out1
U94(z0, f302_out2, z1, z2, z3, z4) → f265_out3
f311_in(z0, z1) → U95(f2_in(s(z0), z1), f314_in(z0, z1), z0, z1)
U95(f2_out1, z0, z1, z2) → f311_out1
U95(z0, f314_out1, z1, z2) → f311_out2
f325_in(z0, z1, z2, z3) → U96(f422_in(z0, z1), f424_in(z2, z0, z3, z1), z0, z1, z2, z3)
U96(f422_out1, z0, z1, z2, z3, z4) → f325_out1
U96(z0, f424_out2, z1, z2, z3, z4) → f325_out3
U96(z0, f424_out3, z1, z2, z3, z4) → f325_out4
f326_in(z0, z1, z2, z3) → U97(f327_in(z0, z1), f328_in(z2, z0, z3, z1), z0, z1, z2, z3)
U97(f327_out1, z0, z1, z2, z3, z4) → f326_out1
U97(z0, f328_out2, z1, z2, z3, z4) → f326_out3
U97(z0, f328_out3, z1, z2, z3, z4) → f326_out4
f414_in(z0, z1, z2, z3) → U98(f415_in(z0, z1, z2, z3), f416_in(z0, z1, z2, z3), z0, z1, z2, z3)
U98(f415_out1, z0, z1, z2, z3, z4) → f414_out1
U98(z0, f416_out1, z1, z2, z3, z4) → f414_out2
f460_in(z0, z1, z2, z3) → U99(f461_in(z0, z1, z2, z3), f462_in(z0, z1, z2, z3), z0, z1, z2, z3)
U99(f461_out1, z0, z1, z2, z3, z4) → f460_out1
U99(z0, f462_out1, z1, z2, z3, z4) → f460_out2
f470_in(z0, z1, z2) → U100(f2_in(0, z0), f476_in(z1, z0, z2), z0, z1, z2)
U100(f2_out1, z0, z1, z2, z3) → f470_out1
U100(z0, f476_out1, z1, z2, z3) → f470_out2
U100(z0, f476_out3, z1, z2, z3) → f470_out4
f471_in(z0, z1, z2, z3) → U101(f521_in(z0, z1, z2), f522_in(z0, z1, z2, z3), z0, z1, z2, z3)
U101(f521_out1, z0, z1, z2, z3, z4) → f471_out1
U101(z0, f522_out2, z1, z2, z3, z4) → f471_out3
f531_in(z0, z1) → U102(f2_in(s(z0), z1), f534_in(z0, z1), z0, z1)
U102(f2_out1, z0, z1, z2) → f531_out1
U102(z0, f534_out1, z1, z2) → f531_out2
f542_in(z0, z1, z2, z3) → U103(f585_in(z0, z1), f586_in(z2, z0, z3, z1), z0, z1, z2, z3)
U103(f585_out1, z0, z1, z2, z3, z4) → f542_out1
U103(z0, f586_out2, z1, z2, z3, z4) → f542_out3
U103(z0, f586_out3, z1, z2, z3, z4) → f542_out4
f543_in(z0, z1, z2, z3) → U104(f574_in(z0, z1), f575_in(z2, z0, z3, z1), z0, z1, z2, z3)
U104(f574_out1, z0, z1, z2, z3, z4) → f543_out1
U104(z0, f575_out2, z1, z2, z3, z4) → f543_out3
U104(z0, f575_out3, z1, z2, z3, z4) → f543_out4
f578_in(z0, z1, z2, z3) → U105(f579_in(z0, z1, z2, z3), f580_in(z0, z1, z2, z3), z0, z1, z2, z3)
U105(f579_out1, z0, z1, z2, z3, z4) → f578_out1
U105(z0, f580_out1, z1, z2, z3, z4) → f578_out2
f589_in(z0, z1, z2, z3) → U106(f590_in(z0, z1, z2, z3), f591_in(z0, z1, z2, z3), z0, z1, z2, z3)
U106(f590_out1, z0, z1, z2, z3, z4) → f589_out1
U106(z0, f591_out1, z1, z2, z3, z4) → f589_out2
f599_in(z0, z1, z2) → U107(f2_in(0, z0), f602_in(z1, z0, z2), z0, z1, z2)
U107(f2_out1, z0, z1, z2, z3) → f599_out1
U107(z0, f602_out1, z1, z2, z3) → f599_out2
U107(z0, f602_out3, z1, z2, z3) → f599_out4
f600_in(z0, z1, z2, z3) → U108(f607_in(z0, z1, z2), f608_in(z0, z1, z2, z3), z0, z1, z2, z3)
U108(f607_out1, z0, z1, z2, z3, z4) → f600_out1
U108(z0, f608_out2, z1, z2, z3, z4) → f600_out3
f700_in(z0, z1) → U109(f2_in(s(z0), z1), f703_in(z0, z1), z0, z1)
U109(f2_out1, z0, z1, z2) → f700_out1
U109(z0, f703_out1, z1, z2) → f700_out2

Tuples:

F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F61_IN(0, s(z0), x2) → c186(U72'(f63_out1, 0, s(z0), x2), F63_IN(0, s(z0)))
F61_IN(s(z0), s(z1), x2) → c186(U72'(U27(f63_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F63_IN(s(z0), s(z1)))

S tuples:

F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))

K tuples:

F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0), F118_IN(z1, z0, z2))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0), F267_IN(z1, z0, z2))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0), F476_IN(z1, z0, z2))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0), F602_IN(z1, z0, z2))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, U17, U18, U19, U20, U21, U22, U23, U24, f33_in, U25, U26, f63_in, U27, f585_in, U28, f586_in, U29, f211_in, U30, f212_in, U31, f422_in, U32, f424_in, U33, f574_in, U34, f575_in, U35, f602_in, U36, f607_in, U37, f608_in, U38, f86_in, U39, f87_in, U40, f169_in, U41, f170_in, U42, f267_in, U43, f301_in, U44, f302_in, U45, f327_in, U46, f328_in, U47, f476_in, U48, f521_in, U49, f522_in, U50, f590_in, U51, f591_in, U52, f27_in, U53, f28_in, U54, f118_in, U55, f134_in, U56, f135_in, U57, f216_in, U58, f217_in, U59, f461_in, U60, f462_in, U61, f579_in, U62, f580_in, U63, f95_in, U64, f96_in, U65, f174_in, U66, f175_in, U67, f415_in, U68, f416_in, U69, f52_in, U70, f53_in, U71, f61_in, U72, U73, f78_in, U74, U75, f123_in, U76, U77, f138_in, U78, U79, f159_in, U80, U81, f23_in, U82, f25_in, U83, f49_in, U84, f92_in, U85, f113_in, U86, f114_in, U87, f154_in, U88, f167_in, U89, f168_in, U90, f173_in, U91, f215_in, U92, f264_in, U93, f265_in, U94, f311_in, U95, f325_in, U96, f326_in, U97, f414_in, U98, f460_in, U99, f470_in, U100, f471_in, U101, f531_in, U102, f542_in, U103, f543_in, U104, f578_in, U105, f589_in, U106, f599_in, U107, f600_in, U108, f700_in, U109

Defined Pair Symbols:

F78_IN, F138_IN, F159_IN, F585_IN, F211_IN, F422_IN, F574_IN, F86_IN, F169_IN, F327_IN, F27_IN, F2_IN, F33_IN, F63_IN, F586_IN, F212_IN, F424_IN, F575_IN, F607_IN, F608_IN, F87_IN, F170_IN, F301_IN, F302_IN, F328_IN, F521_IN, F522_IN, F590_IN, F591_IN, F28_IN, F134_IN, F135_IN, F216_IN, F217_IN, F461_IN, F462_IN, F579_IN, F580_IN, F95_IN, F96_IN, F174_IN, F175_IN, F415_IN, F416_IN, F52_IN, F53_IN, U72', U74', U78', U80', F23_IN, F25_IN, F49_IN, F92_IN, F113_IN, F114_IN, F154_IN, F167_IN, F168_IN, F173_IN, F215_IN, F264_IN, F265_IN, F311_IN, F325_IN, F326_IN, F414_IN, F460_IN, F470_IN, F471_IN, F531_IN, F542_IN, F543_IN, F578_IN, F589_IN, F599_IN, F600_IN, F700_IN, F61_IN

Compound Symbols:

c189, c195, c198, c, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c83, c84, c88, c92, c97, c102, c107, c112, c114, c118, c123, c128, c130, c134, c139, c141, c143, c145, c149, c154, c156, c158, c160, c162, c164, c166, c168, c170, c172, c174, c176, c178, c180, c182, c184, c187, c190, c196, c199, c201, c205, c209, c212, c215, c219, c222, c225, c229, c233, c236, c239, c243, c246, c249, c253, c257, c260, c263, c267, c270, c273, c277, c281, c284, c287, c291, c294, c186

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

Removed 5 trailing tuple parts

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → U1(f25_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U2(f23_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U3(f113_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f114_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f154_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U7(f168_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U8(f167_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U9(f264_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U10(f265_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U11(f311_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U12(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U13(f326_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U14(f325_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U15(f470_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U16(f471_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U17(f531_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U18(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U19(f543_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U20(f542_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U21(f599_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U22(f600_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U23(f700_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U24(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f25_out1, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out3, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out4, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out1, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out3, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out4, z0, tree(z1, z2, z3)) → f2_out1
U3(f113_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U4(f114_out1, z0, tree(z1, z2, z3)) → f2_out1
U4(f114_out3, z0, tree(z1, z2, z3)) → f2_out1
U5(f154_out1, s(z0), tree(0, z1, z2)) → f2_out1
U5(f154_out2, s(z0), tree(0, z1, z2)) → f2_out1
U6(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U7(f168_out1, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out3, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out4, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out1, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out3, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out4, z0, tree(z1, z2, z3)) → f2_out1
U9(f264_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U10(f265_out1, z0, tree(z1, z2, z3)) → f2_out1
U10(f265_out3, z0, tree(z1, z2, z3)) → f2_out1
U11(f311_out1, s(z0), tree(0, z1, z2)) → f2_out1
U11(f311_out2, s(z0), tree(0, z1, z2)) → f2_out1
U12(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U13(f326_out1, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out3, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out4, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out3, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out4, z0, tree(z1, z2, z3)) → f2_out1
U15(f470_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U16(f471_out1, z0, tree(z1, z2, z3)) → f2_out1
U16(f471_out3, z0, tree(z1, z2, z3)) → f2_out1
U17(f531_out1, s(z0), tree(0, z1, z2)) → f2_out1
U17(f531_out2, s(z0), tree(0, z1, z2)) → f2_out1
U18(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U19(f543_out1, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out3, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out4, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out1, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out3, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out4, z0, tree(z1, z2, z3)) → f2_out1
U21(f599_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U22(f600_out1, z0, tree(z1, z2, z3)) → f2_out1
U22(f600_out3, z0, tree(z1, z2, z3)) → f2_out1
U23(f700_out1, s(z0), tree(0, z1, z2)) → f2_out1
U23(f700_out2, s(z0), tree(0, z1, z2)) → f2_out1
U24(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f33_in(z0, z1) → f33_out1
f33_in(z0, tree(z1, z2, z3)) → U25(f33_in(z0, z2), z0, tree(z1, z2, z3))
f33_in(z0, tree(z1, z2, z3)) → U26(f33_in(z0, z2), z0, tree(z1, z2, z3))
U25(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
U26(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
f63_in(0, s(z0)) → f63_out1
f63_in(s(z0), s(z1)) → U27(f63_in(z0, z1), s(z0), s(z1))
U27(f63_out1, s(z0), s(z1)) → f63_out1
f585_in(z0, tree(z1, z2, z3)) → U28(f33_in(z0, z2), z0, tree(z1, z2, z3))
U28(f33_out1, z0, tree(z1, z2, z3)) → f585_out1
f586_in(z0, z1, z2, z3) → U29(f589_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f589_out1, z0, z1, z2, z3) → f586_out2
U29(f589_out2, z0, z1, z2, z3) → f586_out3
f211_in(z0, tree(z1, z2, z3)) → U30(f33_in(z0, z2), z0, tree(z1, z2, z3))
U30(f33_out1, z0, tree(z1, z2, z3)) → f211_out1
f212_in(z0, z1, z2, z3) → U31(f215_in(z0, z1, z2, z3), z0, z1, z2, z3)
U31(f215_out1, z0, z1, z2, z3) → f212_out2
U31(f215_out2, z0, z1, z2, z3) → f212_out3
f422_in(z0, tree(z1, z2, z3)) → U32(f33_in(z0, z2), z0, tree(z1, z2, z3))
U32(f33_out1, z0, tree(z1, z2, z3)) → f422_out1
f424_in(z0, z1, z2, z3) → U33(f460_in(z0, z1, z2, z3), z0, z1, z2, z3)
U33(f460_out1, z0, z1, z2, z3) → f424_out2
U33(f460_out2, z0, z1, z2, z3) → f424_out3
f574_in(z0, tree(z1, z2, z3)) → U34(f33_in(z0, z2), z0, tree(z1, z2, z3))
U34(f33_out1, z0, tree(z1, z2, z3)) → f574_out1
f575_in(z0, z1, z2, z3) → U35(f578_in(z0, z1, z2, z3), z0, z1, z2, z3)
U35(f578_out1, z0, z1, z2, z3) → f575_out2
U35(f578_out2, z0, z1, z2, z3) → f575_out3
f602_in(z0, z1, z2) → U36(f123_in(z0, z2), z0, z1, z2)
U36(f123_out1, z0, z1, z2) → f602_out3
f607_in(s(z0), s(z1), z2) → U37(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U37(f138_out1, s(z0), s(z1), z2) → f607_out1
f608_in(z0, z1, z2, z3) → U38(f78_in(z1, z0, z3), z0, z1, z2, z3)
U38(f78_out1, z0, z1, z2, z3) → f608_out2
f86_in(z0, tree(z1, z2, z3)) → U39(f33_in(z0, z2), z0, tree(z1, z2, z3))
U39(f33_out1, z0, tree(z1, z2, z3)) → f86_out1
f87_in(z0, z1, z2, z3) → U40(f92_in(z0, z1, z2, z3), z0, z1, z2, z3)
U40(f92_out1, z0, z1, z2, z3) → f87_out2
U40(f92_out2, z0, z1, z2, z3) → f87_out3
f169_in(z0, tree(z1, z2, z3)) → U41(f33_in(z0, z2), z0, tree(z1, z2, z3))
U41(f33_out1, z0, tree(z1, z2, z3)) → f169_out1
f170_in(z0, z1, z2, z3) → U42(f173_in(z0, z1, z2, z3), z0, z1, z2, z3)
U42(f173_out1, z0, z1, z2, z3) → f170_out2
U42(f173_out2, z0, z1, z2, z3) → f170_out3
f267_in(z0, z1, z2) → U43(f123_in(z0, z2), z0, z1, z2)
U43(f123_out1, z0, z1, z2) → f267_out3
f301_in(s(z0), s(z1), z2) → U44(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U44(f138_out1, s(z0), s(z1), z2) → f301_out1
f302_in(z0, z1, z2, z3) → U45(f78_in(z1, z0, z3), z0, z1, z2, z3)
U45(f78_out1, z0, z1, z2, z3) → f302_out2
f327_in(z0, tree(z1, z2, z3)) → U46(f33_in(z0, z2), z0, tree(z1, z2, z3))
U46(f33_out1, z0, tree(z1, z2, z3)) → f327_out1
f328_in(z0, z1, z2, z3) → U47(f414_in(z0, z1, z2, z3), z0, z1, z2, z3)
U47(f414_out1, z0, z1, z2, z3) → f328_out2
U47(f414_out2, z0, z1, z2, z3) → f328_out3
f476_in(z0, z1, z2) → U48(f123_in(z0, z2), z0, z1, z2)
U48(f123_out1, z0, z1, z2) → f476_out3
f521_in(s(z0), s(z1), z2) → U49(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U49(f138_out1, s(z0), s(z1), z2) → f521_out1
f522_in(z0, z1, z2, z3) → U50(f78_in(z1, z0, z3), z0, z1, z2, z3)
U50(f78_out1, z0, z1, z2, z3) → f522_out2
f590_in(z0, z1, z2, z3) → U51(f61_in(z0, z1, z2), z0, z1, z2, z3)
U51(f61_out1, z0, z1, z2, z3) → f590_out1
f591_in(z0, z1, z2, z3) → U52(f78_in(z1, z0, z3), z0, z1, z2, z3)
U52(f78_out1, z0, z1, z2, z3) → f591_out1
f27_in(z0, tree(z1, z2, z3)) → U53(f33_in(z0, z2), z0, tree(z1, z2, z3))
U53(f33_out1, z0, tree(z1, z2, z3)) → f27_out1
f28_in(z0, z1, z2, z3) → U54(f49_in(z0, z1, z2, z3), z0, z1, z2, z3)
U54(f49_out1, z0, z1, z2, z3) → f28_out2
U54(f49_out2, z0, z1, z2, z3) → f28_out3
f118_in(z0, z1, z2) → U55(f123_in(z0, z2), z0, z1, z2)
U55(f123_out1, z0, z1, z2) → f118_out3
f134_in(s(z0), s(z1), z2) → U56(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U56(f138_out1, s(z0), s(z1), z2) → f134_out1
f135_in(z0, z1, z2, z3) → U57(f78_in(z1, z0, z3), z0, z1, z2, z3)
U57(f78_out1, z0, z1, z2, z3) → f135_out2
f216_in(z0, z1, z2, z3) → U58(f61_in(z0, z1, z2), z0, z1, z2, z3)
U58(f61_out1, z0, z1, z2, z3) → f216_out1
f217_in(z0, z1, z2, z3) → U59(f78_in(z1, z0, z3), z0, z1, z2, z3)
U59(f78_out1, z0, z1, z2, z3) → f217_out1
f461_in(z0, z1, z2, z3) → U60(f61_in(z0, z1, z2), z0, z1, z2, z3)
U60(f61_out1, z0, z1, z2, z3) → f461_out1
f462_in(z0, z1, z2, z3) → U61(f78_in(z1, z0, z3), z0, z1, z2, z3)
U61(f78_out1, z0, z1, z2, z3) → f462_out1
f579_in(z0, z1, z2, z3) → U62(f61_in(z0, z1, z2), z0, z1, z2, z3)
U62(f61_out1, z0, z1, z2, z3) → f579_out1
f580_in(z0, z1, z2, z3) → U63(f78_in(z1, z0, z3), z0, z1, z2, z3)
U63(f78_out1, z0, z1, z2, z3) → f580_out1
f95_in(z0, z1, z2, z3) → U64(f61_in(z0, z1, z2), z0, z1, z2, z3)
U64(f61_out1, z0, z1, z2, z3) → f95_out1
f96_in(z0, z1, z2, z3) → U65(f78_in(z1, z0, z3), z0, z1, z2, z3)
U65(f78_out1, z0, z1, z2, z3) → f96_out1
f174_in(z0, z1, z2, z3) → U66(f61_in(z0, z1, z2), z0, z1, z2, z3)
U66(f61_out1, z0, z1, z2, z3) → f174_out1
f175_in(z0, z1, z2, z3) → U67(f78_in(z1, z0, z3), z0, z1, z2, z3)
U67(f78_out1, z0, z1, z2, z3) → f175_out1
f415_in(z0, z1, z2, z3) → U68(f61_in(z0, z1, z2), z0, z1, z2, z3)
U68(f61_out1, z0, z1, z2, z3) → f415_out1
f416_in(z0, z1, z2, z3) → U69(f78_in(z1, z0, z3), z0, z1, z2, z3)
U69(f78_out1, z0, z1, z2, z3) → f416_out1
f52_in(z0, z1, z2, z3) → U70(f61_in(z0, z1, z2), z0, z1, z2, z3)
U70(f61_out1, z0, z1, z2, z3) → f52_out1
f53_in(z0, z1, z2, z3) → U71(f78_in(z1, z0, z3), z0, z1, z2, z3)
U71(f78_out1, z0, z1, z2, z3) → f53_out1
f61_in(z0, z1, z2) → U72(f63_in(z0, z1), z0, z1, z2)
U72(f63_out1, z0, z1, z2) → U73(f2_in(z0, z2), z0, z1, z2)
U73(f2_out1, z0, z1, z2) → f61_out1
f78_in(z0, z1, z2) → U74(f63_in(z0, z1), z0, z1, z2)
U74(f63_out1, z0, z1, z2) → U75(f2_in(z1, z2), z0, z1, z2)
U75(f2_out1, z0, z1, z2) → f78_out1
f123_in(z0, z1) → U76(f127_in(z0), z0, z1)
U76(f127_out1, z0, z1) → U77(f2_in(0, z1), z0, z1)
U77(f2_out1, z0, z1) → f123_out1
f138_in(z0, z1, z2) → U78(f63_in(z0, z1), z0, z1, z2)
U78(f63_out1, z0, z1, z2) → U79(f2_in(s(z0), z2), z0, z1, z2)
U79(f2_out1, z0, z1, z2) → f138_out1
f159_in(z0, z1, z2) → U80(f63_in(z0, z1), z0, z1, z2)
U80(f63_out1, z0, z1, z2) → U81(f2_in(s(z1), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f159_out1
f23_in(z0, z1, z2, z3) → U82(f86_in(z0, z1), f87_in(z2, z0, z3, z1), z0, z1, z2, z3)
U82(f86_out1, z0, z1, z2, z3, z4) → f23_out1
U82(z0, f87_out2, z1, z2, z3, z4) → f23_out3
U82(z0, f87_out3, z1, z2, z3, z4) → f23_out4
f25_in(z0, z1, z2, z3) → U83(f27_in(z0, z1), f28_in(z2, z0, z3, z1), z0, z1, z2, z3)
U83(f27_out1, z0, z1, z2, z3, z4) → f25_out1
U83(z0, f28_out2, z1, z2, z3, z4) → f25_out3
U83(z0, f28_out3, z1, z2, z3, z4) → f25_out4
f49_in(z0, z1, z2, z3) → U84(f52_in(z0, z1, z2, z3), f53_in(z0, z1, z2, z3), z0, z1, z2, z3)
U84(f52_out1, z0, z1, z2, z3, z4) → f49_out1
U84(z0, f53_out1, z1, z2, z3, z4) → f49_out2
f92_in(z0, z1, z2, z3) → U85(f95_in(z0, z1, z2, z3), f96_in(z0, z1, z2, z3), z0, z1, z2, z3)
U85(f95_out1, z0, z1, z2, z3, z4) → f92_out1
U85(z0, f96_out1, z1, z2, z3, z4) → f92_out2
f113_in(z0, z1, z2) → U86(f2_in(0, z0), f118_in(z1, z0, z2), z0, z1, z2)
U86(f2_out1, z0, z1, z2, z3) → f113_out1
U86(z0, f118_out1, z1, z2, z3) → f113_out2
U86(z0, f118_out3, z1, z2, z3) → f113_out4
f114_in(z0, z1, z2, z3) → U87(f134_in(z0, z1, z2), f135_in(z0, z1, z2, z3), z0, z1, z2, z3)
U87(f134_out1, z0, z1, z2, z3, z4) → f114_out1
U87(z0, f135_out2, z1, z2, z3, z4) → f114_out3
f154_in(z0, z1) → U88(f2_in(s(z0), z1), f157_in(z0, z1), z0, z1)
U88(f2_out1, z0, z1, z2) → f154_out1
U88(z0, f157_out1, z1, z2) → f154_out2
f167_in(z0, z1, z2, z3) → U89(f211_in(z0, z1), f212_in(z2, z0, z3, z1), z0, z1, z2, z3)
U89(f211_out1, z0, z1, z2, z3, z4) → f167_out1
U89(z0, f212_out2, z1, z2, z3, z4) → f167_out3
U89(z0, f212_out3, z1, z2, z3, z4) → f167_out4
f168_in(z0, z1, z2, z3) → U90(f169_in(z0, z1), f170_in(z2, z0, z3, z1), z0, z1, z2, z3)
U90(f169_out1, z0, z1, z2, z3, z4) → f168_out1
U90(z0, f170_out2, z1, z2, z3, z4) → f168_out3
U90(z0, f170_out3, z1, z2, z3, z4) → f168_out4
f173_in(z0, z1, z2, z3) → U91(f174_in(z0, z1, z2, z3), f175_in(z0, z1, z2, z3), z0, z1, z2, z3)
U91(f174_out1, z0, z1, z2, z3, z4) → f173_out1
U91(z0, f175_out1, z1, z2, z3, z4) → f173_out2
f215_in(z0, z1, z2, z3) → U92(f216_in(z0, z1, z2, z3), f217_in(z0, z1, z2, z3), z0, z1, z2, z3)
U92(f216_out1, z0, z1, z2, z3, z4) → f215_out1
U92(z0, f217_out1, z1, z2, z3, z4) → f215_out2
f264_in(z0, z1, z2) → U93(f2_in(0, z0), f267_in(z1, z0, z2), z0, z1, z2)
U93(f2_out1, z0, z1, z2, z3) → f264_out1
U93(z0, f267_out1, z1, z2, z3) → f264_out2
U93(z0, f267_out3, z1, z2, z3) → f264_out4
f265_in(z0, z1, z2, z3) → U94(f301_in(z0, z1, z2), f302_in(z0, z1, z2, z3), z0, z1, z2, z3)
U94(f301_out1, z0, z1, z2, z3, z4) → f265_out1
U94(z0, f302_out2, z1, z2, z3, z4) → f265_out3
f311_in(z0, z1) → U95(f2_in(s(z0), z1), f314_in(z0, z1), z0, z1)
U95(f2_out1, z0, z1, z2) → f311_out1
U95(z0, f314_out1, z1, z2) → f311_out2
f325_in(z0, z1, z2, z3) → U96(f422_in(z0, z1), f424_in(z2, z0, z3, z1), z0, z1, z2, z3)
U96(f422_out1, z0, z1, z2, z3, z4) → f325_out1
U96(z0, f424_out2, z1, z2, z3, z4) → f325_out3
U96(z0, f424_out3, z1, z2, z3, z4) → f325_out4
f326_in(z0, z1, z2, z3) → U97(f327_in(z0, z1), f328_in(z2, z0, z3, z1), z0, z1, z2, z3)
U97(f327_out1, z0, z1, z2, z3, z4) → f326_out1
U97(z0, f328_out2, z1, z2, z3, z4) → f326_out3
U97(z0, f328_out3, z1, z2, z3, z4) → f326_out4
f414_in(z0, z1, z2, z3) → U98(f415_in(z0, z1, z2, z3), f416_in(z0, z1, z2, z3), z0, z1, z2, z3)
U98(f415_out1, z0, z1, z2, z3, z4) → f414_out1
U98(z0, f416_out1, z1, z2, z3, z4) → f414_out2
f460_in(z0, z1, z2, z3) → U99(f461_in(z0, z1, z2, z3), f462_in(z0, z1, z2, z3), z0, z1, z2, z3)
U99(f461_out1, z0, z1, z2, z3, z4) → f460_out1
U99(z0, f462_out1, z1, z2, z3, z4) → f460_out2
f470_in(z0, z1, z2) → U100(f2_in(0, z0), f476_in(z1, z0, z2), z0, z1, z2)
U100(f2_out1, z0, z1, z2, z3) → f470_out1
U100(z0, f476_out1, z1, z2, z3) → f470_out2
U100(z0, f476_out3, z1, z2, z3) → f470_out4
f471_in(z0, z1, z2, z3) → U101(f521_in(z0, z1, z2), f522_in(z0, z1, z2, z3), z0, z1, z2, z3)
U101(f521_out1, z0, z1, z2, z3, z4) → f471_out1
U101(z0, f522_out2, z1, z2, z3, z4) → f471_out3
f531_in(z0, z1) → U102(f2_in(s(z0), z1), f534_in(z0, z1), z0, z1)
U102(f2_out1, z0, z1, z2) → f531_out1
U102(z0, f534_out1, z1, z2) → f531_out2
f542_in(z0, z1, z2, z3) → U103(f585_in(z0, z1), f586_in(z2, z0, z3, z1), z0, z1, z2, z3)
U103(f585_out1, z0, z1, z2, z3, z4) → f542_out1
U103(z0, f586_out2, z1, z2, z3, z4) → f542_out3
U103(z0, f586_out3, z1, z2, z3, z4) → f542_out4
f543_in(z0, z1, z2, z3) → U104(f574_in(z0, z1), f575_in(z2, z0, z3, z1), z0, z1, z2, z3)
U104(f574_out1, z0, z1, z2, z3, z4) → f543_out1
U104(z0, f575_out2, z1, z2, z3, z4) → f543_out3
U104(z0, f575_out3, z1, z2, z3, z4) → f543_out4
f578_in(z0, z1, z2, z3) → U105(f579_in(z0, z1, z2, z3), f580_in(z0, z1, z2, z3), z0, z1, z2, z3)
U105(f579_out1, z0, z1, z2, z3, z4) → f578_out1
U105(z0, f580_out1, z1, z2, z3, z4) → f578_out2
f589_in(z0, z1, z2, z3) → U106(f590_in(z0, z1, z2, z3), f591_in(z0, z1, z2, z3), z0, z1, z2, z3)
U106(f590_out1, z0, z1, z2, z3, z4) → f589_out1
U106(z0, f591_out1, z1, z2, z3, z4) → f589_out2
f599_in(z0, z1, z2) → U107(f2_in(0, z0), f602_in(z1, z0, z2), z0, z1, z2)
U107(f2_out1, z0, z1, z2, z3) → f599_out1
U107(z0, f602_out1, z1, z2, z3) → f599_out2
U107(z0, f602_out3, z1, z2, z3) → f599_out4
f600_in(z0, z1, z2, z3) → U108(f607_in(z0, z1, z2), f608_in(z0, z1, z2, z3), z0, z1, z2, z3)
U108(f607_out1, z0, z1, z2, z3, z4) → f600_out1
U108(z0, f608_out2, z1, z2, z3, z4) → f600_out3
f700_in(z0, z1) → U109(f2_in(s(z0), z1), f703_in(z0, z1), z0, z1)
U109(f2_out1, z0, z1, z2) → f700_out1
U109(z0, f703_out1, z1, z2) → f700_out2

Tuples:

F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F61_IN(s(z0), s(z1), x2) → c186(U72'(U27(f63_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F63_IN(s(z0), s(z1)))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0))
F61_IN(0, s(z0), x2) → c186(U72'(f63_out1, 0, s(z0), x2))

S tuples:

F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))

K tuples:

F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, U17, U18, U19, U20, U21, U22, U23, U24, f33_in, U25, U26, f63_in, U27, f585_in, U28, f586_in, U29, f211_in, U30, f212_in, U31, f422_in, U32, f424_in, U33, f574_in, U34, f575_in, U35, f602_in, U36, f607_in, U37, f608_in, U38, f86_in, U39, f87_in, U40, f169_in, U41, f170_in, U42, f267_in, U43, f301_in, U44, f302_in, U45, f327_in, U46, f328_in, U47, f476_in, U48, f521_in, U49, f522_in, U50, f590_in, U51, f591_in, U52, f27_in, U53, f28_in, U54, f118_in, U55, f134_in, U56, f135_in, U57, f216_in, U58, f217_in, U59, f461_in, U60, f462_in, U61, f579_in, U62, f580_in, U63, f95_in, U64, f96_in, U65, f174_in, U66, f175_in, U67, f415_in, U68, f416_in, U69, f52_in, U70, f53_in, U71, f61_in, U72, U73, f78_in, U74, U75, f123_in, U76, U77, f138_in, U78, U79, f159_in, U80, U81, f23_in, U82, f25_in, U83, f49_in, U84, f92_in, U85, f113_in, U86, f114_in, U87, f154_in, U88, f167_in, U89, f168_in, U90, f173_in, U91, f215_in, U92, f264_in, U93, f265_in, U94, f311_in, U95, f325_in, U96, f326_in, U97, f414_in, U98, f460_in, U99, f470_in, U100, f471_in, U101, f531_in, U102, f542_in, U103, f543_in, U104, f578_in, U105, f589_in, U106, f599_in, U107, f600_in, U108, f700_in, U109

Defined Pair Symbols:

F78_IN, F138_IN, F159_IN, F585_IN, F211_IN, F422_IN, F574_IN, F86_IN, F169_IN, F327_IN, F27_IN, F2_IN, F33_IN, F63_IN, F586_IN, F212_IN, F424_IN, F575_IN, F607_IN, F608_IN, F87_IN, F170_IN, F301_IN, F302_IN, F328_IN, F521_IN, F522_IN, F590_IN, F591_IN, F28_IN, F134_IN, F135_IN, F216_IN, F217_IN, F461_IN, F462_IN, F579_IN, F580_IN, F95_IN, F96_IN, F174_IN, F175_IN, F415_IN, F416_IN, F52_IN, F53_IN, U72', U74', U78', U80', F23_IN, F25_IN, F49_IN, F92_IN, F114_IN, F154_IN, F167_IN, F168_IN, F173_IN, F215_IN, F265_IN, F311_IN, F325_IN, F326_IN, F414_IN, F460_IN, F471_IN, F531_IN, F542_IN, F543_IN, F578_IN, F589_IN, F600_IN, F700_IN, F61_IN, F113_IN, F264_IN, F470_IN, F599_IN

Compound Symbols:

c189, c195, c198, c, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c83, c84, c88, c92, c97, c102, c107, c112, c114, c118, c123, c128, c130, c134, c139, c141, c143, c145, c149, c154, c156, c158, c160, c162, c164, c166, c168, c170, c172, c174, c176, c178, c180, c182, c184, c187, c190, c196, c199, c201, c205, c209, c212, c219, c222, c225, c229, c233, c236, c243, c246, c249, c253, c257, c260, c267, c270, c273, c277, c281, c284, c291, c294, c186, c215, c239, c263, c287, c186

(45) 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.

F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))

We considered the (Usable) Rules:

f63_in(0, s(z0)) → f63_out1
f63_in(s(z0), s(z1)) → U27(f63_in(z0, z1), s(z0), s(z1))
U27(f63_out1, s(z0), s(z1)) → f63_out1

And the Tuples:

F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F61_IN(s(z0), s(z1), x2) → c186(U72'(U27(f63_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F63_IN(s(z0), s(z1)))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0))
F61_IN(0, s(z0), x2) → c186(U72'(f63_out1, 0, s(z0), x2))

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

POL(0) = 0   
POL(F113_IN(x₁, x₂, x₃)) = x₃² + x₂·x₃ + x₁·x₃ + x₁² + x₁·x₂ + x₂²   
POL(F114_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₃·x₄ + x₂·x₄ + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂·x₃ + x₂²   
POL(F134_IN(x₁, x₂, x₃)) = x₃² + x₁·x₃ + x₁·x₂   
POL(F135_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₃·x₄ + x₁·x₄   
POL(F138_IN(x₁, x₂, x₃)) = x₁ + x₃ + x₃² + x₁·x₃   
POL(F154_IN(x₁, x₂)) = x₂ + x₂² + x₁·x₂   
POL(F159_IN(x₁, x₂, x₃)) = [1] + x₁ + x₃ + x₃² + x₂·x₃   
POL(F167_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₃·x₄ + x₁² + x₁·x₃ + x₂·x₃ + x₂²   
POL(F168_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₃·x₄ + x₁² + x₁·x₃ + x₂·x₃ + x₂²   
POL(F169_IN(x₁, x₂)) = 0   
POL(F170_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F173_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F174_IN(x₁, x₂, x₃, x₄)) = [1] + x₃ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F175_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₁·x₄   
POL(F211_IN(x₁, x₂)) = 0   
POL(F212_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F215_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F216_IN(x₁, x₂, x₃, x₄)) = [1] + x₃ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F217_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₁·x₄   
POL(F23_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₃·x₄ + x₂·x₄ + x₁² + x₁·x₂ + x₁·x₃ + x₂·x₃ + x₂²   
POL(F25_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₃·x₄ + x₁² + x₁·x₂ + x₁·x₃ + x₂·x₃ + x₂²   
POL(F264_IN(x₁, x₂, x₃)) = x₁ + x₂ + x₃ + x₃² + x₂·x₃ + x₁·x₃ + x₁² + x₁·x₂ + x₂²   
POL(F265_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃²   
POL(F27_IN(x₁, x₂)) = 0   
POL(F28_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F2_IN(x₁, x₂)) = x₂² + x₁·x₂   
POL(F301_IN(x₁, x₂, x₃)) = x₃² + x₁·x₃ + x₁·x₂   
POL(F302_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₁·x₄   
POL(F311_IN(x₁, x₂)) = [1] + x₂ + x₂² + x₁·x₂   
POL(F325_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₃·x₄ + x₁² + x₁·x₃ + x₂·x₃ + x₂²   
POL(F326_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₃·x₄ + x₁² + x₁·x₃ + x₂·x₃ + x₂²   
POL(F327_IN(x₁, x₂)) = 0   
POL(F328_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F33_IN(x₁, x₂)) = 0   
POL(F414_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F415_IN(x₁, x₂, x₃, x₄)) = [1] + x₃ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F416_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₁·x₄   
POL(F422_IN(x₁, x₂)) = 0   
POL(F424_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F460_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F461_IN(x₁, x₂, x₃, x₄)) = [1] + x₃ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F462_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₁·x₄   
POL(F470_IN(x₁, x₂, x₃)) = [1] + x₁ + x₂ + x₃ + x₃² + x₂·x₃ + x₁·x₃ + x₁² + x₁·x₂ + x₂²   
POL(F471_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₃·x₄ + x₂·x₄ + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F49_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F521_IN(x₁, x₂, x₃)) = x₃² + x₁·x₃ + x₁·x₂   
POL(F522_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₃·x₄ + x₁·x₄   
POL(F52_IN(x₁, x₂, x₃, x₄)) = [1] + x₃ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F531_IN(x₁, x₂)) = [1] + x₂ + x₂² + x₁·x₂   
POL(F53_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₁·x₄   
POL(F542_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₃·x₄ + x₂·x₄ + x₁·x₄ + x₁² + x₁·x₃ + x₂·x₃ + x₂²   
POL(F543_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₃·x₄ + x₂·x₄ + x₁² + x₁·x₂ + x₁·x₃ + x₂·x₃ + x₂²   
POL(F574_IN(x₁, x₂)) = 0   
POL(F575_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F578_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F579_IN(x₁, x₂, x₃, x₄)) = [1] + x₃ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F580_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₁·x₄   
POL(F585_IN(x₁, x₂)) = 0   
POL(F586_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F589_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F590_IN(x₁, x₂, x₃, x₄)) = [1] + x₃ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F591_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₁·x₄   
POL(F599_IN(x₁, x₂, x₃)) = [1] + x₂ + x₃ + x₃² + x₂·x₃ + x₁·x₃ + x₁² + x₁·x₂ + x₂²   
POL(F600_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₃·x₄ + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂·x₃ + x₂²   
POL(F607_IN(x₁, x₂, x₃)) = x₃² + x₁·x₃ + x₁·x₂   
POL(F608_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₃·x₄ + x₁·x₄   
POL(F61_IN(x₁, x₂, x₃)) = [1] + x₃ + x₃² + x₁·x₃ + x₁·x₂ + x₂²   
POL(F63_IN(x₁, x₂)) = x₁   
POL(F700_IN(x₁, x₂)) = [1] + x₂ + x₂² + x₁·x₂   
POL(F78_IN(x₁, x₂, x₃)) = x₁ + x₂ + x₃ + x₃² + x₂·x₃   
POL(F86_IN(x₁, x₂)) = 0   
POL(F87_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F92_IN(x₁, x₂, x₃, x₄)) = [1] + x₁ + x₂ + x₃ + x₄ + x₄² + x₁·x₄ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F95_IN(x₁, x₂, x₃, x₄)) = [1] + x₃ + x₁·x₂ + x₁·x₃ + x₃² + x₂²   
POL(F96_IN(x₁, x₂, x₃, x₄)) = x₁ + x₂ + x₄ + x₄² + x₁·x₄   
POL(U27(x₁, x₂, x₃)) = 0   
POL(U72'(x₁, x₂, x₃, x₄)) = [1] + x₄ + x₄² + x₂·x₄ + x₃²   
POL(U74'(x₁, x₂, x₃, x₄)) = x₃ + x₄² + x₃·x₄ + x₁·x₄ + x₁·x₃   
POL(U78'(x₁, x₂, x₃, x₄)) = x₄ + x₄² + x₂·x₄   
POL(U80'(x₁, x₂, x₃, x₄)) = x₄ + x₄² + x₃·x₄   
POL(c(x₁)) = x₁   
POL(c10(x₁)) = x₁   
POL(c102(x₁)) = x₁   
POL(c107(x₁)) = x₁   
POL(c11(x₁)) = x₁   
POL(c112(x₁)) = x₁   
POL(c114(x₁)) = x₁   
POL(c118(x₁)) = x₁   
POL(c12(x₁)) = x₁   
POL(c123(x₁)) = x₁   
POL(c128(x₁)) = x₁   
POL(c13(x₁)) = x₁   
POL(c130(x₁)) = x₁   
POL(c134(x₁)) = x₁   
POL(c139(x₁)) = x₁   
POL(c14(x₁)) = x₁   
POL(c141(x₁)) = x₁   
POL(c143(x₁)) = x₁   
POL(c145(x₁)) = x₁   
POL(c149(x₁)) = x₁   
POL(c15(x₁)) = x₁   
POL(c154(x₁)) = x₁   
POL(c156(x₁)) = x₁   
POL(c158(x₁)) = x₁   
POL(c16(x₁)) = x₁   
POL(c160(x₁)) = x₁   
POL(c162(x₁)) = x₁   
POL(c164(x₁)) = x₁   
POL(c166(x₁)) = x₁   
POL(c168(x₁)) = x₁   
POL(c17(x₁)) = x₁   
POL(c170(x₁)) = x₁   
POL(c172(x₁)) = x₁   
POL(c174(x₁)) = x₁   
POL(c176(x₁)) = x₁   
POL(c178(x₁)) = x₁   
POL(c18(x₁)) = x₁   
POL(c180(x₁)) = x₁   
POL(c182(x₁)) = x₁   
POL(c184(x₁)) = x₁   
POL(c186(x₁)) = x₁   
POL(c186(x₁, x₂)) = x₁ + x₂   
POL(c187(x₁)) = x₁   
POL(c189(x₁, x₂)) = x₁ + x₂   
POL(c19(x₁)) = x₁   
POL(c190(x₁)) = x₁   
POL(c195(x₁, x₂)) = x₁ + x₂   
POL(c196(x₁)) = x₁   
POL(c198(x₁, x₂)) = x₁ + x₂   
POL(c199(x₁)) = x₁   
POL(c2(x₁)) = x₁   
POL(c20(x₁)) = x₁   
POL(c201(x₁, x₂)) = x₁ + x₂   
POL(c205(x₁, x₂)) = x₁ + x₂   
POL(c209(x₁, x₂)) = x₁ + x₂   
POL(c21(x₁)) = x₁   
POL(c212(x₁, x₂)) = x₁ + x₂   
POL(c215(x₁)) = x₁   
POL(c219(x₁, x₂)) = x₁ + x₂   
POL(c22(x₁)) = x₁   
POL(c222(x₁)) = x₁   
POL(c225(x₁, x₂)) = x₁ + x₂   
POL(c229(x₁, x₂)) = x₁ + x₂   
POL(c23(x₁)) = x₁   
POL(c233(x₁, x₂)) = x₁ + x₂   
POL(c236(x₁, x₂)) = x₁ + x₂   
POL(c239(x₁)) = x₁   
POL(c24(x₁)) = x₁   
POL(c243(x₁, x₂)) = x₁ + x₂   
POL(c246(x₁)) = x₁   
POL(c249(x₁, x₂)) = x₁ + x₂   
POL(c25(x₁)) = x₁   
POL(c253(x₁, x₂)) = x₁ + x₂   
POL(c257(x₁, x₂)) = x₁ + x₂   
POL(c260(x₁, x₂)) = x₁ + x₂   
POL(c263(x₁)) = x₁   
POL(c267(x₁, x₂)) = x₁ + x₂   
POL(c270(x₁)) = x₁   
POL(c273(x₁, x₂)) = x₁ + x₂   
POL(c277(x₁, x₂)) = x₁ + x₂   
POL(c281(x₁, x₂)) = x₁ + x₂   
POL(c284(x₁, x₂)) = x₁ + x₂   
POL(c287(x₁)) = x₁   
POL(c291(x₁, x₂)) = x₁ + x₂   
POL(c294(x₁)) = x₁   
POL(c3(x₁)) = x₁   
POL(c4(x₁)) = x₁   
POL(c5(x₁)) = x₁   
POL(c6(x₁)) = x₁   
POL(c7(x₁)) = x₁   
POL(c8(x₁)) = x₁   
POL(c83(x₁)) = x₁   
POL(c84(x₁)) = x₁   
POL(c88(x₁)) = x₁   
POL(c9(x₁)) = x₁   
POL(c92(x₁)) = x₁   
POL(c97(x₁)) = x₁   
POL(f63_in(x₁, x₂)) = 0   
POL(f63_out1) = 0   
POL(s(x₁)) = [1] + x₁   
POL(tree(x₁, x₂, x₃)) = [1] + x₁ + x₂ + x₃   

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → f2_out1
f2_in(z0, tree(z1, z2, z3)) → U1(f25_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U2(f23_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U3(f113_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U4(f114_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U5(f154_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U6(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U7(f168_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U8(f167_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U9(f264_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U10(f265_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U11(f311_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U12(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U13(f326_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U14(f325_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U15(f470_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U16(f471_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U17(f531_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U18(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U19(f543_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(z0, tree(z1, z2, z3)) → U20(f542_in(z1, z3, z0, z2), z0, tree(z1, z2, z3))
f2_in(0, tree(s(z0), z1, z2)) → U21(f599_in(z1, z0, z2), 0, tree(s(z0), z1, z2))
f2_in(z0, tree(z1, z2, z3)) → U22(f600_in(z0, z1, z2, z3), z0, tree(z1, z2, z3))
f2_in(s(z0), tree(0, z1, z2)) → U23(f700_in(z0, z2), s(z0), tree(0, z1, z2))
f2_in(s(z0), tree(s(z1), z2, z3)) → U24(f159_in(z1, z0, z3), s(z0), tree(s(z1), z2, z3))
U1(f25_out1, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out3, z0, tree(z1, z2, z3)) → f2_out1
U1(f25_out4, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out1, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out3, z0, tree(z1, z2, z3)) → f2_out1
U2(f23_out4, z0, tree(z1, z2, z3)) → f2_out1
U3(f113_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U3(f113_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U4(f114_out1, z0, tree(z1, z2, z3)) → f2_out1
U4(f114_out3, z0, tree(z1, z2, z3)) → f2_out1
U5(f154_out1, s(z0), tree(0, z1, z2)) → f2_out1
U5(f154_out2, s(z0), tree(0, z1, z2)) → f2_out1
U6(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U7(f168_out1, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out3, z0, tree(z1, z2, z3)) → f2_out1
U7(f168_out4, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out1, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out3, z0, tree(z1, z2, z3)) → f2_out1
U8(f167_out4, z0, tree(z1, z2, z3)) → f2_out1
U9(f264_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U9(f264_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U10(f265_out1, z0, tree(z1, z2, z3)) → f2_out1
U10(f265_out3, z0, tree(z1, z2, z3)) → f2_out1
U11(f311_out1, s(z0), tree(0, z1, z2)) → f2_out1
U11(f311_out2, s(z0), tree(0, z1, z2)) → f2_out1
U12(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U13(f326_out1, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out3, z0, tree(z1, z2, z3)) → f2_out1
U13(f326_out4, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out1, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out3, z0, tree(z1, z2, z3)) → f2_out1
U14(f325_out4, z0, tree(z1, z2, z3)) → f2_out1
U15(f470_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U15(f470_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U16(f471_out1, z0, tree(z1, z2, z3)) → f2_out1
U16(f471_out3, z0, tree(z1, z2, z3)) → f2_out1
U17(f531_out1, s(z0), tree(0, z1, z2)) → f2_out1
U17(f531_out2, s(z0), tree(0, z1, z2)) → f2_out1
U18(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
U19(f543_out1, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out3, z0, tree(z1, z2, z3)) → f2_out1
U19(f543_out4, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out1, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out3, z0, tree(z1, z2, z3)) → f2_out1
U20(f542_out4, z0, tree(z1, z2, z3)) → f2_out1
U21(f599_out1, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out2, 0, tree(s(z0), z1, z2)) → f2_out1
U21(f599_out4, 0, tree(s(z0), z1, z2)) → f2_out1
U22(f600_out1, z0, tree(z1, z2, z3)) → f2_out1
U22(f600_out3, z0, tree(z1, z2, z3)) → f2_out1
U23(f700_out1, s(z0), tree(0, z1, z2)) → f2_out1
U23(f700_out2, s(z0), tree(0, z1, z2)) → f2_out1
U24(f159_out1, s(z0), tree(s(z1), z2, z3)) → f2_out1
f33_in(z0, z1) → f33_out1
f33_in(z0, tree(z1, z2, z3)) → U25(f33_in(z0, z2), z0, tree(z1, z2, z3))
f33_in(z0, tree(z1, z2, z3)) → U26(f33_in(z0, z2), z0, tree(z1, z2, z3))
U25(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
U26(f33_out1, z0, tree(z1, z2, z3)) → f33_out1
f63_in(0, s(z0)) → f63_out1
f63_in(s(z0), s(z1)) → U27(f63_in(z0, z1), s(z0), s(z1))
U27(f63_out1, s(z0), s(z1)) → f63_out1
f585_in(z0, tree(z1, z2, z3)) → U28(f33_in(z0, z2), z0, tree(z1, z2, z3))
U28(f33_out1, z0, tree(z1, z2, z3)) → f585_out1
f586_in(z0, z1, z2, z3) → U29(f589_in(z0, z1, z2, z3), z0, z1, z2, z3)
U29(f589_out1, z0, z1, z2, z3) → f586_out2
U29(f589_out2, z0, z1, z2, z3) → f586_out3
f211_in(z0, tree(z1, z2, z3)) → U30(f33_in(z0, z2), z0, tree(z1, z2, z3))
U30(f33_out1, z0, tree(z1, z2, z3)) → f211_out1
f212_in(z0, z1, z2, z3) → U31(f215_in(z0, z1, z2, z3), z0, z1, z2, z3)
U31(f215_out1, z0, z1, z2, z3) → f212_out2
U31(f215_out2, z0, z1, z2, z3) → f212_out3
f422_in(z0, tree(z1, z2, z3)) → U32(f33_in(z0, z2), z0, tree(z1, z2, z3))
U32(f33_out1, z0, tree(z1, z2, z3)) → f422_out1
f424_in(z0, z1, z2, z3) → U33(f460_in(z0, z1, z2, z3), z0, z1, z2, z3)
U33(f460_out1, z0, z1, z2, z3) → f424_out2
U33(f460_out2, z0, z1, z2, z3) → f424_out3
f574_in(z0, tree(z1, z2, z3)) → U34(f33_in(z0, z2), z0, tree(z1, z2, z3))
U34(f33_out1, z0, tree(z1, z2, z3)) → f574_out1
f575_in(z0, z1, z2, z3) → U35(f578_in(z0, z1, z2, z3), z0, z1, z2, z3)
U35(f578_out1, z0, z1, z2, z3) → f575_out2
U35(f578_out2, z0, z1, z2, z3) → f575_out3
f602_in(z0, z1, z2) → U36(f123_in(z0, z2), z0, z1, z2)
U36(f123_out1, z0, z1, z2) → f602_out3
f607_in(s(z0), s(z1), z2) → U37(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U37(f138_out1, s(z0), s(z1), z2) → f607_out1
f608_in(z0, z1, z2, z3) → U38(f78_in(z1, z0, z3), z0, z1, z2, z3)
U38(f78_out1, z0, z1, z2, z3) → f608_out2
f86_in(z0, tree(z1, z2, z3)) → U39(f33_in(z0, z2), z0, tree(z1, z2, z3))
U39(f33_out1, z0, tree(z1, z2, z3)) → f86_out1
f87_in(z0, z1, z2, z3) → U40(f92_in(z0, z1, z2, z3), z0, z1, z2, z3)
U40(f92_out1, z0, z1, z2, z3) → f87_out2
U40(f92_out2, z0, z1, z2, z3) → f87_out3
f169_in(z0, tree(z1, z2, z3)) → U41(f33_in(z0, z2), z0, tree(z1, z2, z3))
U41(f33_out1, z0, tree(z1, z2, z3)) → f169_out1
f170_in(z0, z1, z2, z3) → U42(f173_in(z0, z1, z2, z3), z0, z1, z2, z3)
U42(f173_out1, z0, z1, z2, z3) → f170_out2
U42(f173_out2, z0, z1, z2, z3) → f170_out3
f267_in(z0, z1, z2) → U43(f123_in(z0, z2), z0, z1, z2)
U43(f123_out1, z0, z1, z2) → f267_out3
f301_in(s(z0), s(z1), z2) → U44(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U44(f138_out1, s(z0), s(z1), z2) → f301_out1
f302_in(z0, z1, z2, z3) → U45(f78_in(z1, z0, z3), z0, z1, z2, z3)
U45(f78_out1, z0, z1, z2, z3) → f302_out2
f327_in(z0, tree(z1, z2, z3)) → U46(f33_in(z0, z2), z0, tree(z1, z2, z3))
U46(f33_out1, z0, tree(z1, z2, z3)) → f327_out1
f328_in(z0, z1, z2, z3) → U47(f414_in(z0, z1, z2, z3), z0, z1, z2, z3)
U47(f414_out1, z0, z1, z2, z3) → f328_out2
U47(f414_out2, z0, z1, z2, z3) → f328_out3
f476_in(z0, z1, z2) → U48(f123_in(z0, z2), z0, z1, z2)
U48(f123_out1, z0, z1, z2) → f476_out3
f521_in(s(z0), s(z1), z2) → U49(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U49(f138_out1, s(z0), s(z1), z2) → f521_out1
f522_in(z0, z1, z2, z3) → U50(f78_in(z1, z0, z3), z0, z1, z2, z3)
U50(f78_out1, z0, z1, z2, z3) → f522_out2
f590_in(z0, z1, z2, z3) → U51(f61_in(z0, z1, z2), z0, z1, z2, z3)
U51(f61_out1, z0, z1, z2, z3) → f590_out1
f591_in(z0, z1, z2, z3) → U52(f78_in(z1, z0, z3), z0, z1, z2, z3)
U52(f78_out1, z0, z1, z2, z3) → f591_out1
f27_in(z0, tree(z1, z2, z3)) → U53(f33_in(z0, z2), z0, tree(z1, z2, z3))
U53(f33_out1, z0, tree(z1, z2, z3)) → f27_out1
f28_in(z0, z1, z2, z3) → U54(f49_in(z0, z1, z2, z3), z0, z1, z2, z3)
U54(f49_out1, z0, z1, z2, z3) → f28_out2
U54(f49_out2, z0, z1, z2, z3) → f28_out3
f118_in(z0, z1, z2) → U55(f123_in(z0, z2), z0, z1, z2)
U55(f123_out1, z0, z1, z2) → f118_out3
f134_in(s(z0), s(z1), z2) → U56(f138_in(z0, z1, z2), s(z0), s(z1), z2)
U56(f138_out1, s(z0), s(z1), z2) → f134_out1
f135_in(z0, z1, z2, z3) → U57(f78_in(z1, z0, z3), z0, z1, z2, z3)
U57(f78_out1, z0, z1, z2, z3) → f135_out2
f216_in(z0, z1, z2, z3) → U58(f61_in(z0, z1, z2), z0, z1, z2, z3)
U58(f61_out1, z0, z1, z2, z3) → f216_out1
f217_in(z0, z1, z2, z3) → U59(f78_in(z1, z0, z3), z0, z1, z2, z3)
U59(f78_out1, z0, z1, z2, z3) → f217_out1
f461_in(z0, z1, z2, z3) → U60(f61_in(z0, z1, z2), z0, z1, z2, z3)
U60(f61_out1, z0, z1, z2, z3) → f461_out1
f462_in(z0, z1, z2, z3) → U61(f78_in(z1, z0, z3), z0, z1, z2, z3)
U61(f78_out1, z0, z1, z2, z3) → f462_out1
f579_in(z0, z1, z2, z3) → U62(f61_in(z0, z1, z2), z0, z1, z2, z3)
U62(f61_out1, z0, z1, z2, z3) → f579_out1
f580_in(z0, z1, z2, z3) → U63(f78_in(z1, z0, z3), z0, z1, z2, z3)
U63(f78_out1, z0, z1, z2, z3) → f580_out1
f95_in(z0, z1, z2, z3) → U64(f61_in(z0, z1, z2), z0, z1, z2, z3)
U64(f61_out1, z0, z1, z2, z3) → f95_out1
f96_in(z0, z1, z2, z3) → U65(f78_in(z1, z0, z3), z0, z1, z2, z3)
U65(f78_out1, z0, z1, z2, z3) → f96_out1
f174_in(z0, z1, z2, z3) → U66(f61_in(z0, z1, z2), z0, z1, z2, z3)
U66(f61_out1, z0, z1, z2, z3) → f174_out1
f175_in(z0, z1, z2, z3) → U67(f78_in(z1, z0, z3), z0, z1, z2, z3)
U67(f78_out1, z0, z1, z2, z3) → f175_out1
f415_in(z0, z1, z2, z3) → U68(f61_in(z0, z1, z2), z0, z1, z2, z3)
U68(f61_out1, z0, z1, z2, z3) → f415_out1
f416_in(z0, z1, z2, z3) → U69(f78_in(z1, z0, z3), z0, z1, z2, z3)
U69(f78_out1, z0, z1, z2, z3) → f416_out1
f52_in(z0, z1, z2, z3) → U70(f61_in(z0, z1, z2), z0, z1, z2, z3)
U70(f61_out1, z0, z1, z2, z3) → f52_out1
f53_in(z0, z1, z2, z3) → U71(f78_in(z1, z0, z3), z0, z1, z2, z3)
U71(f78_out1, z0, z1, z2, z3) → f53_out1
f61_in(z0, z1, z2) → U72(f63_in(z0, z1), z0, z1, z2)
U72(f63_out1, z0, z1, z2) → U73(f2_in(z0, z2), z0, z1, z2)
U73(f2_out1, z0, z1, z2) → f61_out1
f78_in(z0, z1, z2) → U74(f63_in(z0, z1), z0, z1, z2)
U74(f63_out1, z0, z1, z2) → U75(f2_in(z1, z2), z0, z1, z2)
U75(f2_out1, z0, z1, z2) → f78_out1
f123_in(z0, z1) → U76(f127_in(z0), z0, z1)
U76(f127_out1, z0, z1) → U77(f2_in(0, z1), z0, z1)
U77(f2_out1, z0, z1) → f123_out1
f138_in(z0, z1, z2) → U78(f63_in(z0, z1), z0, z1, z2)
U78(f63_out1, z0, z1, z2) → U79(f2_in(s(z0), z2), z0, z1, z2)
U79(f2_out1, z0, z1, z2) → f138_out1
f159_in(z0, z1, z2) → U80(f63_in(z0, z1), z0, z1, z2)
U80(f63_out1, z0, z1, z2) → U81(f2_in(s(z1), z2), z0, z1, z2)
U81(f2_out1, z0, z1, z2) → f159_out1
f23_in(z0, z1, z2, z3) → U82(f86_in(z0, z1), f87_in(z2, z0, z3, z1), z0, z1, z2, z3)
U82(f86_out1, z0, z1, z2, z3, z4) → f23_out1
U82(z0, f87_out2, z1, z2, z3, z4) → f23_out3
U82(z0, f87_out3, z1, z2, z3, z4) → f23_out4
f25_in(z0, z1, z2, z3) → U83(f27_in(z0, z1), f28_in(z2, z0, z3, z1), z0, z1, z2, z3)
U83(f27_out1, z0, z1, z2, z3, z4) → f25_out1
U83(z0, f28_out2, z1, z2, z3, z4) → f25_out3
U83(z0, f28_out3, z1, z2, z3, z4) → f25_out4
f49_in(z0, z1, z2, z3) → U84(f52_in(z0, z1, z2, z3), f53_in(z0, z1, z2, z3), z0, z1, z2, z3)
U84(f52_out1, z0, z1, z2, z3, z4) → f49_out1
U84(z0, f53_out1, z1, z2, z3, z4) → f49_out2
f92_in(z0, z1, z2, z3) → U85(f95_in(z0, z1, z2, z3), f96_in(z0, z1, z2, z3), z0, z1, z2, z3)
U85(f95_out1, z0, z1, z2, z3, z4) → f92_out1
U85(z0, f96_out1, z1, z2, z3, z4) → f92_out2
f113_in(z0, z1, z2) → U86(f2_in(0, z0), f118_in(z1, z0, z2), z0, z1, z2)
U86(f2_out1, z0, z1, z2, z3) → f113_out1
U86(z0, f118_out1, z1, z2, z3) → f113_out2
U86(z0, f118_out3, z1, z2, z3) → f113_out4
f114_in(z0, z1, z2, z3) → U87(f134_in(z0, z1, z2), f135_in(z0, z1, z2, z3), z0, z1, z2, z3)
U87(f134_out1, z0, z1, z2, z3, z4) → f114_out1
U87(z0, f135_out2, z1, z2, z3, z4) → f114_out3
f154_in(z0, z1) → U88(f2_in(s(z0), z1), f157_in(z0, z1), z0, z1)
U88(f2_out1, z0, z1, z2) → f154_out1
U88(z0, f157_out1, z1, z2) → f154_out2
f167_in(z0, z1, z2, z3) → U89(f211_in(z0, z1), f212_in(z2, z0, z3, z1), z0, z1, z2, z3)
U89(f211_out1, z0, z1, z2, z3, z4) → f167_out1
U89(z0, f212_out2, z1, z2, z3, z4) → f167_out3
U89(z0, f212_out3, z1, z2, z3, z4) → f167_out4
f168_in(z0, z1, z2, z3) → U90(f169_in(z0, z1), f170_in(z2, z0, z3, z1), z0, z1, z2, z3)
U90(f169_out1, z0, z1, z2, z3, z4) → f168_out1
U90(z0, f170_out2, z1, z2, z3, z4) → f168_out3
U90(z0, f170_out3, z1, z2, z3, z4) → f168_out4
f173_in(z0, z1, z2, z3) → U91(f174_in(z0, z1, z2, z3), f175_in(z0, z1, z2, z3), z0, z1, z2, z3)
U91(f174_out1, z0, z1, z2, z3, z4) → f173_out1
U91(z0, f175_out1, z1, z2, z3, z4) → f173_out2
f215_in(z0, z1, z2, z3) → U92(f216_in(z0, z1, z2, z3), f217_in(z0, z1, z2, z3), z0, z1, z2, z3)
U92(f216_out1, z0, z1, z2, z3, z4) → f215_out1
U92(z0, f217_out1, z1, z2, z3, z4) → f215_out2
f264_in(z0, z1, z2) → U93(f2_in(0, z0), f267_in(z1, z0, z2), z0, z1, z2)
U93(f2_out1, z0, z1, z2, z3) → f264_out1
U93(z0, f267_out1, z1, z2, z3) → f264_out2
U93(z0, f267_out3, z1, z2, z3) → f264_out4
f265_in(z0, z1, z2, z3) → U94(f301_in(z0, z1, z2), f302_in(z0, z1, z2, z3), z0, z1, z2, z3)
U94(f301_out1, z0, z1, z2, z3, z4) → f265_out1
U94(z0, f302_out2, z1, z2, z3, z4) → f265_out3
f311_in(z0, z1) → U95(f2_in(s(z0), z1), f314_in(z0, z1), z0, z1)
U95(f2_out1, z0, z1, z2) → f311_out1
U95(z0, f314_out1, z1, z2) → f311_out2
f325_in(z0, z1, z2, z3) → U96(f422_in(z0, z1), f424_in(z2, z0, z3, z1), z0, z1, z2, z3)
U96(f422_out1, z0, z1, z2, z3, z4) → f325_out1
U96(z0, f424_out2, z1, z2, z3, z4) → f325_out3
U96(z0, f424_out3, z1, z2, z3, z4) → f325_out4
f326_in(z0, z1, z2, z3) → U97(f327_in(z0, z1), f328_in(z2, z0, z3, z1), z0, z1, z2, z3)
U97(f327_out1, z0, z1, z2, z3, z4) → f326_out1
U97(z0, f328_out2, z1, z2, z3, z4) → f326_out3
U97(z0, f328_out3, z1, z2, z3, z4) → f326_out4
f414_in(z0, z1, z2, z3) → U98(f415_in(z0, z1, z2, z3), f416_in(z0, z1, z2, z3), z0, z1, z2, z3)
U98(f415_out1, z0, z1, z2, z3, z4) → f414_out1
U98(z0, f416_out1, z1, z2, z3, z4) → f414_out2
f460_in(z0, z1, z2, z3) → U99(f461_in(z0, z1, z2, z3), f462_in(z0, z1, z2, z3), z0, z1, z2, z3)
U99(f461_out1, z0, z1, z2, z3, z4) → f460_out1
U99(z0, f462_out1, z1, z2, z3, z4) → f460_out2
f470_in(z0, z1, z2) → U100(f2_in(0, z0), f476_in(z1, z0, z2), z0, z1, z2)
U100(f2_out1, z0, z1, z2, z3) → f470_out1
U100(z0, f476_out1, z1, z2, z3) → f470_out2
U100(z0, f476_out3, z1, z2, z3) → f470_out4
f471_in(z0, z1, z2, z3) → U101(f521_in(z0, z1, z2), f522_in(z0, z1, z2, z3), z0, z1, z2, z3)
U101(f521_out1, z0, z1, z2, z3, z4) → f471_out1
U101(z0, f522_out2, z1, z2, z3, z4) → f471_out3
f531_in(z0, z1) → U102(f2_in(s(z0), z1), f534_in(z0, z1), z0, z1)
U102(f2_out1, z0, z1, z2) → f531_out1
U102(z0, f534_out1, z1, z2) → f531_out2
f542_in(z0, z1, z2, z3) → U103(f585_in(z0, z1), f586_in(z2, z0, z3, z1), z0, z1, z2, z3)
U103(f585_out1, z0, z1, z2, z3, z4) → f542_out1
U103(z0, f586_out2, z1, z2, z3, z4) → f542_out3
U103(z0, f586_out3, z1, z2, z3, z4) → f542_out4
f543_in(z0, z1, z2, z3) → U104(f574_in(z0, z1), f575_in(z2, z0, z3, z1), z0, z1, z2, z3)
U104(f574_out1, z0, z1, z2, z3, z4) → f543_out1
U104(z0, f575_out2, z1, z2, z3, z4) → f543_out3
U104(z0, f575_out3, z1, z2, z3, z4) → f543_out4
f578_in(z0, z1, z2, z3) → U105(f579_in(z0, z1, z2, z3), f580_in(z0, z1, z2, z3), z0, z1, z2, z3)
U105(f579_out1, z0, z1, z2, z3, z4) → f578_out1
U105(z0, f580_out1, z1, z2, z3, z4) → f578_out2
f589_in(z0, z1, z2, z3) → U106(f590_in(z0, z1, z2, z3), f591_in(z0, z1, z2, z3), z0, z1, z2, z3)
U106(f590_out1, z0, z1, z2, z3, z4) → f589_out1
U106(z0, f591_out1, z1, z2, z3, z4) → f589_out2
f599_in(z0, z1, z2) → U107(f2_in(0, z0), f602_in(z1, z0, z2), z0, z1, z2)
U107(f2_out1, z0, z1, z2, z3) → f599_out1
U107(z0, f602_out1, z1, z2, z3) → f599_out2
U107(z0, f602_out3, z1, z2, z3) → f599_out4
f600_in(z0, z1, z2, z3) → U108(f607_in(z0, z1, z2), f608_in(z0, z1, z2, z3), z0, z1, z2, z3)
U108(f607_out1, z0, z1, z2, z3, z4) → f600_out1
U108(z0, f608_out2, z1, z2, z3, z4) → f600_out3
f700_in(z0, z1) → U109(f2_in(s(z0), z1), f703_in(z0, z1), z0, z1)
U109(f2_out1, z0, z1, z2) → f700_out1
U109(z0, f703_out1, z1, z2) → f700_out2

Tuples:

F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F61_IN(s(z0), s(z1), x2) → c186(U72'(U27(f63_in(z0, z1), s(z0), s(z1)), s(z0), s(z1), x2), F63_IN(s(z0), s(z1)))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0))
F61_IN(0, s(z0), x2) → c186(U72'(f63_out1, 0, s(z0), x2))

S tuples:none
K tuples:

F2_IN(z0, tree(z1, z2, z3)) → c3(F23_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c4(F113_IN(z1, z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c7(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c8(F168_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c9(F167_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c10(F264_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c11(F265_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c13(F159_IN(z1, z0, z3))
F2_IN(z0, tree(z1, z2, z3)) → c14(F326_IN(z1, z3, z0, z2))
F2_IN(0, tree(s(z0), z1, z2)) → c16(F470_IN(z1, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c17(F471_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c18(F531_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c19(F159_IN(z1, z0, z3))
F2_IN(0, tree(s(z0), z1, z2)) → c22(F599_IN(z1, z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c24(F700_IN(z0, z2))
F2_IN(s(z0), tree(s(z1), z2, z3)) → c25(F159_IN(z1, z0, z3))
F575_IN(z0, z1, z2, z3) → c107(F578_IN(z0, z1, z2, z3))
F608_IN(z0, z1, z2, z3) → c114(F78_IN(z1, z0, z3))
F25_IN(z0, z1, z2, z3) → c205(F27_IN(z0, z1), F28_IN(z2, z0, z3, z1))
F114_IN(z0, z1, z2, z3) → c219(F134_IN(z0, z1, z2), F135_IN(z0, z1, z2, z3))
F154_IN(z0, z1) → c222(F2_IN(s(z0), z1))
F265_IN(z0, z1, z2, z3) → c243(F301_IN(z0, z1, z2), F302_IN(z0, z1, z2, z3))
F311_IN(z0, z1) → c246(F2_IN(s(z0), z1))
F326_IN(z0, z1, z2, z3) → c253(F327_IN(z0, z1), F328_IN(z2, z0, z3, z1))
F460_IN(z0, z1, z2, z3) → c260(F461_IN(z0, z1, z2, z3), F462_IN(z0, z1, z2, z3))
F542_IN(z0, z1, z2, z3) → c273(F585_IN(z0, z1), F586_IN(z2, z0, z3, z1))
F543_IN(z0, z1, z2, z3) → c277(F574_IN(z0, z1), F575_IN(z2, z0, z3, z1))
F600_IN(z0, z1, z2, z3) → c291(F607_IN(z0, z1, z2), F608_IN(z0, z1, z2, z3))
F159_IN(z0, z1, z2) → c198(U80'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F585_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F574_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F327_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F27_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F586_IN(z0, z1, z2, z3) → c92(F589_IN(z0, z1, z2, z3))
F607_IN(s(z0), s(z1), z2) → c112(F138_IN(z0, z1, z2))
F301_IN(s(z0), s(z1), z2) → c128(F138_IN(z0, z1, z2))
F302_IN(z0, z1, z2, z3) → c130(F78_IN(z1, z0, z3))
F328_IN(z0, z1, z2, z3) → c134(F414_IN(z0, z1, z2, z3))
F28_IN(z0, z1, z2, z3) → c149(F49_IN(z0, z1, z2, z3))
F134_IN(s(z0), s(z1), z2) → c154(F138_IN(z0, z1, z2))
F135_IN(z0, z1, z2, z3) → c156(F78_IN(z1, z0, z3))
F461_IN(z0, z1, z2, z3) → c162(F61_IN(z0, z1, z2))
F462_IN(z0, z1, z2, z3) → c164(F78_IN(z1, z0, z3))
U80'(f63_out1, z0, z1, z2) → c199(F2_IN(s(z1), z2))
F23_IN(z0, z1, z2, z3) → c201(F86_IN(z0, z1), F87_IN(z2, z0, z3, z1))
F49_IN(z0, z1, z2, z3) → c209(F52_IN(z0, z1, z2, z3), F53_IN(z0, z1, z2, z3))
F167_IN(z0, z1, z2, z3) → c225(F211_IN(z0, z1), F212_IN(z2, z0, z3, z1))
F168_IN(z0, z1, z2, z3) → c229(F169_IN(z0, z1), F170_IN(z2, z0, z3, z1))
F414_IN(z0, z1, z2, z3) → c257(F415_IN(z0, z1, z2, z3), F416_IN(z0, z1, z2, z3))
F471_IN(z0, z1, z2, z3) → c267(F521_IN(z0, z1, z2), F522_IN(z0, z1, z2, z3))
F531_IN(z0, z1) → c270(F2_IN(s(z0), z1))
F578_IN(z0, z1, z2, z3) → c281(F579_IN(z0, z1, z2, z3), F580_IN(z0, z1, z2, z3))
F589_IN(z0, z1, z2, z3) → c284(F590_IN(z0, z1, z2, z3), F591_IN(z0, z1, z2, z3))
F700_IN(z0, z1) → c294(F2_IN(s(z0), z1))
F86_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F87_IN(z0, z1, z2, z3) → c118(F92_IN(z0, z1, z2, z3))
F52_IN(z0, z1, z2, z3) → c182(F61_IN(z0, z1, z2))
F53_IN(z0, z1, z2, z3) → c184(F78_IN(z1, z0, z3))
F211_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F212_IN(z0, z1, z2, z3) → c97(F215_IN(z0, z1, z2, z3))
F169_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F170_IN(z0, z1, z2, z3) → c123(F173_IN(z0, z1, z2, z3))
F415_IN(z0, z1, z2, z3) → c178(F61_IN(z0, z1, z2))
F416_IN(z0, z1, z2, z3) → c180(F78_IN(z1, z0, z3))
F521_IN(s(z0), s(z1), z2) → c139(F138_IN(z0, z1, z2))
F522_IN(z0, z1, z2, z3) → c141(F78_IN(z1, z0, z3))
F579_IN(z0, z1, z2, z3) → c166(F61_IN(z0, z1, z2))
F580_IN(z0, z1, z2, z3) → c168(F78_IN(z1, z0, z3))
F590_IN(z0, z1, z2, z3) → c143(F61_IN(z0, z1, z2))
F591_IN(z0, z1, z2, z3) → c145(F78_IN(z1, z0, z3))
F92_IN(z0, z1, z2, z3) → c212(F95_IN(z0, z1, z2, z3), F96_IN(z0, z1, z2, z3))
F215_IN(z0, z1, z2, z3) → c236(F216_IN(z0, z1, z2, z3), F217_IN(z0, z1, z2, z3))
F173_IN(z0, z1, z2, z3) → c233(F174_IN(z0, z1, z2, z3), F175_IN(z0, z1, z2, z3))
F138_IN(z0, z1, z2) → c195(U78'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
F95_IN(z0, z1, z2, z3) → c170(F61_IN(z0, z1, z2))
F96_IN(z0, z1, z2, z3) → c172(F78_IN(z1, z0, z3))
F216_IN(z0, z1, z2, z3) → c158(F61_IN(z0, z1, z2))
F217_IN(z0, z1, z2, z3) → c160(F78_IN(z1, z0, z3))
F174_IN(z0, z1, z2, z3) → c174(F61_IN(z0, z1, z2))
F175_IN(z0, z1, z2, z3) → c176(F78_IN(z1, z0, z3))
U78'(f63_out1, z0, z1, z2) → c196(F2_IN(s(z0), z2))
F78_IN(z0, z1, z2) → c189(U74'(f63_in(z0, z1), z0, z1, z2), F63_IN(z0, z1))
U72'(f63_out1, z0, z1, z2) → c187(F2_IN(z0, z2))
U74'(f63_out1, z0, z1, z2) → c190(F2_IN(z1, z2))
F2_IN(z0, tree(z1, z2, z3)) → c2(F25_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c5(F114_IN(z0, z1, z2, z3))
F2_IN(s(z0), tree(0, z1, z2)) → c6(F154_IN(z0, z2))
F2_IN(s(z0), tree(0, z1, z2)) → c12(F311_IN(z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c15(F325_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c20(F543_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c21(F542_IN(z1, z3, z0, z2))
F2_IN(z0, tree(z1, z2, z3)) → c23(F600_IN(z0, z1, z2, z3))
F325_IN(z0, z1, z2, z3) → c249(F422_IN(z0, z1), F424_IN(z2, z0, z3, z1))
F422_IN(z0, tree(z1, z2, z3)) → c(F33_IN(z0, z2))
F424_IN(z0, z1, z2, z3) → c102(F460_IN(z0, z1, z2, z3))
F33_IN(z0, tree(z1, z2, z3)) → c83(F33_IN(z0, z2))
F33_IN(z0, tree(z1, z2, z3)) → c84(F33_IN(z0, z2))
F113_IN(z0, z1, z2) → c215(F2_IN(0, z0))
F264_IN(z0, z1, z2) → c239(F2_IN(0, z0))
F470_IN(z0, z1, z2) → c263(F2_IN(0, z0))
F599_IN(z0, z1, z2) → c287(F2_IN(0, z0))
F63_IN(s(z0), s(z1)) → c88(F63_IN(z0, z1))

Defined Rule Symbols:

f2_in, U1, U2, U3, U4, U5, U6, U7, U8, U9, U10, U11, U12, U13, U14, U15, U16, U17, U18, U19, U20, U21, U22, U23, U24, f33_in, U25, U26, f63_in, U27, f585_in, U28, f586_in, U29, f211_in, U30, f212_in, U31, f422_in, U32, f424_in, U33, f574_in, U34, f575_in, U35, f602_in, U36, f607_in, U37, f608_in, U38, f86_in, U39, f87_in, U40, f169_in, U41, f170_in, U42, f267_in, U43, f301_in, U44, f302_in, U45, f327_in, U46, f328_in, U47, f476_in, U48, f521_in, U49, f522_in, U50, f590_in, U51, f591_in, U52, f27_in, U53, f28_in, U54, f118_in, U55, f134_in, U56, f135_in, U57, f216_in, U58, f217_in, U59, f461_in, U60, f462_in, U61, f579_in, U62, f580_in, U63, f95_in, U64, f96_in, U65, f174_in, U66, f175_in, U67, f415_in, U68, f416_in, U69, f52_in, U70, f53_in, U71, f61_in, U72, U73, f78_in, U74, U75, f123_in, U76, U77, f138_in, U78, U79, f159_in, U80, U81, f23_in, U82, f25_in, U83, f49_in, U84, f92_in, U85, f113_in, U86, f114_in, U87, f154_in, U88, f167_in, U89, f168_in, U90, f173_in, U91, f215_in, U92, f264_in, U93, f265_in, U94, f311_in, U95, f325_in, U96, f326_in, U97, f414_in, U98, f460_in, U99, f470_in, U100, f471_in, U101, f531_in, U102, f542_in, U103, f543_in, U104, f578_in, U105, f589_in, U106, f599_in, U107, f600_in, U108, f700_in, U109

Defined Pair Symbols:

F78_IN, F138_IN, F159_IN, F585_IN, F211_IN, F422_IN, F574_IN, F86_IN, F169_IN, F327_IN, F27_IN, F2_IN, F33_IN, F63_IN, F586_IN, F212_IN, F424_IN, F575_IN, F607_IN, F608_IN, F87_IN, F170_IN, F301_IN, F302_IN, F328_IN, F521_IN, F522_IN, F590_IN, F591_IN, F28_IN, F134_IN, F135_IN, F216_IN, F217_IN, F461_IN, F462_IN, F579_IN, F580_IN, F95_IN, F96_IN, F174_IN, F175_IN, F415_IN, F416_IN, F52_IN, F53_IN, U72', U74', U78', U80', F23_IN, F25_IN, F49_IN, F92_IN, F114_IN, F154_IN, F167_IN, F168_IN, F173_IN, F215_IN, F265_IN, F311_IN, F325_IN, F326_IN, F414_IN, F460_IN, F471_IN, F531_IN, F542_IN, F543_IN, F578_IN, F589_IN, F600_IN, F700_IN, F61_IN, F113_IN, F264_IN, F470_IN, F599_IN

Compound Symbols:

c189, c195, c198, c, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c83, c84, c88, c92, c97, c102, c107, c112, c114, c118, c123, c128, c130, c134, c139, c141, c143, c145, c149, c154, c156, c158, c160, c162, c164, c166, c168, c170, c172, c174, c176, c178, c180, c182, c184, c187, c190, c196, c199, c201, c205, c209, c212, c219, c222, c225, c229, c233, c236, c243, c246, c249, c253, c257, c260, c267, c270, c273, c277, c281, c284, c291, c294, c186, c215, c239, c263, c287, c186

(47) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

(48) BOUNDS(O(1), O(1))