Left Termination of the query pattern prime_in_1(g) w.r.t. the given Prolog program could not be shown:

(0) Obligation:

Clauses:

div(X, Y, Z) :- quot(X, Y, Y, Z).
quot(0, s(Y), s(Z), 0).
quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U).
quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U).
prime(s(s(X))) :- pr(s(s(X)), s(X)).
pr(X, s(0)).
pr(X, s(s(Y))) :- ','(not_divides(s(s(Y)), X), pr(X, s(Y))).
not_divides(Y, X) :- ','(div(X, Y, U), ','(times(U, Y, Z), neq(X, Z))).
neq(s(X), 0).
neq(0, s(X)).
neq(s(X), s(Y)) :- neq(X, Y).
times(0, Y, 0).
times(s(X), Y, Z) :- ','(times(X, Y, U), add(U, Y, Z)).
add(X, 0, X).
add(0, X, X).
add(s(X), Y, s(Z)) :- add(X, Y, Z).

Queries:

prime(g).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: prime(T1)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: prime(T1), SCOPE: 1, CLAUSE: 4\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: pr(s(s(T3)), s(T3))\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: pr(s(s(T3)), s(T3)), SCOPE: 2, CLAUSE: 5 | pr(s(s(T3)), s(T3)), SCOPE: 2, CLAUSE: 6\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: pr(s(s(T3)), s(T3)), SCOPE: 2, CLAUSE: 5\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: pr(s(s(T3)), s(T3)), SCOPE: 2, CLAUSE: 6\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: ','(not_divides(s(s(T14)), s(s(s(T14)))), pr(s(s(s(T14))), s(T14)))\n\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: not_divides(s(s(T14)), s(s(s(T14))))\n\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: pr(s(s(s(T14))), s(T14))\n\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: not_divides(s(s(T14)), s(s(s(T14)))), SCOPE: 3, CLAUSE: 7\n\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ','(div(s(s(s(T20))), s(s(T20)), X38), ','(times(X38, s(s(T20)), X39), neq(s(s(s(T20))), X39)))\n\nT20 is ground\nX38 is free; \nX39 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: div(s(s(s(T20))), s(s(T20)), X38)\n\nT20 is ground\nX38 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: ','(times(T22, s(s(T20)), X39), neq(s(s(s(T20))), X39))\n\nT20 is ground\nT22 is ground\nX39 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: div(s(s(s(T20))), s(s(T20)), X38), SCOPE: 4, CLAUSE: 0\n\nT20 is ground\nX38 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: quot(s(s(s(T27))), s(s(T27)), s(s(T27)), X68)\n\nT27 is ground\nX68 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: quot(s(s(s(T27))), s(s(T27)), s(s(T27)), X68), SCOPE: 5, CLAUSE: 1 | quot(s(s(s(T27))), s(s(T27)), s(s(T27)), X68), SCOPE: 5, CLAUSE: 2 | quot(s(s(s(T27))), s(s(T27)), s(s(T27)), X68), SCOPE: 5, CLAUSE: 3\n\nT27 is ground\nX68 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: quot(s(s(s(T27))), s(s(T27)), s(s(T27)), X68), SCOPE: 5, CLAUSE: 2 | quot(s(s(s(T27))), s(s(T27)), s(s(T27)), X68), SCOPE: 5, CLAUSE: 3\n\nT27 is ground\nX68 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: quot(s(s(s(T27))), s(s(T27)), s(s(T27)), X68), SCOPE: 5, CLAUSE: 2\n\nT27 is ground\nX68 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: quot(s(s(s(T27))), s(s(T27)), s(s(T27)), X68), SCOPE: 5, CLAUSE: 3\n\nT27 is ground\nX68 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: quot(s(s(T35)), s(T35), s(s(T35)), X122)\n\nT35 is ground\nX122 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: quot(s(s(T35)), s(T35), s(s(T35)), X122), SCOPE: 6, CLAUSE: 1 | quot(s(s(T35)), s(T35), s(s(T35)), X122), SCOPE: 6, CLAUSE: 2 | quot(s(s(T35)), s(T35), s(s(T35)), X122), SCOPE: 6, CLAUSE: 3\n\nT35 is ground\nX122 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: quot(s(s(T35)), s(T35), s(s(T35)), X122), SCOPE: 6, CLAUSE: 2 | quot(s(s(T35)), s(T35), s(s(T35)), X122), SCOPE: 6, CLAUSE: 3\n\nT35 is ground\nX122 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: quot(s(s(T35)), s(T35), s(s(T35)), X122), SCOPE: 6, CLAUSE: 2\n\nT35 is ground\nX122 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: quot(s(s(T35)), s(T35), s(s(T35)), X122), SCOPE: 6, CLAUSE: 3\n\nT35 is ground\nX122 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: quot(s(T45), T45, s(s(T45)), X176)\n\nT45 is ground\nX176 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: quot(s(T45), T45, s(s(T45)), X176), SCOPE: 7, CLAUSE: 1 | quot(s(T45), T45, s(s(T45)), X176), SCOPE: 7, CLAUSE: 2 | quot(s(T45), T45, s(s(T45)), X176), SCOPE: 7, CLAUSE: 3\n\nT45 is ground\nX176 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: quot(s(T45), T45, s(s(T45)), X176), SCOPE: 7, CLAUSE: 2 | quot(s(T45), T45, s(s(T45)), X176), SCOPE: 7, CLAUSE: 3\n\nT45 is ground\nX176 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: quot(s(T45), T45, s(s(T45)), X176), SCOPE: 7, CLAUSE: 2\n\nT45 is ground\nX176 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: quot(s(T45), T45, s(s(T45)), X176), SCOPE: 7, CLAUSE: 3\n\nT45 is ground\nX176 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: quot(s(T57), T57, s(s(s(T57))), X212)\n\nT57 is ground\nX212 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: quot(s(T57), T57, s(s(s(T57))), X212), SCOPE: 8, CLAUSE: 1 | quot(s(T57), T57, s(s(s(T57))), X212), SCOPE: 8, CLAUSE: 2 | quot(s(T57), T57, s(s(s(T57))), X212), SCOPE: 8, CLAUSE: 3\n\nT57 is ground\nX212 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: quot(s(T57), T57, s(s(s(T57))), X212), SCOPE: 8, CLAUSE: 2 | quot(s(T57), T57, s(s(s(T57))), X212), SCOPE: 8, CLAUSE: 3\n\nT57 is ground\nX212 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: quot(s(T57), T57, s(s(s(T57))), X212), SCOPE: 8, CLAUSE: 2\n\nT57 is ground\nX212 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: quot(s(T57), T57, s(s(s(T57))), X212), SCOPE: 8, CLAUSE: 3\n\nT57 is ground\nX212 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: quot(s(T69), T69, s(s(s(s(T69)))), X252)\n\nT69 is ground\nX252 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: quot(s(T69), T69, s(s(s(s(T69)))), X252), SCOPE: 9, CLAUSE: 1 | quot(s(T69), T69, s(s(s(s(T69)))), X252), SCOPE: 9, CLAUSE: 2 | quot(s(T69), T69, s(s(s(s(T69)))), X252), SCOPE: 9, CLAUSE: 3\n\nT69 is ground\nX252 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: quot(s(T69), T69, s(s(s(s(T69)))), X252), SCOPE: 9, CLAUSE: 2 | quot(s(T69), T69, s(s(s(s(T69)))), X252), SCOPE: 9, CLAUSE: 3\n\nT69 is ground\nX252 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: quot(s(T69), T69, s(s(s(s(T69)))), X252), SCOPE: 9, CLAUSE: 2\n\nT69 is ground\nX252 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: quot(s(T69), T69, s(s(s(s(T69)))), X252), SCOPE: 9, CLAUSE: 3\n\nT69 is ground\nX252 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: quot(s(T81), T81, s(s(s(s(s(T81))))), X292)\n\nT81 is ground\nX292 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: quot(s(T81), T81, s(s(s(s(s(T81))))), X292), SCOPE: 10, CLAUSE: 1 | quot(s(T81), T81, s(s(s(s(s(T81))))), X292), SCOPE: 10, CLAUSE: 2 | quot(s(T81), T81, s(s(s(s(s(T81))))), X292), SCOPE: 10, CLAUSE: 3\n\nT81 is ground\nX292 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: quot(s(T81), T81, s(s(s(s(s(T81))))), X292), SCOPE: 10, CLAUSE: 2 | quot(s(T81), T81, s(s(s(s(s(T81))))), X292), SCOPE: 10, CLAUSE: 3\n\nT81 is ground\nX292 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: quot(s(T81), T81, s(s(s(s(s(T81))))), X292), SCOPE: 10, CLAUSE: 2\n\nT81 is ground\nX292 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: quot(s(T81), T81, s(s(s(s(s(T81))))), X292), SCOPE: 10, CLAUSE: 3\n\nT81 is ground\nX292 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: quot(s(T93), T93, s(s(s(s(s(s(T93)))))), X332)\n\nT93 is ground\nX332 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: quot(s(T93), T93, s(s(s(s(s(s(T93)))))), X332), SCOPE: 11, CLAUSE: 1 | quot(s(T93), T93, s(s(s(s(s(s(T93)))))), X332), SCOPE: 11, CLAUSE: 2 | quot(s(T93), T93, s(s(s(s(s(s(T93)))))), X332), SCOPE: 11, CLAUSE: 3\n\nT93 is ground\nX332 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: quot(s(T93), T93, s(s(s(s(s(s(T93)))))), X332), SCOPE: 11, CLAUSE: 2 | quot(s(T93), T93, s(s(s(s(s(s(T93)))))), X332), SCOPE: 11, CLAUSE: 3\n\nT93 is ground\nX332 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: quot(s(T93), T93, s(s(s(s(s(s(T93)))))), X332), SCOPE: 11, CLAUSE: 2\n\nT93 is ground\nX332 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: quot(s(T93), T93, s(s(s(s(s(s(T93)))))), X332), SCOPE: 11, CLAUSE: 3\n\nT93 is ground\nX332 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: quot(s(T105), T105, s(s(s(s(s(s(s(T105))))))), X372)\n\nT105 is ground\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: quot(s(T105), T105, s(s(s(s(s(s(s(T105))))))), X372), SCOPE: 12, CLAUSE: 1 | quot(s(T105), T105, s(s(s(s(s(s(s(T105))))))), X372), SCOPE: 12, CLAUSE: 2 | quot(s(T105), T105, s(s(s(s(s(s(s(T105))))))), X372), SCOPE: 12, CLAUSE: 3\n\nT105 is ground\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: quot(s(T105), T105, s(s(s(s(s(s(s(T105))))))), X372), SCOPE: 12, CLAUSE: 2 | quot(s(T105), T105, s(s(s(s(s(s(s(T105))))))), X372), SCOPE: 12, CLAUSE: 3\n\nT105 is ground\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: quot(s(T105), T105, s(s(s(s(s(s(s(T105))))))), X372), SCOPE: 12, CLAUSE: 2\n\nT105 is ground\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: quot(s(T105), T105, s(s(s(s(s(s(s(T105))))))), X372), SCOPE: 12, CLAUSE: 3\n\nT105 is ground\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: quot(s(T117), T117, s(s(s(s(s(s(s(s(T117)))))))), X412)\n\nT117 is ground\nX412 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: quot(s(T117), T117, s(T120), X412)\n\nT117 is ground\nT120 is ground\nX412 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: quot(s(T117), T117, s(T120), X412), SCOPE: 13, CLAUSE: 1 | quot(s(T117), T117, s(T120), X412), SCOPE: 13, CLAUSE: 2 | quot(s(T117), T117, s(T120), X412), SCOPE: 13, CLAUSE: 3\n\nT117 is ground\nT120 is ground\nX412 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: quot(s(T117), T117, s(T120), X412), SCOPE: 13, CLAUSE: 2 | quot(s(T117), T117, s(T120), X412), SCOPE: 13, CLAUSE: 3\n\nT117 is ground\nT120 is ground\nX412 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: quot(s(T117), T117, s(T120), X412), SCOPE: 13, CLAUSE: 2\n\nT117 is ground\nT120 is ground\nX412 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: quot(s(T117), T117, s(T120), X412), SCOPE: 13, CLAUSE: 3\n\nT117 is ground\nT120 is ground\nX412 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: quot(s(T137), T137, s(T138), X461)\n\nT137 is ground\nT138 is ground\nX461 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: quot(s(0), s(T147), s(T147), X486)\n\nT147 is ground\nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: quot(s(0), s(T147), s(T147), X486), SCOPE: 14, CLAUSE: 1 | quot(s(0), s(T147), s(T147), X486), SCOPE: 14, CLAUSE: 2 | quot(s(0), s(T147), s(T147), X486), SCOPE: 14, CLAUSE: 3\n\nT147 is ground\nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: quot(s(0), s(T147), s(T147), X486), SCOPE: 14, CLAUSE: 2 | quot(s(0), s(T147), s(T147), X486), SCOPE: 14, CLAUSE: 3\n\nT147 is ground\nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: quot(s(0), s(T147), s(T147), X486), SCOPE: 14, CLAUSE: 2\n\nT147 is ground\nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: quot(s(0), s(T147), s(T147), X486), SCOPE: 14, CLAUSE: 3\n\nT147 is ground\nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: quot(0, T157, s(T157), X533)\n\nT157 is ground\nX533 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: quot(0, T157, s(T157), X533), SCOPE: 15, CLAUSE: 1 | quot(0, T157, s(T157), X533), SCOPE: 15, CLAUSE: 2 | quot(0, T157, s(T157), X533), SCOPE: 15, CLAUSE: 3\n\nT157 is ground\nX533 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: quot(0, T157, s(T157), X533), SCOPE: 15, CLAUSE: 1\n\nT157 is ground\nX533 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: quot(0, T157, s(T157), X533), SCOPE: 15, CLAUSE: 2 | quot(0, T157, s(T157), X533), SCOPE: 15, CLAUSE: 3\n\nT157 is ground\nX533 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: quot(0, T157, s(T157), X533), SCOPE: 15, CLAUSE: 3\n\nT157 is ground\nX533 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: quot(0, s(0), s(0), X565)\n\nX565 is free", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: quot(0, s(0), s(0), X565), SCOPE: 16, CLAUSE: 1 | quot(0, s(0), s(0), X565), SCOPE: 16, CLAUSE: 2 | quot(0, s(0), s(0), X565), SCOPE: 16, CLAUSE: 3\n\nX565 is free", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: quot(0, s(0), s(0), X565), SCOPE: 16, CLAUSE: 1\n\nX565 is free", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: quot(0, s(0), s(0), X565), SCOPE: 16, CLAUSE: 2 | quot(0, s(0), s(0), X565), SCOPE: 16, CLAUSE: 3\n\nX565 is free", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: quot(0, s(0), s(0), X565), SCOPE: 16, CLAUSE: 3\n\nX565 is free", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X602)\n\nX602 is free", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X602), SCOPE: 17, CLAUSE: 1 | quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X602), SCOPE: 17, CLAUSE: 2 | quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X602), SCOPE: 17, CLAUSE: 3\n\nX602 is free", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X602), SCOPE: 17, CLAUSE: 2 | quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X602), SCOPE: 17, CLAUSE: 3\n\nX602 is free", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X602), SCOPE: 17, CLAUSE: 2\n\nX602 is free", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: quot(s(0), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X602), SCOPE: 17, CLAUSE: 3\n\nX602 is free", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X645)\n\nX645 is free", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X645), SCOPE: 18, CLAUSE: 1 | quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X645), SCOPE: 18, CLAUSE: 2 | quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X645), SCOPE: 18, CLAUSE: 3\n\nX645 is free", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X645), SCOPE: 18, CLAUSE: 1\n\nX645 is free", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X645), SCOPE: 18, CLAUSE: 2 | quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X645), SCOPE: 18, CLAUSE: 3\n\nX645 is free", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: quot(0, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X645), SCOPE: 18, CLAUSE: 3\n\nX645 is free", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X679)\n\nX679 is free", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X679), SCOPE: 19, CLAUSE: 1 | quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X679), SCOPE: 19, CLAUSE: 2 | quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X679), SCOPE: 19, CLAUSE: 3\n\nX679 is free", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X679), SCOPE: 19, CLAUSE: 2 | quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X679), SCOPE: 19, CLAUSE: 3\n\nX679 is free", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X679), SCOPE: 19, CLAUSE: 2\n\nX679 is free", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X679), SCOPE: 19, CLAUSE: 3\n\nX679 is free", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X722)\n\nX722 is free", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X722), SCOPE: 20, CLAUSE: 1 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X722), SCOPE: 20, CLAUSE: 2 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X722), SCOPE: 20, CLAUSE: 3\n\nX722 is free", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X722), SCOPE: 20, CLAUSE: 1\n\nX722 is free", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X722), SCOPE: 20, CLAUSE: 2 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X722), SCOPE: 20, CLAUSE: 3\n\nX722 is free", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X722), SCOPE: 20, CLAUSE: 3\n\nX722 is free", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X756)\n\nX756 is free", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X756), SCOPE: 21, CLAUSE: 1 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X756), SCOPE: 21, CLAUSE: 2 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X756), SCOPE: 21, CLAUSE: 3\n\nX756 is free", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X756), SCOPE: 21, CLAUSE: 2 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X756), SCOPE: 21, CLAUSE: 3\n\nX756 is free", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X756), SCOPE: 21, CLAUSE: 2\n\nX756 is free", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X756), SCOPE: 21, CLAUSE: 3\n\nX756 is free", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X799)\n\nX799 is free", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X799), SCOPE: 22, CLAUSE: 1 | quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X799), SCOPE: 22, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X799), SCOPE: 22, CLAUSE: 3\n\nX799 is free", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X799), SCOPE: 22, CLAUSE: 1\n\nX799 is free", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X799), SCOPE: 22, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X799), SCOPE: 22, CLAUSE: 3\n\nX799 is free", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: quot(0, s(s(s(s(0)))), s(s(s(s(s(0))))), X799), SCOPE: 22, CLAUSE: 3\n\nX799 is free", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X833)\n\nX833 is free", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X833), SCOPE: 23, CLAUSE: 1 | quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X833), SCOPE: 23, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X833), SCOPE: 23, CLAUSE: 3\n\nX833 is free", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X833), SCOPE: 23, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X833), SCOPE: 23, CLAUSE: 3\n\nX833 is free", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X833), SCOPE: 23, CLAUSE: 2\n\nX833 is free", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X833), SCOPE: 23, CLAUSE: 3\n\nX833 is free", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: quot(0, s(s(s(0))), s(s(s(s(0)))), X876)\n\nX876 is free", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: quot(0, s(s(s(0))), s(s(s(s(0)))), X876), SCOPE: 24, CLAUSE: 1 | quot(0, s(s(s(0))), s(s(s(s(0)))), X876), SCOPE: 24, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(0)))), X876), SCOPE: 24, CLAUSE: 3\n\nX876 is free", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: quot(0, s(s(s(0))), s(s(s(s(0)))), X876), SCOPE: 24, CLAUSE: 1\n\nX876 is free", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: quot(0, s(s(s(0))), s(s(s(s(0)))), X876), SCOPE: 24, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(0)))), X876), SCOPE: 24, CLAUSE: 3\n\nX876 is free", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: quot(0, s(s(s(0))), s(s(s(s(0)))), X876), SCOPE: 24, CLAUSE: 3\n\nX876 is free", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: quot(s(0), s(s(s(0))), s(s(s(0))), X910)\n\nX910 is free", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: quot(s(0), s(s(s(0))), s(s(s(0))), X910), SCOPE: 25, CLAUSE: 1 | quot(s(0), s(s(s(0))), s(s(s(0))), X910), SCOPE: 25, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(0))), X910), SCOPE: 25, CLAUSE: 3\n\nX910 is free", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: quot(s(0), s(s(s(0))), s(s(s(0))), X910), SCOPE: 25, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(0))), X910), SCOPE: 25, CLAUSE: 3\n\nX910 is free", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: quot(s(0), s(s(s(0))), s(s(s(0))), X910), SCOPE: 25, CLAUSE: 2\n\nX910 is free", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: quot(s(0), s(s(s(0))), s(s(s(0))), X910), SCOPE: 25, CLAUSE: 3\n\nX910 is free", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: quot(0, s(s(0)), s(s(s(0))), X953)\n\nX953 is free", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: quot(0, s(s(0)), s(s(s(0))), X953), SCOPE: 26, CLAUSE: 1 | quot(0, s(s(0)), s(s(s(0))), X953), SCOPE: 26, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(0))), X953), SCOPE: 26, CLAUSE: 3\n\nX953 is free", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: quot(0, s(s(0)), s(s(s(0))), X953), SCOPE: 26, CLAUSE: 1\n\nX953 is free", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: quot(0, s(s(0)), s(s(s(0))), X953), SCOPE: 26, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(0))), X953), SCOPE: 26, CLAUSE: 3\n\nX953 is free", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: quot(0, s(s(0)), s(s(s(0))), X953), SCOPE: 26, CLAUSE: 3\n\nX953 is free", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: quot(s(0), s(s(0)), s(s(0)), X987)\n\nX987 is free", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: quot(s(0), s(s(0)), s(s(0)), X987), SCOPE: 27, CLAUSE: 1 | quot(s(0), s(s(0)), s(s(0)), X987), SCOPE: 27, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(0)), X987), SCOPE: 27, CLAUSE: 3\n\nX987 is free", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: quot(s(0), s(s(0)), s(s(0)), X987), SCOPE: 27, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(0)), X987), SCOPE: 27, CLAUSE: 3\n\nX987 is free", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: quot(s(0), s(s(0)), s(s(0)), X987), SCOPE: 27, CLAUSE: 2\n\nX987 is free", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: quot(s(0), s(s(0)), s(s(0)), X987), SCOPE: 27, CLAUSE: 3\n\nX987 is free", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: quot(0, s(0), s(s(0)), X1030)\n\nX1030 is free", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: quot(0, s(0), s(s(0)), X1030), SCOPE: 28, CLAUSE: 1 | quot(0, s(0), s(s(0)), X1030), SCOPE: 28, CLAUSE: 2 | quot(0, s(0), s(s(0)), X1030), SCOPE: 28, CLAUSE: 3\n\nX1030 is free", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: quot(0, s(0), s(s(0)), X1030), SCOPE: 28, CLAUSE: 1\n\nX1030 is free", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: quot(0, s(0), s(s(0)), X1030), SCOPE: 28, CLAUSE: 2 | quot(0, s(0), s(s(0)), X1030), SCOPE: 28, CLAUSE: 3\n\nX1030 is free", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: quot(0, s(0), s(s(0)), X1030), SCOPE: 28, CLAUSE: 3\n\nX1030 is free", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: times(T22, s(s(T20)), X39)\n\nT20 is ground\nT22 is ground\nX39 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: neq(s(s(s(T20))), T187)\n\nT20 is ground\nT187 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: times(T22, s(s(T20)), X39), SCOPE: 29, CLAUSE: 11 | times(T22, s(s(T20)), X39), SCOPE: 29, CLAUSE: 12\n\nT20 is ground\nT22 is ground\nX39 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: times(T22, s(s(T20)), X39), SCOPE: 29, CLAUSE: 11\n\nT20 is ground\nT22 is ground\nX39 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: times(T22, s(s(T20)), X39), SCOPE: 29, CLAUSE: 12\n\nT20 is ground\nT22 is ground\nX39 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: ','(times(T199, s(s(T200)), X1081), add(X1081, s(s(T200)), X1082))\n\nT199 is ground\nT200 is ground\nX1082 is free; \nX1081 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: times(T199, s(s(T200)), X1081)\n\nT199 is ground\nT200 is ground\nX1081 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: add(T203, s(s(T200)), X1082)\n\nT200 is ground\nT203 is ground\nX1082 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: add(T203, s(s(T200)), X1082), SCOPE: 30, CLAUSE: 13 | add(T203, s(s(T200)), X1082), SCOPE: 30, CLAUSE: 14 | add(T203, s(s(T200)), X1082), SCOPE: 30, CLAUSE: 15\n\nT200 is ground\nT203 is ground\nX1082 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: add(T203, s(s(T200)), X1082), SCOPE: 30, CLAUSE: 14 | add(T203, s(s(T200)), X1082), SCOPE: 30, CLAUSE: 15\n\nT200 is ground\nT203 is ground\nX1082 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: add(T203, s(s(T200)), X1082), SCOPE: 30, CLAUSE: 14\n\nT200 is ground\nT203 is ground\nX1082 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: add(T203, s(s(T200)), X1082), SCOPE: 30, CLAUSE: 15\n\nT200 is ground\nT203 is ground\nX1082 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: add(T220, s(s(T221)), X1112)\n\nT220 is ground\nT221 is ground\nX1112 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: neq(s(s(s(T20))), T187), SCOPE: 31, CLAUSE: 8 | neq(s(s(s(T20))), T187), SCOPE: 31, CLAUSE: 9 | neq(s(s(s(T20))), T187), SCOPE: 31, CLAUSE: 10\n\nT20 is ground\nT187 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: neq(s(s(s(T20))), T187), SCOPE: 31, CLAUSE: 8\n\nT20 is ground\nT187 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: neq(s(s(s(T20))), T187), SCOPE: 31, CLAUSE: 9 | neq(s(s(s(T20))), T187), SCOPE: 31, CLAUSE: 10\n\nT20 is ground\nT187 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: neq(s(s(s(T20))), T187), SCOPE: 31, CLAUSE: 10\n\nT20 is ground\nT187 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: neq(s(s(T237)), T238)\n\nT237 is ground\nT238 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: neq(s(s(T237)), T238), SCOPE: 32, CLAUSE: 8 | neq(s(s(T237)), T238), SCOPE: 32, CLAUSE: 9 | neq(s(s(T237)), T238), SCOPE: 32, CLAUSE: 10\n\nT237 is ground\nT238 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: neq(s(s(T237)), T238), SCOPE: 32, CLAUSE: 8\n\nT237 is ground\nT238 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: neq(s(s(T237)), T238), SCOPE: 32, CLAUSE: 9 | neq(s(s(T237)), T238), SCOPE: 32, CLAUSE: 10\n\nT237 is ground\nT238 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: neq(s(s(T237)), T238), SCOPE: 32, CLAUSE: 10\n\nT237 is ground\nT238 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
227 [label="227: neq(s(T250), T251)\n\nT250 is ground\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
228 [label="228: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
229 [label="229: neq(s(T250), T251), SCOPE: 33, CLAUSE: 8 | neq(s(T250), T251), SCOPE: 33, CLAUSE: 9 | neq(s(T250), T251), SCOPE: 33, CLAUSE: 10\n\nT250 is ground\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="230: neq(s(T250), T251), SCOPE: 33, CLAUSE: 8\n\nT250 is ground\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
231 [label="231: neq(s(T250), T251), SCOPE: 33, CLAUSE: 9 | neq(s(T250), T251), SCOPE: 33, CLAUSE: 10\n\nT250 is ground\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
232 [label="232: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
233 [label="233: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
234 [label="234: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
235 [label="235: neq(s(T250), T251), SCOPE: 33, CLAUSE: 10\n\nT250 is ground\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
236 [label="236: neq(T263, T264)\n\nT263 is ground\nT264 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
237 [label="237: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
238 [label="238: neq(T263, T264), SCOPE: 34, CLAUSE: 8 | neq(T263, T264), SCOPE: 34, CLAUSE: 9 | neq(T263, T264), SCOPE: 34, CLAUSE: 10\n\nT263 is ground\nT264 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
239 [label="239: neq(T263, T264), SCOPE: 34, CLAUSE: 8\n\nT263 is ground\nT264 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
240 [label="240: neq(T263, T264), SCOPE: 34, CLAUSE: 9 | neq(T263, T264), SCOPE: 34, CLAUSE: 10\n\nT263 is ground\nT264 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
241 [label="241: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
242 [label="242: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
243 [label="243: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
244 [label="244: neq(T263, T264), SCOPE: 34, CLAUSE: 9\n\nT263 is ground\nT264 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
245 [label="245: neq(T263, T264), SCOPE: 34, CLAUSE: 10\n\nT263 is ground\nT264 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
246 [label="246: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
247 [label="247: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
248 [label="248: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
249 [label="249: neq(T281, T282)\n\nT281 is ground\nT282 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
250 [label="250: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
251 [label="251: pr(s(s(s(T14))), s(T14)), SCOPE: 35, CLAUSE: 5 | pr(s(s(s(T14))), s(T14)), SCOPE: 35, CLAUSE: 6\n\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
252 [label="252: pr(s(s(s(T14))), s(T14)), SCOPE: 35, CLAUSE: 5\n\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
253 [label="253: pr(s(s(s(T14))), s(T14)), SCOPE: 35, CLAUSE: 6\n\nT14 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
254 [label="254: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
255 [label="255: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
256 [label="256: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
257 [label="257: ','(not_divides(s(s(T297)), s(s(s(s(T297))))), pr(s(s(s(s(T297)))), s(T297)))\n\nT297 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
258 [label="258: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
259 [label="259: not_divides(s(s(T297)), s(s(s(s(T297)))))\n\nT297 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
260 [label="260: pr(s(s(s(s(T297)))), s(T297))\n\nT297 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
261 [label="261: not_divides(s(s(T297)), s(s(s(s(T297))))), SCOPE: 36, CLAUSE: 7\n\nT297 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
262 [label="262: ','(div(s(s(s(s(T303)))), s(s(T303)), X1231), ','(times(X1231, s(s(T303)), X1232), neq(s(s(s(s(T303)))), X1232)))\n\nT303 is ground\nX1231 is free; \nX1232 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
263 [label="263: div(s(s(s(s(T303)))), s(s(T303)), X1231)\n\nT303 is ground\nX1231 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
264 [label="264: ','(times(T305, s(s(T303)), X1232), neq(s(s(s(s(T303)))), X1232))\n\nT303 is ground\nT305 is ground\nX1232 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
265 [label="265: div(s(s(s(s(T303)))), s(s(T303)), X1231), SCOPE: 37, CLAUSE: 0\n\nT303 is ground\nX1231 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
266 [label="266: quot(s(s(s(s(T310)))), s(s(T310)), s(s(T310)), X1261)\n\nT310 is ground\nX1261 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
267 [label="267: quot(s(s(s(s(T310)))), s(s(T310)), s(s(T310)), X1261), SCOPE: 38, CLAUSE: 1 | quot(s(s(s(s(T310)))), s(s(T310)), s(s(T310)), X1261), SCOPE: 38, CLAUSE: 2 | quot(s(s(s(s(T310)))), s(s(T310)), s(s(T310)), X1261), SCOPE: 38, CLAUSE: 3\n\nT310 is ground\nX1261 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
268 [label="268: quot(s(s(s(s(T310)))), s(s(T310)), s(s(T310)), X1261), SCOPE: 38, CLAUSE: 2 | quot(s(s(s(s(T310)))), s(s(T310)), s(s(T310)), X1261), SCOPE: 38, CLAUSE: 3\n\nT310 is ground\nX1261 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
269 [label="269: quot(s(s(s(s(T310)))), s(s(T310)), s(s(T310)), X1261), SCOPE: 38, CLAUSE: 2\n\nT310 is ground\nX1261 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
270 [label="270: quot(s(s(s(s(T310)))), s(s(T310)), s(s(T310)), X1261), SCOPE: 38, CLAUSE: 3\n\nT310 is ground\nX1261 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
271 [label="271: quot(s(s(s(T318))), s(T318), s(s(T318)), X1315)\n\nT318 is ground\nX1315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
272 [label="272: quot(s(s(s(T318))), s(T318), s(s(T318)), X1315), SCOPE: 39, CLAUSE: 1 | quot(s(s(s(T318))), s(T318), s(s(T318)), X1315), SCOPE: 39, CLAUSE: 2 | quot(s(s(s(T318))), s(T318), s(s(T318)), X1315), SCOPE: 39, CLAUSE: 3\n\nT318 is ground\nX1315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
273 [label="273: quot(s(s(s(T318))), s(T318), s(s(T318)), X1315), SCOPE: 39, CLAUSE: 2 | quot(s(s(s(T318))), s(T318), s(s(T318)), X1315), SCOPE: 39, CLAUSE: 3\n\nT318 is ground\nX1315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
274 [label="274: quot(s(s(s(T318))), s(T318), s(s(T318)), X1315), SCOPE: 39, CLAUSE: 2\n\nT318 is ground\nX1315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
275 [label="275: quot(s(s(s(T318))), s(T318), s(s(T318)), X1315), SCOPE: 39, CLAUSE: 3\n\nT318 is ground\nX1315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
276 [label="276: quot(s(s(T328)), T328, s(s(T328)), X1369)\n\nT328 is ground\nX1369 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
277 [label="277: quot(s(s(T328)), T328, s(s(T328)), X1369), SCOPE: 40, CLAUSE: 1 | quot(s(s(T328)), T328, s(s(T328)), X1369), SCOPE: 40, CLAUSE: 2 | quot(s(s(T328)), T328, s(s(T328)), X1369), SCOPE: 40, CLAUSE: 3\n\nT328 is ground\nX1369 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
278 [label="278: quot(s(s(T328)), T328, s(s(T328)), X1369), SCOPE: 40, CLAUSE: 2 | quot(s(s(T328)), T328, s(s(T328)), X1369), SCOPE: 40, CLAUSE: 3\n\nT328 is ground\nX1369 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
279 [label="279: quot(s(s(T328)), T328, s(s(T328)), X1369), SCOPE: 40, CLAUSE: 2\n\nT328 is ground\nX1369 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
280 [label="280: quot(s(s(T328)), T328, s(s(T328)), X1369), SCOPE: 40, CLAUSE: 3\n\nT328 is ground\nX1369 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
281 [label="281: quot(s(s(T340)), T340, s(s(s(T340))), X1405)\n\nT340 is ground\nX1405 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
282 [label="282: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
283 [label="283: quot(s(s(T340)), T340, s(s(s(T340))), X1405), SCOPE: 41, CLAUSE: 1 | quot(s(s(T340)), T340, s(s(s(T340))), X1405), SCOPE: 41, CLAUSE: 2 | quot(s(s(T340)), T340, s(s(s(T340))), X1405), SCOPE: 41, CLAUSE: 3\n\nT340 is ground\nX1405 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
284 [label="284: quot(s(s(T340)), T340, s(s(s(T340))), X1405), SCOPE: 41, CLAUSE: 2 | quot(s(s(T340)), T340, s(s(s(T340))), X1405), SCOPE: 41, CLAUSE: 3\n\nT340 is ground\nX1405 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
285 [label="285: quot(s(s(T340)), T340, s(s(s(T340))), X1405), SCOPE: 41, CLAUSE: 2\n\nT340 is ground\nX1405 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
286 [label="286: quot(s(s(T340)), T340, s(s(s(T340))), X1405), SCOPE: 41, CLAUSE: 3\n\nT340 is ground\nX1405 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
287 [label="287: quot(s(s(T352)), T352, s(s(s(s(T352)))), X1445)\n\nT352 is ground\nX1445 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
288 [label="288: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
289 [label="289: quot(s(s(T352)), T352, s(s(s(s(T352)))), X1445), SCOPE: 42, CLAUSE: 1 | quot(s(s(T352)), T352, s(s(s(s(T352)))), X1445), SCOPE: 42, CLAUSE: 2 | quot(s(s(T352)), T352, s(s(s(s(T352)))), X1445), SCOPE: 42, CLAUSE: 3\n\nT352 is ground\nX1445 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
290 [label="290: quot(s(s(T352)), T352, s(s(s(s(T352)))), X1445), SCOPE: 42, CLAUSE: 2 | quot(s(s(T352)), T352, s(s(s(s(T352)))), X1445), SCOPE: 42, CLAUSE: 3\n\nT352 is ground\nX1445 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
291 [label="291: quot(s(s(T352)), T352, s(s(s(s(T352)))), X1445), SCOPE: 42, CLAUSE: 2\n\nT352 is ground\nX1445 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
292 [label="292: quot(s(s(T352)), T352, s(s(s(s(T352)))), X1445), SCOPE: 42, CLAUSE: 3\n\nT352 is ground\nX1445 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
293 [label="293: quot(s(s(T364)), T364, s(s(s(s(s(T364))))), X1485)\n\nT364 is ground\nX1485 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
294 [label="294: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
295 [label="295: quot(s(s(T364)), T364, s(s(s(s(s(T364))))), X1485), SCOPE: 43, CLAUSE: 1 | quot(s(s(T364)), T364, s(s(s(s(s(T364))))), X1485), SCOPE: 43, CLAUSE: 2 | quot(s(s(T364)), T364, s(s(s(s(s(T364))))), X1485), SCOPE: 43, CLAUSE: 3\n\nT364 is ground\nX1485 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
296 [label="296: quot(s(s(T364)), T364, s(s(s(s(s(T364))))), X1485), SCOPE: 43, CLAUSE: 2 | quot(s(s(T364)), T364, s(s(s(s(s(T364))))), X1485), SCOPE: 43, CLAUSE: 3\n\nT364 is ground\nX1485 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
297 [label="297: quot(s(s(T364)), T364, s(s(s(s(s(T364))))), X1485), SCOPE: 43, CLAUSE: 2\n\nT364 is ground\nX1485 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
298 [label="298: quot(s(s(T364)), T364, s(s(s(s(s(T364))))), X1485), SCOPE: 43, CLAUSE: 3\n\nT364 is ground\nX1485 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
299 [label="299: quot(s(s(T376)), T376, s(s(s(s(s(s(T376)))))), X1525)\n\nT376 is ground\nX1525 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
300 [label="300: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
301 [label="301: quot(s(s(T376)), T376, s(s(s(s(s(s(T376)))))), X1525), SCOPE: 44, CLAUSE: 1 | quot(s(s(T376)), T376, s(s(s(s(s(s(T376)))))), X1525), SCOPE: 44, CLAUSE: 2 | quot(s(s(T376)), T376, s(s(s(s(s(s(T376)))))), X1525), SCOPE: 44, CLAUSE: 3\n\nT376 is ground\nX1525 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
302 [label="302: quot(s(s(T376)), T376, s(s(s(s(s(s(T376)))))), X1525), SCOPE: 44, CLAUSE: 2 | quot(s(s(T376)), T376, s(s(s(s(s(s(T376)))))), X1525), SCOPE: 44, CLAUSE: 3\n\nT376 is ground\nX1525 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
303 [label="303: quot(s(s(T376)), T376, s(s(s(s(s(s(T376)))))), X1525), SCOPE: 44, CLAUSE: 2\n\nT376 is ground\nX1525 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
304 [label="304: quot(s(s(T376)), T376, s(s(s(s(s(s(T376)))))), X1525), SCOPE: 44, CLAUSE: 3\n\nT376 is ground\nX1525 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
305 [label="305: quot(s(s(T388)), T388, s(s(s(s(s(s(s(T388))))))), X1565)\n\nT388 is ground\nX1565 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
306 [label="306: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
307 [label="307: quot(s(s(T388)), T388, s(s(s(s(s(s(s(T388))))))), X1565), SCOPE: 45, CLAUSE: 1 | quot(s(s(T388)), T388, s(s(s(s(s(s(s(T388))))))), X1565), SCOPE: 45, CLAUSE: 2 | quot(s(s(T388)), T388, s(s(s(s(s(s(s(T388))))))), X1565), SCOPE: 45, CLAUSE: 3\n\nT388 is ground\nX1565 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
308 [label="308: quot(s(s(T388)), T388, s(s(s(s(s(s(s(T388))))))), X1565), SCOPE: 45, CLAUSE: 2 | quot(s(s(T388)), T388, s(s(s(s(s(s(s(T388))))))), X1565), SCOPE: 45, CLAUSE: 3\n\nT388 is ground\nX1565 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
309 [label="309: quot(s(s(T388)), T388, s(s(s(s(s(s(s(T388))))))), X1565), SCOPE: 45, CLAUSE: 2\n\nT388 is ground\nX1565 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
310 [label="310: quot(s(s(T388)), T388, s(s(s(s(s(s(s(T388))))))), X1565), SCOPE: 45, CLAUSE: 3\n\nT388 is ground\nX1565 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
311 [label="311: quot(s(s(T400)), T400, s(s(s(s(s(s(s(s(T400)))))))), X1605)\n\nT400 is ground\nX1605 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
312 [label="312: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
313 [label="313: quot(s(s(T400)), T400, s(T403), X1605)\n\nT400 is ground\nT403 is ground\nX1605 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
314 [label="314: quot(s(s(T400)), T400, s(T403), X1605), SCOPE: 46, CLAUSE: 1 | quot(s(s(T400)), T400, s(T403), X1605), SCOPE: 46, CLAUSE: 2 | quot(s(s(T400)), T400, s(T403), X1605), SCOPE: 46, CLAUSE: 3\n\nT400 is ground\nT403 is ground\nX1605 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
315 [label="315: quot(s(s(T400)), T400, s(T403), X1605), SCOPE: 46, CLAUSE: 2 | quot(s(s(T400)), T400, s(T403), X1605), SCOPE: 46, CLAUSE: 3\n\nT400 is ground\nT403 is ground\nX1605 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
316 [label="316: quot(s(s(T400)), T400, s(T403), X1605), SCOPE: 46, CLAUSE: 2\n\nT400 is ground\nT403 is ground\nX1605 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
317 [label="317: quot(s(s(T400)), T400, s(T403), X1605), SCOPE: 46, CLAUSE: 3\n\nT400 is ground\nT403 is ground\nX1605 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
318 [label="318: quot(s(s(T420)), T420, s(T421), X1654)\n\nT420 is ground\nT421 is ground\nX1654 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
319 [label="319: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
320 [label="320: quot(s(s(0)), s(T430), s(T430), X1679)\n\nT430 is ground\nX1679 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
321 [label="321: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
322 [label="322: quot(s(s(0)), s(T430), s(T430), X1679), SCOPE: 47, CLAUSE: 1 | quot(s(s(0)), s(T430), s(T430), X1679), SCOPE: 47, CLAUSE: 2 | quot(s(s(0)), s(T430), s(T430), X1679), SCOPE: 47, CLAUSE: 3\n\nT430 is ground\nX1679 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
323 [label="323: quot(s(s(0)), s(T430), s(T430), X1679), SCOPE: 47, CLAUSE: 2 | quot(s(s(0)), s(T430), s(T430), X1679), SCOPE: 47, CLAUSE: 3\n\nT430 is ground\nX1679 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
324 [label="324: quot(s(s(0)), s(T430), s(T430), X1679), SCOPE: 47, CLAUSE: 2\n\nT430 is ground\nX1679 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
325 [label="325: quot(s(s(0)), s(T430), s(T430), X1679), SCOPE: 47, CLAUSE: 3\n\nT430 is ground\nX1679 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
326 [label="326: quot(s(0), T438, s(T438), X1736)\n\nT438 is ground\nX1736 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
327 [label="327: quot(s(0), T438, s(T438), X1736), SCOPE: 48, CLAUSE: 1 | quot(s(0), T438, s(T438), X1736), SCOPE: 48, CLAUSE: 2 | quot(s(0), T438, s(T438), X1736), SCOPE: 48, CLAUSE: 3\n\nT438 is ground\nX1736 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
328 [label="328: quot(s(0), T438, s(T438), X1736), SCOPE: 48, CLAUSE: 2 | quot(s(0), T438, s(T438), X1736), SCOPE: 48, CLAUSE: 3\n\nT438 is ground\nX1736 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
329 [label="329: quot(s(0), T438, s(T438), X1736), SCOPE: 48, CLAUSE: 2\n\nT438 is ground\nX1736 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
330 [label="330: quot(s(0), T438, s(T438), X1736), SCOPE: 48, CLAUSE: 3\n\nT438 is ground\nX1736 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
331 [label="331: quot(0, T444, s(s(T444)), X1772)\n\nT444 is ground\nX1772 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
332 [label="332: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
333 [label="333: quot(0, T444, s(s(T444)), X1772), SCOPE: 49, CLAUSE: 1 | quot(0, T444, s(s(T444)), X1772), SCOPE: 49, CLAUSE: 2 | quot(0, T444, s(s(T444)), X1772), SCOPE: 49, CLAUSE: 3\n\nT444 is ground\nX1772 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
334 [label="334: quot(0, T444, s(s(T444)), X1772), SCOPE: 49, CLAUSE: 1\n\nT444 is ground\nX1772 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
335 [label="335: quot(0, T444, s(s(T444)), X1772), SCOPE: 49, CLAUSE: 2 | quot(0, T444, s(s(T444)), X1772), SCOPE: 49, CLAUSE: 3\n\nT444 is ground\nX1772 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
336 [label="336: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
337 [label="337: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
338 [label="338: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
339 [label="339: quot(0, T444, s(s(T444)), X1772), SCOPE: 49, CLAUSE: 3\n\nT444 is ground\nX1772 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
340 [label="340: quot(0, s(s(0)), s(s(0)), X1808)\n\nX1808 is free", fontsize=16, style=filled, fillcolor=lightyellow];
341 [label="341: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
342 [label="342: quot(0, s(s(0)), s(s(0)), X1808), SCOPE: 50, CLAUSE: 1 | quot(0, s(s(0)), s(s(0)), X1808), SCOPE: 50, CLAUSE: 2 | quot(0, s(s(0)), s(s(0)), X1808), SCOPE: 50, CLAUSE: 3\n\nX1808 is free", fontsize=16, style=filled, fillcolor=lightyellow];
343 [label="343: quot(0, s(s(0)), s(s(0)), X1808), SCOPE: 50, CLAUSE: 1\n\nX1808 is free", fontsize=16, style=filled, fillcolor=lightyellow];
344 [label="344: quot(0, s(s(0)), s(s(0)), X1808), SCOPE: 50, CLAUSE: 2 | quot(0, s(s(0)), s(s(0)), X1808), SCOPE: 50, CLAUSE: 3\n\nX1808 is free", fontsize=16, style=filled, fillcolor=lightyellow];
345 [label="345: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
346 [label="346: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
347 [label="347: quot(0, s(s(0)), s(s(0)), X1808), SCOPE: 50, CLAUSE: 3\n\nX1808 is free", fontsize=16, style=filled, fillcolor=lightyellow];
348 [label="348: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
349 [label="349: quot(s(0), s(0), s(0), X1842)\n\nX1842 is free", fontsize=16, style=filled, fillcolor=lightyellow];
350 [label="350: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
351 [label="351: quot(s(0), s(0), s(0), X1842), SCOPE: 51, CLAUSE: 1 | quot(s(0), s(0), s(0), X1842), SCOPE: 51, CLAUSE: 2 | quot(s(0), s(0), s(0), X1842), SCOPE: 51, CLAUSE: 3\n\nX1842 is free", fontsize=16, style=filled, fillcolor=lightyellow];
352 [label="352: quot(s(0), s(0), s(0), X1842), SCOPE: 51, CLAUSE: 2 | quot(s(0), s(0), s(0), X1842), SCOPE: 51, CLAUSE: 3\n\nX1842 is free", fontsize=16, style=filled, fillcolor=lightyellow];
353 [label="353: quot(s(0), s(0), s(0), X1842), SCOPE: 51, CLAUSE: 2\n\nX1842 is free", fontsize=16, style=filled, fillcolor=lightyellow];
354 [label="354: quot(s(0), s(0), s(0), X1842), SCOPE: 51, CLAUSE: 3\n\nX1842 is free", fontsize=16, style=filled, fillcolor=lightyellow];
355 [label="355: quot(0, 0, s(0), X1905)\n\nX1905 is free", fontsize=16, style=filled, fillcolor=lightyellow];
356 [label="356: quot(0, 0, s(0), X1905), SCOPE: 52, CLAUSE: 1 | quot(0, 0, s(0), X1905), SCOPE: 52, CLAUSE: 2 | quot(0, 0, s(0), X1905), SCOPE: 52, CLAUSE: 3\n\nX1905 is free", fontsize=16, style=filled, fillcolor=lightyellow];
357 [label="357: quot(0, 0, s(0), X1905), SCOPE: 52, CLAUSE: 2 | quot(0, 0, s(0), X1905), SCOPE: 52, CLAUSE: 3\n\nX1905 is free", fontsize=16, style=filled, fillcolor=lightyellow];
358 [label="358: quot(0, 0, s(0), X1905), SCOPE: 52, CLAUSE: 3\n\nX1905 is free", fontsize=16, style=filled, fillcolor=lightyellow];
359 [label="359: quot(0, s(0), s(0), X1937)\n\nX1937 is free", fontsize=16, style=filled, fillcolor=lightyellow];
360 [label="360: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
361 [label="361: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
362 [label="362: quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1957)\n\nX1957 is free", fontsize=16, style=filled, fillcolor=lightyellow];
363 [label="363: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
364 [label="364: quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1957), SCOPE: 53, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1957), SCOPE: 53, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1957), SCOPE: 53, CLAUSE: 3\n\nX1957 is free", fontsize=16, style=filled, fillcolor=lightyellow];
365 [label="365: quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1957), SCOPE: 53, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1957), SCOPE: 53, CLAUSE: 3\n\nX1957 is free", fontsize=16, style=filled, fillcolor=lightyellow];
366 [label="366: quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1957), SCOPE: 53, CLAUSE: 2\n\nX1957 is free", fontsize=16, style=filled, fillcolor=lightyellow];
367 [label="367: quot(s(s(0)), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X1957), SCOPE: 53, CLAUSE: 3\n\nX1957 is free", fontsize=16, style=filled, fillcolor=lightyellow];
368 [label="368: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2014)\n\nX2014 is free", fontsize=16, style=filled, fillcolor=lightyellow];
369 [label="369: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2014), SCOPE: 54, CLAUSE: 1 | quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2014), SCOPE: 54, CLAUSE: 2 | quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2014), SCOPE: 54, CLAUSE: 3\n\nX2014 is free", fontsize=16, style=filled, fillcolor=lightyellow];
370 [label="370: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2014), SCOPE: 54, CLAUSE: 2 | quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2014), SCOPE: 54, CLAUSE: 3\n\nX2014 is free", fontsize=16, style=filled, fillcolor=lightyellow];
371 [label="371: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2014), SCOPE: 54, CLAUSE: 2\n\nX2014 is free", fontsize=16, style=filled, fillcolor=lightyellow];
372 [label="372: quot(s(0), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X2014), SCOPE: 54, CLAUSE: 3\n\nX2014 is free", fontsize=16, style=filled, fillcolor=lightyellow];
373 [label="373: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2054)\n\nX2054 is free", fontsize=16, style=filled, fillcolor=lightyellow];
374 [label="374: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2054), SCOPE: 55, CLAUSE: 1 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2054), SCOPE: 55, CLAUSE: 2 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2054), SCOPE: 55, CLAUSE: 3\n\nX2054 is free", fontsize=16, style=filled, fillcolor=lightyellow];
375 [label="375: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2054), SCOPE: 55, CLAUSE: 1\n\nX2054 is free", fontsize=16, style=filled, fillcolor=lightyellow];
376 [label="376: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2054), SCOPE: 55, CLAUSE: 2 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2054), SCOPE: 55, CLAUSE: 3\n\nX2054 is free", fontsize=16, style=filled, fillcolor=lightyellow];
377 [label="377: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
378 [label="378: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
379 [label="379: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X2054), SCOPE: 55, CLAUSE: 3\n\nX2054 is free", fontsize=16, style=filled, fillcolor=lightyellow];
380 [label="380: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
381 [label="381: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
382 [label="382: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
383 [label="383: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X2091)\n\nX2091 is free", fontsize=16, style=filled, fillcolor=lightyellow];
384 [label="384: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
385 [label="385: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X2091), SCOPE: 56, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X2091), SCOPE: 56, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X2091), SCOPE: 56, CLAUSE: 3\n\nX2091 is free", fontsize=16, style=filled, fillcolor=lightyellow];
386 [label="386: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X2091), SCOPE: 56, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X2091), SCOPE: 56, CLAUSE: 3\n\nX2091 is free", fontsize=16, style=filled, fillcolor=lightyellow];
387 [label="387: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X2091), SCOPE: 56, CLAUSE: 2\n\nX2091 is free", fontsize=16, style=filled, fillcolor=lightyellow];
388 [label="388: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X2091), SCOPE: 56, CLAUSE: 3\n\nX2091 is free", fontsize=16, style=filled, fillcolor=lightyellow];
389 [label="389: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X2148)\n\nX2148 is free", fontsize=16, style=filled, fillcolor=lightyellow];
390 [label="390: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X2148), SCOPE: 57, CLAUSE: 1 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X2148), SCOPE: 57, CLAUSE: 2 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X2148), SCOPE: 57, CLAUSE: 3\n\nX2148 is free", fontsize=16, style=filled, fillcolor=lightyellow];
391 [label="391: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X2148), SCOPE: 57, CLAUSE: 2 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X2148), SCOPE: 57, CLAUSE: 3\n\nX2148 is free", fontsize=16, style=filled, fillcolor=lightyellow];
392 [label="392: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X2148), SCOPE: 57, CLAUSE: 2\n\nX2148 is free", fontsize=16, style=filled, fillcolor=lightyellow];
393 [label="393: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X2148), SCOPE: 57, CLAUSE: 3\n\nX2148 is free", fontsize=16, style=filled, fillcolor=lightyellow];
394 [label="394: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X2188)\n\nX2188 is free", fontsize=16, style=filled, fillcolor=lightyellow];
395 [label="395: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X2188), SCOPE: 58, CLAUSE: 1 | quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X2188), SCOPE: 58, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X2188), SCOPE: 58, CLAUSE: 3\n\nX2188 is free", fontsize=16, style=filled, fillcolor=lightyellow];
396 [label="396: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X2188), SCOPE: 58, CLAUSE: 1\n\nX2188 is free", fontsize=16, style=filled, fillcolor=lightyellow];
397 [label="397: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X2188), SCOPE: 58, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X2188), SCOPE: 58, CLAUSE: 3\n\nX2188 is free", fontsize=16, style=filled, fillcolor=lightyellow];
398 [label="398: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
399 [label="399: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
400 [label="400: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X2188), SCOPE: 58, CLAUSE: 3\n\nX2188 is free", fontsize=16, style=filled, fillcolor=lightyellow];
401 [label="401: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
402 [label="402: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
403 [label="403: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
404 [label="404: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X2225)\n\nX2225 is free", fontsize=16, style=filled, fillcolor=lightyellow];
405 [label="405: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
406 [label="406: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X2225), SCOPE: 59, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X2225), SCOPE: 59, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X2225), SCOPE: 59, CLAUSE: 3\n\nX2225 is free", fontsize=16, style=filled, fillcolor=lightyellow];
407 [label="407: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X2225), SCOPE: 59, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X2225), SCOPE: 59, CLAUSE: 3\n\nX2225 is free", fontsize=16, style=filled, fillcolor=lightyellow];
408 [label="408: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X2225), SCOPE: 59, CLAUSE: 2\n\nX2225 is free", fontsize=16, style=filled, fillcolor=lightyellow];
409 [label="409: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X2225), SCOPE: 59, CLAUSE: 3\n\nX2225 is free", fontsize=16, style=filled, fillcolor=lightyellow];
410 [label="410: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X2282)\n\nX2282 is free", fontsize=16, style=filled, fillcolor=lightyellow];
411 [label="411: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X2282), SCOPE: 60, CLAUSE: 1 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X2282), SCOPE: 60, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X2282), SCOPE: 60, CLAUSE: 3\n\nX2282 is free", fontsize=16, style=filled, fillcolor=lightyellow];
412 [label="412: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X2282), SCOPE: 60, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X2282), SCOPE: 60, CLAUSE: 3\n\nX2282 is free", fontsize=16, style=filled, fillcolor=lightyellow];
413 [label="413: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X2282), SCOPE: 60, CLAUSE: 2\n\nX2282 is free", fontsize=16, style=filled, fillcolor=lightyellow];
414 [label="414: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(0))))), X2282), SCOPE: 60, CLAUSE: 3\n\nX2282 is free", fontsize=16, style=filled, fillcolor=lightyellow];
415 [label="415: quot(0, s(s(s(0))), s(s(s(s(s(0))))), X2322)\n\nX2322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
416 [label="416: quot(0, s(s(s(0))), s(s(s(s(s(0))))), X2322), SCOPE: 61, CLAUSE: 1 | quot(0, s(s(s(0))), s(s(s(s(s(0))))), X2322), SCOPE: 61, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(s(0))))), X2322), SCOPE: 61, CLAUSE: 3\n\nX2322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
417 [label="417: quot(0, s(s(s(0))), s(s(s(s(s(0))))), X2322), SCOPE: 61, CLAUSE: 1\n\nX2322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
418 [label="418: quot(0, s(s(s(0))), s(s(s(s(s(0))))), X2322), SCOPE: 61, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(s(0))))), X2322), SCOPE: 61, CLAUSE: 3\n\nX2322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
419 [label="419: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
420 [label="420: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
421 [label="421: quot(0, s(s(s(0))), s(s(s(s(s(0))))), X2322), SCOPE: 61, CLAUSE: 3\n\nX2322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
422 [label="422: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
423 [label="423: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
424 [label="424: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
425 [label="425: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X2359)\n\nX2359 is free", fontsize=16, style=filled, fillcolor=lightyellow];
426 [label="426: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
427 [label="427: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X2359), SCOPE: 62, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X2359), SCOPE: 62, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X2359), SCOPE: 62, CLAUSE: 3\n\nX2359 is free", fontsize=16, style=filled, fillcolor=lightyellow];
428 [label="428: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X2359), SCOPE: 62, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X2359), SCOPE: 62, CLAUSE: 3\n\nX2359 is free", fontsize=16, style=filled, fillcolor=lightyellow];
429 [label="429: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X2359), SCOPE: 62, CLAUSE: 2\n\nX2359 is free", fontsize=16, style=filled, fillcolor=lightyellow];
430 [label="430: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(0)))), X2359), SCOPE: 62, CLAUSE: 3\n\nX2359 is free", fontsize=16, style=filled, fillcolor=lightyellow];
431 [label="431: quot(s(0), s(s(s(0))), s(s(s(s(0)))), X2416)\n\nX2416 is free", fontsize=16, style=filled, fillcolor=lightyellow];
432 [label="432: quot(s(0), s(s(s(0))), s(s(s(s(0)))), X2416), SCOPE: 63, CLAUSE: 1 | quot(s(0), s(s(s(0))), s(s(s(s(0)))), X2416), SCOPE: 63, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(0)))), X2416), SCOPE: 63, CLAUSE: 3\n\nX2416 is free", fontsize=16, style=filled, fillcolor=lightyellow];
433 [label="433: quot(s(0), s(s(s(0))), s(s(s(s(0)))), X2416), SCOPE: 63, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(0)))), X2416), SCOPE: 63, CLAUSE: 3\n\nX2416 is free", fontsize=16, style=filled, fillcolor=lightyellow];
434 [label="434: quot(s(0), s(s(s(0))), s(s(s(s(0)))), X2416), SCOPE: 63, CLAUSE: 2\n\nX2416 is free", fontsize=16, style=filled, fillcolor=lightyellow];
435 [label="435: quot(s(0), s(s(s(0))), s(s(s(s(0)))), X2416), SCOPE: 63, CLAUSE: 3\n\nX2416 is free", fontsize=16, style=filled, fillcolor=lightyellow];
436 [label="436: quot(0, s(s(0)), s(s(s(s(0)))), X2456)\n\nX2456 is free", fontsize=16, style=filled, fillcolor=lightyellow];
437 [label="437: quot(0, s(s(0)), s(s(s(s(0)))), X2456), SCOPE: 64, CLAUSE: 1 | quot(0, s(s(0)), s(s(s(s(0)))), X2456), SCOPE: 64, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(0)))), X2456), SCOPE: 64, CLAUSE: 3\n\nX2456 is free", fontsize=16, style=filled, fillcolor=lightyellow];
438 [label="438: quot(0, s(s(0)), s(s(s(s(0)))), X2456), SCOPE: 64, CLAUSE: 1\n\nX2456 is free", fontsize=16, style=filled, fillcolor=lightyellow];
439 [label="439: quot(0, s(s(0)), s(s(s(s(0)))), X2456), SCOPE: 64, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(0)))), X2456), SCOPE: 64, CLAUSE: 3\n\nX2456 is free", fontsize=16, style=filled, fillcolor=lightyellow];
440 [label="440: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
441 [label="441: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
442 [label="442: quot(0, s(s(0)), s(s(s(s(0)))), X2456), SCOPE: 64, CLAUSE: 3\n\nX2456 is free", fontsize=16, style=filled, fillcolor=lightyellow];
443 [label="443: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
444 [label="444: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
445 [label="445: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
446 [label="446: quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2493)\n\nX2493 is free", fontsize=16, style=filled, fillcolor=lightyellow];
447 [label="447: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
448 [label="448: quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2493), SCOPE: 65, CLAUSE: 1 | quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2493), SCOPE: 65, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2493), SCOPE: 65, CLAUSE: 3\n\nX2493 is free", fontsize=16, style=filled, fillcolor=lightyellow];
449 [label="449: quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2493), SCOPE: 65, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2493), SCOPE: 65, CLAUSE: 3\n\nX2493 is free", fontsize=16, style=filled, fillcolor=lightyellow];
450 [label="450: quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2493), SCOPE: 65, CLAUSE: 2\n\nX2493 is free", fontsize=16, style=filled, fillcolor=lightyellow];
451 [label="451: quot(s(s(0)), s(s(s(0))), s(s(s(0))), X2493), SCOPE: 65, CLAUSE: 3\n\nX2493 is free", fontsize=16, style=filled, fillcolor=lightyellow];
452 [label="452: quot(s(0), s(s(0)), s(s(s(0))), X2550)\n\nX2550 is free", fontsize=16, style=filled, fillcolor=lightyellow];
453 [label="453: quot(s(0), s(s(0)), s(s(s(0))), X2550), SCOPE: 66, CLAUSE: 1 | quot(s(0), s(s(0)), s(s(s(0))), X2550), SCOPE: 66, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(0))), X2550), SCOPE: 66, CLAUSE: 3\n\nX2550 is free", fontsize=16, style=filled, fillcolor=lightyellow];
454 [label="454: quot(s(0), s(s(0)), s(s(s(0))), X2550), SCOPE: 66, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(0))), X2550), SCOPE: 66, CLAUSE: 3\n\nX2550 is free", fontsize=16, style=filled, fillcolor=lightyellow];
455 [label="455: quot(s(0), s(s(0)), s(s(s(0))), X2550), SCOPE: 66, CLAUSE: 2\n\nX2550 is free", fontsize=16, style=filled, fillcolor=lightyellow];
456 [label="456: quot(s(0), s(s(0)), s(s(s(0))), X2550), SCOPE: 66, CLAUSE: 3\n\nX2550 is free", fontsize=16, style=filled, fillcolor=lightyellow];
457 [label="457: quot(0, s(0), s(s(s(0))), X2590)\n\nX2590 is free", fontsize=16, style=filled, fillcolor=lightyellow];
458 [label="458: quot(0, s(0), s(s(s(0))), X2590), SCOPE: 67, CLAUSE: 1 | quot(0, s(0), s(s(s(0))), X2590), SCOPE: 67, CLAUSE: 2 | quot(0, s(0), s(s(s(0))), X2590), SCOPE: 67, CLAUSE: 3\n\nX2590 is free", fontsize=16, style=filled, fillcolor=lightyellow];
459 [label="459: quot(0, s(0), s(s(s(0))), X2590), SCOPE: 67, CLAUSE: 1\n\nX2590 is free", fontsize=16, style=filled, fillcolor=lightyellow];
460 [label="460: quot(0, s(0), s(s(s(0))), X2590), SCOPE: 67, CLAUSE: 2 | quot(0, s(0), s(s(s(0))), X2590), SCOPE: 67, CLAUSE: 3\n\nX2590 is free", fontsize=16, style=filled, fillcolor=lightyellow];
461 [label="461: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
462 [label="462: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
463 [label="463: quot(0, s(0), s(s(s(0))), X2590), SCOPE: 67, CLAUSE: 3\n\nX2590 is free", fontsize=16, style=filled, fillcolor=lightyellow];
464 [label="464: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
465 [label="465: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
466 [label="466: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
467 [label="467: quot(s(s(0)), s(s(0)), s(s(0)), X2627)\n\nX2627 is free", fontsize=16, style=filled, fillcolor=lightyellow];
468 [label="468: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
469 [label="469: quot(s(s(0)), s(s(0)), s(s(0)), X2627), SCOPE: 68, CLAUSE: 1 | quot(s(s(0)), s(s(0)), s(s(0)), X2627), SCOPE: 68, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(0)), X2627), SCOPE: 68, CLAUSE: 3\n\nX2627 is free", fontsize=16, style=filled, fillcolor=lightyellow];
470 [label="470: quot(s(s(0)), s(s(0)), s(s(0)), X2627), SCOPE: 68, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(0)), X2627), SCOPE: 68, CLAUSE: 3\n\nX2627 is free", fontsize=16, style=filled, fillcolor=lightyellow];
471 [label="471: quot(s(s(0)), s(s(0)), s(s(0)), X2627), SCOPE: 68, CLAUSE: 2\n\nX2627 is free", fontsize=16, style=filled, fillcolor=lightyellow];
472 [label="472: quot(s(s(0)), s(s(0)), s(s(0)), X2627), SCOPE: 68, CLAUSE: 3\n\nX2627 is free", fontsize=16, style=filled, fillcolor=lightyellow];
473 [label="473: quot(s(0), s(0), s(s(0)), X2684)\n\nX2684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
474 [label="474: quot(s(0), s(0), s(s(0)), X2684), SCOPE: 69, CLAUSE: 1 | quot(s(0), s(0), s(s(0)), X2684), SCOPE: 69, CLAUSE: 2 | quot(s(0), s(0), s(s(0)), X2684), SCOPE: 69, CLAUSE: 3\n\nX2684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
475 [label="475: quot(s(0), s(0), s(s(0)), X2684), SCOPE: 69, CLAUSE: 2 | quot(s(0), s(0), s(s(0)), X2684), SCOPE: 69, CLAUSE: 3\n\nX2684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
476 [label="476: quot(s(0), s(0), s(s(0)), X2684), SCOPE: 69, CLAUSE: 2\n\nX2684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
477 [label="477: quot(s(0), s(0), s(s(0)), X2684), SCOPE: 69, CLAUSE: 3\n\nX2684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
478 [label="478: quot(0, 0, s(s(0)), X2744)\n\nX2744 is free", fontsize=16, style=filled, fillcolor=lightyellow];
479 [label="479: quot(0, 0, s(s(0)), X2744), SCOPE: 70, CLAUSE: 1 | quot(0, 0, s(s(0)), X2744), SCOPE: 70, CLAUSE: 2 | quot(0, 0, s(s(0)), X2744), SCOPE: 70, CLAUSE: 3\n\nX2744 is free", fontsize=16, style=filled, fillcolor=lightyellow];
480 [label="480: quot(0, 0, s(s(0)), X2744), SCOPE: 70, CLAUSE: 2 | quot(0, 0, s(s(0)), X2744), SCOPE: 70, CLAUSE: 3\n\nX2744 is free", fontsize=16, style=filled, fillcolor=lightyellow];
481 [label="481: quot(0, 0, s(s(0)), X2744), SCOPE: 70, CLAUSE: 3\n\nX2744 is free", fontsize=16, style=filled, fillcolor=lightyellow];
482 [label="482: quot(0, s(s(0)), s(s(0)), X2776)\n\nX2776 is free", fontsize=16, style=filled, fillcolor=lightyellow];
483 [label="483: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
484 [label="484: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
485 [label="485: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
486 [label="486: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
487 [label="487: times(T305, s(s(T303)), X1232)\n\nT303 is ground\nT305 is ground\nX1232 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
488 [label="488: neq(s(s(s(s(T303)))), T474)\n\nT303 is ground\nT474 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
489 [label="489: pr(s(s(s(s(T297)))), s(T297)), SCOPE: 71, CLAUSE: 5 | pr(s(s(s(s(T297)))), s(T297)), SCOPE: 71, CLAUSE: 6\n\nT297 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
490 [label="490: pr(s(s(s(s(T297)))), s(T297)), SCOPE: 71, CLAUSE: 5\n\nT297 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
491 [label="491: pr(s(s(s(s(T297)))), s(T297)), SCOPE: 71, CLAUSE: 6\n\nT297 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
492 [label="492: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
493 [label="493: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
494 [label="494: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
495 [label="495: ','(not_divides(s(s(T491)), s(s(s(s(s(T491)))))), pr(s(s(s(s(s(T491))))), s(T491)))\n\nT491 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
496 [label="496: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
497 [label="497: not_divides(s(s(T491)), s(s(s(s(s(T491))))))\n\nT491 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
498 [label="498: pr(s(s(s(s(s(T491))))), s(T491))\n\nT491 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
499 [label="499: not_divides(s(s(T491)), s(s(s(s(s(T491)))))), SCOPE: 72, CLAUSE: 7\n\nT491 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
500 [label="500: ','(div(s(s(s(s(s(T497))))), s(s(T497)), X2833), ','(times(X2833, s(s(T497)), X2834), neq(s(s(s(s(s(T497))))), X2834)))\n\nT497 is ground\nX2833 is free; \nX2834 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
501 [label="501: div(s(s(s(s(s(T497))))), s(s(T497)), X2833)\n\nT497 is ground\nX2833 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
502 [label="502: ','(times(T499, s(s(T497)), X2834), neq(s(s(s(s(s(T497))))), X2834))\n\nT497 is ground\nT499 is ground\nX2834 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
503 [label="503: div(s(s(s(s(s(T497))))), s(s(T497)), X2833), SCOPE: 73, CLAUSE: 0\n\nT497 is ground\nX2833 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
504 [label="504: quot(s(s(s(s(s(T504))))), s(s(T504)), s(s(T504)), X2863)\n\nT504 is ground\nX2863 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
505 [label="505: quot(s(s(s(s(s(T504))))), s(s(T504)), s(s(T504)), X2863), SCOPE: 74, CLAUSE: 1 | quot(s(s(s(s(s(T504))))), s(s(T504)), s(s(T504)), X2863), SCOPE: 74, CLAUSE: 2 | quot(s(s(s(s(s(T504))))), s(s(T504)), s(s(T504)), X2863), SCOPE: 74, CLAUSE: 3\n\nT504 is ground\nX2863 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
506 [label="506: quot(s(s(s(s(s(T504))))), s(s(T504)), s(s(T504)), X2863), SCOPE: 74, CLAUSE: 2 | quot(s(s(s(s(s(T504))))), s(s(T504)), s(s(T504)), X2863), SCOPE: 74, CLAUSE: 3\n\nT504 is ground\nX2863 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
507 [label="507: quot(s(s(s(s(s(T504))))), s(s(T504)), s(s(T504)), X2863), SCOPE: 74, CLAUSE: 2\n\nT504 is ground\nX2863 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
508 [label="508: quot(s(s(s(s(s(T504))))), s(s(T504)), s(s(T504)), X2863), SCOPE: 74, CLAUSE: 3\n\nT504 is ground\nX2863 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
509 [label="509: quot(s(s(s(s(T512)))), s(T512), s(s(T512)), X2917)\n\nT512 is ground\nX2917 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
510 [label="510: quot(s(s(s(s(T512)))), s(T512), s(s(T512)), X2917), SCOPE: 75, CLAUSE: 1 | quot(s(s(s(s(T512)))), s(T512), s(s(T512)), X2917), SCOPE: 75, CLAUSE: 2 | quot(s(s(s(s(T512)))), s(T512), s(s(T512)), X2917), SCOPE: 75, CLAUSE: 3\n\nT512 is ground\nX2917 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
511 [label="511: quot(s(s(s(s(T512)))), s(T512), s(s(T512)), X2917), SCOPE: 75, CLAUSE: 2 | quot(s(s(s(s(T512)))), s(T512), s(s(T512)), X2917), SCOPE: 75, CLAUSE: 3\n\nT512 is ground\nX2917 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
512 [label="512: quot(s(s(s(s(T512)))), s(T512), s(s(T512)), X2917), SCOPE: 75, CLAUSE: 2\n\nT512 is ground\nX2917 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
513 [label="513: quot(s(s(s(s(T512)))), s(T512), s(s(T512)), X2917), SCOPE: 75, CLAUSE: 3\n\nT512 is ground\nX2917 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
514 [label="514: quot(s(s(s(T522))), T522, s(s(T522)), X2971)\n\nT522 is ground\nX2971 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
515 [label="515: quot(s(s(s(T522))), T522, s(s(T522)), X2971), SCOPE: 76, CLAUSE: 1 | quot(s(s(s(T522))), T522, s(s(T522)), X2971), SCOPE: 76, CLAUSE: 2 | quot(s(s(s(T522))), T522, s(s(T522)), X2971), SCOPE: 76, CLAUSE: 3\n\nT522 is ground\nX2971 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
516 [label="516: quot(s(s(s(T522))), T522, s(s(T522)), X2971), SCOPE: 76, CLAUSE: 2 | quot(s(s(s(T522))), T522, s(s(T522)), X2971), SCOPE: 76, CLAUSE: 3\n\nT522 is ground\nX2971 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
517 [label="517: quot(s(s(s(T522))), T522, s(s(T522)), X2971), SCOPE: 76, CLAUSE: 2\n\nT522 is ground\nX2971 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
518 [label="518: quot(s(s(s(T522))), T522, s(s(T522)), X2971), SCOPE: 76, CLAUSE: 3\n\nT522 is ground\nX2971 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
519 [label="519: quot(s(s(s(T534))), T534, s(s(s(T534))), X3007)\n\nT534 is ground\nX3007 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
520 [label="520: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
521 [label="521: quot(s(s(s(T534))), T534, s(s(s(T534))), X3007), SCOPE: 77, CLAUSE: 1 | quot(s(s(s(T534))), T534, s(s(s(T534))), X3007), SCOPE: 77, CLAUSE: 2 | quot(s(s(s(T534))), T534, s(s(s(T534))), X3007), SCOPE: 77, CLAUSE: 3\n\nT534 is ground\nX3007 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
522 [label="522: quot(s(s(s(T534))), T534, s(s(s(T534))), X3007), SCOPE: 77, CLAUSE: 2 | quot(s(s(s(T534))), T534, s(s(s(T534))), X3007), SCOPE: 77, CLAUSE: 3\n\nT534 is ground\nX3007 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
523 [label="523: quot(s(s(s(T534))), T534, s(s(s(T534))), X3007), SCOPE: 77, CLAUSE: 2\n\nT534 is ground\nX3007 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
524 [label="524: quot(s(s(s(T534))), T534, s(s(s(T534))), X3007), SCOPE: 77, CLAUSE: 3\n\nT534 is ground\nX3007 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
525 [label="525: quot(s(s(s(T546))), T546, s(s(s(s(T546)))), X3047)\n\nT546 is ground\nX3047 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
526 [label="526: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
527 [label="527: quot(s(s(s(T546))), T546, s(s(s(s(T546)))), X3047), SCOPE: 78, CLAUSE: 1 | quot(s(s(s(T546))), T546, s(s(s(s(T546)))), X3047), SCOPE: 78, CLAUSE: 2 | quot(s(s(s(T546))), T546, s(s(s(s(T546)))), X3047), SCOPE: 78, CLAUSE: 3\n\nT546 is ground\nX3047 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
528 [label="528: quot(s(s(s(T546))), T546, s(s(s(s(T546)))), X3047), SCOPE: 78, CLAUSE: 2 | quot(s(s(s(T546))), T546, s(s(s(s(T546)))), X3047), SCOPE: 78, CLAUSE: 3\n\nT546 is ground\nX3047 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
529 [label="529: quot(s(s(s(T546))), T546, s(s(s(s(T546)))), X3047), SCOPE: 78, CLAUSE: 2\n\nT546 is ground\nX3047 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
530 [label="530: quot(s(s(s(T546))), T546, s(s(s(s(T546)))), X3047), SCOPE: 78, CLAUSE: 3\n\nT546 is ground\nX3047 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
531 [label="531: quot(s(s(s(T558))), T558, s(s(s(s(s(T558))))), X3087)\n\nT558 is ground\nX3087 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
532 [label="532: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
533 [label="533: quot(s(s(s(T558))), T558, s(s(s(s(s(T558))))), X3087), SCOPE: 79, CLAUSE: 1 | quot(s(s(s(T558))), T558, s(s(s(s(s(T558))))), X3087), SCOPE: 79, CLAUSE: 2 | quot(s(s(s(T558))), T558, s(s(s(s(s(T558))))), X3087), SCOPE: 79, CLAUSE: 3\n\nT558 is ground\nX3087 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
534 [label="534: quot(s(s(s(T558))), T558, s(s(s(s(s(T558))))), X3087), SCOPE: 79, CLAUSE: 2 | quot(s(s(s(T558))), T558, s(s(s(s(s(T558))))), X3087), SCOPE: 79, CLAUSE: 3\n\nT558 is ground\nX3087 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
535 [label="535: quot(s(s(s(T558))), T558, s(s(s(s(s(T558))))), X3087), SCOPE: 79, CLAUSE: 2\n\nT558 is ground\nX3087 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
536 [label="536: quot(s(s(s(T558))), T558, s(s(s(s(s(T558))))), X3087), SCOPE: 79, CLAUSE: 3\n\nT558 is ground\nX3087 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
537 [label="537: quot(s(s(s(T570))), T570, s(s(s(s(s(s(T570)))))), X3127)\n\nT570 is ground\nX3127 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
538 [label="538: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
539 [label="539: quot(s(s(s(T570))), T570, s(s(s(s(s(s(T570)))))), X3127), SCOPE: 80, CLAUSE: 1 | quot(s(s(s(T570))), T570, s(s(s(s(s(s(T570)))))), X3127), SCOPE: 80, CLAUSE: 2 | quot(s(s(s(T570))), T570, s(s(s(s(s(s(T570)))))), X3127), SCOPE: 80, CLAUSE: 3\n\nT570 is ground\nX3127 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
540 [label="540: quot(s(s(s(T570))), T570, s(s(s(s(s(s(T570)))))), X3127), SCOPE: 80, CLAUSE: 2 | quot(s(s(s(T570))), T570, s(s(s(s(s(s(T570)))))), X3127), SCOPE: 80, CLAUSE: 3\n\nT570 is ground\nX3127 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
541 [label="541: quot(s(s(s(T570))), T570, s(s(s(s(s(s(T570)))))), X3127), SCOPE: 80, CLAUSE: 2\n\nT570 is ground\nX3127 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
542 [label="542: quot(s(s(s(T570))), T570, s(s(s(s(s(s(T570)))))), X3127), SCOPE: 80, CLAUSE: 3\n\nT570 is ground\nX3127 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
543 [label="543: quot(s(s(s(T582))), T582, s(s(s(s(s(s(s(T582))))))), X3167)\n\nT582 is ground\nX3167 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
544 [label="544: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
545 [label="545: quot(s(s(s(T582))), T582, s(s(s(s(s(s(s(T582))))))), X3167), SCOPE: 81, CLAUSE: 1 | quot(s(s(s(T582))), T582, s(s(s(s(s(s(s(T582))))))), X3167), SCOPE: 81, CLAUSE: 2 | quot(s(s(s(T582))), T582, s(s(s(s(s(s(s(T582))))))), X3167), SCOPE: 81, CLAUSE: 3\n\nT582 is ground\nX3167 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
546 [label="546: quot(s(s(s(T582))), T582, s(s(s(s(s(s(s(T582))))))), X3167), SCOPE: 81, CLAUSE: 2 | quot(s(s(s(T582))), T582, s(s(s(s(s(s(s(T582))))))), X3167), SCOPE: 81, CLAUSE: 3\n\nT582 is ground\nX3167 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
547 [label="547: quot(s(s(s(T582))), T582, s(s(s(s(s(s(s(T582))))))), X3167), SCOPE: 81, CLAUSE: 2\n\nT582 is ground\nX3167 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
548 [label="548: quot(s(s(s(T582))), T582, s(s(s(s(s(s(s(T582))))))), X3167), SCOPE: 81, CLAUSE: 3\n\nT582 is ground\nX3167 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
549 [label="549: quot(s(s(s(T594))), T594, s(s(s(s(s(s(s(s(T594)))))))), X3207)\n\nT594 is ground\nX3207 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
550 [label="550: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
551 [label="551: quot(s(s(s(T594))), T594, s(T597), X3207)\n\nT594 is ground\nT597 is ground\nX3207 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
552 [label="552: quot(s(s(s(T594))), T594, s(T597), X3207), SCOPE: 82, CLAUSE: 1 | quot(s(s(s(T594))), T594, s(T597), X3207), SCOPE: 82, CLAUSE: 2 | quot(s(s(s(T594))), T594, s(T597), X3207), SCOPE: 82, CLAUSE: 3\n\nT594 is ground\nT597 is ground\nX3207 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
553 [label="553: quot(s(s(s(T594))), T594, s(T597), X3207), SCOPE: 82, CLAUSE: 2 | quot(s(s(s(T594))), T594, s(T597), X3207), SCOPE: 82, CLAUSE: 3\n\nT594 is ground\nT597 is ground\nX3207 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
554 [label="554: quot(s(s(s(T594))), T594, s(T597), X3207), SCOPE: 82, CLAUSE: 2\n\nT594 is ground\nT597 is ground\nX3207 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
555 [label="555: quot(s(s(s(T594))), T594, s(T597), X3207), SCOPE: 82, CLAUSE: 3\n\nT594 is ground\nT597 is ground\nX3207 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
556 [label="556: quot(s(s(s(T614))), T614, s(T615), X3256)\n\nT614 is ground\nT615 is ground\nX3256 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
557 [label="557: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
558 [label="558: quot(s(s(s(0))), s(T624), s(T624), X3281)\n\nT624 is ground\nX3281 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
559 [label="559: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
560 [label="560: quot(s(s(s(0))), s(T624), s(T624), X3281), SCOPE: 83, CLAUSE: 1 | quot(s(s(s(0))), s(T624), s(T624), X3281), SCOPE: 83, CLAUSE: 2 | quot(s(s(s(0))), s(T624), s(T624), X3281), SCOPE: 83, CLAUSE: 3\n\nT624 is ground\nX3281 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
561 [label="561: quot(s(s(s(0))), s(T624), s(T624), X3281), SCOPE: 83, CLAUSE: 2 | quot(s(s(s(0))), s(T624), s(T624), X3281), SCOPE: 83, CLAUSE: 3\n\nT624 is ground\nX3281 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
562 [label="562: quot(s(s(s(0))), s(T624), s(T624), X3281), SCOPE: 83, CLAUSE: 2\n\nT624 is ground\nX3281 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
563 [label="563: quot(s(s(s(0))), s(T624), s(T624), X3281), SCOPE: 83, CLAUSE: 3\n\nT624 is ground\nX3281 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
564 [label="564: quot(s(s(0)), T632, s(T632), X3338)\n\nT632 is ground\nX3338 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
565 [label="565: quot(s(s(0)), T632, s(T632), X3338), SCOPE: 84, CLAUSE: 1 | quot(s(s(0)), T632, s(T632), X3338), SCOPE: 84, CLAUSE: 2 | quot(s(s(0)), T632, s(T632), X3338), SCOPE: 84, CLAUSE: 3\n\nT632 is ground\nX3338 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
566 [label="566: quot(s(s(0)), T632, s(T632), X3338), SCOPE: 84, CLAUSE: 2 | quot(s(s(0)), T632, s(T632), X3338), SCOPE: 84, CLAUSE: 3\n\nT632 is ground\nX3338 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
567 [label="567: quot(s(s(0)), T632, s(T632), X3338), SCOPE: 84, CLAUSE: 2\n\nT632 is ground\nX3338 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
568 [label="568: quot(s(s(0)), T632, s(T632), X3338), SCOPE: 84, CLAUSE: 3\n\nT632 is ground\nX3338 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
569 [label="569: quot(s(0), T638, s(s(T638)), X3374)\n\nT638 is ground\nX3374 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
570 [label="570: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
571 [label="571: quot(s(0), T638, s(s(T638)), X3374), SCOPE: 85, CLAUSE: 1 | quot(s(0), T638, s(s(T638)), X3374), SCOPE: 85, CLAUSE: 2 | quot(s(0), T638, s(s(T638)), X3374), SCOPE: 85, CLAUSE: 3\n\nT638 is ground\nX3374 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
572 [label="572: quot(s(0), T638, s(s(T638)), X3374), SCOPE: 85, CLAUSE: 2 | quot(s(0), T638, s(s(T638)), X3374), SCOPE: 85, CLAUSE: 3\n\nT638 is ground\nX3374 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
573 [label="573: quot(s(0), T638, s(s(T638)), X3374), SCOPE: 85, CLAUSE: 2\n\nT638 is ground\nX3374 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
574 [label="574: quot(s(0), T638, s(s(T638)), X3374), SCOPE: 85, CLAUSE: 3\n\nT638 is ground\nX3374 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
575 [label="575: quot(0, T644, s(s(s(T644))), X3414)\n\nT644 is ground\nX3414 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
576 [label="576: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
577 [label="577: quot(0, T644, s(s(s(T644))), X3414), SCOPE: 86, CLAUSE: 1 | quot(0, T644, s(s(s(T644))), X3414), SCOPE: 86, CLAUSE: 2 | quot(0, T644, s(s(s(T644))), X3414), SCOPE: 86, CLAUSE: 3\n\nT644 is ground\nX3414 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
578 [label="578: quot(0, T644, s(s(s(T644))), X3414), SCOPE: 86, CLAUSE: 1\n\nT644 is ground\nX3414 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
579 [label="579: quot(0, T644, s(s(s(T644))), X3414), SCOPE: 86, CLAUSE: 2 | quot(0, T644, s(s(s(T644))), X3414), SCOPE: 86, CLAUSE: 3\n\nT644 is ground\nX3414 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
580 [label="580: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
581 [label="581: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
582 [label="582: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
583 [label="583: quot(0, T644, s(s(s(T644))), X3414), SCOPE: 86, CLAUSE: 3\n\nT644 is ground\nX3414 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
584 [label="584: quot(0, s(s(s(0))), s(s(s(0))), X3450)\n\nX3450 is free", fontsize=16, style=filled, fillcolor=lightyellow];
585 [label="585: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
586 [label="586: quot(0, s(s(s(0))), s(s(s(0))), X3450), SCOPE: 87, CLAUSE: 1 | quot(0, s(s(s(0))), s(s(s(0))), X3450), SCOPE: 87, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(0))), X3450), SCOPE: 87, CLAUSE: 3\n\nX3450 is free", fontsize=16, style=filled, fillcolor=lightyellow];
587 [label="587: quot(0, s(s(s(0))), s(s(s(0))), X3450), SCOPE: 87, CLAUSE: 1\n\nX3450 is free", fontsize=16, style=filled, fillcolor=lightyellow];
588 [label="588: quot(0, s(s(s(0))), s(s(s(0))), X3450), SCOPE: 87, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(0))), X3450), SCOPE: 87, CLAUSE: 3\n\nX3450 is free", fontsize=16, style=filled, fillcolor=lightyellow];
589 [label="589: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
590 [label="590: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
591 [label="591: quot(0, s(s(s(0))), s(s(s(0))), X3450), SCOPE: 87, CLAUSE: 3\n\nX3450 is free", fontsize=16, style=filled, fillcolor=lightyellow];
592 [label="592: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
593 [label="593: quot(s(0), s(s(0)), s(s(0)), X3484)\n\nX3484 is free", fontsize=16, style=filled, fillcolor=lightyellow];
594 [label="594: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
595 [label="595: quot(s(s(0)), s(0), s(0), X3508)\n\nX3508 is free", fontsize=16, style=filled, fillcolor=lightyellow];
596 [label="596: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
597 [label="597: quot(s(s(0)), s(0), s(0), X3508), SCOPE: 88, CLAUSE: 1 | quot(s(s(0)), s(0), s(0), X3508), SCOPE: 88, CLAUSE: 2 | quot(s(s(0)), s(0), s(0), X3508), SCOPE: 88, CLAUSE: 3\n\nX3508 is free", fontsize=16, style=filled, fillcolor=lightyellow];
598 [label="598: quot(s(s(0)), s(0), s(0), X3508), SCOPE: 88, CLAUSE: 2 | quot(s(s(0)), s(0), s(0), X3508), SCOPE: 88, CLAUSE: 3\n\nX3508 is free", fontsize=16, style=filled, fillcolor=lightyellow];
599 [label="599: quot(s(s(0)), s(0), s(0), X3508), SCOPE: 88, CLAUSE: 2\n\nX3508 is free", fontsize=16, style=filled, fillcolor=lightyellow];
600 [label="600: quot(s(s(0)), s(0), s(0), X3508), SCOPE: 88, CLAUSE: 3\n\nX3508 is free", fontsize=16, style=filled, fillcolor=lightyellow];
601 [label="601: quot(s(0), 0, s(0), X3571)\n\nX3571 is free", fontsize=16, style=filled, fillcolor=lightyellow];
602 [label="602: quot(s(0), 0, s(0), X3571), SCOPE: 89, CLAUSE: 1 | quot(s(0), 0, s(0), X3571), SCOPE: 89, CLAUSE: 2 | quot(s(0), 0, s(0), X3571), SCOPE: 89, CLAUSE: 3\n\nX3571 is free", fontsize=16, style=filled, fillcolor=lightyellow];
603 [label="603: quot(s(0), 0, s(0), X3571), SCOPE: 89, CLAUSE: 2 | quot(s(0), 0, s(0), X3571), SCOPE: 89, CLAUSE: 3\n\nX3571 is free", fontsize=16, style=filled, fillcolor=lightyellow];
604 [label="604: quot(s(0), 0, s(0), X3571), SCOPE: 89, CLAUSE: 3\n\nX3571 is free", fontsize=16, style=filled, fillcolor=lightyellow];
605 [label="605: quot(s(0), s(0), s(0), X3610)\n\nX3610 is free", fontsize=16, style=filled, fillcolor=lightyellow];
606 [label="606: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
607 [label="607: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
608 [label="608: quot(s(s(s(0))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X3637)\n\nX3637 is free", fontsize=16, style=filled, fillcolor=lightyellow];
609 [label="609: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
610 [label="610: quot(s(s(s(0))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X3637), SCOPE: 90, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X3637), SCOPE: 90, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X3637), SCOPE: 90, CLAUSE: 3\n\nX3637 is free", fontsize=16, style=filled, fillcolor=lightyellow];
611 [label="611: quot(s(s(s(0))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X3637), SCOPE: 90, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X3637), SCOPE: 90, CLAUSE: 3\n\nX3637 is free", fontsize=16, style=filled, fillcolor=lightyellow];
612 [label="612: quot(s(s(s(0))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X3637), SCOPE: 90, CLAUSE: 2\n\nX3637 is free", fontsize=16, style=filled, fillcolor=lightyellow];
613 [label="613: quot(s(s(s(0))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X3637), SCOPE: 90, CLAUSE: 3\n\nX3637 is free", fontsize=16, style=filled, fillcolor=lightyellow];
614 [label="614: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X3694)\n\nX3694 is free", fontsize=16, style=filled, fillcolor=lightyellow];
615 [label="615: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X3694), SCOPE: 91, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X3694), SCOPE: 91, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X3694), SCOPE: 91, CLAUSE: 3\n\nX3694 is free", fontsize=16, style=filled, fillcolor=lightyellow];
616 [label="616: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X3694), SCOPE: 91, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X3694), SCOPE: 91, CLAUSE: 3\n\nX3694 is free", fontsize=16, style=filled, fillcolor=lightyellow];
617 [label="617: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X3694), SCOPE: 91, CLAUSE: 2\n\nX3694 is free", fontsize=16, style=filled, fillcolor=lightyellow];
618 [label="618: quot(s(s(0)), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X3694), SCOPE: 91, CLAUSE: 3\n\nX3694 is free", fontsize=16, style=filled, fillcolor=lightyellow];
619 [label="619: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X3748)\n\nX3748 is free", fontsize=16, style=filled, fillcolor=lightyellow];
620 [label="620: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X3748), SCOPE: 92, CLAUSE: 1 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X3748), SCOPE: 92, CLAUSE: 2 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X3748), SCOPE: 92, CLAUSE: 3\n\nX3748 is free", fontsize=16, style=filled, fillcolor=lightyellow];
621 [label="621: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X3748), SCOPE: 92, CLAUSE: 2 | quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X3748), SCOPE: 92, CLAUSE: 3\n\nX3748 is free", fontsize=16, style=filled, fillcolor=lightyellow];
622 [label="622: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X3748), SCOPE: 92, CLAUSE: 2\n\nX3748 is free", fontsize=16, style=filled, fillcolor=lightyellow];
623 [label="623: quot(s(0), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X3748), SCOPE: 92, CLAUSE: 3\n\nX3748 is free", fontsize=16, style=filled, fillcolor=lightyellow];
624 [label="624: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3788)\n\nX3788 is free", fontsize=16, style=filled, fillcolor=lightyellow];
625 [label="625: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3788), SCOPE: 93, CLAUSE: 1 | quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3788), SCOPE: 93, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3788), SCOPE: 93, CLAUSE: 3\n\nX3788 is free", fontsize=16, style=filled, fillcolor=lightyellow];
626 [label="626: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3788), SCOPE: 93, CLAUSE: 1\n\nX3788 is free", fontsize=16, style=filled, fillcolor=lightyellow];
627 [label="627: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3788), SCOPE: 93, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3788), SCOPE: 93, CLAUSE: 3\n\nX3788 is free", fontsize=16, style=filled, fillcolor=lightyellow];
628 [label="628: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
629 [label="629: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
630 [label="630: quot(0, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X3788), SCOPE: 93, CLAUSE: 3\n\nX3788 is free", fontsize=16, style=filled, fillcolor=lightyellow];
631 [label="631: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
632 [label="632: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
633 [label="633: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
634 [label="634: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
635 [label="635: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3828)\n\nX3828 is free", fontsize=16, style=filled, fillcolor=lightyellow];
636 [label="636: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
637 [label="637: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3828), SCOPE: 94, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3828), SCOPE: 94, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3828), SCOPE: 94, CLAUSE: 3\n\nX3828 is free", fontsize=16, style=filled, fillcolor=lightyellow];
638 [label="638: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3828), SCOPE: 94, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3828), SCOPE: 94, CLAUSE: 3\n\nX3828 is free", fontsize=16, style=filled, fillcolor=lightyellow];
639 [label="639: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3828), SCOPE: 94, CLAUSE: 2\n\nX3828 is free", fontsize=16, style=filled, fillcolor=lightyellow];
640 [label="640: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X3828), SCOPE: 94, CLAUSE: 3\n\nX3828 is free", fontsize=16, style=filled, fillcolor=lightyellow];
641 [label="641: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3885)\n\nX3885 is free", fontsize=16, style=filled, fillcolor=lightyellow];
642 [label="642: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3885), SCOPE: 95, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3885), SCOPE: 95, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3885), SCOPE: 95, CLAUSE: 3\n\nX3885 is free", fontsize=16, style=filled, fillcolor=lightyellow];
643 [label="643: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3885), SCOPE: 95, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3885), SCOPE: 95, CLAUSE: 3\n\nX3885 is free", fontsize=16, style=filled, fillcolor=lightyellow];
644 [label="644: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3885), SCOPE: 95, CLAUSE: 2\n\nX3885 is free", fontsize=16, style=filled, fillcolor=lightyellow];
645 [label="645: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X3885), SCOPE: 95, CLAUSE: 3\n\nX3885 is free", fontsize=16, style=filled, fillcolor=lightyellow];
646 [label="646: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3939)\n\nX3939 is free", fontsize=16, style=filled, fillcolor=lightyellow];
647 [label="647: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3939), SCOPE: 96, CLAUSE: 1 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3939), SCOPE: 96, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3939), SCOPE: 96, CLAUSE: 3\n\nX3939 is free", fontsize=16, style=filled, fillcolor=lightyellow];
648 [label="648: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3939), SCOPE: 96, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3939), SCOPE: 96, CLAUSE: 3\n\nX3939 is free", fontsize=16, style=filled, fillcolor=lightyellow];
649 [label="649: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3939), SCOPE: 96, CLAUSE: 2\n\nX3939 is free", fontsize=16, style=filled, fillcolor=lightyellow];
650 [label="650: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X3939), SCOPE: 96, CLAUSE: 3\n\nX3939 is free", fontsize=16, style=filled, fillcolor=lightyellow];
651 [label="651: quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3979)\n\nX3979 is free", fontsize=16, style=filled, fillcolor=lightyellow];
652 [label="652: quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3979), SCOPE: 97, CLAUSE: 1 | quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3979), SCOPE: 97, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3979), SCOPE: 97, CLAUSE: 3\n\nX3979 is free", fontsize=16, style=filled, fillcolor=lightyellow];
653 [label="653: quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3979), SCOPE: 97, CLAUSE: 1\n\nX3979 is free", fontsize=16, style=filled, fillcolor=lightyellow];
654 [label="654: quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3979), SCOPE: 97, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3979), SCOPE: 97, CLAUSE: 3\n\nX3979 is free", fontsize=16, style=filled, fillcolor=lightyellow];
655 [label="655: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
656 [label="656: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
657 [label="657: quot(0, s(s(s(0))), s(s(s(s(s(s(0)))))), X3979), SCOPE: 97, CLAUSE: 3\n\nX3979 is free", fontsize=16, style=filled, fillcolor=lightyellow];
658 [label="658: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
659 [label="659: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
660 [label="660: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
661 [label="661: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
662 [label="662: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4019)\n\nX4019 is free", fontsize=16, style=filled, fillcolor=lightyellow];
663 [label="663: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
664 [label="664: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4019), SCOPE: 98, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4019), SCOPE: 98, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4019), SCOPE: 98, CLAUSE: 3\n\nX4019 is free", fontsize=16, style=filled, fillcolor=lightyellow];
665 [label="665: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4019), SCOPE: 98, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4019), SCOPE: 98, CLAUSE: 3\n\nX4019 is free", fontsize=16, style=filled, fillcolor=lightyellow];
666 [label="666: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4019), SCOPE: 98, CLAUSE: 2\n\nX4019 is free", fontsize=16, style=filled, fillcolor=lightyellow];
667 [label="667: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X4019), SCOPE: 98, CLAUSE: 3\n\nX4019 is free", fontsize=16, style=filled, fillcolor=lightyellow];
668 [label="668: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X4076)\n\nX4076 is free", fontsize=16, style=filled, fillcolor=lightyellow];
669 [label="669: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X4076), SCOPE: 99, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X4076), SCOPE: 99, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X4076), SCOPE: 99, CLAUSE: 3\n\nX4076 is free", fontsize=16, style=filled, fillcolor=lightyellow];
670 [label="670: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X4076), SCOPE: 99, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X4076), SCOPE: 99, CLAUSE: 3\n\nX4076 is free", fontsize=16, style=filled, fillcolor=lightyellow];
671 [label="671: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X4076), SCOPE: 99, CLAUSE: 2\n\nX4076 is free", fontsize=16, style=filled, fillcolor=lightyellow];
672 [label="672: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(0))))), X4076), SCOPE: 99, CLAUSE: 3\n\nX4076 is free", fontsize=16, style=filled, fillcolor=lightyellow];
673 [label="673: quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X4130)\n\nX4130 is free", fontsize=16, style=filled, fillcolor=lightyellow];
674 [label="674: quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X4130), SCOPE: 100, CLAUSE: 1 | quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X4130), SCOPE: 100, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X4130), SCOPE: 100, CLAUSE: 3\n\nX4130 is free", fontsize=16, style=filled, fillcolor=lightyellow];
675 [label="675: quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X4130), SCOPE: 100, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X4130), SCOPE: 100, CLAUSE: 3\n\nX4130 is free", fontsize=16, style=filled, fillcolor=lightyellow];
676 [label="676: quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X4130), SCOPE: 100, CLAUSE: 2\n\nX4130 is free", fontsize=16, style=filled, fillcolor=lightyellow];
677 [label="677: quot(s(0), s(s(s(0))), s(s(s(s(s(0))))), X4130), SCOPE: 100, CLAUSE: 3\n\nX4130 is free", fontsize=16, style=filled, fillcolor=lightyellow];
678 [label="678: quot(0, s(s(0)), s(s(s(s(s(0))))), X4170)\n\nX4170 is free", fontsize=16, style=filled, fillcolor=lightyellow];
679 [label="679: quot(0, s(s(0)), s(s(s(s(s(0))))), X4170), SCOPE: 101, CLAUSE: 1 | quot(0, s(s(0)), s(s(s(s(s(0))))), X4170), SCOPE: 101, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(s(0))))), X4170), SCOPE: 101, CLAUSE: 3\n\nX4170 is free", fontsize=16, style=filled, fillcolor=lightyellow];
680 [label="680: quot(0, s(s(0)), s(s(s(s(s(0))))), X4170), SCOPE: 101, CLAUSE: 1\n\nX4170 is free", fontsize=16, style=filled, fillcolor=lightyellow];
681 [label="681: quot(0, s(s(0)), s(s(s(s(s(0))))), X4170), SCOPE: 101, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(s(0))))), X4170), SCOPE: 101, CLAUSE: 3\n\nX4170 is free", fontsize=16, style=filled, fillcolor=lightyellow];
682 [label="682: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
683 [label="683: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
684 [label="684: quot(0, s(s(0)), s(s(s(s(s(0))))), X4170), SCOPE: 101, CLAUSE: 3\n\nX4170 is free", fontsize=16, style=filled, fillcolor=lightyellow];
685 [label="685: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
686 [label="686: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
687 [label="687: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
688 [label="688: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
689 [label="689: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X4210)\n\nX4210 is free", fontsize=16, style=filled, fillcolor=lightyellow];
690 [label="690: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
691 [label="691: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X4210), SCOPE: 102, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X4210), SCOPE: 102, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X4210), SCOPE: 102, CLAUSE: 3\n\nX4210 is free", fontsize=16, style=filled, fillcolor=lightyellow];
692 [label="692: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X4210), SCOPE: 102, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X4210), SCOPE: 102, CLAUSE: 3\n\nX4210 is free", fontsize=16, style=filled, fillcolor=lightyellow];
693 [label="693: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X4210), SCOPE: 102, CLAUSE: 2\n\nX4210 is free", fontsize=16, style=filled, fillcolor=lightyellow];
694 [label="694: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(0)))), X4210), SCOPE: 102, CLAUSE: 3\n\nX4210 is free", fontsize=16, style=filled, fillcolor=lightyellow];
695 [label="695: quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X4267)\n\nX4267 is free", fontsize=16, style=filled, fillcolor=lightyellow];
696 [label="696: quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X4267), SCOPE: 103, CLAUSE: 1 | quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X4267), SCOPE: 103, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X4267), SCOPE: 103, CLAUSE: 3\n\nX4267 is free", fontsize=16, style=filled, fillcolor=lightyellow];
697 [label="697: quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X4267), SCOPE: 103, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X4267), SCOPE: 103, CLAUSE: 3\n\nX4267 is free", fontsize=16, style=filled, fillcolor=lightyellow];
698 [label="698: quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X4267), SCOPE: 103, CLAUSE: 2\n\nX4267 is free", fontsize=16, style=filled, fillcolor=lightyellow];
699 [label="699: quot(s(s(0)), s(s(s(0))), s(s(s(s(0)))), X4267), SCOPE: 103, CLAUSE: 3\n\nX4267 is free", fontsize=16, style=filled, fillcolor=lightyellow];
700 [label="700: quot(s(0), s(s(0)), s(s(s(s(0)))), X4321)\n\nX4321 is free", fontsize=16, style=filled, fillcolor=lightyellow];
701 [label="701: quot(s(0), s(s(0)), s(s(s(s(0)))), X4321), SCOPE: 104, CLAUSE: 1 | quot(s(0), s(s(0)), s(s(s(s(0)))), X4321), SCOPE: 104, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(s(0)))), X4321), SCOPE: 104, CLAUSE: 3\n\nX4321 is free", fontsize=16, style=filled, fillcolor=lightyellow];
702 [label="702: quot(s(0), s(s(0)), s(s(s(s(0)))), X4321), SCOPE: 104, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(s(0)))), X4321), SCOPE: 104, CLAUSE: 3\n\nX4321 is free", fontsize=16, style=filled, fillcolor=lightyellow];
703 [label="703: quot(s(0), s(s(0)), s(s(s(s(0)))), X4321), SCOPE: 104, CLAUSE: 2\n\nX4321 is free", fontsize=16, style=filled, fillcolor=lightyellow];
704 [label="704: quot(s(0), s(s(0)), s(s(s(s(0)))), X4321), SCOPE: 104, CLAUSE: 3\n\nX4321 is free", fontsize=16, style=filled, fillcolor=lightyellow];
705 [label="705: quot(0, s(0), s(s(s(s(0)))), X4361)\n\nX4361 is free", fontsize=16, style=filled, fillcolor=lightyellow];
706 [label="706: quot(0, s(0), s(s(s(s(0)))), X4361), SCOPE: 105, CLAUSE: 1 | quot(0, s(0), s(s(s(s(0)))), X4361), SCOPE: 105, CLAUSE: 2 | quot(0, s(0), s(s(s(s(0)))), X4361), SCOPE: 105, CLAUSE: 3\n\nX4361 is free", fontsize=16, style=filled, fillcolor=lightyellow];
707 [label="707: quot(0, s(0), s(s(s(s(0)))), X4361), SCOPE: 105, CLAUSE: 1\n\nX4361 is free", fontsize=16, style=filled, fillcolor=lightyellow];
708 [label="708: quot(0, s(0), s(s(s(s(0)))), X4361), SCOPE: 105, CLAUSE: 2 | quot(0, s(0), s(s(s(s(0)))), X4361), SCOPE: 105, CLAUSE: 3\n\nX4361 is free", fontsize=16, style=filled, fillcolor=lightyellow];
709 [label="709: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
710 [label="710: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
711 [label="711: quot(0, s(0), s(s(s(s(0)))), X4361), SCOPE: 105, CLAUSE: 3\n\nX4361 is free", fontsize=16, style=filled, fillcolor=lightyellow];
712 [label="712: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
713 [label="713: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
714 [label="714: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
715 [label="715: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
716 [label="716: quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X4401)\n\nX4401 is free", fontsize=16, style=filled, fillcolor=lightyellow];
717 [label="717: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
718 [label="718: quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X4401), SCOPE: 106, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X4401), SCOPE: 106, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X4401), SCOPE: 106, CLAUSE: 3\n\nX4401 is free", fontsize=16, style=filled, fillcolor=lightyellow];
719 [label="719: quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X4401), SCOPE: 106, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X4401), SCOPE: 106, CLAUSE: 3\n\nX4401 is free", fontsize=16, style=filled, fillcolor=lightyellow];
720 [label="720: quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X4401), SCOPE: 106, CLAUSE: 2\n\nX4401 is free", fontsize=16, style=filled, fillcolor=lightyellow];
721 [label="721: quot(s(s(s(0))), s(s(s(0))), s(s(s(0))), X4401), SCOPE: 106, CLAUSE: 3\n\nX4401 is free", fontsize=16, style=filled, fillcolor=lightyellow];
722 [label="722: quot(s(s(0)), s(s(0)), s(s(s(0))), X4458)\n\nX4458 is free", fontsize=16, style=filled, fillcolor=lightyellow];
723 [label="723: quot(s(s(0)), s(s(0)), s(s(s(0))), X4458), SCOPE: 107, CLAUSE: 1 | quot(s(s(0)), s(s(0)), s(s(s(0))), X4458), SCOPE: 107, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(s(0))), X4458), SCOPE: 107, CLAUSE: 3\n\nX4458 is free", fontsize=16, style=filled, fillcolor=lightyellow];
724 [label="724: quot(s(s(0)), s(s(0)), s(s(s(0))), X4458), SCOPE: 107, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(s(0))), X4458), SCOPE: 107, CLAUSE: 3\n\nX4458 is free", fontsize=16, style=filled, fillcolor=lightyellow];
725 [label="725: quot(s(s(0)), s(s(0)), s(s(s(0))), X4458), SCOPE: 107, CLAUSE: 2\n\nX4458 is free", fontsize=16, style=filled, fillcolor=lightyellow];
726 [label="726: quot(s(s(0)), s(s(0)), s(s(s(0))), X4458), SCOPE: 107, CLAUSE: 3\n\nX4458 is free", fontsize=16, style=filled, fillcolor=lightyellow];
727 [label="727: quot(s(0), s(0), s(s(s(0))), X4512)\n\nX4512 is free", fontsize=16, style=filled, fillcolor=lightyellow];
728 [label="728: quot(s(0), s(0), s(s(s(0))), X4512), SCOPE: 108, CLAUSE: 1 | quot(s(0), s(0), s(s(s(0))), X4512), SCOPE: 108, CLAUSE: 2 | quot(s(0), s(0), s(s(s(0))), X4512), SCOPE: 108, CLAUSE: 3\n\nX4512 is free", fontsize=16, style=filled, fillcolor=lightyellow];
729 [label="729: quot(s(0), s(0), s(s(s(0))), X4512), SCOPE: 108, CLAUSE: 2 | quot(s(0), s(0), s(s(s(0))), X4512), SCOPE: 108, CLAUSE: 3\n\nX4512 is free", fontsize=16, style=filled, fillcolor=lightyellow];
730 [label="730: quot(s(0), s(0), s(s(s(0))), X4512), SCOPE: 108, CLAUSE: 2\n\nX4512 is free", fontsize=16, style=filled, fillcolor=lightyellow];
731 [label="731: quot(s(0), s(0), s(s(s(0))), X4512), SCOPE: 108, CLAUSE: 3\n\nX4512 is free", fontsize=16, style=filled, fillcolor=lightyellow];
732 [label="732: quot(0, 0, s(s(s(0))), X4572)\n\nX4572 is free", fontsize=16, style=filled, fillcolor=lightyellow];
733 [label="733: quot(0, 0, s(s(s(0))), X4572), SCOPE: 109, CLAUSE: 1 | quot(0, 0, s(s(s(0))), X4572), SCOPE: 109, CLAUSE: 2 | quot(0, 0, s(s(s(0))), X4572), SCOPE: 109, CLAUSE: 3\n\nX4572 is free", fontsize=16, style=filled, fillcolor=lightyellow];
734 [label="734: quot(0, 0, s(s(s(0))), X4572), SCOPE: 109, CLAUSE: 2 | quot(0, 0, s(s(s(0))), X4572), SCOPE: 109, CLAUSE: 3\n\nX4572 is free", fontsize=16, style=filled, fillcolor=lightyellow];
735 [label="735: quot(0, 0, s(s(s(0))), X4572), SCOPE: 109, CLAUSE: 3\n\nX4572 is free", fontsize=16, style=filled, fillcolor=lightyellow];
736 [label="736: quot(0, s(s(s(0))), s(s(s(0))), X4604)\n\nX4604 is free", fontsize=16, style=filled, fillcolor=lightyellow];
737 [label="737: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
738 [label="738: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
739 [label="739: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
740 [label="740: quot(s(s(s(0))), s(s(0)), s(s(0)), X4627)\n\nX4627 is free", fontsize=16, style=filled, fillcolor=lightyellow];
741 [label="741: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
742 [label="742: quot(s(s(s(0))), s(s(0)), s(s(0)), X4627), SCOPE: 110, CLAUSE: 1 | quot(s(s(s(0))), s(s(0)), s(s(0)), X4627), SCOPE: 110, CLAUSE: 2 | quot(s(s(s(0))), s(s(0)), s(s(0)), X4627), SCOPE: 110, CLAUSE: 3\n\nX4627 is free", fontsize=16, style=filled, fillcolor=lightyellow];
743 [label="743: quot(s(s(s(0))), s(s(0)), s(s(0)), X4627), SCOPE: 110, CLAUSE: 2 | quot(s(s(s(0))), s(s(0)), s(s(0)), X4627), SCOPE: 110, CLAUSE: 3\n\nX4627 is free", fontsize=16, style=filled, fillcolor=lightyellow];
744 [label="744: quot(s(s(s(0))), s(s(0)), s(s(0)), X4627), SCOPE: 110, CLAUSE: 2\n\nX4627 is free", fontsize=16, style=filled, fillcolor=lightyellow];
745 [label="745: quot(s(s(s(0))), s(s(0)), s(s(0)), X4627), SCOPE: 110, CLAUSE: 3\n\nX4627 is free", fontsize=16, style=filled, fillcolor=lightyellow];
746 [label="746: quot(s(s(0)), s(0), s(s(0)), X4684)\n\nX4684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
747 [label="747: quot(s(s(0)), s(0), s(s(0)), X4684), SCOPE: 111, CLAUSE: 1 | quot(s(s(0)), s(0), s(s(0)), X4684), SCOPE: 111, CLAUSE: 2 | quot(s(s(0)), s(0), s(s(0)), X4684), SCOPE: 111, CLAUSE: 3\n\nX4684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
748 [label="748: quot(s(s(0)), s(0), s(s(0)), X4684), SCOPE: 111, CLAUSE: 2 | quot(s(s(0)), s(0), s(s(0)), X4684), SCOPE: 111, CLAUSE: 3\n\nX4684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
749 [label="749: quot(s(s(0)), s(0), s(s(0)), X4684), SCOPE: 111, CLAUSE: 2\n\nX4684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
750 [label="750: quot(s(s(0)), s(0), s(s(0)), X4684), SCOPE: 111, CLAUSE: 3\n\nX4684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
751 [label="751: quot(s(0), 0, s(s(0)), X4744)\n\nX4744 is free", fontsize=16, style=filled, fillcolor=lightyellow];
752 [label="752: quot(s(0), 0, s(s(0)), X4744), SCOPE: 112, CLAUSE: 1 | quot(s(0), 0, s(s(0)), X4744), SCOPE: 112, CLAUSE: 2 | quot(s(0), 0, s(s(0)), X4744), SCOPE: 112, CLAUSE: 3\n\nX4744 is free", fontsize=16, style=filled, fillcolor=lightyellow];
753 [label="753: quot(s(0), 0, s(s(0)), X4744), SCOPE: 112, CLAUSE: 2 | quot(s(0), 0, s(s(0)), X4744), SCOPE: 112, CLAUSE: 3\n\nX4744 is free", fontsize=16, style=filled, fillcolor=lightyellow];
754 [label="754: quot(s(0), 0, s(s(0)), X4744), SCOPE: 112, CLAUSE: 3\n\nX4744 is free", fontsize=16, style=filled, fillcolor=lightyellow];
755 [label="755: quot(s(0), s(s(0)), s(s(0)), X4783)\n\nX4783 is free", fontsize=16, style=filled, fillcolor=lightyellow];
756 [label="756: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
757 [label="757: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
758 [label="758: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
759 [label="759: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
760 [label="760: times(T499, s(s(T497)), X2834)\n\nT497 is ground\nT499 is ground\nX2834 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
761 [label="761: neq(s(s(s(s(s(T497))))), T674)\n\nT497 is ground\nT674 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
762 [label="762: pr(s(s(s(s(s(T491))))), s(T491)), SCOPE: 113, CLAUSE: 5 | pr(s(s(s(s(s(T491))))), s(T491)), SCOPE: 113, CLAUSE: 6\n\nT491 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
763 [label="763: pr(s(s(s(s(s(T491))))), s(T491)), SCOPE: 113, CLAUSE: 5\n\nT491 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
764 [label="764: pr(s(s(s(s(s(T491))))), s(T491)), SCOPE: 113, CLAUSE: 6\n\nT491 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
765 [label="765: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
766 [label="766: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
767 [label="767: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
768 [label="768: ','(not_divides(s(s(T691)), s(s(s(s(s(s(T691))))))), pr(s(s(s(s(s(s(T691)))))), s(T691)))\n\nT691 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
769 [label="769: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
770 [label="770: not_divides(s(s(T691)), s(s(s(s(s(s(T691)))))))\n\nT691 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
771 [label="771: pr(s(s(s(s(s(s(T691)))))), s(T691))\n\nT691 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
772 [label="772: not_divides(s(s(T691)), s(s(s(s(s(s(T691))))))), SCOPE: 114, CLAUSE: 7\n\nT691 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
773 [label="773: ','(div(s(s(s(s(s(s(T697)))))), s(s(T697)), X4847), ','(times(X4847, s(s(T697)), X4848), neq(s(s(s(s(s(s(T697)))))), X4848)))\n\nT697 is ground\nX4847 is free; \nX4848 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
774 [label="774: div(s(s(s(s(s(s(T697)))))), s(s(T697)), X4847)\n\nT697 is ground\nX4847 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
775 [label="775: ','(times(T699, s(s(T697)), X4848), neq(s(s(s(s(s(s(T697)))))), X4848))\n\nT697 is ground\nT699 is ground\nX4848 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
776 [label="776: div(s(s(s(s(s(s(T697)))))), s(s(T697)), X4847), SCOPE: 115, CLAUSE: 0\n\nT697 is ground\nX4847 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
777 [label="777: quot(s(s(s(s(s(s(T704)))))), s(s(T704)), s(s(T704)), X4877)\n\nT704 is ground\nX4877 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
778 [label="778: quot(s(s(s(s(s(s(T704)))))), s(s(T704)), s(s(T704)), X4877), SCOPE: 116, CLAUSE: 1 | quot(s(s(s(s(s(s(T704)))))), s(s(T704)), s(s(T704)), X4877), SCOPE: 116, CLAUSE: 2 | quot(s(s(s(s(s(s(T704)))))), s(s(T704)), s(s(T704)), X4877), SCOPE: 116, CLAUSE: 3\n\nT704 is ground\nX4877 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
779 [label="779: quot(s(s(s(s(s(s(T704)))))), s(s(T704)), s(s(T704)), X4877), SCOPE: 116, CLAUSE: 2 | quot(s(s(s(s(s(s(T704)))))), s(s(T704)), s(s(T704)), X4877), SCOPE: 116, CLAUSE: 3\n\nT704 is ground\nX4877 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
780 [label="780: quot(s(s(s(s(s(s(T704)))))), s(s(T704)), s(s(T704)), X4877), SCOPE: 116, CLAUSE: 2\n\nT704 is ground\nX4877 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
781 [label="781: quot(s(s(s(s(s(s(T704)))))), s(s(T704)), s(s(T704)), X4877), SCOPE: 116, CLAUSE: 3\n\nT704 is ground\nX4877 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
782 [label="782: quot(s(s(s(s(s(T712))))), s(T712), s(s(T712)), X4931)\n\nT712 is ground\nX4931 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
783 [label="783: quot(s(s(s(s(s(T712))))), s(T712), s(s(T712)), X4931), SCOPE: 117, CLAUSE: 1 | quot(s(s(s(s(s(T712))))), s(T712), s(s(T712)), X4931), SCOPE: 117, CLAUSE: 2 | quot(s(s(s(s(s(T712))))), s(T712), s(s(T712)), X4931), SCOPE: 117, CLAUSE: 3\n\nT712 is ground\nX4931 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
784 [label="784: quot(s(s(s(s(s(T712))))), s(T712), s(s(T712)), X4931), SCOPE: 117, CLAUSE: 2 | quot(s(s(s(s(s(T712))))), s(T712), s(s(T712)), X4931), SCOPE: 117, CLAUSE: 3\n\nT712 is ground\nX4931 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
785 [label="785: quot(s(s(s(s(s(T712))))), s(T712), s(s(T712)), X4931), SCOPE: 117, CLAUSE: 2\n\nT712 is ground\nX4931 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
786 [label="786: quot(s(s(s(s(s(T712))))), s(T712), s(s(T712)), X4931), SCOPE: 117, CLAUSE: 3\n\nT712 is ground\nX4931 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
787 [label="787: quot(s(s(s(s(T722)))), T722, s(s(T722)), X4985)\n\nT722 is ground\nX4985 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
788 [label="788: quot(s(s(s(s(T722)))), T722, s(s(T722)), X4985), SCOPE: 118, CLAUSE: 1 | quot(s(s(s(s(T722)))), T722, s(s(T722)), X4985), SCOPE: 118, CLAUSE: 2 | quot(s(s(s(s(T722)))), T722, s(s(T722)), X4985), SCOPE: 118, CLAUSE: 3\n\nT722 is ground\nX4985 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
789 [label="789: quot(s(s(s(s(T722)))), T722, s(s(T722)), X4985), SCOPE: 118, CLAUSE: 2 | quot(s(s(s(s(T722)))), T722, s(s(T722)), X4985), SCOPE: 118, CLAUSE: 3\n\nT722 is ground\nX4985 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
790 [label="790: quot(s(s(s(s(T722)))), T722, s(s(T722)), X4985), SCOPE: 118, CLAUSE: 2\n\nT722 is ground\nX4985 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
791 [label="791: quot(s(s(s(s(T722)))), T722, s(s(T722)), X4985), SCOPE: 118, CLAUSE: 3\n\nT722 is ground\nX4985 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
792 [label="792: quot(s(s(s(s(T734)))), T734, s(s(s(T734))), X5021)\n\nT734 is ground\nX5021 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
793 [label="793: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
794 [label="794: quot(s(s(s(s(T734)))), T734, s(s(s(T734))), X5021), SCOPE: 119, CLAUSE: 1 | quot(s(s(s(s(T734)))), T734, s(s(s(T734))), X5021), SCOPE: 119, CLAUSE: 2 | quot(s(s(s(s(T734)))), T734, s(s(s(T734))), X5021), SCOPE: 119, CLAUSE: 3\n\nT734 is ground\nX5021 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
795 [label="795: quot(s(s(s(s(T734)))), T734, s(s(s(T734))), X5021), SCOPE: 119, CLAUSE: 2 | quot(s(s(s(s(T734)))), T734, s(s(s(T734))), X5021), SCOPE: 119, CLAUSE: 3\n\nT734 is ground\nX5021 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
796 [label="796: quot(s(s(s(s(T734)))), T734, s(s(s(T734))), X5021), SCOPE: 119, CLAUSE: 2\n\nT734 is ground\nX5021 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
797 [label="797: quot(s(s(s(s(T734)))), T734, s(s(s(T734))), X5021), SCOPE: 119, CLAUSE: 3\n\nT734 is ground\nX5021 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
798 [label="798: quot(s(s(s(s(T746)))), T746, s(s(s(s(T746)))), X5061)\n\nT746 is ground\nX5061 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
799 [label="799: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
800 [label="800: quot(s(s(s(s(T746)))), T746, s(s(s(s(T746)))), X5061), SCOPE: 120, CLAUSE: 1 | quot(s(s(s(s(T746)))), T746, s(s(s(s(T746)))), X5061), SCOPE: 120, CLAUSE: 2 | quot(s(s(s(s(T746)))), T746, s(s(s(s(T746)))), X5061), SCOPE: 120, CLAUSE: 3\n\nT746 is ground\nX5061 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
801 [label="801: quot(s(s(s(s(T746)))), T746, s(s(s(s(T746)))), X5061), SCOPE: 120, CLAUSE: 2 | quot(s(s(s(s(T746)))), T746, s(s(s(s(T746)))), X5061), SCOPE: 120, CLAUSE: 3\n\nT746 is ground\nX5061 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
802 [label="802: quot(s(s(s(s(T746)))), T746, s(s(s(s(T746)))), X5061), SCOPE: 120, CLAUSE: 2\n\nT746 is ground\nX5061 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
803 [label="803: quot(s(s(s(s(T746)))), T746, s(s(s(s(T746)))), X5061), SCOPE: 120, CLAUSE: 3\n\nT746 is ground\nX5061 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
804 [label="804: quot(s(s(s(s(T758)))), T758, s(s(s(s(s(T758))))), X5101)\n\nT758 is ground\nX5101 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
805 [label="805: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
806 [label="806: quot(s(s(s(s(T758)))), T758, s(s(s(s(s(T758))))), X5101), SCOPE: 121, CLAUSE: 1 | quot(s(s(s(s(T758)))), T758, s(s(s(s(s(T758))))), X5101), SCOPE: 121, CLAUSE: 2 | quot(s(s(s(s(T758)))), T758, s(s(s(s(s(T758))))), X5101), SCOPE: 121, CLAUSE: 3\n\nT758 is ground\nX5101 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
807 [label="807: quot(s(s(s(s(T758)))), T758, s(s(s(s(s(T758))))), X5101), SCOPE: 121, CLAUSE: 2 | quot(s(s(s(s(T758)))), T758, s(s(s(s(s(T758))))), X5101), SCOPE: 121, CLAUSE: 3\n\nT758 is ground\nX5101 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
808 [label="808: quot(s(s(s(s(T758)))), T758, s(s(s(s(s(T758))))), X5101), SCOPE: 121, CLAUSE: 2\n\nT758 is ground\nX5101 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
809 [label="809: quot(s(s(s(s(T758)))), T758, s(s(s(s(s(T758))))), X5101), SCOPE: 121, CLAUSE: 3\n\nT758 is ground\nX5101 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
810 [label="810: quot(s(s(s(s(T770)))), T770, s(s(s(s(s(s(T770)))))), X5141)\n\nT770 is ground\nX5141 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
811 [label="811: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
812 [label="812: quot(s(s(s(s(T770)))), T770, s(s(s(s(s(s(T770)))))), X5141), SCOPE: 122, CLAUSE: 1 | quot(s(s(s(s(T770)))), T770, s(s(s(s(s(s(T770)))))), X5141), SCOPE: 122, CLAUSE: 2 | quot(s(s(s(s(T770)))), T770, s(s(s(s(s(s(T770)))))), X5141), SCOPE: 122, CLAUSE: 3\n\nT770 is ground\nX5141 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
813 [label="813: quot(s(s(s(s(T770)))), T770, s(s(s(s(s(s(T770)))))), X5141), SCOPE: 122, CLAUSE: 2 | quot(s(s(s(s(T770)))), T770, s(s(s(s(s(s(T770)))))), X5141), SCOPE: 122, CLAUSE: 3\n\nT770 is ground\nX5141 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
814 [label="814: quot(s(s(s(s(T770)))), T770, s(s(s(s(s(s(T770)))))), X5141), SCOPE: 122, CLAUSE: 2\n\nT770 is ground\nX5141 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
815 [label="815: quot(s(s(s(s(T770)))), T770, s(s(s(s(s(s(T770)))))), X5141), SCOPE: 122, CLAUSE: 3\n\nT770 is ground\nX5141 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
816 [label="816: quot(s(s(s(s(T782)))), T782, s(s(s(s(s(s(s(T782))))))), X5181)\n\nT782 is ground\nX5181 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
817 [label="817: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
818 [label="818: quot(s(s(s(s(T782)))), T782, s(s(s(s(s(s(s(T782))))))), X5181), SCOPE: 123, CLAUSE: 1 | quot(s(s(s(s(T782)))), T782, s(s(s(s(s(s(s(T782))))))), X5181), SCOPE: 123, CLAUSE: 2 | quot(s(s(s(s(T782)))), T782, s(s(s(s(s(s(s(T782))))))), X5181), SCOPE: 123, CLAUSE: 3\n\nT782 is ground\nX5181 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
819 [label="819: quot(s(s(s(s(T782)))), T782, s(s(s(s(s(s(s(T782))))))), X5181), SCOPE: 123, CLAUSE: 2 | quot(s(s(s(s(T782)))), T782, s(s(s(s(s(s(s(T782))))))), X5181), SCOPE: 123, CLAUSE: 3\n\nT782 is ground\nX5181 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
820 [label="820: quot(s(s(s(s(T782)))), T782, s(s(s(s(s(s(s(T782))))))), X5181), SCOPE: 123, CLAUSE: 2\n\nT782 is ground\nX5181 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
821 [label="821: quot(s(s(s(s(T782)))), T782, s(s(s(s(s(s(s(T782))))))), X5181), SCOPE: 123, CLAUSE: 3\n\nT782 is ground\nX5181 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
822 [label="822: quot(s(s(s(s(T794)))), T794, s(s(s(s(s(s(s(s(T794)))))))), X5221)\n\nT794 is ground\nX5221 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
823 [label="823: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
824 [label="824: quot(s(s(s(s(T794)))), T794, s(T797), X5221)\n\nT794 is ground\nT797 is ground\nX5221 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
825 [label="825: quot(s(s(s(s(T794)))), T794, s(T797), X5221), SCOPE: 124, CLAUSE: 1 | quot(s(s(s(s(T794)))), T794, s(T797), X5221), SCOPE: 124, CLAUSE: 2 | quot(s(s(s(s(T794)))), T794, s(T797), X5221), SCOPE: 124, CLAUSE: 3\n\nT794 is ground\nT797 is ground\nX5221 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
826 [label="826: quot(s(s(s(s(T794)))), T794, s(T797), X5221), SCOPE: 124, CLAUSE: 2 | quot(s(s(s(s(T794)))), T794, s(T797), X5221), SCOPE: 124, CLAUSE: 3\n\nT794 is ground\nT797 is ground\nX5221 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
827 [label="827: quot(s(s(s(s(T794)))), T794, s(T797), X5221), SCOPE: 124, CLAUSE: 2\n\nT794 is ground\nT797 is ground\nX5221 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
828 [label="828: quot(s(s(s(s(T794)))), T794, s(T797), X5221), SCOPE: 124, CLAUSE: 3\n\nT794 is ground\nT797 is ground\nX5221 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
829 [label="829: quot(s(s(s(s(T814)))), T814, s(T815), X5270)\n\nT814 is ground\nT815 is ground\nX5270 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
830 [label="830: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
831 [label="831: quot(s(s(s(s(0)))), s(T824), s(T824), X5295)\n\nT824 is ground\nX5295 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
832 [label="832: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
833 [label="833: quot(s(s(s(s(0)))), s(T824), s(T824), X5295), SCOPE: 125, CLAUSE: 1 | quot(s(s(s(s(0)))), s(T824), s(T824), X5295), SCOPE: 125, CLAUSE: 2 | quot(s(s(s(s(0)))), s(T824), s(T824), X5295), SCOPE: 125, CLAUSE: 3\n\nT824 is ground\nX5295 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
834 [label="834: quot(s(s(s(s(0)))), s(T824), s(T824), X5295), SCOPE: 125, CLAUSE: 2 | quot(s(s(s(s(0)))), s(T824), s(T824), X5295), SCOPE: 125, CLAUSE: 3\n\nT824 is ground\nX5295 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
835 [label="835: quot(s(s(s(s(0)))), s(T824), s(T824), X5295), SCOPE: 125, CLAUSE: 2\n\nT824 is ground\nX5295 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
836 [label="836: quot(s(s(s(s(0)))), s(T824), s(T824), X5295), SCOPE: 125, CLAUSE: 3\n\nT824 is ground\nX5295 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
837 [label="837: quot(s(s(s(0))), T832, s(T832), X5352)\n\nT832 is ground\nX5352 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
838 [label="838: quot(s(s(s(0))), T832, s(T832), X5352), SCOPE: 126, CLAUSE: 1 | quot(s(s(s(0))), T832, s(T832), X5352), SCOPE: 126, CLAUSE: 2 | quot(s(s(s(0))), T832, s(T832), X5352), SCOPE: 126, CLAUSE: 3\n\nT832 is ground\nX5352 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
839 [label="839: quot(s(s(s(0))), T832, s(T832), X5352), SCOPE: 126, CLAUSE: 2 | quot(s(s(s(0))), T832, s(T832), X5352), SCOPE: 126, CLAUSE: 3\n\nT832 is ground\nX5352 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
840 [label="840: quot(s(s(s(0))), T832, s(T832), X5352), SCOPE: 126, CLAUSE: 2\n\nT832 is ground\nX5352 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
841 [label="841: quot(s(s(s(0))), T832, s(T832), X5352), SCOPE: 126, CLAUSE: 3\n\nT832 is ground\nX5352 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
842 [label="842: quot(s(s(0)), T838, s(s(T838)), X5388)\n\nT838 is ground\nX5388 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
843 [label="843: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
844 [label="844: quot(s(s(0)), T838, s(s(T838)), X5388), SCOPE: 127, CLAUSE: 1 | quot(s(s(0)), T838, s(s(T838)), X5388), SCOPE: 127, CLAUSE: 2 | quot(s(s(0)), T838, s(s(T838)), X5388), SCOPE: 127, CLAUSE: 3\n\nT838 is ground\nX5388 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
845 [label="845: quot(s(s(0)), T838, s(s(T838)), X5388), SCOPE: 127, CLAUSE: 2 | quot(s(s(0)), T838, s(s(T838)), X5388), SCOPE: 127, CLAUSE: 3\n\nT838 is ground\nX5388 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
846 [label="846: quot(s(s(0)), T838, s(s(T838)), X5388), SCOPE: 127, CLAUSE: 2\n\nT838 is ground\nX5388 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
847 [label="847: quot(s(s(0)), T838, s(s(T838)), X5388), SCOPE: 127, CLAUSE: 3\n\nT838 is ground\nX5388 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
848 [label="848: quot(s(0), T844, s(s(s(T844))), X5428)\n\nT844 is ground\nX5428 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
849 [label="849: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
850 [label="850: quot(s(0), T844, s(s(s(T844))), X5428), SCOPE: 128, CLAUSE: 1 | quot(s(0), T844, s(s(s(T844))), X5428), SCOPE: 128, CLAUSE: 2 | quot(s(0), T844, s(s(s(T844))), X5428), SCOPE: 128, CLAUSE: 3\n\nT844 is ground\nX5428 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
851 [label="851: quot(s(0), T844, s(s(s(T844))), X5428), SCOPE: 128, CLAUSE: 2 | quot(s(0), T844, s(s(s(T844))), X5428), SCOPE: 128, CLAUSE: 3\n\nT844 is ground\nX5428 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
852 [label="852: quot(s(0), T844, s(s(s(T844))), X5428), SCOPE: 128, CLAUSE: 2\n\nT844 is ground\nX5428 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
853 [label="853: quot(s(0), T844, s(s(s(T844))), X5428), SCOPE: 128, CLAUSE: 3\n\nT844 is ground\nX5428 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
854 [label="854: quot(0, T850, s(s(s(s(T850)))), X5468)\n\nT850 is ground\nX5468 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
855 [label="855: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
856 [label="856: quot(0, T850, s(s(s(s(T850)))), X5468), SCOPE: 129, CLAUSE: 1 | quot(0, T850, s(s(s(s(T850)))), X5468), SCOPE: 129, CLAUSE: 2 | quot(0, T850, s(s(s(s(T850)))), X5468), SCOPE: 129, CLAUSE: 3\n\nT850 is ground\nX5468 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
857 [label="857: quot(0, T850, s(s(s(s(T850)))), X5468), SCOPE: 129, CLAUSE: 1\n\nT850 is ground\nX5468 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
858 [label="858: quot(0, T850, s(s(s(s(T850)))), X5468), SCOPE: 129, CLAUSE: 2 | quot(0, T850, s(s(s(s(T850)))), X5468), SCOPE: 129, CLAUSE: 3\n\nT850 is ground\nX5468 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
859 [label="859: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
860 [label="860: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
861 [label="861: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
862 [label="862: quot(0, T850, s(s(s(s(T850)))), X5468), SCOPE: 129, CLAUSE: 3\n\nT850 is ground\nX5468 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
863 [label="863: quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X5504)\n\nX5504 is free", fontsize=16, style=filled, fillcolor=lightyellow];
864 [label="864: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
865 [label="865: quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X5504), SCOPE: 130, CLAUSE: 1 | quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X5504), SCOPE: 130, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X5504), SCOPE: 130, CLAUSE: 3\n\nX5504 is free", fontsize=16, style=filled, fillcolor=lightyellow];
866 [label="866: quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X5504), SCOPE: 130, CLAUSE: 1\n\nX5504 is free", fontsize=16, style=filled, fillcolor=lightyellow];
867 [label="867: quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X5504), SCOPE: 130, CLAUSE: 2 | quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X5504), SCOPE: 130, CLAUSE: 3\n\nX5504 is free", fontsize=16, style=filled, fillcolor=lightyellow];
868 [label="868: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
869 [label="869: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
870 [label="870: quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X5504), SCOPE: 130, CLAUSE: 3\n\nX5504 is free", fontsize=16, style=filled, fillcolor=lightyellow];
871 [label="871: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
872 [label="872: quot(s(0), s(s(s(0))), s(s(s(0))), X5538)\n\nX5538 is free", fontsize=16, style=filled, fillcolor=lightyellow];
873 [label="873: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
874 [label="874: quot(s(s(0)), s(s(0)), s(s(0)), X5562)\n\nX5562 is free", fontsize=16, style=filled, fillcolor=lightyellow];
875 [label="875: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
876 [label="876: quot(s(s(s(0))), s(0), s(0), X5586)\n\nX5586 is free", fontsize=16, style=filled, fillcolor=lightyellow];
877 [label="877: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
878 [label="878: quot(s(s(s(0))), s(0), s(0), X5586), SCOPE: 131, CLAUSE: 1 | quot(s(s(s(0))), s(0), s(0), X5586), SCOPE: 131, CLAUSE: 2 | quot(s(s(s(0))), s(0), s(0), X5586), SCOPE: 131, CLAUSE: 3\n\nX5586 is free", fontsize=16, style=filled, fillcolor=lightyellow];
879 [label="879: quot(s(s(s(0))), s(0), s(0), X5586), SCOPE: 131, CLAUSE: 2 | quot(s(s(s(0))), s(0), s(0), X5586), SCOPE: 131, CLAUSE: 3\n\nX5586 is free", fontsize=16, style=filled, fillcolor=lightyellow];
880 [label="880: quot(s(s(s(0))), s(0), s(0), X5586), SCOPE: 131, CLAUSE: 2\n\nX5586 is free", fontsize=16, style=filled, fillcolor=lightyellow];
881 [label="881: quot(s(s(s(0))), s(0), s(0), X5586), SCOPE: 131, CLAUSE: 3\n\nX5586 is free", fontsize=16, style=filled, fillcolor=lightyellow];
882 [label="882: quot(s(s(0)), 0, s(0), X5649)\n\nX5649 is free", fontsize=16, style=filled, fillcolor=lightyellow];
883 [label="883: quot(s(s(0)), 0, s(0), X5649), SCOPE: 132, CLAUSE: 1 | quot(s(s(0)), 0, s(0), X5649), SCOPE: 132, CLAUSE: 2 | quot(s(s(0)), 0, s(0), X5649), SCOPE: 132, CLAUSE: 3\n\nX5649 is free", fontsize=16, style=filled, fillcolor=lightyellow];
884 [label="884: quot(s(s(0)), 0, s(0), X5649), SCOPE: 132, CLAUSE: 2 | quot(s(s(0)), 0, s(0), X5649), SCOPE: 132, CLAUSE: 3\n\nX5649 is free", fontsize=16, style=filled, fillcolor=lightyellow];
885 [label="885: quot(s(s(0)), 0, s(0), X5649), SCOPE: 132, CLAUSE: 3\n\nX5649 is free", fontsize=16, style=filled, fillcolor=lightyellow];
886 [label="886: quot(s(s(0)), s(0), s(0), X5688)\n\nX5688 is free", fontsize=16, style=filled, fillcolor=lightyellow];
887 [label="887: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
888 [label="888: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
889 [label="889: quot(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X5715)\n\nX5715 is free", fontsize=16, style=filled, fillcolor=lightyellow];
890 [label="890: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
891 [label="891: quot(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X5715), SCOPE: 133, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X5715), SCOPE: 133, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X5715), SCOPE: 133, CLAUSE: 3\n\nX5715 is free", fontsize=16, style=filled, fillcolor=lightyellow];
892 [label="892: quot(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X5715), SCOPE: 133, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X5715), SCOPE: 133, CLAUSE: 3\n\nX5715 is free", fontsize=16, style=filled, fillcolor=lightyellow];
893 [label="893: quot(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X5715), SCOPE: 133, CLAUSE: 2\n\nX5715 is free", fontsize=16, style=filled, fillcolor=lightyellow];
894 [label="894: quot(s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X5715), SCOPE: 133, CLAUSE: 3\n\nX5715 is free", fontsize=16, style=filled, fillcolor=lightyellow];
895 [label="895: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X5772)\n\nX5772 is free", fontsize=16, style=filled, fillcolor=lightyellow];
896 [label="896: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X5772), SCOPE: 134, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X5772), SCOPE: 134, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X5772), SCOPE: 134, CLAUSE: 3\n\nX5772 is free", fontsize=16, style=filled, fillcolor=lightyellow];
897 [label="897: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X5772), SCOPE: 134, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X5772), SCOPE: 134, CLAUSE: 3\n\nX5772 is free", fontsize=16, style=filled, fillcolor=lightyellow];
898 [label="898: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X5772), SCOPE: 134, CLAUSE: 2\n\nX5772 is free", fontsize=16, style=filled, fillcolor=lightyellow];
899 [label="899: quot(s(s(s(0))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X5772), SCOPE: 134, CLAUSE: 3\n\nX5772 is free", fontsize=16, style=filled, fillcolor=lightyellow];
900 [label="900: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X5826)\n\nX5826 is free", fontsize=16, style=filled, fillcolor=lightyellow];
901 [label="901: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X5826), SCOPE: 135, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X5826), SCOPE: 135, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X5826), SCOPE: 135, CLAUSE: 3\n\nX5826 is free", fontsize=16, style=filled, fillcolor=lightyellow];
902 [label="902: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X5826), SCOPE: 135, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X5826), SCOPE: 135, CLAUSE: 3\n\nX5826 is free", fontsize=16, style=filled, fillcolor=lightyellow];
903 [label="903: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X5826), SCOPE: 135, CLAUSE: 2\n\nX5826 is free", fontsize=16, style=filled, fillcolor=lightyellow];
904 [label="904: quot(s(s(0)), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X5826), SCOPE: 135, CLAUSE: 3\n\nX5826 is free", fontsize=16, style=filled, fillcolor=lightyellow];
905 [label="905: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X5880)\n\nX5880 is free", fontsize=16, style=filled, fillcolor=lightyellow];
906 [label="906: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X5880), SCOPE: 136, CLAUSE: 1 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X5880), SCOPE: 136, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X5880), SCOPE: 136, CLAUSE: 3\n\nX5880 is free", fontsize=16, style=filled, fillcolor=lightyellow];
907 [label="907: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X5880), SCOPE: 136, CLAUSE: 2 | quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X5880), SCOPE: 136, CLAUSE: 3\n\nX5880 is free", fontsize=16, style=filled, fillcolor=lightyellow];
908 [label="908: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X5880), SCOPE: 136, CLAUSE: 2\n\nX5880 is free", fontsize=16, style=filled, fillcolor=lightyellow];
909 [label="909: quot(s(0), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X5880), SCOPE: 136, CLAUSE: 3\n\nX5880 is free", fontsize=16, style=filled, fillcolor=lightyellow];
910 [label="910: quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X5920)\n\nX5920 is free", fontsize=16, style=filled, fillcolor=lightyellow];
911 [label="911: quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X5920), SCOPE: 137, CLAUSE: 1 | quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X5920), SCOPE: 137, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X5920), SCOPE: 137, CLAUSE: 3\n\nX5920 is free", fontsize=16, style=filled, fillcolor=lightyellow];
912 [label="912: quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X5920), SCOPE: 137, CLAUSE: 1\n\nX5920 is free", fontsize=16, style=filled, fillcolor=lightyellow];
913 [label="913: quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X5920), SCOPE: 137, CLAUSE: 2 | quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X5920), SCOPE: 137, CLAUSE: 3\n\nX5920 is free", fontsize=16, style=filled, fillcolor=lightyellow];
914 [label="914: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
915 [label="915: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
916 [label="916: quot(0, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X5920), SCOPE: 137, CLAUSE: 3\n\nX5920 is free", fontsize=16, style=filled, fillcolor=lightyellow];
917 [label="917: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
918 [label="918: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
919 [label="919: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
920 [label="920: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
921 [label="921: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
922 [label="922: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X5963)\n\nX5963 is free", fontsize=16, style=filled, fillcolor=lightyellow];
923 [label="923: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
924 [label="924: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X5963), SCOPE: 138, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X5963), SCOPE: 138, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X5963), SCOPE: 138, CLAUSE: 3\n\nX5963 is free", fontsize=16, style=filled, fillcolor=lightyellow];
925 [label="925: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X5963), SCOPE: 138, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X5963), SCOPE: 138, CLAUSE: 3\n\nX5963 is free", fontsize=16, style=filled, fillcolor=lightyellow];
926 [label="926: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X5963), SCOPE: 138, CLAUSE: 2\n\nX5963 is free", fontsize=16, style=filled, fillcolor=lightyellow];
927 [label="927: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X5963), SCOPE: 138, CLAUSE: 3\n\nX5963 is free", fontsize=16, style=filled, fillcolor=lightyellow];
928 [label="928: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6020)\n\nX6020 is free", fontsize=16, style=filled, fillcolor=lightyellow];
929 [label="929: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6020), SCOPE: 139, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6020), SCOPE: 139, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6020), SCOPE: 139, CLAUSE: 3\n\nX6020 is free", fontsize=16, style=filled, fillcolor=lightyellow];
930 [label="930: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6020), SCOPE: 139, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6020), SCOPE: 139, CLAUSE: 3\n\nX6020 is free", fontsize=16, style=filled, fillcolor=lightyellow];
931 [label="931: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6020), SCOPE: 139, CLAUSE: 2\n\nX6020 is free", fontsize=16, style=filled, fillcolor=lightyellow];
932 [label="932: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X6020), SCOPE: 139, CLAUSE: 3\n\nX6020 is free", fontsize=16, style=filled, fillcolor=lightyellow];
933 [label="933: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6074)\n\nX6074 is free", fontsize=16, style=filled, fillcolor=lightyellow];
934 [label="934: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6074), SCOPE: 140, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6074), SCOPE: 140, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6074), SCOPE: 140, CLAUSE: 3\n\nX6074 is free", fontsize=16, style=filled, fillcolor=lightyellow];
935 [label="935: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6074), SCOPE: 140, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6074), SCOPE: 140, CLAUSE: 3\n\nX6074 is free", fontsize=16, style=filled, fillcolor=lightyellow];
936 [label="936: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6074), SCOPE: 140, CLAUSE: 2\n\nX6074 is free", fontsize=16, style=filled, fillcolor=lightyellow];
937 [label="937: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X6074), SCOPE: 140, CLAUSE: 3\n\nX6074 is free", fontsize=16, style=filled, fillcolor=lightyellow];
938 [label="938: quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X6128)\n\nX6128 is free", fontsize=16, style=filled, fillcolor=lightyellow];
939 [label="939: quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X6128), SCOPE: 141, CLAUSE: 1 | quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X6128), SCOPE: 141, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X6128), SCOPE: 141, CLAUSE: 3\n\nX6128 is free", fontsize=16, style=filled, fillcolor=lightyellow];
940 [label="940: quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X6128), SCOPE: 141, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X6128), SCOPE: 141, CLAUSE: 3\n\nX6128 is free", fontsize=16, style=filled, fillcolor=lightyellow];
941 [label="941: quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X6128), SCOPE: 141, CLAUSE: 2\n\nX6128 is free", fontsize=16, style=filled, fillcolor=lightyellow];
942 [label="942: quot(s(0), s(s(s(0))), s(s(s(s(s(s(0)))))), X6128), SCOPE: 141, CLAUSE: 3\n\nX6128 is free", fontsize=16, style=filled, fillcolor=lightyellow];
943 [label="943: quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X6168)\n\nX6168 is free", fontsize=16, style=filled, fillcolor=lightyellow];
944 [label="944: quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X6168), SCOPE: 142, CLAUSE: 1 | quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X6168), SCOPE: 142, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X6168), SCOPE: 142, CLAUSE: 3\n\nX6168 is free", fontsize=16, style=filled, fillcolor=lightyellow];
945 [label="945: quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X6168), SCOPE: 142, CLAUSE: 1\n\nX6168 is free", fontsize=16, style=filled, fillcolor=lightyellow];
946 [label="946: quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X6168), SCOPE: 142, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X6168), SCOPE: 142, CLAUSE: 3\n\nX6168 is free", fontsize=16, style=filled, fillcolor=lightyellow];
947 [label="947: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
948 [label="948: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
949 [label="949: quot(0, s(s(0)), s(s(s(s(s(s(0)))))), X6168), SCOPE: 142, CLAUSE: 3\n\nX6168 is free", fontsize=16, style=filled, fillcolor=lightyellow];
950 [label="950: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
951 [label="951: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
952 [label="952: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
953 [label="953: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
954 [label="954: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
955 [label="955: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6211)\n\nX6211 is free", fontsize=16, style=filled, fillcolor=lightyellow];
956 [label="956: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
957 [label="957: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6211), SCOPE: 143, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6211), SCOPE: 143, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6211), SCOPE: 143, CLAUSE: 3\n\nX6211 is free", fontsize=16, style=filled, fillcolor=lightyellow];
958 [label="958: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6211), SCOPE: 143, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6211), SCOPE: 143, CLAUSE: 3\n\nX6211 is free", fontsize=16, style=filled, fillcolor=lightyellow];
959 [label="959: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6211), SCOPE: 143, CLAUSE: 2\n\nX6211 is free", fontsize=16, style=filled, fillcolor=lightyellow];
960 [label="960: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X6211), SCOPE: 143, CLAUSE: 3\n\nX6211 is free", fontsize=16, style=filled, fillcolor=lightyellow];
961 [label="961: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6268)\n\nX6268 is free", fontsize=16, style=filled, fillcolor=lightyellow];
962 [label="962: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6268), SCOPE: 144, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6268), SCOPE: 144, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6268), SCOPE: 144, CLAUSE: 3\n\nX6268 is free", fontsize=16, style=filled, fillcolor=lightyellow];
963 [label="963: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6268), SCOPE: 144, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6268), SCOPE: 144, CLAUSE: 3\n\nX6268 is free", fontsize=16, style=filled, fillcolor=lightyellow];
964 [label="964: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6268), SCOPE: 144, CLAUSE: 2\n\nX6268 is free", fontsize=16, style=filled, fillcolor=lightyellow];
965 [label="965: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(0))))), X6268), SCOPE: 144, CLAUSE: 3\n\nX6268 is free", fontsize=16, style=filled, fillcolor=lightyellow];
966 [label="966: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X6322)\n\nX6322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
967 [label="967: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X6322), SCOPE: 145, CLAUSE: 1 | quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X6322), SCOPE: 145, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X6322), SCOPE: 145, CLAUSE: 3\n\nX6322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
968 [label="968: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X6322), SCOPE: 145, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X6322), SCOPE: 145, CLAUSE: 3\n\nX6322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
969 [label="969: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X6322), SCOPE: 145, CLAUSE: 2\n\nX6322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
970 [label="970: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(0))))), X6322), SCOPE: 145, CLAUSE: 3\n\nX6322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
971 [label="971: quot(s(0), s(s(0)), s(s(s(s(s(0))))), X6376)\n\nX6376 is free", fontsize=16, style=filled, fillcolor=lightyellow];
972 [label="972: quot(s(0), s(s(0)), s(s(s(s(s(0))))), X6376), SCOPE: 146, CLAUSE: 1 | quot(s(0), s(s(0)), s(s(s(s(s(0))))), X6376), SCOPE: 146, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(s(s(0))))), X6376), SCOPE: 146, CLAUSE: 3\n\nX6376 is free", fontsize=16, style=filled, fillcolor=lightyellow];
973 [label="973: quot(s(0), s(s(0)), s(s(s(s(s(0))))), X6376), SCOPE: 146, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(s(s(0))))), X6376), SCOPE: 146, CLAUSE: 3\n\nX6376 is free", fontsize=16, style=filled, fillcolor=lightyellow];
974 [label="974: quot(s(0), s(s(0)), s(s(s(s(s(0))))), X6376), SCOPE: 146, CLAUSE: 2\n\nX6376 is free", fontsize=16, style=filled, fillcolor=lightyellow];
975 [label="975: quot(s(0), s(s(0)), s(s(s(s(s(0))))), X6376), SCOPE: 146, CLAUSE: 3\n\nX6376 is free", fontsize=16, style=filled, fillcolor=lightyellow];
976 [label="976: quot(0, s(0), s(s(s(s(s(0))))), X6416)\n\nX6416 is free", fontsize=16, style=filled, fillcolor=lightyellow];
977 [label="977: quot(0, s(0), s(s(s(s(s(0))))), X6416), SCOPE: 147, CLAUSE: 1 | quot(0, s(0), s(s(s(s(s(0))))), X6416), SCOPE: 147, CLAUSE: 2 | quot(0, s(0), s(s(s(s(s(0))))), X6416), SCOPE: 147, CLAUSE: 3\n\nX6416 is free", fontsize=16, style=filled, fillcolor=lightyellow];
978 [label="978: quot(0, s(0), s(s(s(s(s(0))))), X6416), SCOPE: 147, CLAUSE: 1\n\nX6416 is free", fontsize=16, style=filled, fillcolor=lightyellow];
979 [label="979: quot(0, s(0), s(s(s(s(s(0))))), X6416), SCOPE: 147, CLAUSE: 2 | quot(0, s(0), s(s(s(s(s(0))))), X6416), SCOPE: 147, CLAUSE: 3\n\nX6416 is free", fontsize=16, style=filled, fillcolor=lightyellow];
980 [label="980: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
981 [label="981: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
982 [label="982: quot(0, s(0), s(s(s(s(s(0))))), X6416), SCOPE: 147, CLAUSE: 3\n\nX6416 is free", fontsize=16, style=filled, fillcolor=lightyellow];
983 [label="983: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
984 [label="984: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
985 [label="985: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
986 [label="986: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
987 [label="987: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
988 [label="988: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X6459)\n\nX6459 is free", fontsize=16, style=filled, fillcolor=lightyellow];
989 [label="989: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
990 [label="990: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X6459), SCOPE: 148, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X6459), SCOPE: 148, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X6459), SCOPE: 148, CLAUSE: 3\n\nX6459 is free", fontsize=16, style=filled, fillcolor=lightyellow];
991 [label="991: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X6459), SCOPE: 148, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X6459), SCOPE: 148, CLAUSE: 3\n\nX6459 is free", fontsize=16, style=filled, fillcolor=lightyellow];
992 [label="992: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X6459), SCOPE: 148, CLAUSE: 2\n\nX6459 is free", fontsize=16, style=filled, fillcolor=lightyellow];
993 [label="993: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(0)))), X6459), SCOPE: 148, CLAUSE: 3\n\nX6459 is free", fontsize=16, style=filled, fillcolor=lightyellow];
994 [label="994: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X6516)\n\nX6516 is free", fontsize=16, style=filled, fillcolor=lightyellow];
995 [label="995: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X6516), SCOPE: 149, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X6516), SCOPE: 149, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X6516), SCOPE: 149, CLAUSE: 3\n\nX6516 is free", fontsize=16, style=filled, fillcolor=lightyellow];
996 [label="996: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X6516), SCOPE: 149, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X6516), SCOPE: 149, CLAUSE: 3\n\nX6516 is free", fontsize=16, style=filled, fillcolor=lightyellow];
997 [label="997: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X6516), SCOPE: 149, CLAUSE: 2\n\nX6516 is free", fontsize=16, style=filled, fillcolor=lightyellow];
998 [label="998: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(0)))), X6516), SCOPE: 149, CLAUSE: 3\n\nX6516 is free", fontsize=16, style=filled, fillcolor=lightyellow];
999 [label="999: quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X6570)\n\nX6570 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1000 [label="1000: quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X6570), SCOPE: 150, CLAUSE: 1 | quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X6570), SCOPE: 150, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X6570), SCOPE: 150, CLAUSE: 3\n\nX6570 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1001 [label="1001: quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X6570), SCOPE: 150, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X6570), SCOPE: 150, CLAUSE: 3\n\nX6570 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1002 [label="1002: quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X6570), SCOPE: 150, CLAUSE: 2\n\nX6570 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1003 [label="1003: quot(s(s(0)), s(s(0)), s(s(s(s(0)))), X6570), SCOPE: 150, CLAUSE: 3\n\nX6570 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1004 [label="1004: quot(s(0), s(0), s(s(s(s(0)))), X6624)\n\nX6624 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1005 [label="1005: quot(s(0), s(0), s(s(s(s(0)))), X6624), SCOPE: 151, CLAUSE: 1 | quot(s(0), s(0), s(s(s(s(0)))), X6624), SCOPE: 151, CLAUSE: 2 | quot(s(0), s(0), s(s(s(s(0)))), X6624), SCOPE: 151, CLAUSE: 3\n\nX6624 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1006 [label="1006: quot(s(0), s(0), s(s(s(s(0)))), X6624), SCOPE: 151, CLAUSE: 2 | quot(s(0), s(0), s(s(s(s(0)))), X6624), SCOPE: 151, CLAUSE: 3\n\nX6624 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1007 [label="1007: quot(s(0), s(0), s(s(s(s(0)))), X6624), SCOPE: 151, CLAUSE: 2\n\nX6624 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1008 [label="1008: quot(s(0), s(0), s(s(s(s(0)))), X6624), SCOPE: 151, CLAUSE: 3\n\nX6624 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1009 [label="1009: quot(0, 0, s(s(s(s(0)))), X6684)\n\nX6684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1010 [label="1010: quot(0, 0, s(s(s(s(0)))), X6684), SCOPE: 152, CLAUSE: 1 | quot(0, 0, s(s(s(s(0)))), X6684), SCOPE: 152, CLAUSE: 2 | quot(0, 0, s(s(s(s(0)))), X6684), SCOPE: 152, CLAUSE: 3\n\nX6684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1011 [label="1011: quot(0, 0, s(s(s(s(0)))), X6684), SCOPE: 152, CLAUSE: 2 | quot(0, 0, s(s(s(s(0)))), X6684), SCOPE: 152, CLAUSE: 3\n\nX6684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1012 [label="1012: quot(0, 0, s(s(s(s(0)))), X6684), SCOPE: 152, CLAUSE: 3\n\nX6684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1013 [label="1013: quot(0, s(s(s(s(0)))), s(s(s(s(0)))), X6716)\n\nX6716 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1014 [label="1014: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1015 [label="1015: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1016 [label="1016: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1017 [label="1017: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1018 [label="1018: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X6742)\n\nX6742 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1019 [label="1019: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1020 [label="1020: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X6742), SCOPE: 153, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X6742), SCOPE: 153, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X6742), SCOPE: 153, CLAUSE: 3\n\nX6742 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1021 [label="1021: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X6742), SCOPE: 153, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X6742), SCOPE: 153, CLAUSE: 3\n\nX6742 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1022 [label="1022: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X6742), SCOPE: 153, CLAUSE: 2\n\nX6742 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1023 [label="1023: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(0))), X6742), SCOPE: 153, CLAUSE: 3\n\nX6742 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1024 [label="1024: quot(s(s(s(0))), s(s(0)), s(s(s(0))), X6799)\n\nX6799 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1025 [label="1025: quot(s(s(s(0))), s(s(0)), s(s(s(0))), X6799), SCOPE: 154, CLAUSE: 1 | quot(s(s(s(0))), s(s(0)), s(s(s(0))), X6799), SCOPE: 154, CLAUSE: 2 | quot(s(s(s(0))), s(s(0)), s(s(s(0))), X6799), SCOPE: 154, CLAUSE: 3\n\nX6799 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1026 [label="1026: quot(s(s(s(0))), s(s(0)), s(s(s(0))), X6799), SCOPE: 154, CLAUSE: 2 | quot(s(s(s(0))), s(s(0)), s(s(s(0))), X6799), SCOPE: 154, CLAUSE: 3\n\nX6799 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1027 [label="1027: quot(s(s(s(0))), s(s(0)), s(s(s(0))), X6799), SCOPE: 154, CLAUSE: 2\n\nX6799 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1028 [label="1028: quot(s(s(s(0))), s(s(0)), s(s(s(0))), X6799), SCOPE: 154, CLAUSE: 3\n\nX6799 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1029 [label="1029: quot(s(s(0)), s(0), s(s(s(0))), X6853)\n\nX6853 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1030 [label="1030: quot(s(s(0)), s(0), s(s(s(0))), X6853), SCOPE: 155, CLAUSE: 1 | quot(s(s(0)), s(0), s(s(s(0))), X6853), SCOPE: 155, CLAUSE: 2 | quot(s(s(0)), s(0), s(s(s(0))), X6853), SCOPE: 155, CLAUSE: 3\n\nX6853 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1031 [label="1031: quot(s(s(0)), s(0), s(s(s(0))), X6853), SCOPE: 155, CLAUSE: 2 | quot(s(s(0)), s(0), s(s(s(0))), X6853), SCOPE: 155, CLAUSE: 3\n\nX6853 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1032 [label="1032: quot(s(s(0)), s(0), s(s(s(0))), X6853), SCOPE: 155, CLAUSE: 2\n\nX6853 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1033 [label="1033: quot(s(s(0)), s(0), s(s(s(0))), X6853), SCOPE: 155, CLAUSE: 3\n\nX6853 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1034 [label="1034: quot(s(0), 0, s(s(s(0))), X6913)\n\nX6913 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1035 [label="1035: quot(s(0), 0, s(s(s(0))), X6913), SCOPE: 156, CLAUSE: 1 | quot(s(0), 0, s(s(s(0))), X6913), SCOPE: 156, CLAUSE: 2 | quot(s(0), 0, s(s(s(0))), X6913), SCOPE: 156, CLAUSE: 3\n\nX6913 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1036 [label="1036: quot(s(0), 0, s(s(s(0))), X6913), SCOPE: 156, CLAUSE: 2 | quot(s(0), 0, s(s(s(0))), X6913), SCOPE: 156, CLAUSE: 3\n\nX6913 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1037 [label="1037: quot(s(0), 0, s(s(s(0))), X6913), SCOPE: 156, CLAUSE: 3\n\nX6913 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1038 [label="1038: quot(s(0), s(s(s(0))), s(s(s(0))), X6952)\n\nX6952 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1039 [label="1039: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1040 [label="1040: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1041 [label="1041: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1042 [label="1042: quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X6982)\n\nX6982 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1043 [label="1043: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1044 [label="1044: quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X6982), SCOPE: 157, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X6982), SCOPE: 157, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X6982), SCOPE: 157, CLAUSE: 3\n\nX6982 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1045 [label="1045: quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X6982), SCOPE: 157, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X6982), SCOPE: 157, CLAUSE: 3\n\nX6982 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1046 [label="1046: quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X6982), SCOPE: 157, CLAUSE: 2\n\nX6982 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1047 [label="1047: quot(s(s(s(s(0)))), s(s(0)), s(s(0)), X6982), SCOPE: 157, CLAUSE: 3\n\nX6982 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1048 [label="1048: quot(s(s(s(0))), s(0), s(s(0)), X7039)\n\nX7039 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1049 [label="1049: quot(s(s(s(0))), s(0), s(s(0)), X7039), SCOPE: 158, CLAUSE: 1 | quot(s(s(s(0))), s(0), s(s(0)), X7039), SCOPE: 158, CLAUSE: 2 | quot(s(s(s(0))), s(0), s(s(0)), X7039), SCOPE: 158, CLAUSE: 3\n\nX7039 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1050 [label="1050: quot(s(s(s(0))), s(0), s(s(0)), X7039), SCOPE: 158, CLAUSE: 2 | quot(s(s(s(0))), s(0), s(s(0)), X7039), SCOPE: 158, CLAUSE: 3\n\nX7039 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1051 [label="1051: quot(s(s(s(0))), s(0), s(s(0)), X7039), SCOPE: 158, CLAUSE: 2\n\nX7039 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1052 [label="1052: quot(s(s(s(0))), s(0), s(s(0)), X7039), SCOPE: 158, CLAUSE: 3\n\nX7039 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1053 [label="1053: quot(s(s(0)), 0, s(s(0)), X7099)\n\nX7099 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1054 [label="1054: quot(s(s(0)), 0, s(s(0)), X7099), SCOPE: 159, CLAUSE: 1 | quot(s(s(0)), 0, s(s(0)), X7099), SCOPE: 159, CLAUSE: 2 | quot(s(s(0)), 0, s(s(0)), X7099), SCOPE: 159, CLAUSE: 3\n\nX7099 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1055 [label="1055: quot(s(s(0)), 0, s(s(0)), X7099), SCOPE: 159, CLAUSE: 2 | quot(s(s(0)), 0, s(s(0)), X7099), SCOPE: 159, CLAUSE: 3\n\nX7099 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1056 [label="1056: quot(s(s(0)), 0, s(s(0)), X7099), SCOPE: 159, CLAUSE: 3\n\nX7099 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1057 [label="1057: quot(s(s(0)), s(s(0)), s(s(0)), X7138)\n\nX7138 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1058 [label="1058: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1059 [label="1059: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1060 [label="1060: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1061 [label="1061: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1062 [label="1062: times(T699, s(s(T697)), X4848)\n\nT697 is ground\nT699 is ground\nX4848 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1063 [label="1063: neq(s(s(s(s(s(s(T697)))))), T880)\n\nT697 is ground\nT880 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1064 [label="1064: pr(s(s(s(s(s(s(T691)))))), s(T691)), SCOPE: 160, CLAUSE: 5 | pr(s(s(s(s(s(s(T691)))))), s(T691)), SCOPE: 160, CLAUSE: 6\n\nT691 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1065 [label="1065: pr(s(s(s(s(s(s(T691)))))), s(T691)), SCOPE: 160, CLAUSE: 5\n\nT691 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1066 [label="1066: pr(s(s(s(s(s(s(T691)))))), s(T691)), SCOPE: 160, CLAUSE: 6\n\nT691 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1067 [label="1067: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1068 [label="1068: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1069 [label="1069: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1070 [label="1070: ','(not_divides(s(s(T897)), s(s(s(s(s(s(s(T897)))))))), pr(s(s(s(s(s(s(s(T897))))))), s(T897)))\n\nT897 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1071 [label="1071: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1072 [label="1072: not_divides(s(s(T897)), s(s(s(s(s(s(s(T897))))))))\n\nT897 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1073 [label="1073: pr(s(s(s(s(s(s(s(T897))))))), s(T897))\n\nT897 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1074 [label="1074: not_divides(s(s(T897)), s(s(s(s(s(s(s(T897)))))))), SCOPE: 161, CLAUSE: 7\n\nT897 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1075 [label="1075: ','(div(s(s(s(s(s(s(s(T903))))))), s(s(T903)), X7202), ','(times(X7202, s(s(T903)), X7203), neq(s(s(s(s(s(s(s(T903))))))), X7203)))\n\nT903 is ground\nX7202 is free; \nX7203 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1076 [label="1076: div(s(s(s(s(s(s(s(T903))))))), s(s(T903)), X7202)\n\nT903 is ground\nX7202 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1077 [label="1077: ','(times(T905, s(s(T903)), X7203), neq(s(s(s(s(s(s(s(T903))))))), X7203))\n\nT903 is ground\nT905 is ground\nX7203 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1078 [label="1078: div(s(s(s(s(s(s(s(T903))))))), s(s(T903)), X7202), SCOPE: 162, CLAUSE: 0\n\nT903 is ground\nX7202 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1079 [label="1079: quot(s(s(s(s(s(s(s(T910))))))), s(s(T910)), s(s(T910)), X7232)\n\nT910 is ground\nX7232 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1080 [label="1080: quot(s(s(s(s(s(s(s(T910))))))), s(s(T910)), s(s(T910)), X7232), SCOPE: 163, CLAUSE: 1 | quot(s(s(s(s(s(s(s(T910))))))), s(s(T910)), s(s(T910)), X7232), SCOPE: 163, CLAUSE: 2 | quot(s(s(s(s(s(s(s(T910))))))), s(s(T910)), s(s(T910)), X7232), SCOPE: 163, CLAUSE: 3\n\nT910 is ground\nX7232 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1081 [label="1081: quot(s(s(s(s(s(s(s(T910))))))), s(s(T910)), s(s(T910)), X7232), SCOPE: 163, CLAUSE: 2 | quot(s(s(s(s(s(s(s(T910))))))), s(s(T910)), s(s(T910)), X7232), SCOPE: 163, CLAUSE: 3\n\nT910 is ground\nX7232 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1082 [label="1082: quot(s(s(s(s(s(s(s(T910))))))), s(s(T910)), s(s(T910)), X7232), SCOPE: 163, CLAUSE: 2\n\nT910 is ground\nX7232 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1083 [label="1083: quot(s(s(s(s(s(s(s(T910))))))), s(s(T910)), s(s(T910)), X7232), SCOPE: 163, CLAUSE: 3\n\nT910 is ground\nX7232 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1084 [label="1084: quot(s(s(s(s(s(s(T918)))))), s(T918), s(s(T918)), X7286)\n\nT918 is ground\nX7286 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1085 [label="1085: quot(s(s(s(s(s(s(T918)))))), s(T918), s(s(T918)), X7286), SCOPE: 164, CLAUSE: 1 | quot(s(s(s(s(s(s(T918)))))), s(T918), s(s(T918)), X7286), SCOPE: 164, CLAUSE: 2 | quot(s(s(s(s(s(s(T918)))))), s(T918), s(s(T918)), X7286), SCOPE: 164, CLAUSE: 3\n\nT918 is ground\nX7286 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1086 [label="1086: quot(s(s(s(s(s(s(T918)))))), s(T918), s(s(T918)), X7286), SCOPE: 164, CLAUSE: 2 | quot(s(s(s(s(s(s(T918)))))), s(T918), s(s(T918)), X7286), SCOPE: 164, CLAUSE: 3\n\nT918 is ground\nX7286 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1087 [label="1087: quot(s(s(s(s(s(s(T918)))))), s(T918), s(s(T918)), X7286), SCOPE: 164, CLAUSE: 2\n\nT918 is ground\nX7286 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1088 [label="1088: quot(s(s(s(s(s(s(T918)))))), s(T918), s(s(T918)), X7286), SCOPE: 164, CLAUSE: 3\n\nT918 is ground\nX7286 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1089 [label="1089: quot(s(s(s(s(s(T928))))), T928, s(s(T928)), X7340)\n\nT928 is ground\nX7340 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1090 [label="1090: quot(s(s(s(s(s(T928))))), T928, s(s(T928)), X7340), SCOPE: 165, CLAUSE: 1 | quot(s(s(s(s(s(T928))))), T928, s(s(T928)), X7340), SCOPE: 165, CLAUSE: 2 | quot(s(s(s(s(s(T928))))), T928, s(s(T928)), X7340), SCOPE: 165, CLAUSE: 3\n\nT928 is ground\nX7340 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1091 [label="1091: quot(s(s(s(s(s(T928))))), T928, s(s(T928)), X7340), SCOPE: 165, CLAUSE: 2 | quot(s(s(s(s(s(T928))))), T928, s(s(T928)), X7340), SCOPE: 165, CLAUSE: 3\n\nT928 is ground\nX7340 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1092 [label="1092: quot(s(s(s(s(s(T928))))), T928, s(s(T928)), X7340), SCOPE: 165, CLAUSE: 2\n\nT928 is ground\nX7340 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1093 [label="1093: quot(s(s(s(s(s(T928))))), T928, s(s(T928)), X7340), SCOPE: 165, CLAUSE: 3\n\nT928 is ground\nX7340 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1094 [label="1094: quot(s(s(s(s(s(T940))))), T940, s(s(s(T940))), X7376)\n\nT940 is ground\nX7376 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1095 [label="1095: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1096 [label="1096: quot(s(s(s(s(s(T940))))), T940, s(s(s(T940))), X7376), SCOPE: 166, CLAUSE: 1 | quot(s(s(s(s(s(T940))))), T940, s(s(s(T940))), X7376), SCOPE: 166, CLAUSE: 2 | quot(s(s(s(s(s(T940))))), T940, s(s(s(T940))), X7376), SCOPE: 166, CLAUSE: 3\n\nT940 is ground\nX7376 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1097 [label="1097: quot(s(s(s(s(s(T940))))), T940, s(s(s(T940))), X7376), SCOPE: 166, CLAUSE: 2 | quot(s(s(s(s(s(T940))))), T940, s(s(s(T940))), X7376), SCOPE: 166, CLAUSE: 3\n\nT940 is ground\nX7376 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1098 [label="1098: quot(s(s(s(s(s(T940))))), T940, s(s(s(T940))), X7376), SCOPE: 166, CLAUSE: 2\n\nT940 is ground\nX7376 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1099 [label="1099: quot(s(s(s(s(s(T940))))), T940, s(s(s(T940))), X7376), SCOPE: 166, CLAUSE: 3\n\nT940 is ground\nX7376 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1100 [label="1100: quot(s(s(s(s(s(T952))))), T952, s(s(s(s(T952)))), X7416)\n\nT952 is ground\nX7416 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1101 [label="1101: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1102 [label="1102: quot(s(s(s(s(s(T952))))), T952, s(s(s(s(T952)))), X7416), SCOPE: 167, CLAUSE: 1 | quot(s(s(s(s(s(T952))))), T952, s(s(s(s(T952)))), X7416), SCOPE: 167, CLAUSE: 2 | quot(s(s(s(s(s(T952))))), T952, s(s(s(s(T952)))), X7416), SCOPE: 167, CLAUSE: 3\n\nT952 is ground\nX7416 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1103 [label="1103: quot(s(s(s(s(s(T952))))), T952, s(s(s(s(T952)))), X7416), SCOPE: 167, CLAUSE: 2 | quot(s(s(s(s(s(T952))))), T952, s(s(s(s(T952)))), X7416), SCOPE: 167, CLAUSE: 3\n\nT952 is ground\nX7416 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1104 [label="1104: quot(s(s(s(s(s(T952))))), T952, s(s(s(s(T952)))), X7416), SCOPE: 167, CLAUSE: 2\n\nT952 is ground\nX7416 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1105 [label="1105: quot(s(s(s(s(s(T952))))), T952, s(s(s(s(T952)))), X7416), SCOPE: 167, CLAUSE: 3\n\nT952 is ground\nX7416 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1106 [label="1106: quot(s(s(s(s(s(T964))))), T964, s(s(s(s(s(T964))))), X7456)\n\nT964 is ground\nX7456 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1107 [label="1107: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1108 [label="1108: quot(s(s(s(s(s(T964))))), T964, s(s(s(s(s(T964))))), X7456), SCOPE: 168, CLAUSE: 1 | quot(s(s(s(s(s(T964))))), T964, s(s(s(s(s(T964))))), X7456), SCOPE: 168, CLAUSE: 2 | quot(s(s(s(s(s(T964))))), T964, s(s(s(s(s(T964))))), X7456), SCOPE: 168, CLAUSE: 3\n\nT964 is ground\nX7456 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1109 [label="1109: quot(s(s(s(s(s(T964))))), T964, s(s(s(s(s(T964))))), X7456), SCOPE: 168, CLAUSE: 2 | quot(s(s(s(s(s(T964))))), T964, s(s(s(s(s(T964))))), X7456), SCOPE: 168, CLAUSE: 3\n\nT964 is ground\nX7456 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1110 [label="1110: quot(s(s(s(s(s(T964))))), T964, s(s(s(s(s(T964))))), X7456), SCOPE: 168, CLAUSE: 2\n\nT964 is ground\nX7456 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1111 [label="1111: quot(s(s(s(s(s(T964))))), T964, s(s(s(s(s(T964))))), X7456), SCOPE: 168, CLAUSE: 3\n\nT964 is ground\nX7456 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1112 [label="1112: quot(s(s(s(s(s(T976))))), T976, s(s(s(s(s(s(T976)))))), X7496)\n\nT976 is ground\nX7496 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1113 [label="1113: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1114 [label="1114: quot(s(s(s(s(s(T976))))), T976, s(s(s(s(s(s(T976)))))), X7496), SCOPE: 169, CLAUSE: 1 | quot(s(s(s(s(s(T976))))), T976, s(s(s(s(s(s(T976)))))), X7496), SCOPE: 169, CLAUSE: 2 | quot(s(s(s(s(s(T976))))), T976, s(s(s(s(s(s(T976)))))), X7496), SCOPE: 169, CLAUSE: 3\n\nT976 is ground\nX7496 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1115 [label="1115: quot(s(s(s(s(s(T976))))), T976, s(s(s(s(s(s(T976)))))), X7496), SCOPE: 169, CLAUSE: 2 | quot(s(s(s(s(s(T976))))), T976, s(s(s(s(s(s(T976)))))), X7496), SCOPE: 169, CLAUSE: 3\n\nT976 is ground\nX7496 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1116 [label="1116: quot(s(s(s(s(s(T976))))), T976, s(s(s(s(s(s(T976)))))), X7496), SCOPE: 169, CLAUSE: 2\n\nT976 is ground\nX7496 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1117 [label="1117: quot(s(s(s(s(s(T976))))), T976, s(s(s(s(s(s(T976)))))), X7496), SCOPE: 169, CLAUSE: 3\n\nT976 is ground\nX7496 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1118 [label="1118: quot(s(s(s(s(s(T988))))), T988, s(s(s(s(s(s(s(T988))))))), X7536)\n\nT988 is ground\nX7536 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1119 [label="1119: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1120 [label="1120: quot(s(s(s(s(s(T988))))), T988, s(s(s(s(s(s(s(T988))))))), X7536), SCOPE: 170, CLAUSE: 1 | quot(s(s(s(s(s(T988))))), T988, s(s(s(s(s(s(s(T988))))))), X7536), SCOPE: 170, CLAUSE: 2 | quot(s(s(s(s(s(T988))))), T988, s(s(s(s(s(s(s(T988))))))), X7536), SCOPE: 170, CLAUSE: 3\n\nT988 is ground\nX7536 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1121 [label="1121: quot(s(s(s(s(s(T988))))), T988, s(s(s(s(s(s(s(T988))))))), X7536), SCOPE: 170, CLAUSE: 2 | quot(s(s(s(s(s(T988))))), T988, s(s(s(s(s(s(s(T988))))))), X7536), SCOPE: 170, CLAUSE: 3\n\nT988 is ground\nX7536 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1122 [label="1122: quot(s(s(s(s(s(T988))))), T988, s(s(s(s(s(s(s(T988))))))), X7536), SCOPE: 170, CLAUSE: 2\n\nT988 is ground\nX7536 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1123 [label="1123: quot(s(s(s(s(s(T988))))), T988, s(s(s(s(s(s(s(T988))))))), X7536), SCOPE: 170, CLAUSE: 3\n\nT988 is ground\nX7536 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1124 [label="1124: quot(s(s(s(s(s(T1000))))), T1000, s(s(s(s(s(s(s(s(T1000)))))))), X7576)\n\nT1000 is ground\nX7576 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1125 [label="1125: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1126 [label="1126: quot(s(s(s(s(s(T1000))))), T1000, s(T1003), X7576)\n\nT1000 is ground\nT1003 is ground\nX7576 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1127 [label="1127: quot(s(s(s(s(s(T1000))))), T1000, s(T1003), X7576), SCOPE: 171, CLAUSE: 1 | quot(s(s(s(s(s(T1000))))), T1000, s(T1003), X7576), SCOPE: 171, CLAUSE: 2 | quot(s(s(s(s(s(T1000))))), T1000, s(T1003), X7576), SCOPE: 171, CLAUSE: 3\n\nT1000 is ground\nT1003 is ground\nX7576 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1128 [label="1128: quot(s(s(s(s(s(T1000))))), T1000, s(T1003), X7576), SCOPE: 171, CLAUSE: 2 | quot(s(s(s(s(s(T1000))))), T1000, s(T1003), X7576), SCOPE: 171, CLAUSE: 3\n\nT1000 is ground\nT1003 is ground\nX7576 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1129 [label="1129: quot(s(s(s(s(s(T1000))))), T1000, s(T1003), X7576), SCOPE: 171, CLAUSE: 2\n\nT1000 is ground\nT1003 is ground\nX7576 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1130 [label="1130: quot(s(s(s(s(s(T1000))))), T1000, s(T1003), X7576), SCOPE: 171, CLAUSE: 3\n\nT1000 is ground\nT1003 is ground\nX7576 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1131 [label="1131: quot(s(s(s(s(s(T1020))))), T1020, s(T1021), X7625)\n\nT1020 is ground\nT1021 is ground\nX7625 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1132 [label="1132: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1133 [label="1133: quot(s(s(s(s(s(0))))), s(T1030), s(T1030), X7650)\n\nT1030 is ground\nX7650 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1134 [label="1134: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1135 [label="1135: quot(s(s(s(s(s(0))))), s(T1030), s(T1030), X7650), SCOPE: 172, CLAUSE: 1 | quot(s(s(s(s(s(0))))), s(T1030), s(T1030), X7650), SCOPE: 172, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(T1030), s(T1030), X7650), SCOPE: 172, CLAUSE: 3\n\nT1030 is ground\nX7650 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1136 [label="1136: quot(s(s(s(s(s(0))))), s(T1030), s(T1030), X7650), SCOPE: 172, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(T1030), s(T1030), X7650), SCOPE: 172, CLAUSE: 3\n\nT1030 is ground\nX7650 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1137 [label="1137: quot(s(s(s(s(s(0))))), s(T1030), s(T1030), X7650), SCOPE: 172, CLAUSE: 2\n\nT1030 is ground\nX7650 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1138 [label="1138: quot(s(s(s(s(s(0))))), s(T1030), s(T1030), X7650), SCOPE: 172, CLAUSE: 3\n\nT1030 is ground\nX7650 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1139 [label="1139: quot(s(s(s(s(0)))), T1038, s(T1038), X7707)\n\nT1038 is ground\nX7707 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1140 [label="1140: quot(s(s(s(s(0)))), T1038, s(T1038), X7707), SCOPE: 173, CLAUSE: 1 | quot(s(s(s(s(0)))), T1038, s(T1038), X7707), SCOPE: 173, CLAUSE: 2 | quot(s(s(s(s(0)))), T1038, s(T1038), X7707), SCOPE: 173, CLAUSE: 3\n\nT1038 is ground\nX7707 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1141 [label="1141: quot(s(s(s(s(0)))), T1038, s(T1038), X7707), SCOPE: 173, CLAUSE: 2 | quot(s(s(s(s(0)))), T1038, s(T1038), X7707), SCOPE: 173, CLAUSE: 3\n\nT1038 is ground\nX7707 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1142 [label="1142: quot(s(s(s(s(0)))), T1038, s(T1038), X7707), SCOPE: 173, CLAUSE: 2\n\nT1038 is ground\nX7707 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1143 [label="1143: quot(s(s(s(s(0)))), T1038, s(T1038), X7707), SCOPE: 173, CLAUSE: 3\n\nT1038 is ground\nX7707 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1144 [label="1144: quot(s(s(s(0))), T1044, s(s(T1044)), X7743)\n\nT1044 is ground\nX7743 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1145 [label="1145: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1146 [label="1146: quot(s(s(s(0))), T1044, s(s(T1044)), X7743), SCOPE: 174, CLAUSE: 1 | quot(s(s(s(0))), T1044, s(s(T1044)), X7743), SCOPE: 174, CLAUSE: 2 | quot(s(s(s(0))), T1044, s(s(T1044)), X7743), SCOPE: 174, CLAUSE: 3\n\nT1044 is ground\nX7743 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1147 [label="1147: quot(s(s(s(0))), T1044, s(s(T1044)), X7743), SCOPE: 174, CLAUSE: 2 | quot(s(s(s(0))), T1044, s(s(T1044)), X7743), SCOPE: 174, CLAUSE: 3\n\nT1044 is ground\nX7743 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1148 [label="1148: quot(s(s(s(0))), T1044, s(s(T1044)), X7743), SCOPE: 174, CLAUSE: 2\n\nT1044 is ground\nX7743 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1149 [label="1149: quot(s(s(s(0))), T1044, s(s(T1044)), X7743), SCOPE: 174, CLAUSE: 3\n\nT1044 is ground\nX7743 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1150 [label="1150: quot(s(s(0)), T1050, s(s(s(T1050))), X7783)\n\nT1050 is ground\nX7783 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1151 [label="1151: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1152 [label="1152: quot(s(s(0)), T1050, s(s(s(T1050))), X7783), SCOPE: 175, CLAUSE: 1 | quot(s(s(0)), T1050, s(s(s(T1050))), X7783), SCOPE: 175, CLAUSE: 2 | quot(s(s(0)), T1050, s(s(s(T1050))), X7783), SCOPE: 175, CLAUSE: 3\n\nT1050 is ground\nX7783 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1153 [label="1153: quot(s(s(0)), T1050, s(s(s(T1050))), X7783), SCOPE: 175, CLAUSE: 2 | quot(s(s(0)), T1050, s(s(s(T1050))), X7783), SCOPE: 175, CLAUSE: 3\n\nT1050 is ground\nX7783 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1154 [label="1154: quot(s(s(0)), T1050, s(s(s(T1050))), X7783), SCOPE: 175, CLAUSE: 2\n\nT1050 is ground\nX7783 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1155 [label="1155: quot(s(s(0)), T1050, s(s(s(T1050))), X7783), SCOPE: 175, CLAUSE: 3\n\nT1050 is ground\nX7783 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1156 [label="1156: quot(s(0), T1056, s(s(s(s(T1056)))), X7823)\n\nT1056 is ground\nX7823 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1157 [label="1157: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1158 [label="1158: quot(s(0), T1056, s(s(s(s(T1056)))), X7823), SCOPE: 176, CLAUSE: 1 | quot(s(0), T1056, s(s(s(s(T1056)))), X7823), SCOPE: 176, CLAUSE: 2 | quot(s(0), T1056, s(s(s(s(T1056)))), X7823), SCOPE: 176, CLAUSE: 3\n\nT1056 is ground\nX7823 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1159 [label="1159: quot(s(0), T1056, s(s(s(s(T1056)))), X7823), SCOPE: 176, CLAUSE: 2 | quot(s(0), T1056, s(s(s(s(T1056)))), X7823), SCOPE: 176, CLAUSE: 3\n\nT1056 is ground\nX7823 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1160 [label="1160: quot(s(0), T1056, s(s(s(s(T1056)))), X7823), SCOPE: 176, CLAUSE: 2\n\nT1056 is ground\nX7823 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1161 [label="1161: quot(s(0), T1056, s(s(s(s(T1056)))), X7823), SCOPE: 176, CLAUSE: 3\n\nT1056 is ground\nX7823 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1162 [label="1162: quot(0, T1062, s(s(s(s(s(T1062))))), X7863)\n\nT1062 is ground\nX7863 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1163 [label="1163: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1164 [label="1164: quot(0, T1062, s(s(s(s(s(T1062))))), X7863), SCOPE: 177, CLAUSE: 1 | quot(0, T1062, s(s(s(s(s(T1062))))), X7863), SCOPE: 177, CLAUSE: 2 | quot(0, T1062, s(s(s(s(s(T1062))))), X7863), SCOPE: 177, CLAUSE: 3\n\nT1062 is ground\nX7863 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1165 [label="1165: quot(0, T1062, s(s(s(s(s(T1062))))), X7863), SCOPE: 177, CLAUSE: 1\n\nT1062 is ground\nX7863 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1166 [label="1166: quot(0, T1062, s(s(s(s(s(T1062))))), X7863), SCOPE: 177, CLAUSE: 2 | quot(0, T1062, s(s(s(s(s(T1062))))), X7863), SCOPE: 177, CLAUSE: 3\n\nT1062 is ground\nX7863 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1167 [label="1167: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1168 [label="1168: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1169 [label="1169: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1170 [label="1170: quot(0, T1062, s(s(s(s(s(T1062))))), X7863), SCOPE: 177, CLAUSE: 3\n\nT1062 is ground\nX7863 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1171 [label="1171: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X7899)\n\nX7899 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1172 [label="1172: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1173 [label="1173: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X7899), SCOPE: 178, CLAUSE: 1 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X7899), SCOPE: 178, CLAUSE: 2 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X7899), SCOPE: 178, CLAUSE: 3\n\nX7899 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1174 [label="1174: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X7899), SCOPE: 178, CLAUSE: 1\n\nX7899 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1175 [label="1175: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X7899), SCOPE: 178, CLAUSE: 2 | quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X7899), SCOPE: 178, CLAUSE: 3\n\nX7899 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1176 [label="1176: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1177 [label="1177: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1178 [label="1178: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X7899), SCOPE: 178, CLAUSE: 3\n\nX7899 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1179 [label="1179: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1180 [label="1180: quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X7933)\n\nX7933 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1181 [label="1181: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1182 [label="1182: quot(s(s(0)), s(s(s(0))), s(s(s(0))), X7957)\n\nX7957 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1183 [label="1183: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1184 [label="1184: quot(s(s(s(0))), s(s(0)), s(s(0)), X7981)\n\nX7981 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1185 [label="1185: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1186 [label="1186: quot(s(s(s(s(0)))), s(0), s(0), X8005)\n\nX8005 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1187 [label="1187: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1188 [label="1188: quot(s(s(s(s(0)))), s(0), s(0), X8005), SCOPE: 179, CLAUSE: 1 | quot(s(s(s(s(0)))), s(0), s(0), X8005), SCOPE: 179, CLAUSE: 2 | quot(s(s(s(s(0)))), s(0), s(0), X8005), SCOPE: 179, CLAUSE: 3\n\nX8005 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1189 [label="1189: quot(s(s(s(s(0)))), s(0), s(0), X8005), SCOPE: 179, CLAUSE: 2 | quot(s(s(s(s(0)))), s(0), s(0), X8005), SCOPE: 179, CLAUSE: 3\n\nX8005 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1190 [label="1190: quot(s(s(s(s(0)))), s(0), s(0), X8005), SCOPE: 179, CLAUSE: 2\n\nX8005 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1191 [label="1191: quot(s(s(s(s(0)))), s(0), s(0), X8005), SCOPE: 179, CLAUSE: 3\n\nX8005 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1192 [label="1192: quot(s(s(s(0))), 0, s(0), X8068)\n\nX8068 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1193 [label="1193: quot(s(s(s(0))), 0, s(0), X8068), SCOPE: 180, CLAUSE: 1 | quot(s(s(s(0))), 0, s(0), X8068), SCOPE: 180, CLAUSE: 2 | quot(s(s(s(0))), 0, s(0), X8068), SCOPE: 180, CLAUSE: 3\n\nX8068 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1194 [label="1194: quot(s(s(s(0))), 0, s(0), X8068), SCOPE: 180, CLAUSE: 2 | quot(s(s(s(0))), 0, s(0), X8068), SCOPE: 180, CLAUSE: 3\n\nX8068 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1195 [label="1195: quot(s(s(s(0))), 0, s(0), X8068), SCOPE: 180, CLAUSE: 3\n\nX8068 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1196 [label="1196: quot(s(s(s(0))), s(0), s(0), X8107)\n\nX8107 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1197 [label="1197: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1198 [label="1198: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1199 [label="1199: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8134)\n\nX8134 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1200 [label="1200: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1201 [label="1201: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8134), SCOPE: 181, CLAUSE: 1 | quot(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8134), SCOPE: 181, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8134), SCOPE: 181, CLAUSE: 3\n\nX8134 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1202 [label="1202: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8134), SCOPE: 181, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8134), SCOPE: 181, CLAUSE: 3\n\nX8134 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1203 [label="1203: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8134), SCOPE: 181, CLAUSE: 2\n\nX8134 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1204 [label="1204: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X8134), SCOPE: 181, CLAUSE: 3\n\nX8134 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1205 [label="1205: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8191)\n\nX8191 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1206 [label="1206: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8191), SCOPE: 182, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8191), SCOPE: 182, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8191), SCOPE: 182, CLAUSE: 3\n\nX8191 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1207 [label="1207: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8191), SCOPE: 182, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8191), SCOPE: 182, CLAUSE: 3\n\nX8191 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1208 [label="1208: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8191), SCOPE: 182, CLAUSE: 2\n\nX8191 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1209 [label="1209: quot(s(s(s(s(0)))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X8191), SCOPE: 182, CLAUSE: 3\n\nX8191 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1210 [label="1210: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8245)\n\nX8245 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1211 [label="1211: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8245), SCOPE: 183, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8245), SCOPE: 183, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8245), SCOPE: 183, CLAUSE: 3\n\nX8245 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1212 [label="1212: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8245), SCOPE: 183, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8245), SCOPE: 183, CLAUSE: 3\n\nX8245 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1213 [label="1213: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8245), SCOPE: 183, CLAUSE: 2\n\nX8245 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1214 [label="1214: quot(s(s(s(0))), s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X8245), SCOPE: 183, CLAUSE: 3\n\nX8245 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1215 [label="1215: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8299)\n\nX8299 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1216 [label="1216: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8299), SCOPE: 184, CLAUSE: 1 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8299), SCOPE: 184, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8299), SCOPE: 184, CLAUSE: 3\n\nX8299 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1217 [label="1217: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8299), SCOPE: 184, CLAUSE: 2 | quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8299), SCOPE: 184, CLAUSE: 3\n\nX8299 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1218 [label="1218: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8299), SCOPE: 184, CLAUSE: 2\n\nX8299 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1219 [label="1219: quot(s(s(0)), s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X8299), SCOPE: 184, CLAUSE: 3\n\nX8299 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1220 [label="1220: quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8353)\n\nX8353 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1221 [label="1221: quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8353), SCOPE: 185, CLAUSE: 1 | quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8353), SCOPE: 185, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8353), SCOPE: 185, CLAUSE: 3\n\nX8353 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1222 [label="1222: quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8353), SCOPE: 185, CLAUSE: 2 | quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8353), SCOPE: 185, CLAUSE: 3\n\nX8353 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1223 [label="1223: quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8353), SCOPE: 185, CLAUSE: 2\n\nX8353 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1224 [label="1224: quot(s(0), s(s(s(0))), s(s(s(s(s(s(s(0))))))), X8353), SCOPE: 185, CLAUSE: 3\n\nX8353 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1225 [label="1225: quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X8393)\n\nX8393 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1226 [label="1226: quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X8393), SCOPE: 186, CLAUSE: 1 | quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X8393), SCOPE: 186, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X8393), SCOPE: 186, CLAUSE: 3\n\nX8393 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1227 [label="1227: quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X8393), SCOPE: 186, CLAUSE: 1\n\nX8393 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1228 [label="1228: quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X8393), SCOPE: 186, CLAUSE: 2 | quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X8393), SCOPE: 186, CLAUSE: 3\n\nX8393 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1229 [label="1229: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1230 [label="1230: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1231 [label="1231: quot(0, s(s(0)), s(s(s(s(s(s(s(0))))))), X8393), SCOPE: 186, CLAUSE: 3\n\nX8393 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1232 [label="1232: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1233 [label="1233: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1234 [label="1234: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1235 [label="1235: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1236 [label="1236: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1237 [label="1237: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1238 [label="1238: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8439)\n\nX8439 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1239 [label="1239: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1240 [label="1240: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8439), SCOPE: 187, CLAUSE: 1 | quot(s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8439), SCOPE: 187, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8439), SCOPE: 187, CLAUSE: 3\n\nX8439 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1241 [label="1241: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8439), SCOPE: 187, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8439), SCOPE: 187, CLAUSE: 3\n\nX8439 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1242 [label="1242: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8439), SCOPE: 187, CLAUSE: 2\n\nX8439 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1243 [label="1243: quot(s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X8439), SCOPE: 187, CLAUSE: 3\n\nX8439 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1244 [label="1244: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8496)\n\nX8496 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1245 [label="1245: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8496), SCOPE: 188, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8496), SCOPE: 188, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8496), SCOPE: 188, CLAUSE: 3\n\nX8496 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1246 [label="1246: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8496), SCOPE: 188, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8496), SCOPE: 188, CLAUSE: 3\n\nX8496 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1247 [label="1247: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8496), SCOPE: 188, CLAUSE: 2\n\nX8496 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1248 [label="1248: quot(s(s(s(s(0)))), s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X8496), SCOPE: 188, CLAUSE: 3\n\nX8496 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1249 [label="1249: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8550)\n\nX8550 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1250 [label="1250: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8550), SCOPE: 189, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8550), SCOPE: 189, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8550), SCOPE: 189, CLAUSE: 3\n\nX8550 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1251 [label="1251: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8550), SCOPE: 189, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8550), SCOPE: 189, CLAUSE: 3\n\nX8550 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1252 [label="1252: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8550), SCOPE: 189, CLAUSE: 2\n\nX8550 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1253 [label="1253: quot(s(s(s(0))), s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X8550), SCOPE: 189, CLAUSE: 3\n\nX8550 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1254 [label="1254: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X8604)\n\nX8604 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1255 [label="1255: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X8604), SCOPE: 190, CLAUSE: 1 | quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X8604), SCOPE: 190, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X8604), SCOPE: 190, CLAUSE: 3\n\nX8604 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1256 [label="1256: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X8604), SCOPE: 190, CLAUSE: 2 | quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X8604), SCOPE: 190, CLAUSE: 3\n\nX8604 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1257 [label="1257: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X8604), SCOPE: 190, CLAUSE: 2\n\nX8604 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1258 [label="1258: quot(s(s(0)), s(s(s(0))), s(s(s(s(s(s(0)))))), X8604), SCOPE: 190, CLAUSE: 3\n\nX8604 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1259 [label="1259: quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X8658)\n\nX8658 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1260 [label="1260: quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X8658), SCOPE: 191, CLAUSE: 1 | quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X8658), SCOPE: 191, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X8658), SCOPE: 191, CLAUSE: 3\n\nX8658 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1261 [label="1261: quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X8658), SCOPE: 191, CLAUSE: 2 | quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X8658), SCOPE: 191, CLAUSE: 3\n\nX8658 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1262 [label="1262: quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X8658), SCOPE: 191, CLAUSE: 2\n\nX8658 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1263 [label="1263: quot(s(0), s(s(0)), s(s(s(s(s(s(0)))))), X8658), SCOPE: 191, CLAUSE: 3\n\nX8658 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1264 [label="1264: quot(0, s(0), s(s(s(s(s(s(0)))))), X8698)\n\nX8698 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1265 [label="1265: quot(0, s(0), s(s(s(s(s(s(0)))))), X8698), SCOPE: 192, CLAUSE: 1 | quot(0, s(0), s(s(s(s(s(s(0)))))), X8698), SCOPE: 192, CLAUSE: 2 | quot(0, s(0), s(s(s(s(s(s(0)))))), X8698), SCOPE: 192, CLAUSE: 3\n\nX8698 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1266 [label="1266: quot(0, s(0), s(s(s(s(s(s(0)))))), X8698), SCOPE: 192, CLAUSE: 1\n\nX8698 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1267 [label="1267: quot(0, s(0), s(s(s(s(s(s(0)))))), X8698), SCOPE: 192, CLAUSE: 2 | quot(0, s(0), s(s(s(s(s(s(0)))))), X8698), SCOPE: 192, CLAUSE: 3\n\nX8698 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1268 [label="1268: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1269 [label="1269: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1270 [label="1270: quot(0, s(0), s(s(s(s(s(s(0)))))), X8698), SCOPE: 192, CLAUSE: 3\n\nX8698 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1271 [label="1271: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1272 [label="1272: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1273 [label="1273: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1274 [label="1274: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1275 [label="1275: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1276 [label="1276: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1277 [label="1277: quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8744)\n\nX8744 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1278 [label="1278: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1279 [label="1279: quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8744), SCOPE: 193, CLAUSE: 1 | quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8744), SCOPE: 193, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8744), SCOPE: 193, CLAUSE: 3\n\nX8744 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1280 [label="1280: quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8744), SCOPE: 193, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8744), SCOPE: 193, CLAUSE: 3\n\nX8744 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1281 [label="1281: quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8744), SCOPE: 193, CLAUSE: 2\n\nX8744 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1282 [label="1282: quot(s(s(s(s(s(0))))), s(s(s(s(s(0))))), s(s(s(s(s(0))))), X8744), SCOPE: 193, CLAUSE: 3\n\nX8744 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1283 [label="1283: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X8801)\n\nX8801 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1284 [label="1284: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X8801), SCOPE: 194, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X8801), SCOPE: 194, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X8801), SCOPE: 194, CLAUSE: 3\n\nX8801 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1285 [label="1285: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X8801), SCOPE: 194, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X8801), SCOPE: 194, CLAUSE: 3\n\nX8801 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1286 [label="1286: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X8801), SCOPE: 194, CLAUSE: 2\n\nX8801 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1287 [label="1287: quot(s(s(s(s(0)))), s(s(s(s(0)))), s(s(s(s(s(0))))), X8801), SCOPE: 194, CLAUSE: 3\n\nX8801 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1288 [label="1288: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X8855)\n\nX8855 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1289 [label="1289: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X8855), SCOPE: 195, CLAUSE: 1 | quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X8855), SCOPE: 195, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X8855), SCOPE: 195, CLAUSE: 3\n\nX8855 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1290 [label="1290: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X8855), SCOPE: 195, CLAUSE: 2 | quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X8855), SCOPE: 195, CLAUSE: 3\n\nX8855 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1291 [label="1291: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X8855), SCOPE: 195, CLAUSE: 2\n\nX8855 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1292 [label="1292: quot(s(s(s(0))), s(s(s(0))), s(s(s(s(s(0))))), X8855), SCOPE: 195, CLAUSE: 3\n\nX8855 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1293 [label="1293: quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X8909)\n\nX8909 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1294 [label="1294: quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X8909), SCOPE: 196, CLAUSE: 1 | quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X8909), SCOPE: 196, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X8909), SCOPE: 196, CLAUSE: 3\n\nX8909 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1295 [label="1295: quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X8909), SCOPE: 196, CLAUSE: 2 | quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X8909), SCOPE: 196, CLAUSE: 3\n\nX8909 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1296 [label="1296: quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X8909), SCOPE: 196, CLAUSE: 2\n\nX8909 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1297 [label="1297: quot(s(s(0)), s(s(0)), s(s(s(s(s(0))))), X8909), SCOPE: 196, CLAUSE: 3\n\nX8909 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1298 [label="1298: quot(s(0), s(0), s(s(s(s(s(0))))), X8963)\n\nX8963 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1299 [label="1299: quot(s(0), s(0), s(s(s(s(s(0))))), X8963), SCOPE: 197, CLAUSE: 1 | quot(s(0), s(0), s(s(s(s(s(0))))), X8963), SCOPE: 197, CLAUSE: 2 | quot(s(0), s(0), s(s(s(s(s(0))))), X8963), SCOPE: 197, CLAUSE: 3\n\nX8963 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1300 [label="1300: quot(s(0), s(0), s(s(s(s(s(0))))), X8963), SCOPE: 197, CLAUSE: 2 | quot(s(0), s(0), s(s(s(s(s(0))))), X8963), SCOPE: 197, CLAUSE: 3\n\nX8963 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1301 [label="1301: quot(s(0), s(0), s(s(s(s(s(0))))), X8963), SCOPE: 197, CLAUSE: 2\n\nX8963 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1302 [label="1302: quot(s(0), s(0), s(s(s(s(s(0))))), X8963), SCOPE: 197, CLAUSE: 3\n\nX8963 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1303 [label="1303: quot(0, 0, s(s(s(s(s(0))))), X9023)\n\nX9023 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1304 [label="1304: quot(0, 0, s(s(s(s(s(0))))), X9023), SCOPE: 198, CLAUSE: 1 | quot(0, 0, s(s(s(s(s(0))))), X9023), SCOPE: 198, CLAUSE: 2 | quot(0, 0, s(s(s(s(s(0))))), X9023), SCOPE: 198, CLAUSE: 3\n\nX9023 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1305 [label="1305: quot(0, 0, s(s(s(s(s(0))))), X9023), SCOPE: 198, CLAUSE: 2 | quot(0, 0, s(s(s(s(s(0))))), X9023), SCOPE: 198, CLAUSE: 3\n\nX9023 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1306 [label="1306: quot(0, 0, s(s(s(s(s(0))))), X9023), SCOPE: 198, CLAUSE: 3\n\nX9023 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1307 [label="1307: quot(0, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X9055)\n\nX9055 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1308 [label="1308: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1309 [label="1309: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1310 [label="1310: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1311 [label="1311: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1312 [label="1312: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1313 [label="1313: quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X9084)\n\nX9084 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1314 [label="1314: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1315 [label="1315: quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X9084), SCOPE: 199, CLAUSE: 1 | quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X9084), SCOPE: 199, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X9084), SCOPE: 199, CLAUSE: 3\n\nX9084 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1316 [label="1316: quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X9084), SCOPE: 199, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X9084), SCOPE: 199, CLAUSE: 3\n\nX9084 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1317 [label="1317: quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X9084), SCOPE: 199, CLAUSE: 2\n\nX9084 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1318 [label="1318: quot(s(s(s(s(s(0))))), s(s(s(s(0)))), s(s(s(s(0)))), X9084), SCOPE: 199, CLAUSE: 3\n\nX9084 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1319 [label="1319: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X9141)\n\nX9141 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1320 [label="1320: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X9141), SCOPE: 200, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X9141), SCOPE: 200, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X9141), SCOPE: 200, CLAUSE: 3\n\nX9141 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1321 [label="1321: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X9141), SCOPE: 200, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X9141), SCOPE: 200, CLAUSE: 3\n\nX9141 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1322 [label="1322: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X9141), SCOPE: 200, CLAUSE: 2\n\nX9141 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1323 [label="1323: quot(s(s(s(s(0)))), s(s(s(0))), s(s(s(s(0)))), X9141), SCOPE: 200, CLAUSE: 3\n\nX9141 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1324 [label="1324: quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X9195)\n\nX9195 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1325 [label="1325: quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X9195), SCOPE: 201, CLAUSE: 1 | quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X9195), SCOPE: 201, CLAUSE: 2 | quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X9195), SCOPE: 201, CLAUSE: 3\n\nX9195 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1326 [label="1326: quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X9195), SCOPE: 201, CLAUSE: 2 | quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X9195), SCOPE: 201, CLAUSE: 3\n\nX9195 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1327 [label="1327: quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X9195), SCOPE: 201, CLAUSE: 2\n\nX9195 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1328 [label="1328: quot(s(s(s(0))), s(s(0)), s(s(s(s(0)))), X9195), SCOPE: 201, CLAUSE: 3\n\nX9195 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1329 [label="1329: quot(s(s(0)), s(0), s(s(s(s(0)))), X9249)\n\nX9249 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1330 [label="1330: quot(s(s(0)), s(0), s(s(s(s(0)))), X9249), SCOPE: 202, CLAUSE: 1 | quot(s(s(0)), s(0), s(s(s(s(0)))), X9249), SCOPE: 202, CLAUSE: 2 | quot(s(s(0)), s(0), s(s(s(s(0)))), X9249), SCOPE: 202, CLAUSE: 3\n\nX9249 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1331 [label="1331: quot(s(s(0)), s(0), s(s(s(s(0)))), X9249), SCOPE: 202, CLAUSE: 2 | quot(s(s(0)), s(0), s(s(s(s(0)))), X9249), SCOPE: 202, CLAUSE: 3\n\nX9249 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1332 [label="1332: quot(s(s(0)), s(0), s(s(s(s(0)))), X9249), SCOPE: 202, CLAUSE: 2\n\nX9249 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1333 [label="1333: quot(s(s(0)), s(0), s(s(s(s(0)))), X9249), SCOPE: 202, CLAUSE: 3\n\nX9249 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1334 [label="1334: quot(s(0), 0, s(s(s(s(0)))), X9309)\n\nX9309 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1335 [label="1335: quot(s(0), 0, s(s(s(s(0)))), X9309), SCOPE: 203, CLAUSE: 1 | quot(s(0), 0, s(s(s(s(0)))), X9309), SCOPE: 203, CLAUSE: 2 | quot(s(0), 0, s(s(s(s(0)))), X9309), SCOPE: 203, CLAUSE: 3\n\nX9309 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1336 [label="1336: quot(s(0), 0, s(s(s(s(0)))), X9309), SCOPE: 203, CLAUSE: 2 | quot(s(0), 0, s(s(s(s(0)))), X9309), SCOPE: 203, CLAUSE: 3\n\nX9309 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1337 [label="1337: quot(s(0), 0, s(s(s(s(0)))), X9309), SCOPE: 203, CLAUSE: 3\n\nX9309 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1338 [label="1338: quot(s(0), s(s(s(s(0)))), s(s(s(s(0)))), X9348)\n\nX9348 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1339 [label="1339: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1340 [label="1340: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1341 [label="1341: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1342 [label="1342: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1343 [label="1343: quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X9381)\n\nX9381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1344 [label="1344: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1345 [label="1345: quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X9381), SCOPE: 204, CLAUSE: 1 | quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X9381), SCOPE: 204, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X9381), SCOPE: 204, CLAUSE: 3\n\nX9381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1346 [label="1346: quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X9381), SCOPE: 204, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X9381), SCOPE: 204, CLAUSE: 3\n\nX9381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1347 [label="1347: quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X9381), SCOPE: 204, CLAUSE: 2\n\nX9381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1348 [label="1348: quot(s(s(s(s(s(0))))), s(s(s(0))), s(s(s(0))), X9381), SCOPE: 204, CLAUSE: 3\n\nX9381 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1349 [label="1349: quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X9438)\n\nX9438 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1350 [label="1350: quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X9438), SCOPE: 205, CLAUSE: 1 | quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X9438), SCOPE: 205, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X9438), SCOPE: 205, CLAUSE: 3\n\nX9438 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1351 [label="1351: quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X9438), SCOPE: 205, CLAUSE: 2 | quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X9438), SCOPE: 205, CLAUSE: 3\n\nX9438 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1352 [label="1352: quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X9438), SCOPE: 205, CLAUSE: 2\n\nX9438 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1353 [label="1353: quot(s(s(s(s(0)))), s(s(0)), s(s(s(0))), X9438), SCOPE: 205, CLAUSE: 3\n\nX9438 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1354 [label="1354: quot(s(s(s(0))), s(0), s(s(s(0))), X9492)\n\nX9492 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1355 [label="1355: quot(s(s(s(0))), s(0), s(s(s(0))), X9492), SCOPE: 206, CLAUSE: 1 | quot(s(s(s(0))), s(0), s(s(s(0))), X9492), SCOPE: 206, CLAUSE: 2 | quot(s(s(s(0))), s(0), s(s(s(0))), X9492), SCOPE: 206, CLAUSE: 3\n\nX9492 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1356 [label="1356: quot(s(s(s(0))), s(0), s(s(s(0))), X9492), SCOPE: 206, CLAUSE: 2 | quot(s(s(s(0))), s(0), s(s(s(0))), X9492), SCOPE: 206, CLAUSE: 3\n\nX9492 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1357 [label="1357: quot(s(s(s(0))), s(0), s(s(s(0))), X9492), SCOPE: 206, CLAUSE: 2\n\nX9492 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1358 [label="1358: quot(s(s(s(0))), s(0), s(s(s(0))), X9492), SCOPE: 206, CLAUSE: 3\n\nX9492 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1359 [label="1359: quot(s(s(0)), 0, s(s(s(0))), X9552)\n\nX9552 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1360 [label="1360: quot(s(s(0)), 0, s(s(s(0))), X9552), SCOPE: 207, CLAUSE: 1 | quot(s(s(0)), 0, s(s(s(0))), X9552), SCOPE: 207, CLAUSE: 2 | quot(s(s(0)), 0, s(s(s(0))), X9552), SCOPE: 207, CLAUSE: 3\n\nX9552 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1361 [label="1361: quot(s(s(0)), 0, s(s(s(0))), X9552), SCOPE: 207, CLAUSE: 2 | quot(s(s(0)), 0, s(s(s(0))), X9552), SCOPE: 207, CLAUSE: 3\n\nX9552 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1362 [label="1362: quot(s(s(0)), 0, s(s(s(0))), X9552), SCOPE: 207, CLAUSE: 3\n\nX9552 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1363 [label="1363: quot(s(s(0)), s(s(s(0))), s(s(s(0))), X9591)\n\nX9591 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1364 [label="1364: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1365 [label="1365: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1366 [label="1366: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1367 [label="1367: quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X9621)\n\nX9621 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1368 [label="1368: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1369 [label="1369: quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X9621), SCOPE: 208, CLAUSE: 1 | quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X9621), SCOPE: 208, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X9621), SCOPE: 208, CLAUSE: 3\n\nX9621 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1370 [label="1370: quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X9621), SCOPE: 208, CLAUSE: 2 | quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X9621), SCOPE: 208, CLAUSE: 3\n\nX9621 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1371 [label="1371: quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X9621), SCOPE: 208, CLAUSE: 2\n\nX9621 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1372 [label="1372: quot(s(s(s(s(s(0))))), s(s(0)), s(s(0)), X9621), SCOPE: 208, CLAUSE: 3\n\nX9621 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1373 [label="1373: quot(s(s(s(s(0)))), s(0), s(s(0)), X9678)\n\nX9678 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1374 [label="1374: quot(s(s(s(s(0)))), s(0), s(s(0)), X9678), SCOPE: 209, CLAUSE: 1 | quot(s(s(s(s(0)))), s(0), s(s(0)), X9678), SCOPE: 209, CLAUSE: 2 | quot(s(s(s(s(0)))), s(0), s(s(0)), X9678), SCOPE: 209, CLAUSE: 3\n\nX9678 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1375 [label="1375: quot(s(s(s(s(0)))), s(0), s(s(0)), X9678), SCOPE: 209, CLAUSE: 2 | quot(s(s(s(s(0)))), s(0), s(s(0)), X9678), SCOPE: 209, CLAUSE: 3\n\nX9678 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1376 [label="1376: quot(s(s(s(s(0)))), s(0), s(s(0)), X9678), SCOPE: 209, CLAUSE: 2\n\nX9678 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1377 [label="1377: quot(s(s(s(s(0)))), s(0), s(s(0)), X9678), SCOPE: 209, CLAUSE: 3\n\nX9678 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1378 [label="1378: quot(s(s(s(0))), 0, s(s(0)), X9738)\n\nX9738 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1379 [label="1379: quot(s(s(s(0))), 0, s(s(0)), X9738), SCOPE: 210, CLAUSE: 1 | quot(s(s(s(0))), 0, s(s(0)), X9738), SCOPE: 210, CLAUSE: 2 | quot(s(s(s(0))), 0, s(s(0)), X9738), SCOPE: 210, CLAUSE: 3\n\nX9738 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1380 [label="1380: quot(s(s(s(0))), 0, s(s(0)), X9738), SCOPE: 210, CLAUSE: 2 | quot(s(s(s(0))), 0, s(s(0)), X9738), SCOPE: 210, CLAUSE: 3\n\nX9738 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1381 [label="1381: quot(s(s(s(0))), 0, s(s(0)), X9738), SCOPE: 210, CLAUSE: 3\n\nX9738 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1382 [label="1382: quot(s(s(s(0))), s(s(0)), s(s(0)), X9777)\n\nX9777 is free", fontsize=16, style=filled, fillcolor=lightyellow];
1383 [label="1383: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1384 [label="1384: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1385 [label="1385: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1386 [label="1386: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1387 [label="1387: times(T905, s(s(T903)), X7203)\n\nT903 is ground\nT905 is ground\nX7203 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1388 [label="1388: neq(s(s(s(s(s(s(s(T903))))))), T1092)\n\nT903 is ground\nT1092 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1389 [label="1389: pr(s(s(s(s(s(s(s(T897))))))), s(T897)), SCOPE: 211, CLAUSE: 5 | pr(s(s(s(s(s(s(s(T897))))))), s(T897)), SCOPE: 211, CLAUSE: 6\n\nT897 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1390 [label="1390: pr(s(s(s(s(s(s(s(T897))))))), s(T897)), SCOPE: 211, CLAUSE: 5\n\nT897 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1391 [label="1391: pr(s(s(s(s(s(s(s(T897))))))), s(T897)), SCOPE: 211, CLAUSE: 6\n\nT897 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1392 [label="1392: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1393 [label="1393: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1394 [label="1394: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1395 [label="1395: ','(not_divides(s(s(T1109)), s(s(s(s(s(s(s(s(T1109))))))))), pr(s(s(s(s(s(s(s(s(T1109)))))))), s(T1109)))\n\nT1109 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1396 [label="1396: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1397 [label="1397: ','(not_divides(s(s(T1109)), s(T1111)), pr(s(T1111), s(T1109)))\n\nT1109 is ground\nT1111 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1398 [label="1398: not_divides(s(s(T1109)), s(T1111))\n\nT1109 is ground\nT1111 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1399 [label="1399: pr(s(T1111), s(T1109))\n\nT1109 is ground\nT1111 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1400 [label="1400: not_divides(s(s(T1109)), s(T1111)), SCOPE: 212, CLAUSE: 7\n\nT1109 is ground\nT1111 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1401 [label="1401: ','(div(s(T1123), s(s(T1122)), X9845), ','(times(X9845, s(s(T1122)), X9846), neq(s(T1123), X9846)))\n\nT1122 is ground\nT1123 is ground\nX9845 is free; \nX9846 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1402 [label="1402: div(s(T1123), s(s(T1122)), X9845)\n\nT1122 is ground\nT1123 is ground\nX9845 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1403 [label="1403: ','(times(T1126, s(s(T1122)), X9846), neq(s(T1123), X9846))\n\nT1122 is ground\nT1123 is ground\nT1126 is ground\nX9846 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1404 [label="1404: div(s(T1123), s(s(T1122)), X9845), SCOPE: 213, CLAUSE: 0\n\nT1122 is ground\nT1123 is ground\nX9845 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1405 [label="1405: quot(s(T1135), s(s(T1136)), s(s(T1136)), X9875)\n\nT1135 is ground\nT1136 is ground\nX9875 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1406 [label="1406: quot(s(T1135), s(s(T1136)), s(s(T1136)), X9875), SCOPE: 214, CLAUSE: 1 | quot(s(T1135), s(s(T1136)), s(s(T1136)), X9875), SCOPE: 214, CLAUSE: 2 | quot(s(T1135), s(s(T1136)), s(s(T1136)), X9875), SCOPE: 214, CLAUSE: 3\n\nT1135 is ground\nT1136 is ground\nX9875 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1407 [label="1407: quot(s(T1135), s(s(T1136)), s(s(T1136)), X9875), SCOPE: 214, CLAUSE: 2 | quot(s(T1135), s(s(T1136)), s(s(T1136)), X9875), SCOPE: 214, CLAUSE: 3\n\nT1135 is ground\nT1136 is ground\nX9875 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1408 [label="1408: quot(s(T1135), s(s(T1136)), s(s(T1136)), X9875), SCOPE: 214, CLAUSE: 2\n\nT1135 is ground\nT1136 is ground\nX9875 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1409 [label="1409: quot(s(T1135), s(s(T1136)), s(s(T1136)), X9875), SCOPE: 214, CLAUSE: 3\n\nT1135 is ground\nT1136 is ground\nX9875 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1410 [label="1410: quot(T1151, s(T1152), s(s(T1152)), X9919)\n\nT1151 is ground\nT1152 is ground\nX9919 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1411 [label="1411: quot(T1151, s(T1152), s(s(T1152)), X9919), SCOPE: 215, CLAUSE: 1 | quot(T1151, s(T1152), s(s(T1152)), X9919), SCOPE: 215, CLAUSE: 2 | quot(T1151, s(T1152), s(s(T1152)), X9919), SCOPE: 215, CLAUSE: 3\n\nT1151 is ground\nT1152 is ground\nX9919 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1412 [label="1412: quot(T1151, s(T1152), s(s(T1152)), X9919), SCOPE: 215, CLAUSE: 1\n\nT1151 is ground\nT1152 is ground\nX9919 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1413 [label="1413: quot(T1151, s(T1152), s(s(T1152)), X9919), SCOPE: 215, CLAUSE: 2 | quot(T1151, s(T1152), s(s(T1152)), X9919), SCOPE: 215, CLAUSE: 3\n\nT1151 is ground\nT1152 is ground\nX9919 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1414 [label="1414: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1415 [label="1415: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1416 [label="1416: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1417 [label="1417: quot(T1151, s(T1152), s(s(T1152)), X9919), SCOPE: 215, CLAUSE: 2\n\nT1151 is ground\nT1152 is ground\nX9919 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1418 [label="1418: quot(T1151, s(T1152), s(s(T1152)), X9919), SCOPE: 215, CLAUSE: 3\n\nT1151 is ground\nT1152 is ground\nX9919 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1419 [label="1419: quot(T1168, T1169, s(s(T1169)), X9960)\n\nT1168 is ground\nT1169 is ground\nX9960 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1420 [label="1420: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1421 [label="1421: quot(T1168, T1169, s(s(T1169)), X9960), SCOPE: 216, CLAUSE: 1 | quot(T1168, T1169, s(s(T1169)), X9960), SCOPE: 216, CLAUSE: 2 | quot(T1168, T1169, s(s(T1169)), X9960), SCOPE: 216, CLAUSE: 3\n\nT1168 is ground\nT1169 is ground\nX9960 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1422 [label="1422: quot(T1168, T1169, s(s(T1169)), X9960), SCOPE: 216, CLAUSE: 1\n\nT1168 is ground\nT1169 is ground\nX9960 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1423 [label="1423: quot(T1168, T1169, s(s(T1169)), X9960), SCOPE: 216, CLAUSE: 2 | quot(T1168, T1169, s(s(T1169)), X9960), SCOPE: 216, CLAUSE: 3\n\nT1168 is ground\nT1169 is ground\nX9960 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1424 [label="1424: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1425 [label="1425: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1426 [label="1426: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1427 [label="1427: quot(T1168, T1169, s(s(T1169)), X9960), SCOPE: 216, CLAUSE: 2\n\nT1168 is ground\nT1169 is ground\nX9960 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1428 [label="1428: quot(T1168, T1169, s(s(T1169)), X9960), SCOPE: 216, CLAUSE: 3\n\nT1168 is ground\nT1169 is ground\nX9960 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1429 [label="1429: quot(T1185, T1186, s(s(s(T1186))), X10005)\n\nT1185 is ground\nT1186 is ground\nX10005 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1430 [label="1430: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1431 [label="1431: quot(T1185, T1186, s(s(s(T1186))), X10005), SCOPE: 217, CLAUSE: 1 | quot(T1185, T1186, s(s(s(T1186))), X10005), SCOPE: 217, CLAUSE: 2 | quot(T1185, T1186, s(s(s(T1186))), X10005), SCOPE: 217, CLAUSE: 3\n\nT1185 is ground\nT1186 is ground\nX10005 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1432 [label="1432: quot(T1185, T1186, s(s(s(T1186))), X10005), SCOPE: 217, CLAUSE: 1\n\nT1185 is ground\nT1186 is ground\nX10005 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1433 [label="1433: quot(T1185, T1186, s(s(s(T1186))), X10005), SCOPE: 217, CLAUSE: 2 | quot(T1185, T1186, s(s(s(T1186))), X10005), SCOPE: 217, CLAUSE: 3\n\nT1185 is ground\nT1186 is ground\nX10005 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1434 [label="1434: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1435 [label="1435: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1436 [label="1436: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1437 [label="1437: quot(T1185, T1186, s(s(s(T1186))), X10005), SCOPE: 217, CLAUSE: 2\n\nT1185 is ground\nT1186 is ground\nX10005 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1438 [label="1438: quot(T1185, T1186, s(s(s(T1186))), X10005), SCOPE: 217, CLAUSE: 3\n\nT1185 is ground\nT1186 is ground\nX10005 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1439 [label="1439: quot(T1202, T1203, s(s(s(s(T1203)))), X10050)\n\nT1202 is ground\nT1203 is ground\nX10050 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1440 [label="1440: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1441 [label="1441: quot(T1202, T1203, s(s(s(s(T1203)))), X10050), SCOPE: 218, CLAUSE: 1 | quot(T1202, T1203, s(s(s(s(T1203)))), X10050), SCOPE: 218, CLAUSE: 2 | quot(T1202, T1203, s(s(s(s(T1203)))), X10050), SCOPE: 218, CLAUSE: 3\n\nT1202 is ground\nT1203 is ground\nX10050 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1442 [label="1442: quot(T1202, T1203, s(s(s(s(T1203)))), X10050), SCOPE: 218, CLAUSE: 1\n\nT1202 is ground\nT1203 is ground\nX10050 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1443 [label="1443: quot(T1202, T1203, s(s(s(s(T1203)))), X10050), SCOPE: 218, CLAUSE: 2 | quot(T1202, T1203, s(s(s(s(T1203)))), X10050), SCOPE: 218, CLAUSE: 3\n\nT1202 is ground\nT1203 is ground\nX10050 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1444 [label="1444: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1445 [label="1445: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1446 [label="1446: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1447 [label="1447: quot(T1202, T1203, s(s(s(s(T1203)))), X10050), SCOPE: 218, CLAUSE: 2\n\nT1202 is ground\nT1203 is ground\nX10050 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1448 [label="1448: quot(T1202, T1203, s(s(s(s(T1203)))), X10050), SCOPE: 218, CLAUSE: 3\n\nT1202 is ground\nT1203 is ground\nX10050 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1449 [label="1449: quot(T1219, T1220, s(s(s(s(s(T1220))))), X10095)\n\nT1219 is ground\nT1220 is ground\nX10095 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1450 [label="1450: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1451 [label="1451: quot(T1219, T1220, s(s(s(s(s(T1220))))), X10095), SCOPE: 219, CLAUSE: 1 | quot(T1219, T1220, s(s(s(s(s(T1220))))), X10095), SCOPE: 219, CLAUSE: 2 | quot(T1219, T1220, s(s(s(s(s(T1220))))), X10095), SCOPE: 219, CLAUSE: 3\n\nT1219 is ground\nT1220 is ground\nX10095 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1452 [label="1452: quot(T1219, T1220, s(s(s(s(s(T1220))))), X10095), SCOPE: 219, CLAUSE: 1\n\nT1219 is ground\nT1220 is ground\nX10095 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1453 [label="1453: quot(T1219, T1220, s(s(s(s(s(T1220))))), X10095), SCOPE: 219, CLAUSE: 2 | quot(T1219, T1220, s(s(s(s(s(T1220))))), X10095), SCOPE: 219, CLAUSE: 3\n\nT1219 is ground\nT1220 is ground\nX10095 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1454 [label="1454: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1455 [label="1455: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1456 [label="1456: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1457 [label="1457: quot(T1219, T1220, s(s(s(s(s(T1220))))), X10095), SCOPE: 219, CLAUSE: 2\n\nT1219 is ground\nT1220 is ground\nX10095 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1458 [label="1458: quot(T1219, T1220, s(s(s(s(s(T1220))))), X10095), SCOPE: 219, CLAUSE: 3\n\nT1219 is ground\nT1220 is ground\nX10095 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1459 [label="1459: quot(T1236, T1237, s(s(s(s(s(s(T1237)))))), X10140)\n\nT1236 is ground\nT1237 is ground\nX10140 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1460 [label="1460: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1461 [label="1461: quot(T1236, T1237, s(s(s(s(s(s(T1237)))))), X10140), SCOPE: 220, CLAUSE: 1 | quot(T1236, T1237, s(s(s(s(s(s(T1237)))))), X10140), SCOPE: 220, CLAUSE: 2 | quot(T1236, T1237, s(s(s(s(s(s(T1237)))))), X10140), SCOPE: 220, CLAUSE: 3\n\nT1236 is ground\nT1237 is ground\nX10140 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1462 [label="1462: quot(T1236, T1237, s(s(s(s(s(s(T1237)))))), X10140), SCOPE: 220, CLAUSE: 1\n\nT1236 is ground\nT1237 is ground\nX10140 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1463 [label="1463: quot(T1236, T1237, s(s(s(s(s(s(T1237)))))), X10140), SCOPE: 220, CLAUSE: 2 | quot(T1236, T1237, s(s(s(s(s(s(T1237)))))), X10140), SCOPE: 220, CLAUSE: 3\n\nT1236 is ground\nT1237 is ground\nX10140 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1464 [label="1464: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1465 [label="1465: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1466 [label="1466: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1467 [label="1467: quot(T1236, T1237, s(s(s(s(s(s(T1237)))))), X10140), SCOPE: 220, CLAUSE: 2\n\nT1236 is ground\nT1237 is ground\nX10140 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1468 [label="1468: quot(T1236, T1237, s(s(s(s(s(s(T1237)))))), X10140), SCOPE: 220, CLAUSE: 3\n\nT1236 is ground\nT1237 is ground\nX10140 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1469 [label="1469: quot(T1253, T1254, s(s(s(s(s(s(s(T1254))))))), X10185)\n\nT1253 is ground\nT1254 is ground\nX10185 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1470 [label="1470: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1471 [label="1471: quot(T1253, T1254, s(s(s(s(s(s(s(T1254))))))), X10185), SCOPE: 221, CLAUSE: 1 | quot(T1253, T1254, s(s(s(s(s(s(s(T1254))))))), X10185), SCOPE: 221, CLAUSE: 2 | quot(T1253, T1254, s(s(s(s(s(s(s(T1254))))))), X10185), SCOPE: 221, CLAUSE: 3\n\nT1253 is ground\nT1254 is ground\nX10185 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1472 [label="1472: quot(T1253, T1254, s(s(s(s(s(s(s(T1254))))))), X10185), SCOPE: 221, CLAUSE: 1\n\nT1253 is ground\nT1254 is ground\nX10185 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1473 [label="1473: quot(T1253, T1254, s(s(s(s(s(s(s(T1254))))))), X10185), SCOPE: 221, CLAUSE: 2 | quot(T1253, T1254, s(s(s(s(s(s(s(T1254))))))), X10185), SCOPE: 221, CLAUSE: 3\n\nT1253 is ground\nT1254 is ground\nX10185 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1474 [label="1474: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1475 [label="1475: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1476 [label="1476: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1477 [label="1477: quot(T1253, T1254, s(s(s(s(s(s(s(T1254))))))), X10185), SCOPE: 221, CLAUSE: 2\n\nT1253 is ground\nT1254 is ground\nX10185 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1478 [label="1478: quot(T1253, T1254, s(s(s(s(s(s(s(T1254))))))), X10185), SCOPE: 221, CLAUSE: 3\n\nT1253 is ground\nT1254 is ground\nX10185 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1479 [label="1479: quot(T1270, T1271, s(s(s(s(s(s(s(s(T1271)))))))), X10230)\n\nT1270 is ground\nT1271 is ground\nX10230 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1480 [label="1480: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1481 [label="1481: quot(T1270, T1271, s(T1274), X10230)\n\nT1270 is ground\nT1271 is ground\nT1274 is ground\nX10230 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1482 [label="1482: quot(T1270, T1271, s(T1274), X10230), SCOPE: 222, CLAUSE: 1 | quot(T1270, T1271, s(T1274), X10230), SCOPE: 222, CLAUSE: 2 | quot(T1270, T1271, s(T1274), X10230), SCOPE: 222, CLAUSE: 3\n\nT1270 is ground\nT1271 is ground\nT1274 is ground\nX10230 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1483 [label="1483: quot(T1270, T1271, s(T1274), X10230), SCOPE: 222, CLAUSE: 1\n\nT1270 is ground\nT1271 is ground\nT1274 is ground\nX10230 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1484 [label="1484: quot(T1270, T1271, s(T1274), X10230), SCOPE: 222, CLAUSE: 2 | quot(T1270, T1271, s(T1274), X10230), SCOPE: 222, CLAUSE: 3\n\nT1270 is ground\nT1271 is ground\nT1274 is ground\nX10230 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1485 [label="1485: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1486 [label="1486: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1487 [label="1487: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1488 [label="1488: quot(T1270, T1271, s(T1274), X10230), SCOPE: 222, CLAUSE: 2\n\nT1270 is ground\nT1271 is ground\nT1274 is ground\nX10230 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1489 [label="1489: quot(T1270, T1271, s(T1274), X10230), SCOPE: 222, CLAUSE: 3\n\nT1270 is ground\nT1271 is ground\nT1274 is ground\nX10230 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1490 [label="1490: quot(T1301, T1302, s(T1303), X10279)\n\nT1301 is ground\nT1302 is ground\nT1303 is ground\nX10279 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1491 [label="1491: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1492 [label="1492: quot(T1312, s(T1313), s(T1313), X10299)\n\nT1312 is ground\nT1313 is ground\nX10299 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1493 [label="1493: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1494 [label="1494: quot(T1312, s(T1313), s(T1313), X10299), SCOPE: 223, CLAUSE: 1 | quot(T1312, s(T1313), s(T1313), X10299), SCOPE: 223, CLAUSE: 2 | quot(T1312, s(T1313), s(T1313), X10299), SCOPE: 223, CLAUSE: 3\n\nT1312 is ground\nT1313 is ground\nX10299 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1495 [label="1495: quot(T1312, s(T1313), s(T1313), X10299), SCOPE: 223, CLAUSE: 1\n\nT1312 is ground\nT1313 is ground\nX10299 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1496 [label="1496: quot(T1312, s(T1313), s(T1313), X10299), SCOPE: 223, CLAUSE: 2 | quot(T1312, s(T1313), s(T1313), X10299), SCOPE: 223, CLAUSE: 3\n\nT1312 is ground\nT1313 is ground\nX10299 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1497 [label="1497: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1498 [label="1498: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1499 [label="1499: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1500 [label="1500: quot(T1312, s(T1313), s(T1313), X10299), SCOPE: 223, CLAUSE: 2\n\nT1312 is ground\nT1313 is ground\nX10299 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1501 [label="1501: quot(T1312, s(T1313), s(T1313), X10299), SCOPE: 223, CLAUSE: 3\n\nT1312 is ground\nT1313 is ground\nX10299 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1502 [label="1502: quot(T1329, T1330, s(T1330), X10343)\n\nT1329 is ground\nT1330 is ground\nX10343 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1503 [label="1503: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1504 [label="1504: quot(T1329, T1330, s(T1330), X10343), SCOPE: 224, CLAUSE: 1 | quot(T1329, T1330, s(T1330), X10343), SCOPE: 224, CLAUSE: 2 | quot(T1329, T1330, s(T1330), X10343), SCOPE: 224, CLAUSE: 3\n\nT1329 is ground\nT1330 is ground\nX10343 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1505 [label="1505: quot(T1329, T1330, s(T1330), X10343), SCOPE: 224, CLAUSE: 1\n\nT1329 is ground\nT1330 is ground\nX10343 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1506 [label="1506: quot(T1329, T1330, s(T1330), X10343), SCOPE: 224, CLAUSE: 2 | quot(T1329, T1330, s(T1330), X10343), SCOPE: 224, CLAUSE: 3\n\nT1329 is ground\nT1330 is ground\nX10343 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1507 [label="1507: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1508 [label="1508: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1509 [label="1509: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1510 [label="1510: quot(T1329, T1330, s(T1330), X10343), SCOPE: 224, CLAUSE: 2\n\nT1329 is ground\nT1330 is ground\nX10343 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1511 [label="1511: quot(T1329, T1330, s(T1330), X10343), SCOPE: 224, CLAUSE: 3\n\nT1329 is ground\nT1330 is ground\nX10343 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1512 [label="1512: quot(T1346, T1347, s(s(T1347)), X10388)\n\nT1346 is ground\nT1347 is ground\nX10388 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1513 [label="1513: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1514 [label="1514: quot(T1352, s(0), s(0), X10408)\n\nT1352 is ground\nX10408 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1515 [label="1515: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1516 [label="1516: quot(T1352, s(0), s(0), X10408), SCOPE: 225, CLAUSE: 1 | quot(T1352, s(0), s(0), X10408), SCOPE: 225, CLAUSE: 2 | quot(T1352, s(0), s(0), X10408), SCOPE: 225, CLAUSE: 3\n\nT1352 is ground\nX10408 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1517 [label="1517: quot(T1352, s(0), s(0), X10408), SCOPE: 225, CLAUSE: 1\n\nT1352 is ground\nX10408 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1518 [label="1518: quot(T1352, s(0), s(0), X10408), SCOPE: 225, CLAUSE: 2 | quot(T1352, s(0), s(0), X10408), SCOPE: 225, CLAUSE: 3\n\nT1352 is ground\nX10408 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1519 [label="1519: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1520 [label="1520: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1521 [label="1521: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1522 [label="1522: quot(T1352, s(0), s(0), X10408), SCOPE: 225, CLAUSE: 2\n\nT1352 is ground\nX10408 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1523 [label="1523: quot(T1352, s(0), s(0), X10408), SCOPE: 225, CLAUSE: 3\n\nT1352 is ground\nX10408 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1524 [label="1524: quot(T1357, 0, s(0), X10452)\n\nT1357 is ground\nX10452 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1525 [label="1525: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1526 [label="1526: quot(T1357, 0, s(0), X10452), SCOPE: 226, CLAUSE: 1 | quot(T1357, 0, s(0), X10452), SCOPE: 226, CLAUSE: 2 | quot(T1357, 0, s(0), X10452), SCOPE: 226, CLAUSE: 3\n\nT1357 is ground\nX10452 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1527 [label="1527: quot(T1357, 0, s(0), X10452), SCOPE: 226, CLAUSE: 2 | quot(T1357, 0, s(0), X10452), SCOPE: 226, CLAUSE: 3\n\nT1357 is ground\nX10452 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1528 [label="1528: quot(T1357, 0, s(0), X10452), SCOPE: 226, CLAUSE: 3\n\nT1357 is ground\nX10452 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1529 [label="1529: quot(T1363, s(0), s(0), X10490)\n\nT1363 is ground\nX10490 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1530 [label="1530: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1531 [label="1531: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1532 [label="1532: quot(T1368, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X10512)\n\nT1368 is ground\nX10512 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1533 [label="1533: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1534 [label="1534: quot(T1368, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X10512), SCOPE: 227, CLAUSE: 1 | quot(T1368, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X10512), SCOPE: 227, CLAUSE: 2 | quot(T1368, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X10512), SCOPE: 227, CLAUSE: 3\n\nT1368 is ground\nX10512 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1535 [label="1535: quot(T1368, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X10512), SCOPE: 227, CLAUSE: 1\n\nT1368 is ground\nX10512 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1536 [label="1536: quot(T1368, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X10512), SCOPE: 227, CLAUSE: 2 | quot(T1368, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X10512), SCOPE: 227, CLAUSE: 3\n\nT1368 is ground\nX10512 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1537 [label="1537: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1538 [label="1538: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1539 [label="1539: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1540 [label="1540: quot(T1368, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X10512), SCOPE: 227, CLAUSE: 2\n\nT1368 is ground\nX10512 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1541 [label="1541: quot(T1368, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X10512), SCOPE: 227, CLAUSE: 3\n\nT1368 is ground\nX10512 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1542 [label="1542: quot(T1373, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X10556)\n\nT1373 is ground\nX10556 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1543 [label="1543: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1544 [label="1544: quot(T1373, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X10556), SCOPE: 228, CLAUSE: 1 | quot(T1373, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X10556), SCOPE: 228, CLAUSE: 2 | quot(T1373, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X10556), SCOPE: 228, CLAUSE: 3\n\nT1373 is ground\nX10556 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1545 [label="1545: quot(T1373, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X10556), SCOPE: 228, CLAUSE: 1\n\nT1373 is ground\nX10556 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1546 [label="1546: quot(T1373, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X10556), SCOPE: 228, CLAUSE: 2 | quot(T1373, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X10556), SCOPE: 228, CLAUSE: 3\n\nT1373 is ground\nX10556 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1547 [label="1547: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1548 [label="1548: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1549 [label="1549: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1550 [label="1550: quot(T1373, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X10556), SCOPE: 228, CLAUSE: 2\n\nT1373 is ground\nX10556 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1551 [label="1551: quot(T1373, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), X10556), SCOPE: 228, CLAUSE: 3\n\nT1373 is ground\nX10556 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1552 [label="1552: quot(T1378, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X10601)\n\nT1378 is ground\nX10601 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1553 [label="1553: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1554 [label="1554: quot(T1378, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X10601), SCOPE: 229, CLAUSE: 1 | quot(T1378, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X10601), SCOPE: 229, CLAUSE: 2 | quot(T1378, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X10601), SCOPE: 229, CLAUSE: 3\n\nT1378 is ground\nX10601 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1555 [label="1555: quot(T1378, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X10601), SCOPE: 229, CLAUSE: 1\n\nT1378 is ground\nX10601 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1556 [label="1556: quot(T1378, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X10601), SCOPE: 229, CLAUSE: 2 | quot(T1378, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X10601), SCOPE: 229, CLAUSE: 3\n\nT1378 is ground\nX10601 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1557 [label="1557: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1558 [label="1558: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1559 [label="1559: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1560 [label="1560: quot(T1378, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X10601), SCOPE: 229, CLAUSE: 2\n\nT1378 is ground\nX10601 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1561 [label="1561: quot(T1378, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), X10601), SCOPE: 229, CLAUSE: 3\n\nT1378 is ground\nX10601 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1562 [label="1562: quot(T1383, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X10646)\n\nT1383 is ground\nX10646 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1563 [label="1563: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1564 [label="1564: quot(T1383, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X10646), SCOPE: 230, CLAUSE: 1 | quot(T1383, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X10646), SCOPE: 230, CLAUSE: 2 | quot(T1383, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X10646), SCOPE: 230, CLAUSE: 3\n\nT1383 is ground\nX10646 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1565 [label="1565: quot(T1383, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X10646), SCOPE: 230, CLAUSE: 1\n\nT1383 is ground\nX10646 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1566 [label="1566: quot(T1383, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X10646), SCOPE: 230, CLAUSE: 2 | quot(T1383, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X10646), SCOPE: 230, CLAUSE: 3\n\nT1383 is ground\nX10646 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1567 [label="1567: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1568 [label="1568: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1569 [label="1569: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1570 [label="1570: quot(T1383, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X10646), SCOPE: 230, CLAUSE: 2\n\nT1383 is ground\nX10646 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1571 [label="1571: quot(T1383, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), X10646), SCOPE: 230, CLAUSE: 3\n\nT1383 is ground\nX10646 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1572 [label="1572: quot(T1388, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X10691)\n\nT1388 is ground\nX10691 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1573 [label="1573: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1574 [label="1574: quot(T1388, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X10691), SCOPE: 231, CLAUSE: 1 | quot(T1388, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X10691), SCOPE: 231, CLAUSE: 2 | quot(T1388, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X10691), SCOPE: 231, CLAUSE: 3\n\nT1388 is ground\nX10691 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1575 [label="1575: quot(T1388, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X10691), SCOPE: 231, CLAUSE: 1\n\nT1388 is ground\nX10691 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1576 [label="1576: quot(T1388, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X10691), SCOPE: 231, CLAUSE: 2 | quot(T1388, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X10691), SCOPE: 231, CLAUSE: 3\n\nT1388 is ground\nX10691 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1577 [label="1577: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1578 [label="1578: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1579 [label="1579: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1580 [label="1580: quot(T1388, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X10691), SCOPE: 231, CLAUSE: 2\n\nT1388 is ground\nX10691 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1581 [label="1581: quot(T1388, s(s(s(0))), s(s(s(s(s(s(s(0))))))), X10691), SCOPE: 231, CLAUSE: 3\n\nT1388 is ground\nX10691 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1582 [label="1582: quot(T1393, s(s(0)), s(s(s(s(s(s(s(0))))))), X10736)\n\nT1393 is ground\nX10736 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1583 [label="1583: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1584 [label="1584: quot(T1393, s(s(0)), s(s(s(s(s(s(s(0))))))), X10736), SCOPE: 232, CLAUSE: 1 | quot(T1393, s(s(0)), s(s(s(s(s(s(s(0))))))), X10736), SCOPE: 232, CLAUSE: 2 | quot(T1393, s(s(0)), s(s(s(s(s(s(s(0))))))), X10736), SCOPE: 232, CLAUSE: 3\n\nT1393 is ground\nX10736 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1585 [label="1585: quot(T1393, s(s(0)), s(s(s(s(s(s(s(0))))))), X10736), SCOPE: 232, CLAUSE: 1\n\nT1393 is ground\nX10736 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1586 [label="1586: quot(T1393, s(s(0)), s(s(s(s(s(s(s(0))))))), X10736), SCOPE: 232, CLAUSE: 2 | quot(T1393, s(s(0)), s(s(s(s(s(s(s(0))))))), X10736), SCOPE: 232, CLAUSE: 3\n\nT1393 is ground\nX10736 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1587 [label="1587: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1588 [label="1588: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1589 [label="1589: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1590 [label="1590: quot(T1393, s(s(0)), s(s(s(s(s(s(s(0))))))), X10736), SCOPE: 232, CLAUSE: 2\n\nT1393 is ground\nX10736 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1591 [label="1591: quot(T1393, s(s(0)), s(s(s(s(s(s(s(0))))))), X10736), SCOPE: 232, CLAUSE: 3\n\nT1393 is ground\nX10736 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1592 [label="1592: quot(T1398, s(0), s(s(s(s(s(s(s(0))))))), X10781)\n\nT1398 is ground\nX10781 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1593 [label="1593: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1594 [label="1594: quot(T1398, s(0), s(s(s(s(s(s(s(0))))))), X10781), SCOPE: 233, CLAUSE: 1 | quot(T1398, s(0), s(s(s(s(s(s(s(0))))))), X10781), SCOPE: 233, CLAUSE: 2 | quot(T1398, s(0), s(s(s(s(s(s(s(0))))))), X10781), SCOPE: 233, CLAUSE: 3\n\nT1398 is ground\nX10781 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1595 [label="1595: quot(T1398, s(0), s(s(s(s(s(s(s(0))))))), X10781), SCOPE: 233, CLAUSE: 1\n\nT1398 is ground\nX10781 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1596 [label="1596: quot(T1398, s(0), s(s(s(s(s(s(s(0))))))), X10781), SCOPE: 233, CLAUSE: 2 | quot(T1398, s(0), s(s(s(s(s(s(s(0))))))), X10781), SCOPE: 233, CLAUSE: 3\n\nT1398 is ground\nX10781 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1597 [label="1597: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1598 [label="1598: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1599 [label="1599: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1600 [label="1600: quot(T1398, s(0), s(s(s(s(s(s(s(0))))))), X10781), SCOPE: 233, CLAUSE: 2\n\nT1398 is ground\nX10781 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1601 [label="1601: quot(T1398, s(0), s(s(s(s(s(s(s(0))))))), X10781), SCOPE: 233, CLAUSE: 3\n\nT1398 is ground\nX10781 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1602 [label="1602: quot(T1403, 0, s(s(s(s(s(s(s(0))))))), X10826)\n\nT1403 is ground\nX10826 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1603 [label="1603: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1604 [label="1604: quot(T1403, 0, s(s(s(s(s(s(s(0))))))), X10826), SCOPE: 234, CLAUSE: 1 | quot(T1403, 0, s(s(s(s(s(s(s(0))))))), X10826), SCOPE: 234, CLAUSE: 2 | quot(T1403, 0, s(s(s(s(s(s(s(0))))))), X10826), SCOPE: 234, CLAUSE: 3\n\nT1403 is ground\nX10826 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1605 [label="1605: quot(T1403, 0, s(s(s(s(s(s(s(0))))))), X10826), SCOPE: 234, CLAUSE: 2 | quot(T1403, 0, s(s(s(s(s(s(s(0))))))), X10826), SCOPE: 234, CLAUSE: 3\n\nT1403 is ground\nX10826 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1606 [label="1606: quot(T1403, 0, s(s(s(s(s(s(s(0))))))), X10826), SCOPE: 234, CLAUSE: 3\n\nT1403 is ground\nX10826 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1607 [label="1607: quot(T1409, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), X10864)\n\nT1409 is ground\nX10864 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1608 [label="1608: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1609 [label="1609: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1610 [label="1610: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1611 [label="1611: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1612 [label="1612: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1613 [label="1613: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1614 [label="1614: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1615 [label="1615: quot(T1419, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X10901)\n\nT1419 is ground\nX10901 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1616 [label="1616: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1617 [label="1617: quot(T1419, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X10901), SCOPE: 235, CLAUSE: 1 | quot(T1419, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X10901), SCOPE: 235, CLAUSE: 2 | quot(T1419, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X10901), SCOPE: 235, CLAUSE: 3\n\nT1419 is ground\nX10901 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1618 [label="1618: quot(T1419, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X10901), SCOPE: 235, CLAUSE: 1\n\nT1419 is ground\nX10901 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1619 [label="1619: quot(T1419, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X10901), SCOPE: 235, CLAUSE: 2 | quot(T1419, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X10901), SCOPE: 235, CLAUSE: 3\n\nT1419 is ground\nX10901 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1620 [label="1620: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1621 [label="1621: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1622 [label="1622: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1623 [label="1623: quot(T1419, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X10901), SCOPE: 235, CLAUSE: 2\n\nT1419 is ground\nX10901 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1624 [label="1624: quot(T1419, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X10901), SCOPE: 235, CLAUSE: 3\n\nT1419 is ground\nX10901 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1625 [label="1625: quot(T1424, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X10945)\n\nT1424 is ground\nX10945 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1626 [label="1626: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1627 [label="1627: quot(T1424, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X10945), SCOPE: 236, CLAUSE: 1 | quot(T1424, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X10945), SCOPE: 236, CLAUSE: 2 | quot(T1424, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X10945), SCOPE: 236, CLAUSE: 3\n\nT1424 is ground\nX10945 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1628 [label="1628: quot(T1424, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X10945), SCOPE: 236, CLAUSE: 1\n\nT1424 is ground\nX10945 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1629 [label="1629: quot(T1424, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X10945), SCOPE: 236, CLAUSE: 2 | quot(T1424, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X10945), SCOPE: 236, CLAUSE: 3\n\nT1424 is ground\nX10945 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1630 [label="1630: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1631 [label="1631: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1632 [label="1632: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1633 [label="1633: quot(T1424, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X10945), SCOPE: 236, CLAUSE: 2\n\nT1424 is ground\nX10945 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1634 [label="1634: quot(T1424, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), X10945), SCOPE: 236, CLAUSE: 3\n\nT1424 is ground\nX10945 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1635 [label="1635: quot(T1429, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X10990)\n\nT1429 is ground\nX10990 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1636 [label="1636: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1637 [label="1637: quot(T1429, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X10990), SCOPE: 237, CLAUSE: 1 | quot(T1429, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X10990), SCOPE: 237, CLAUSE: 2 | quot(T1429, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X10990), SCOPE: 237, CLAUSE: 3\n\nT1429 is ground\nX10990 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1638 [label="1638: quot(T1429, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X10990), SCOPE: 237, CLAUSE: 1\n\nT1429 is ground\nX10990 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1639 [label="1639: quot(T1429, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X10990), SCOPE: 237, CLAUSE: 2 | quot(T1429, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X10990), SCOPE: 237, CLAUSE: 3\n\nT1429 is ground\nX10990 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1640 [label="1640: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1641 [label="1641: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1642 [label="1642: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1643 [label="1643: quot(T1429, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X10990), SCOPE: 237, CLAUSE: 2\n\nT1429 is ground\nX10990 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1644 [label="1644: quot(T1429, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), X10990), SCOPE: 237, CLAUSE: 3\n\nT1429 is ground\nX10990 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1645 [label="1645: quot(T1434, s(s(s(0))), s(s(s(s(s(s(0)))))), X11035)\n\nT1434 is ground\nX11035 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1646 [label="1646: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1647 [label="1647: quot(T1434, s(s(s(0))), s(s(s(s(s(s(0)))))), X11035), SCOPE: 238, CLAUSE: 1 | quot(T1434, s(s(s(0))), s(s(s(s(s(s(0)))))), X11035), SCOPE: 238, CLAUSE: 2 | quot(T1434, s(s(s(0))), s(s(s(s(s(s(0)))))), X11035), SCOPE: 238, CLAUSE: 3\n\nT1434 is ground\nX11035 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1648 [label="1648: quot(T1434, s(s(s(0))), s(s(s(s(s(s(0)))))), X11035), SCOPE: 238, CLAUSE: 1\n\nT1434 is ground\nX11035 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1649 [label="1649: quot(T1434, s(s(s(0))), s(s(s(s(s(s(0)))))), X11035), SCOPE: 238, CLAUSE: 2 | quot(T1434, s(s(s(0))), s(s(s(s(s(s(0)))))), X11035), SCOPE: 238, CLAUSE: 3\n\nT1434 is ground\nX11035 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1650 [label="1650: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1651 [label="1651: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1652 [label="1652: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1653 [label="1653: quot(T1434, s(s(s(0))), s(s(s(s(s(s(0)))))), X11035), SCOPE: 238, CLAUSE: 2\n\nT1434 is ground\nX11035 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1654 [label="1654: quot(T1434, s(s(s(0))), s(s(s(s(s(s(0)))))), X11035), SCOPE: 238, CLAUSE: 3\n\nT1434 is ground\nX11035 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1655 [label="1655: quot(T1439, s(s(0)), s(s(s(s(s(s(0)))))), X11080)\n\nT1439 is ground\nX11080 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1656 [label="1656: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1657 [label="1657: quot(T1439, s(s(0)), s(s(s(s(s(s(0)))))), X11080), SCOPE: 239, CLAUSE: 1 | quot(T1439, s(s(0)), s(s(s(s(s(s(0)))))), X11080), SCOPE: 239, CLAUSE: 2 | quot(T1439, s(s(0)), s(s(s(s(s(s(0)))))), X11080), SCOPE: 239, CLAUSE: 3\n\nT1439 is ground\nX11080 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1658 [label="1658: quot(T1439, s(s(0)), s(s(s(s(s(s(0)))))), X11080), SCOPE: 239, CLAUSE: 1\n\nT1439 is ground\nX11080 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1659 [label="1659: quot(T1439, s(s(0)), s(s(s(s(s(s(0)))))), X11080), SCOPE: 239, CLAUSE: 2 | quot(T1439, s(s(0)), s(s(s(s(s(s(0)))))), X11080), SCOPE: 239, CLAUSE: 3\n\nT1439 is ground\nX11080 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1660 [label="1660: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1661 [label="1661: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1662 [label="1662: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1663 [label="1663: quot(T1439, s(s(0)), s(s(s(s(s(s(0)))))), X11080), SCOPE: 239, CLAUSE: 2\n\nT1439 is ground\nX11080 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1664 [label="1664: quot(T1439, s(s(0)), s(s(s(s(s(s(0)))))), X11080), SCOPE: 239, CLAUSE: 3\n\nT1439 is ground\nX11080 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1665 [label="1665: quot(T1444, s(0), s(s(s(s(s(s(0)))))), X11125)\n\nT1444 is ground\nX11125 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1666 [label="1666: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1667 [label="1667: quot(T1444, s(0), s(s(s(s(s(s(0)))))), X11125), SCOPE: 240, CLAUSE: 1 | quot(T1444, s(0), s(s(s(s(s(s(0)))))), X11125), SCOPE: 240, CLAUSE: 2 | quot(T1444, s(0), s(s(s(s(s(s(0)))))), X11125), SCOPE: 240, CLAUSE: 3\n\nT1444 is ground\nX11125 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1668 [label="1668: quot(T1444, s(0), s(s(s(s(s(s(0)))))), X11125), SCOPE: 240, CLAUSE: 1\n\nT1444 is ground\nX11125 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1669 [label="1669: quot(T1444, s(0), s(s(s(s(s(s(0)))))), X11125), SCOPE: 240, CLAUSE: 2 | quot(T1444, s(0), s(s(s(s(s(s(0)))))), X11125), SCOPE: 240, CLAUSE: 3\n\nT1444 is ground\nX11125 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1670 [label="1670: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1671 [label="1671: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1672 [label="1672: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1673 [label="1673: quot(T1444, s(0), s(s(s(s(s(s(0)))))), X11125), SCOPE: 240, CLAUSE: 2\n\nT1444 is ground\nX11125 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1674 [label="1674: quot(T1444, s(0), s(s(s(s(s(s(0)))))), X11125), SCOPE: 240, CLAUSE: 3\n\nT1444 is ground\nX11125 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1675 [label="1675: quot(T1449, 0, s(s(s(s(s(s(0)))))), X11170)\n\nT1449 is ground\nX11170 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1676 [label="1676: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1677 [label="1677: quot(T1449, 0, s(s(s(s(s(s(0)))))), X11170), SCOPE: 241, CLAUSE: 1 | quot(T1449, 0, s(s(s(s(s(s(0)))))), X11170), SCOPE: 241, CLAUSE: 2 | quot(T1449, 0, s(s(s(s(s(s(0)))))), X11170), SCOPE: 241, CLAUSE: 3\n\nT1449 is ground\nX11170 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1678 [label="1678: quot(T1449, 0, s(s(s(s(s(s(0)))))), X11170), SCOPE: 241, CLAUSE: 2 | quot(T1449, 0, s(s(s(s(s(s(0)))))), X11170), SCOPE: 241, CLAUSE: 3\n\nT1449 is ground\nX11170 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1679 [label="1679: quot(T1449, 0, s(s(s(s(s(s(0)))))), X11170), SCOPE: 241, CLAUSE: 3\n\nT1449 is ground\nX11170 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1680 [label="1680: quot(T1455, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), X11208)\n\nT1455 is ground\nX11208 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1681 [label="1681: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1682 [label="1682: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1683 [label="1683: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1684 [label="1684: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1685 [label="1685: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1686 [label="1686: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1687 [label="1687: quot(T1464, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X11242)\n\nT1464 is ground\nX11242 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1688 [label="1688: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1689 [label="1689: quot(T1464, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X11242), SCOPE: 242, CLAUSE: 1 | quot(T1464, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X11242), SCOPE: 242, CLAUSE: 2 | quot(T1464, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X11242), SCOPE: 242, CLAUSE: 3\n\nT1464 is ground\nX11242 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1690 [label="1690: quot(T1464, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X11242), SCOPE: 242, CLAUSE: 1\n\nT1464 is ground\nX11242 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1691 [label="1691: quot(T1464, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X11242), SCOPE: 242, CLAUSE: 2 | quot(T1464, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X11242), SCOPE: 242, CLAUSE: 3\n\nT1464 is ground\nX11242 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1692 [label="1692: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1693 [label="1693: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1694 [label="1694: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1695 [label="1695: quot(T1464, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X11242), SCOPE: 242, CLAUSE: 2\n\nT1464 is ground\nX11242 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1696 [label="1696: quot(T1464, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X11242), SCOPE: 242, CLAUSE: 3\n\nT1464 is ground\nX11242 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1697 [label="1697: quot(T1469, s(s(s(s(0)))), s(s(s(s(s(0))))), X11286)\n\nT1469 is ground\nX11286 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1698 [label="1698: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1699 [label="1699: quot(T1469, s(s(s(s(0)))), s(s(s(s(s(0))))), X11286), SCOPE: 243, CLAUSE: 1 | quot(T1469, s(s(s(s(0)))), s(s(s(s(s(0))))), X11286), SCOPE: 243, CLAUSE: 2 | quot(T1469, s(s(s(s(0)))), s(s(s(s(s(0))))), X11286), SCOPE: 243, CLAUSE: 3\n\nT1469 is ground\nX11286 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1700 [label="1700: quot(T1469, s(s(s(s(0)))), s(s(s(s(s(0))))), X11286), SCOPE: 243, CLAUSE: 1\n\nT1469 is ground\nX11286 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1701 [label="1701: quot(T1469, s(s(s(s(0)))), s(s(s(s(s(0))))), X11286), SCOPE: 243, CLAUSE: 2 | quot(T1469, s(s(s(s(0)))), s(s(s(s(s(0))))), X11286), SCOPE: 243, CLAUSE: 3\n\nT1469 is ground\nX11286 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1702 [label="1702: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1703 [label="1703: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1704 [label="1704: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1705 [label="1705: quot(T1469, s(s(s(s(0)))), s(s(s(s(s(0))))), X11286), SCOPE: 243, CLAUSE: 2\n\nT1469 is ground\nX11286 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1706 [label="1706: quot(T1469, s(s(s(s(0)))), s(s(s(s(s(0))))), X11286), SCOPE: 243, CLAUSE: 3\n\nT1469 is ground\nX11286 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1707 [label="1707: quot(T1474, s(s(s(0))), s(s(s(s(s(0))))), X11331)\n\nT1474 is ground\nX11331 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1708 [label="1708: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1709 [label="1709: quot(T1474, s(s(s(0))), s(s(s(s(s(0))))), X11331), SCOPE: 244, CLAUSE: 1 | quot(T1474, s(s(s(0))), s(s(s(s(s(0))))), X11331), SCOPE: 244, CLAUSE: 2 | quot(T1474, s(s(s(0))), s(s(s(s(s(0))))), X11331), SCOPE: 244, CLAUSE: 3\n\nT1474 is ground\nX11331 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1710 [label="1710: quot(T1474, s(s(s(0))), s(s(s(s(s(0))))), X11331), SCOPE: 244, CLAUSE: 1\n\nT1474 is ground\nX11331 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1711 [label="1711: quot(T1474, s(s(s(0))), s(s(s(s(s(0))))), X11331), SCOPE: 244, CLAUSE: 2 | quot(T1474, s(s(s(0))), s(s(s(s(s(0))))), X11331), SCOPE: 244, CLAUSE: 3\n\nT1474 is ground\nX11331 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1712 [label="1712: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1713 [label="1713: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1714 [label="1714: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1715 [label="1715: quot(T1474, s(s(s(0))), s(s(s(s(s(0))))), X11331), SCOPE: 244, CLAUSE: 2\n\nT1474 is ground\nX11331 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1716 [label="1716: quot(T1474, s(s(s(0))), s(s(s(s(s(0))))), X11331), SCOPE: 244, CLAUSE: 3\n\nT1474 is ground\nX11331 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1717 [label="1717: quot(T1479, s(s(0)), s(s(s(s(s(0))))), X11376)\n\nT1479 is ground\nX11376 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1718 [label="1718: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1719 [label="1719: quot(T1479, s(s(0)), s(s(s(s(s(0))))), X11376), SCOPE: 245, CLAUSE: 1 | quot(T1479, s(s(0)), s(s(s(s(s(0))))), X11376), SCOPE: 245, CLAUSE: 2 | quot(T1479, s(s(0)), s(s(s(s(s(0))))), X11376), SCOPE: 245, CLAUSE: 3\n\nT1479 is ground\nX11376 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1720 [label="1720: quot(T1479, s(s(0)), s(s(s(s(s(0))))), X11376), SCOPE: 245, CLAUSE: 1\n\nT1479 is ground\nX11376 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1721 [label="1721: quot(T1479, s(s(0)), s(s(s(s(s(0))))), X11376), SCOPE: 245, CLAUSE: 2 | quot(T1479, s(s(0)), s(s(s(s(s(0))))), X11376), SCOPE: 245, CLAUSE: 3\n\nT1479 is ground\nX11376 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1722 [label="1722: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1723 [label="1723: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1724 [label="1724: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1725 [label="1725: quot(T1479, s(s(0)), s(s(s(s(s(0))))), X11376), SCOPE: 245, CLAUSE: 2\n\nT1479 is ground\nX11376 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1726 [label="1726: quot(T1479, s(s(0)), s(s(s(s(s(0))))), X11376), SCOPE: 245, CLAUSE: 3\n\nT1479 is ground\nX11376 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1727 [label="1727: quot(T1484, s(0), s(s(s(s(s(0))))), X11421)\n\nT1484 is ground\nX11421 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1728 [label="1728: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1729 [label="1729: quot(T1484, s(0), s(s(s(s(s(0))))), X11421), SCOPE: 246, CLAUSE: 1 | quot(T1484, s(0), s(s(s(s(s(0))))), X11421), SCOPE: 246, CLAUSE: 2 | quot(T1484, s(0), s(s(s(s(s(0))))), X11421), SCOPE: 246, CLAUSE: 3\n\nT1484 is ground\nX11421 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1730 [label="1730: quot(T1484, s(0), s(s(s(s(s(0))))), X11421), SCOPE: 246, CLAUSE: 1\n\nT1484 is ground\nX11421 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1731 [label="1731: quot(T1484, s(0), s(s(s(s(s(0))))), X11421), SCOPE: 246, CLAUSE: 2 | quot(T1484, s(0), s(s(s(s(s(0))))), X11421), SCOPE: 246, CLAUSE: 3\n\nT1484 is ground\nX11421 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1732 [label="1732: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1733 [label="1733: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1734 [label="1734: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1735 [label="1735: quot(T1484, s(0), s(s(s(s(s(0))))), X11421), SCOPE: 246, CLAUSE: 2\n\nT1484 is ground\nX11421 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1736 [label="1736: quot(T1484, s(0), s(s(s(s(s(0))))), X11421), SCOPE: 246, CLAUSE: 3\n\nT1484 is ground\nX11421 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1737 [label="1737: quot(T1489, 0, s(s(s(s(s(0))))), X11466)\n\nT1489 is ground\nX11466 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1738 [label="1738: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1739 [label="1739: quot(T1489, 0, s(s(s(s(s(0))))), X11466), SCOPE: 247, CLAUSE: 1 | quot(T1489, 0, s(s(s(s(s(0))))), X11466), SCOPE: 247, CLAUSE: 2 | quot(T1489, 0, s(s(s(s(s(0))))), X11466), SCOPE: 247, CLAUSE: 3\n\nT1489 is ground\nX11466 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1740 [label="1740: quot(T1489, 0, s(s(s(s(s(0))))), X11466), SCOPE: 247, CLAUSE: 2 | quot(T1489, 0, s(s(s(s(s(0))))), X11466), SCOPE: 247, CLAUSE: 3\n\nT1489 is ground\nX11466 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1741 [label="1741: quot(T1489, 0, s(s(s(s(s(0))))), X11466), SCOPE: 247, CLAUSE: 3\n\nT1489 is ground\nX11466 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1742 [label="1742: quot(T1495, s(s(s(s(s(0))))), s(s(s(s(s(0))))), X11504)\n\nT1495 is ground\nX11504 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1743 [label="1743: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1744 [label="1744: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1745 [label="1745: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1746 [label="1746: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1747 [label="1747: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1748 [label="1748: quot(T1503, s(s(s(s(0)))), s(s(s(s(0)))), X11535)\n\nT1503 is ground\nX11535 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1749 [label="1749: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1750 [label="1750: quot(T1503, s(s(s(s(0)))), s(s(s(s(0)))), X11535), SCOPE: 248, CLAUSE: 1 | quot(T1503, s(s(s(s(0)))), s(s(s(s(0)))), X11535), SCOPE: 248, CLAUSE: 2 | quot(T1503, s(s(s(s(0)))), s(s(s(s(0)))), X11535), SCOPE: 248, CLAUSE: 3\n\nT1503 is ground\nX11535 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1751 [label="1751: quot(T1503, s(s(s(s(0)))), s(s(s(s(0)))), X11535), SCOPE: 248, CLAUSE: 1\n\nT1503 is ground\nX11535 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1752 [label="1752: quot(T1503, s(s(s(s(0)))), s(s(s(s(0)))), X11535), SCOPE: 248, CLAUSE: 2 | quot(T1503, s(s(s(s(0)))), s(s(s(s(0)))), X11535), SCOPE: 248, CLAUSE: 3\n\nT1503 is ground\nX11535 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1753 [label="1753: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1754 [label="1754: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1755 [label="1755: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1756 [label="1756: quot(T1503, s(s(s(s(0)))), s(s(s(s(0)))), X11535), SCOPE: 248, CLAUSE: 2\n\nT1503 is ground\nX11535 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1757 [label="1757: quot(T1503, s(s(s(s(0)))), s(s(s(s(0)))), X11535), SCOPE: 248, CLAUSE: 3\n\nT1503 is ground\nX11535 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1758 [label="1758: quot(T1508, s(s(s(0))), s(s(s(s(0)))), X11579)\n\nT1508 is ground\nX11579 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1759 [label="1759: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1760 [label="1760: quot(T1508, s(s(s(0))), s(s(s(s(0)))), X11579), SCOPE: 249, CLAUSE: 1 | quot(T1508, s(s(s(0))), s(s(s(s(0)))), X11579), SCOPE: 249, CLAUSE: 2 | quot(T1508, s(s(s(0))), s(s(s(s(0)))), X11579), SCOPE: 249, CLAUSE: 3\n\nT1508 is ground\nX11579 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1761 [label="1761: quot(T1508, s(s(s(0))), s(s(s(s(0)))), X11579), SCOPE: 249, CLAUSE: 1\n\nT1508 is ground\nX11579 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1762 [label="1762: quot(T1508, s(s(s(0))), s(s(s(s(0)))), X11579), SCOPE: 249, CLAUSE: 2 | quot(T1508, s(s(s(0))), s(s(s(s(0)))), X11579), SCOPE: 249, CLAUSE: 3\n\nT1508 is ground\nX11579 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1763 [label="1763: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1764 [label="1764: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1765 [label="1765: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1766 [label="1766: quot(T1508, s(s(s(0))), s(s(s(s(0)))), X11579), SCOPE: 249, CLAUSE: 2\n\nT1508 is ground\nX11579 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1767 [label="1767: quot(T1508, s(s(s(0))), s(s(s(s(0)))), X11579), SCOPE: 249, CLAUSE: 3\n\nT1508 is ground\nX11579 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1768 [label="1768: quot(T1513, s(s(0)), s(s(s(s(0)))), X11624)\n\nT1513 is ground\nX11624 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1769 [label="1769: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1770 [label="1770: quot(T1513, s(s(0)), s(s(s(s(0)))), X11624), SCOPE: 250, CLAUSE: 1 | quot(T1513, s(s(0)), s(s(s(s(0)))), X11624), SCOPE: 250, CLAUSE: 2 | quot(T1513, s(s(0)), s(s(s(s(0)))), X11624), SCOPE: 250, CLAUSE: 3\n\nT1513 is ground\nX11624 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1771 [label="1771: quot(T1513, s(s(0)), s(s(s(s(0)))), X11624), SCOPE: 250, CLAUSE: 1\n\nT1513 is ground\nX11624 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1772 [label="1772: quot(T1513, s(s(0)), s(s(s(s(0)))), X11624), SCOPE: 250, CLAUSE: 2 | quot(T1513, s(s(0)), s(s(s(s(0)))), X11624), SCOPE: 250, CLAUSE: 3\n\nT1513 is ground\nX11624 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1773 [label="1773: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1774 [label="1774: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1775 [label="1775: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1776 [label="1776: quot(T1513, s(s(0)), s(s(s(s(0)))), X11624), SCOPE: 250, CLAUSE: 2\n\nT1513 is ground\nX11624 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1777 [label="1777: quot(T1513, s(s(0)), s(s(s(s(0)))), X11624), SCOPE: 250, CLAUSE: 3\n\nT1513 is ground\nX11624 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1778 [label="1778: quot(T1518, s(0), s(s(s(s(0)))), X11669)\n\nT1518 is ground\nX11669 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1779 [label="1779: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1780 [label="1780: quot(T1518, s(0), s(s(s(s(0)))), X11669), SCOPE: 251, CLAUSE: 1 | quot(T1518, s(0), s(s(s(s(0)))), X11669), SCOPE: 251, CLAUSE: 2 | quot(T1518, s(0), s(s(s(s(0)))), X11669), SCOPE: 251, CLAUSE: 3\n\nT1518 is ground\nX11669 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1781 [label="1781: quot(T1518, s(0), s(s(s(s(0)))), X11669), SCOPE: 251, CLAUSE: 1\n\nT1518 is ground\nX11669 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1782 [label="1782: quot(T1518, s(0), s(s(s(s(0)))), X11669), SCOPE: 251, CLAUSE: 2 | quot(T1518, s(0), s(s(s(s(0)))), X11669), SCOPE: 251, CLAUSE: 3\n\nT1518 is ground\nX11669 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1783 [label="1783: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1784 [label="1784: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1785 [label="1785: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1786 [label="1786: quot(T1518, s(0), s(s(s(s(0)))), X11669), SCOPE: 251, CLAUSE: 2\n\nT1518 is ground\nX11669 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1787 [label="1787: quot(T1518, s(0), s(s(s(s(0)))), X11669), SCOPE: 251, CLAUSE: 3\n\nT1518 is ground\nX11669 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1788 [label="1788: quot(T1523, 0, s(s(s(s(0)))), X11714)\n\nT1523 is ground\nX11714 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1789 [label="1789: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1790 [label="1790: quot(T1523, 0, s(s(s(s(0)))), X11714), SCOPE: 252, CLAUSE: 1 | quot(T1523, 0, s(s(s(s(0)))), X11714), SCOPE: 252, CLAUSE: 2 | quot(T1523, 0, s(s(s(s(0)))), X11714), SCOPE: 252, CLAUSE: 3\n\nT1523 is ground\nX11714 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1791 [label="1791: quot(T1523, 0, s(s(s(s(0)))), X11714), SCOPE: 252, CLAUSE: 2 | quot(T1523, 0, s(s(s(s(0)))), X11714), SCOPE: 252, CLAUSE: 3\n\nT1523 is ground\nX11714 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1792 [label="1792: quot(T1523, 0, s(s(s(s(0)))), X11714), SCOPE: 252, CLAUSE: 3\n\nT1523 is ground\nX11714 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1793 [label="1793: quot(T1529, s(s(s(s(0)))), s(s(s(s(0)))), X11752)\n\nT1529 is ground\nX11752 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1794 [label="1794: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1795 [label="1795: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1796 [label="1796: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1797 [label="1797: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1798 [label="1798: quot(T1536, s(s(s(0))), s(s(s(0))), X11780)\n\nT1536 is ground\nX11780 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1799 [label="1799: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1800 [label="1800: quot(T1536, s(s(s(0))), s(s(s(0))), X11780), SCOPE: 253, CLAUSE: 1 | quot(T1536, s(s(s(0))), s(s(s(0))), X11780), SCOPE: 253, CLAUSE: 2 | quot(T1536, s(s(s(0))), s(s(s(0))), X11780), SCOPE: 253, CLAUSE: 3\n\nT1536 is ground\nX11780 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1801 [label="1801: quot(T1536, s(s(s(0))), s(s(s(0))), X11780), SCOPE: 253, CLAUSE: 1\n\nT1536 is ground\nX11780 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1802 [label="1802: quot(T1536, s(s(s(0))), s(s(s(0))), X11780), SCOPE: 253, CLAUSE: 2 | quot(T1536, s(s(s(0))), s(s(s(0))), X11780), SCOPE: 253, CLAUSE: 3\n\nT1536 is ground\nX11780 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1803 [label="1803: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1804 [label="1804: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1805 [label="1805: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1806 [label="1806: quot(T1536, s(s(s(0))), s(s(s(0))), X11780), SCOPE: 253, CLAUSE: 2\n\nT1536 is ground\nX11780 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1807 [label="1807: quot(T1536, s(s(s(0))), s(s(s(0))), X11780), SCOPE: 253, CLAUSE: 3\n\nT1536 is ground\nX11780 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1808 [label="1808: quot(T1541, s(s(0)), s(s(s(0))), X11824)\n\nT1541 is ground\nX11824 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1809 [label="1809: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1810 [label="1810: quot(T1541, s(s(0)), s(s(s(0))), X11824), SCOPE: 254, CLAUSE: 1 | quot(T1541, s(s(0)), s(s(s(0))), X11824), SCOPE: 254, CLAUSE: 2 | quot(T1541, s(s(0)), s(s(s(0))), X11824), SCOPE: 254, CLAUSE: 3\n\nT1541 is ground\nX11824 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1811 [label="1811: quot(T1541, s(s(0)), s(s(s(0))), X11824), SCOPE: 254, CLAUSE: 1\n\nT1541 is ground\nX11824 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1812 [label="1812: quot(T1541, s(s(0)), s(s(s(0))), X11824), SCOPE: 254, CLAUSE: 2 | quot(T1541, s(s(0)), s(s(s(0))), X11824), SCOPE: 254, CLAUSE: 3\n\nT1541 is ground\nX11824 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1813 [label="1813: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1814 [label="1814: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1815 [label="1815: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1816 [label="1816: quot(T1541, s(s(0)), s(s(s(0))), X11824), SCOPE: 254, CLAUSE: 2\n\nT1541 is ground\nX11824 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1817 [label="1817: quot(T1541, s(s(0)), s(s(s(0))), X11824), SCOPE: 254, CLAUSE: 3\n\nT1541 is ground\nX11824 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1818 [label="1818: quot(T1546, s(0), s(s(s(0))), X11869)\n\nT1546 is ground\nX11869 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1819 [label="1819: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1820 [label="1820: quot(T1546, s(0), s(s(s(0))), X11869), SCOPE: 255, CLAUSE: 1 | quot(T1546, s(0), s(s(s(0))), X11869), SCOPE: 255, CLAUSE: 2 | quot(T1546, s(0), s(s(s(0))), X11869), SCOPE: 255, CLAUSE: 3\n\nT1546 is ground\nX11869 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1821 [label="1821: quot(T1546, s(0), s(s(s(0))), X11869), SCOPE: 255, CLAUSE: 1\n\nT1546 is ground\nX11869 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1822 [label="1822: quot(T1546, s(0), s(s(s(0))), X11869), SCOPE: 255, CLAUSE: 2 | quot(T1546, s(0), s(s(s(0))), X11869), SCOPE: 255, CLAUSE: 3\n\nT1546 is ground\nX11869 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1823 [label="1823: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1824 [label="1824: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1825 [label="1825: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1826 [label="1826: quot(T1546, s(0), s(s(s(0))), X11869), SCOPE: 255, CLAUSE: 2\n\nT1546 is ground\nX11869 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1827 [label="1827: quot(T1546, s(0), s(s(s(0))), X11869), SCOPE: 255, CLAUSE: 3\n\nT1546 is ground\nX11869 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1828 [label="1828: quot(T1551, 0, s(s(s(0))), X11914)\n\nT1551 is ground\nX11914 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1829 [label="1829: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1830 [label="1830: quot(T1551, 0, s(s(s(0))), X11914), SCOPE: 256, CLAUSE: 1 | quot(T1551, 0, s(s(s(0))), X11914), SCOPE: 256, CLAUSE: 2 | quot(T1551, 0, s(s(s(0))), X11914), SCOPE: 256, CLAUSE: 3\n\nT1551 is ground\nX11914 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1831 [label="1831: quot(T1551, 0, s(s(s(0))), X11914), SCOPE: 256, CLAUSE: 2 | quot(T1551, 0, s(s(s(0))), X11914), SCOPE: 256, CLAUSE: 3\n\nT1551 is ground\nX11914 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1832 [label="1832: quot(T1551, 0, s(s(s(0))), X11914), SCOPE: 256, CLAUSE: 3\n\nT1551 is ground\nX11914 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1833 [label="1833: quot(T1557, s(s(s(0))), s(s(s(0))), X11952)\n\nT1557 is ground\nX11952 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1834 [label="1834: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1835 [label="1835: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1836 [label="1836: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1837 [label="1837: quot(T1563, s(s(0)), s(s(0)), X11977)\n\nT1563 is ground\nX11977 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1838 [label="1838: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1839 [label="1839: quot(T1563, s(s(0)), s(s(0)), X11977), SCOPE: 257, CLAUSE: 1 | quot(T1563, s(s(0)), s(s(0)), X11977), SCOPE: 257, CLAUSE: 2 | quot(T1563, s(s(0)), s(s(0)), X11977), SCOPE: 257, CLAUSE: 3\n\nT1563 is ground\nX11977 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1840 [label="1840: quot(T1563, s(s(0)), s(s(0)), X11977), SCOPE: 257, CLAUSE: 1\n\nT1563 is ground\nX11977 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1841 [label="1841: quot(T1563, s(s(0)), s(s(0)), X11977), SCOPE: 257, CLAUSE: 2 | quot(T1563, s(s(0)), s(s(0)), X11977), SCOPE: 257, CLAUSE: 3\n\nT1563 is ground\nX11977 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1842 [label="1842: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1843 [label="1843: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1844 [label="1844: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1845 [label="1845: quot(T1563, s(s(0)), s(s(0)), X11977), SCOPE: 257, CLAUSE: 2\n\nT1563 is ground\nX11977 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1846 [label="1846: quot(T1563, s(s(0)), s(s(0)), X11977), SCOPE: 257, CLAUSE: 3\n\nT1563 is ground\nX11977 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1847 [label="1847: quot(T1568, s(0), s(s(0)), X12021)\n\nT1568 is ground\nX12021 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1848 [label="1848: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1849 [label="1849: quot(T1568, s(0), s(s(0)), X12021), SCOPE: 258, CLAUSE: 1 | quot(T1568, s(0), s(s(0)), X12021), SCOPE: 258, CLAUSE: 2 | quot(T1568, s(0), s(s(0)), X12021), SCOPE: 258, CLAUSE: 3\n\nT1568 is ground\nX12021 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1850 [label="1850: quot(T1568, s(0), s(s(0)), X12021), SCOPE: 258, CLAUSE: 1\n\nT1568 is ground\nX12021 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1851 [label="1851: quot(T1568, s(0), s(s(0)), X12021), SCOPE: 258, CLAUSE: 2 | quot(T1568, s(0), s(s(0)), X12021), SCOPE: 258, CLAUSE: 3\n\nT1568 is ground\nX12021 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1852 [label="1852: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1853 [label="1853: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1854 [label="1854: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1855 [label="1855: quot(T1568, s(0), s(s(0)), X12021), SCOPE: 258, CLAUSE: 2\n\nT1568 is ground\nX12021 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1856 [label="1856: quot(T1568, s(0), s(s(0)), X12021), SCOPE: 258, CLAUSE: 3\n\nT1568 is ground\nX12021 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1857 [label="1857: quot(T1573, 0, s(s(0)), X12066)\n\nT1573 is ground\nX12066 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1858 [label="1858: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1859 [label="1859: quot(T1573, 0, s(s(0)), X12066), SCOPE: 259, CLAUSE: 1 | quot(T1573, 0, s(s(0)), X12066), SCOPE: 259, CLAUSE: 2 | quot(T1573, 0, s(s(0)), X12066), SCOPE: 259, CLAUSE: 3\n\nT1573 is ground\nX12066 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1860 [label="1860: quot(T1573, 0, s(s(0)), X12066), SCOPE: 259, CLAUSE: 2 | quot(T1573, 0, s(s(0)), X12066), SCOPE: 259, CLAUSE: 3\n\nT1573 is ground\nX12066 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1861 [label="1861: quot(T1573, 0, s(s(0)), X12066), SCOPE: 259, CLAUSE: 3\n\nT1573 is ground\nX12066 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1862 [label="1862: quot(T1579, s(s(0)), s(s(0)), X12104)\n\nT1579 is ground\nX12104 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1863 [label="1863: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1864 [label="1864: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1865 [label="1865: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1866 [label="1866: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1867 [label="1867: times(T1126, s(s(T1122)), X9846)\n\nT1122 is ground\nT1126 is ground\nX9846 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
1868 [label="1868: neq(s(T1123), T1586)\n\nT1123 is ground\nT1586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1869 [label="1869: pr(s(T1111), s(T1109)), SCOPE: 260, CLAUSE: 5 | pr(s(T1111), s(T1109)), SCOPE: 260, CLAUSE: 6\n\nT1109 is ground\nT1111 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1870 [label="1870: pr(s(T1111), s(T1109)), SCOPE: 260, CLAUSE: 5\n\nT1109 is ground\nT1111 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1871 [label="1871: pr(s(T1111), s(T1109)), SCOPE: 260, CLAUSE: 6\n\nT1109 is ground\nT1111 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1872 [label="1872: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1873 [label="1873: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1874 [label="1874: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1875 [label="1875: ','(not_divides(s(s(T1603)), s(T1602)), pr(s(T1602), s(T1603)))\n\nT1602 is ground\nT1603 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1876 [label="1876: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1877 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 1877 [arrowhead = none ];
1877 -> 2;

1878 [label="EVAL with clause\nprime(s(s(X2))) :- pr(s(s(X2)), s(X2)).\nand substitution\nX2 -> T3\nT1 -> s(s(T3))", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 1878 [arrowhead = none ];
1878 -> 3;

1879 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 1879 [arrowhead = none ];
1879 -> 4;

1880 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 1880 [arrowhead = none ];
1880 -> 5;

1881 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5 -> 1881 [arrowhead = none ];
1881 -> 6;

1882 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
5 -> 1882 [arrowhead = none ];
1882 -> 7;

1883 [label="EVAL with clause\npr(X8, s(0)).\nand substitution\nT3 -> 0\nX8 -> s(s(0))\nT8 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 1883 [arrowhead = none ];
1883 -> 8;

1884 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 1884 [arrowhead = none ];
1884 -> 9;

1885 [label="EVAL with clause\npr(X14, s(s(X15))) :- ','(not_divides(s(s(X15)), X14), pr(X14, s(X15))).\nand substitution\nT3 -> s(T14)\nX14 -> s(s(s(T14)))\nX15 -> T14\nT13 -> s(T14)", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 1885 [arrowhead = none ];
1885 -> 11;

1886 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 1886 [arrowhead = none ];
1886 -> 12;

1887 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 1887 [arrowhead = none ];
1887 -> 10;

1888 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
11 -> 1888 [arrowhead = none ];
1888 -> 13;

1889 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
11 -> 1889 [arrowhead = none ];
1889 -> 14;

1890 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
13 -> 1890 [arrowhead = none ];
1890 -> 15;

1891 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
14 -> 1891 [arrowhead = none ];
1891 -> 251;

1892 [label="ONLY EVAL with clause\nnot_divides(X36, X37) :- ','(div(X37, X36, X38), ','(times(X38, X36, X39), neq(X37, X39))).\nand substitution\nT14 -> T20\nX36 -> s(s(T20))\nX37 -> s(s(s(T20)))", fontsize=14, style = filled, fillcolor = white];
15 -> 1892 [arrowhead = none ];
1892 -> 16;

1893 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
16 -> 1893 [arrowhead = none ];
1893 -> 17;

1894 [label="SPLIT 2\nnew knowledge:\nT22 is ground\nreplacements:\nX38 -> T22", fontsize=14, style = filled, fillcolor = violet];
16 -> 1894 [arrowhead = none ];
1894 -> 18;

1895 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
17 -> 1895 [arrowhead = none ];
1895 -> 19;

1896 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
18 -> 1896 [arrowhead = none ];
1896 -> 190;

1897 [label="SPLIT 2\nnew knowledge:\nT187 is ground\nreplacements:\nX39 -> T187", fontsize=14, style = filled, fillcolor = violet];
18 -> 1897 [arrowhead = none ];
1897 -> 191;

1898 [label="ONLY EVAL with clause\ndiv(X65, X66, X67) :- quot(X65, X66, X66, X67).\nand substitution\nT20 -> T27\nX65 -> s(s(s(T27)))\nX66 -> s(s(T27))\nX38 -> X68\nX67 -> X68", fontsize=14, style = filled, fillcolor = white];
19 -> 1898 [arrowhead = none ];
1898 -> 20;

1899 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
20 -> 1899 [arrowhead = none ];
1899 -> 21;

1900 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
21 -> 1900 [arrowhead = none ];
1900 -> 22;

1901 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
22 -> 1901 [arrowhead = none ];
1901 -> 23;

1902 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
22 -> 1902 [arrowhead = none ];
1902 -> 24;

1903 [label="ONLY EVAL with clause\nquot(s(X118), s(X119), X120, X121) :- quot(X118, X119, X120, X121).\nand substitution\nT27 -> T35\nX118 -> s(s(T35))\nX119 -> s(T35)\nX120 -> s(s(T35))\nX68 -> X122\nX121 -> X122", fontsize=14, style = filled, fillcolor = white];
23 -> 1903 [arrowhead = none ];
1903 -> 25;

1904 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
24 -> 1904 [arrowhead = none ];
1904 -> 189;

1905 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
25 -> 1905 [arrowhead = none ];
1905 -> 26;

1906 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
26 -> 1906 [arrowhead = none ];
1906 -> 27;

1907 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
27 -> 1907 [arrowhead = none ];
1907 -> 28;

1908 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
27 -> 1908 [arrowhead = none ];
1908 -> 29;

1909 [label="ONLY EVAL with clause\nquot(s(X172), s(X173), X174, X175) :- quot(X172, X173, X174, X175).\nand substitution\nT35 -> T45\nX172 -> s(T45)\nX173 -> T45\nX174 -> s(s(T45))\nX122 -> X176\nX175 -> X176", fontsize=14, style = filled, fillcolor = white];
28 -> 1909 [arrowhead = none ];
1909 -> 30;

1910 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
29 -> 1910 [arrowhead = none ];
1910 -> 188;

1911 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
30 -> 1911 [arrowhead = none ];
1911 -> 31;

1912 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
31 -> 1912 [arrowhead = none ];
1912 -> 32;

1913 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
32 -> 1913 [arrowhead = none ];
1913 -> 33;

1914 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
32 -> 1914 [arrowhead = none ];
1914 -> 34;

1915 [label="EVAL with clause\nquot(s(X208), s(X209), X210, X211) :- quot(X208, X209, X210, X211).\nand substitution\nT45 -> s(T57)\nX208 -> s(T57)\nX209 -> T57\nT56 -> s(T57)\nX210 -> s(s(s(T57)))\nX176 -> X212\nX211 -> X212", fontsize=14, style = filled, fillcolor = lightblue];
33 -> 1915 [arrowhead = none ];
1915 -> 35;

1916 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
33 -> 1916 [arrowhead = none ];
1916 -> 36;

1917 [label="EVAL with clause\nquot(X984, 0, s(X985), s(X986)) :- quot(X984, s(X985), s(X985), X986).\nand substitution\nT45 -> 0\nX984 -> s(0)\nT182 -> 0\nX985 -> s(0)\nX986 -> X987\nX176 -> s(X987)", fontsize=14, style = filled, fillcolor = lightblue];
34 -> 1917 [arrowhead = none ];
1917 -> 173;

1918 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
34 -> 1918 [arrowhead = none ];
1918 -> 174;

1919 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
35 -> 1919 [arrowhead = none ];
1919 -> 37;

1920 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
37 -> 1920 [arrowhead = none ];
1920 -> 38;

1921 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
38 -> 1921 [arrowhead = none ];
1921 -> 39;

1922 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
38 -> 1922 [arrowhead = none ];
1922 -> 40;

1923 [label="EVAL with clause\nquot(s(X248), s(X249), X250, X251) :- quot(X248, X249, X250, X251).\nand substitution\nT57 -> s(T69)\nX248 -> s(T69)\nX249 -> T69\nT68 -> s(T69)\nX250 -> s(s(s(s(T69))))\nX212 -> X252\nX251 -> X252", fontsize=14, style = filled, fillcolor = lightblue];
39 -> 1923 [arrowhead = none ];
1923 -> 41;

1924 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
39 -> 1924 [arrowhead = none ];
1924 -> 42;

1925 [label="EVAL with clause\nquot(X907, 0, s(X908), s(X909)) :- quot(X907, s(X908), s(X908), X909).\nand substitution\nT57 -> 0\nX907 -> s(0)\nT179 -> 0\nX908 -> s(s(0))\nX909 -> X910\nX212 -> s(X910)", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 1925 [arrowhead = none ];
1925 -> 158;

1926 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 1926 [arrowhead = none ];
1926 -> 159;

1927 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
41 -> 1927 [arrowhead = none ];
1927 -> 43;

1928 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
43 -> 1928 [arrowhead = none ];
1928 -> 44;

1929 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
44 -> 1929 [arrowhead = none ];
1929 -> 45;

1930 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
44 -> 1930 [arrowhead = none ];
1930 -> 46;

1931 [label="EVAL with clause\nquot(s(X288), s(X289), X290, X291) :- quot(X288, X289, X290, X291).\nand substitution\nT69 -> s(T81)\nX288 -> s(T81)\nX289 -> T81\nT80 -> s(T81)\nX290 -> s(s(s(s(s(T81)))))\nX252 -> X292\nX291 -> X292", fontsize=14, style = filled, fillcolor = lightblue];
45 -> 1931 [arrowhead = none ];
1931 -> 47;

1932 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
45 -> 1932 [arrowhead = none ];
1932 -> 48;

1933 [label="EVAL with clause\nquot(X830, 0, s(X831), s(X832)) :- quot(X830, s(X831), s(X831), X832).\nand substitution\nT69 -> 0\nX830 -> s(0)\nT176 -> 0\nX831 -> s(s(s(0)))\nX832 -> X833\nX252 -> s(X833)", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 1933 [arrowhead = none ];
1933 -> 143;

1934 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 1934 [arrowhead = none ];
1934 -> 144;

1935 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
47 -> 1935 [arrowhead = none ];
1935 -> 49;

1936 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
49 -> 1936 [arrowhead = none ];
1936 -> 50;

1937 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
50 -> 1937 [arrowhead = none ];
1937 -> 51;

1938 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
50 -> 1938 [arrowhead = none ];
1938 -> 52;

1939 [label="EVAL with clause\nquot(s(X328), s(X329), X330, X331) :- quot(X328, X329, X330, X331).\nand substitution\nT81 -> s(T93)\nX328 -> s(T93)\nX329 -> T93\nT92 -> s(T93)\nX330 -> s(s(s(s(s(s(T93))))))\nX292 -> X332\nX331 -> X332", fontsize=14, style = filled, fillcolor = lightblue];
51 -> 1939 [arrowhead = none ];
1939 -> 53;

1940 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
51 -> 1940 [arrowhead = none ];
1940 -> 54;

1941 [label="EVAL with clause\nquot(X753, 0, s(X754), s(X755)) :- quot(X753, s(X754), s(X754), X755).\nand substitution\nT81 -> 0\nX753 -> s(0)\nT173 -> 0\nX754 -> s(s(s(s(0))))\nX755 -> X756\nX292 -> s(X756)", fontsize=14, style = filled, fillcolor = lightblue];
52 -> 1941 [arrowhead = none ];
1941 -> 128;

1942 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
52 -> 1942 [arrowhead = none ];
1942 -> 129;

1943 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
53 -> 1943 [arrowhead = none ];
1943 -> 55;

1944 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
55 -> 1944 [arrowhead = none ];
1944 -> 56;

1945 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
56 -> 1945 [arrowhead = none ];
1945 -> 57;

1946 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
56 -> 1946 [arrowhead = none ];
1946 -> 58;

1947 [label="EVAL with clause\nquot(s(X368), s(X369), X370, X371) :- quot(X368, X369, X370, X371).\nand substitution\nT93 -> s(T105)\nX368 -> s(T105)\nX369 -> T105\nT104 -> s(T105)\nX370 -> s(s(s(s(s(s(s(T105)))))))\nX332 -> X372\nX371 -> X372", fontsize=14, style = filled, fillcolor = lightblue];
57 -> 1947 [arrowhead = none ];
1947 -> 59;

1948 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
57 -> 1948 [arrowhead = none ];
1948 -> 60;

1949 [label="EVAL with clause\nquot(X676, 0, s(X677), s(X678)) :- quot(X676, s(X677), s(X677), X678).\nand substitution\nT93 -> 0\nX676 -> s(0)\nT170 -> 0\nX677 -> s(s(s(s(s(0)))))\nX678 -> X679\nX332 -> s(X679)", fontsize=14, style = filled, fillcolor = lightblue];
58 -> 1949 [arrowhead = none ];
1949 -> 113;

1950 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
58 -> 1950 [arrowhead = none ];
1950 -> 114;

1951 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
59 -> 1951 [arrowhead = none ];
1951 -> 61;

1952 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
61 -> 1952 [arrowhead = none ];
1952 -> 62;

1953 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
62 -> 1953 [arrowhead = none ];
1953 -> 63;

1954 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
62 -> 1954 [arrowhead = none ];
1954 -> 64;

1955 [label="EVAL with clause\nquot(s(X408), s(X409), X410, X411) :- quot(X408, X409, X410, X411).\nand substitution\nT105 -> s(T117)\nX408 -> s(T117)\nX409 -> T117\nT116 -> s(T117)\nX410 -> s(s(s(s(s(s(s(s(T117))))))))\nX372 -> X412\nX411 -> X412", fontsize=14, style = filled, fillcolor = lightblue];
63 -> 1955 [arrowhead = none ];
1955 -> 65;

1956 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
63 -> 1956 [arrowhead = none ];
1956 -> 66;

1957 [label="EVAL with clause\nquot(X599, 0, s(X600), s(X601)) :- quot(X599, s(X600), s(X600), X601).\nand substitution\nT105 -> 0\nX599 -> s(0)\nT167 -> 0\nX600 -> s(s(s(s(s(s(0))))))\nX601 -> X602\nX372 -> s(X602)", fontsize=14, style = filled, fillcolor = lightblue];
64 -> 1957 [arrowhead = none ];
1957 -> 98;

1958 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
64 -> 1958 [arrowhead = none ];
1958 -> 99;

1959 [label="GENERALIZATION\nT120 <-- s(s(s(s(s(s(s(T117)))))))\n\nNew Knowledge:\nT120 is ground", fontsize=14, style = filled, fillcolor = violet];
65 -> 1959 [arrowhead = none ];
1959 -> 67;

1960 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
67 -> 1960 [arrowhead = none ];
1960 -> 68;

1961 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
68 -> 1961 [arrowhead = none ];
1961 -> 69;

1962 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
69 -> 1962 [arrowhead = none ];
1962 -> 70;

1963 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
69 -> 1963 [arrowhead = none ];
1963 -> 71;

1964 [label="EVAL with clause\nquot(s(X457), s(X458), X459, X460) :- quot(X457, X458, X459, X460).\nand substitution\nT117 -> s(T137)\nX457 -> s(T137)\nX458 -> T137\nT136 -> s(T137)\nT120 -> T138\nX459 -> s(T138)\nX412 -> X461\nX460 -> X461", fontsize=14, style = filled, fillcolor = lightblue];
70 -> 1964 [arrowhead = none ];
1964 -> 72;

1965 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
70 -> 1965 [arrowhead = none ];
1965 -> 73;

1966 [label="EVAL with clause\nquot(X483, 0, s(X484), s(X485)) :- quot(X483, s(X484), s(X484), X485).\nand substitution\nT117 -> 0\nX483 -> s(0)\nT146 -> 0\nT120 -> T147\nX484 -> T147\nX485 -> X486\nX412 -> s(X486)", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 1966 [arrowhead = none ];
1966 -> 74;

1967 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 1967 [arrowhead = none ];
1967 -> 75;

1968 [label="INSTANCE with matching:\nT117 -> T137\nT120 -> T138\nX412 -> X461", fontsize=14, style = filled, fillcolor = lightgrey];
72 -> 1968 [arrowhead = none , style=dashed];
1968 -> 67[style=dashed];

1969 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
74 -> 1969 [arrowhead = none ];
1969 -> 76;

1970 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
76 -> 1970 [arrowhead = none ];
1970 -> 77;

1971 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
77 -> 1971 [arrowhead = none ];
1971 -> 78;

1972 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
77 -> 1972 [arrowhead = none ];
1972 -> 79;

1973 [label="ONLY EVAL with clause\nquot(s(X529), s(X530), X531, X532) :- quot(X529, X530, X531, X532).\nand substitution\nX529 -> 0\nT147 -> T157\nX530 -> T157\nX531 -> s(T157)\nX486 -> X533\nX532 -> X533", fontsize=14, style = filled, fillcolor = white];
78 -> 1973 [arrowhead = none ];
1973 -> 80;

1974 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
79 -> 1974 [arrowhead = none ];
1974 -> 97;

1975 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
80 -> 1975 [arrowhead = none ];
1975 -> 81;

1976 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
81 -> 1976 [arrowhead = none ];
1976 -> 82;

1977 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
81 -> 1977 [arrowhead = none ];
1977 -> 83;

1978 [label="EVAL with clause\nquot(0, s(X546), s(X547), 0).\nand substitution\nX546 -> T164\nT157 -> s(T164)\nX547 -> s(T164)\nX533 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 1978 [arrowhead = none ];
1978 -> 84;

1979 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 1979 [arrowhead = none ];
1979 -> 85;

1980 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
83 -> 1980 [arrowhead = none ];
1980 -> 87;

1981 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
84 -> 1981 [arrowhead = none ];
1981 -> 86;

1982 [label="EVAL with clause\nquot(X562, 0, s(X563), s(X564)) :- quot(X562, s(X563), s(X563), X564).\nand substitution\nX562 -> 0\nT157 -> 0\nX563 -> 0\nX564 -> X565\nX533 -> s(X565)", fontsize=14, style = filled, fillcolor = lightblue];
87 -> 1982 [arrowhead = none ];
1982 -> 88;

1983 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
87 -> 1983 [arrowhead = none ];
1983 -> 89;

1984 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
88 -> 1984 [arrowhead = none ];
1984 -> 90;

1985 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
90 -> 1985 [arrowhead = none ];
1985 -> 91;

1986 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
90 -> 1986 [arrowhead = none ];
1986 -> 92;

1987 [label="ONLY EVAL with clause\nquot(0, s(X579), s(X580), 0).\nand substitution\nX579 -> 0\nX580 -> 0\nX565 -> 0", fontsize=14, style = filled, fillcolor = white];
91 -> 1987 [arrowhead = none ];
1987 -> 93;

1988 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
92 -> 1988 [arrowhead = none ];
1988 -> 95;

1989 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
93 -> 1989 [arrowhead = none ];
1989 -> 94;

1990 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
95 -> 1990 [arrowhead = none ];
1990 -> 96;

1991 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
98 -> 1991 [arrowhead = none ];
1991 -> 100;

1992 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
100 -> 1992 [arrowhead = none ];
1992 -> 101;

1993 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
101 -> 1993 [arrowhead = none ];
1993 -> 102;

1994 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
101 -> 1994 [arrowhead = none ];
1994 -> 103;

1995 [label="ONLY EVAL with clause\nquot(s(X641), s(X642), X643, X644) :- quot(X641, X642, X643, X644).\nand substitution\nX641 -> 0\nX642 -> s(s(s(s(s(s(0))))))\nX643 -> s(s(s(s(s(s(s(0)))))))\nX602 -> X645\nX644 -> X645", fontsize=14, style = filled, fillcolor = white];
102 -> 1995 [arrowhead = none ];
1995 -> 104;

1996 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
103 -> 1996 [arrowhead = none ];
1996 -> 112;

1997 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
104 -> 1997 [arrowhead = none ];
1997 -> 105;

1998 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
105 -> 1998 [arrowhead = none ];
1998 -> 106;

1999 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
105 -> 1999 [arrowhead = none ];
1999 -> 107;

2000 [label="ONLY EVAL with clause\nquot(0, s(X656), s(X657), 0).\nand substitution\nX656 -> s(s(s(s(s(0)))))\nX657 -> s(s(s(s(s(s(0))))))\nX645 -> 0", fontsize=14, style = filled, fillcolor = white];
106 -> 2000 [arrowhead = none ];
2000 -> 108;

2001 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
107 -> 2001 [arrowhead = none ];
2001 -> 110;

2002 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
108 -> 2002 [arrowhead = none ];
2002 -> 109;

2003 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
110 -> 2003 [arrowhead = none ];
2003 -> 111;

2004 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
113 -> 2004 [arrowhead = none ];
2004 -> 115;

2005 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
115 -> 2005 [arrowhead = none ];
2005 -> 116;

2006 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
116 -> 2006 [arrowhead = none ];
2006 -> 117;

2007 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
116 -> 2007 [arrowhead = none ];
2007 -> 118;

2008 [label="ONLY EVAL with clause\nquot(s(X718), s(X719), X720, X721) :- quot(X718, X719, X720, X721).\nand substitution\nX718 -> 0\nX719 -> s(s(s(s(s(0)))))\nX720 -> s(s(s(s(s(s(0))))))\nX679 -> X722\nX721 -> X722", fontsize=14, style = filled, fillcolor = white];
117 -> 2008 [arrowhead = none ];
2008 -> 119;

2009 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
118 -> 2009 [arrowhead = none ];
2009 -> 127;

2010 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
119 -> 2010 [arrowhead = none ];
2010 -> 120;

2011 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
120 -> 2011 [arrowhead = none ];
2011 -> 121;

2012 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
120 -> 2012 [arrowhead = none ];
2012 -> 122;

2013 [label="ONLY EVAL with clause\nquot(0, s(X733), s(X734), 0).\nand substitution\nX733 -> s(s(s(s(0))))\nX734 -> s(s(s(s(s(0)))))\nX722 -> 0", fontsize=14, style = filled, fillcolor = white];
121 -> 2013 [arrowhead = none ];
2013 -> 123;

2014 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
122 -> 2014 [arrowhead = none ];
2014 -> 125;

2015 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
123 -> 2015 [arrowhead = none ];
2015 -> 124;

2016 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
125 -> 2016 [arrowhead = none ];
2016 -> 126;

2017 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
128 -> 2017 [arrowhead = none ];
2017 -> 130;

2018 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
130 -> 2018 [arrowhead = none ];
2018 -> 131;

2019 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
131 -> 2019 [arrowhead = none ];
2019 -> 132;

2020 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
131 -> 2020 [arrowhead = none ];
2020 -> 133;

2021 [label="ONLY EVAL with clause\nquot(s(X795), s(X796), X797, X798) :- quot(X795, X796, X797, X798).\nand substitution\nX795 -> 0\nX796 -> s(s(s(s(0))))\nX797 -> s(s(s(s(s(0)))))\nX756 -> X799\nX798 -> X799", fontsize=14, style = filled, fillcolor = white];
132 -> 2021 [arrowhead = none ];
2021 -> 134;

2022 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
133 -> 2022 [arrowhead = none ];
2022 -> 142;

2023 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
134 -> 2023 [arrowhead = none ];
2023 -> 135;

2024 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
135 -> 2024 [arrowhead = none ];
2024 -> 136;

2025 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
135 -> 2025 [arrowhead = none ];
2025 -> 137;

2026 [label="ONLY EVAL with clause\nquot(0, s(X810), s(X811), 0).\nand substitution\nX810 -> s(s(s(0)))\nX811 -> s(s(s(s(0))))\nX799 -> 0", fontsize=14, style = filled, fillcolor = white];
136 -> 2026 [arrowhead = none ];
2026 -> 138;

2027 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
137 -> 2027 [arrowhead = none ];
2027 -> 140;

2028 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
138 -> 2028 [arrowhead = none ];
2028 -> 139;

2029 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
140 -> 2029 [arrowhead = none ];
2029 -> 141;

2030 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
143 -> 2030 [arrowhead = none ];
2030 -> 145;

2031 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
145 -> 2031 [arrowhead = none ];
2031 -> 146;

2032 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
146 -> 2032 [arrowhead = none ];
2032 -> 147;

2033 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
146 -> 2033 [arrowhead = none ];
2033 -> 148;

2034 [label="ONLY EVAL with clause\nquot(s(X872), s(X873), X874, X875) :- quot(X872, X873, X874, X875).\nand substitution\nX872 -> 0\nX873 -> s(s(s(0)))\nX874 -> s(s(s(s(0))))\nX833 -> X876\nX875 -> X876", fontsize=14, style = filled, fillcolor = white];
147 -> 2034 [arrowhead = none ];
2034 -> 149;

2035 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
148 -> 2035 [arrowhead = none ];
2035 -> 157;

2036 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
149 -> 2036 [arrowhead = none ];
2036 -> 150;

2037 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
150 -> 2037 [arrowhead = none ];
2037 -> 151;

2038 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
150 -> 2038 [arrowhead = none ];
2038 -> 152;

2039 [label="ONLY EVAL with clause\nquot(0, s(X887), s(X888), 0).\nand substitution\nX887 -> s(s(0))\nX888 -> s(s(s(0)))\nX876 -> 0", fontsize=14, style = filled, fillcolor = white];
151 -> 2039 [arrowhead = none ];
2039 -> 153;

2040 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
152 -> 2040 [arrowhead = none ];
2040 -> 155;

2041 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
153 -> 2041 [arrowhead = none ];
2041 -> 154;

2042 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
155 -> 2042 [arrowhead = none ];
2042 -> 156;

2043 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
158 -> 2043 [arrowhead = none ];
2043 -> 160;

2044 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
160 -> 2044 [arrowhead = none ];
2044 -> 161;

2045 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
161 -> 2045 [arrowhead = none ];
2045 -> 162;

2046 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
161 -> 2046 [arrowhead = none ];
2046 -> 163;

2047 [label="ONLY EVAL with clause\nquot(s(X949), s(X950), X951, X952) :- quot(X949, X950, X951, X952).\nand substitution\nX949 -> 0\nX950 -> s(s(0))\nX951 -> s(s(s(0)))\nX910 -> X953\nX952 -> X953", fontsize=14, style = filled, fillcolor = white];
162 -> 2047 [arrowhead = none ];
2047 -> 164;

2048 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
163 -> 2048 [arrowhead = none ];
2048 -> 172;

2049 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
164 -> 2049 [arrowhead = none ];
2049 -> 165;

2050 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
165 -> 2050 [arrowhead = none ];
2050 -> 166;

2051 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
165 -> 2051 [arrowhead = none ];
2051 -> 167;

2052 [label="ONLY EVAL with clause\nquot(0, s(X964), s(X965), 0).\nand substitution\nX964 -> s(0)\nX965 -> s(s(0))\nX953 -> 0", fontsize=14, style = filled, fillcolor = white];
166 -> 2052 [arrowhead = none ];
2052 -> 168;

2053 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
167 -> 2053 [arrowhead = none ];
2053 -> 170;

2054 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
168 -> 2054 [arrowhead = none ];
2054 -> 169;

2055 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
170 -> 2055 [arrowhead = none ];
2055 -> 171;

2056 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
173 -> 2056 [arrowhead = none ];
2056 -> 175;

2057 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
175 -> 2057 [arrowhead = none ];
2057 -> 176;

2058 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
176 -> 2058 [arrowhead = none ];
2058 -> 177;

2059 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
176 -> 2059 [arrowhead = none ];
2059 -> 178;

2060 [label="ONLY EVAL with clause\nquot(s(X1026), s(X1027), X1028, X1029) :- quot(X1026, X1027, X1028, X1029).\nand substitution\nX1026 -> 0\nX1027 -> s(0)\nX1028 -> s(s(0))\nX987 -> X1030\nX1029 -> X1030", fontsize=14, style = filled, fillcolor = white];
177 -> 2060 [arrowhead = none ];
2060 -> 179;

2061 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
178 -> 2061 [arrowhead = none ];
2061 -> 187;

2062 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
179 -> 2062 [arrowhead = none ];
2062 -> 180;

2063 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
180 -> 2063 [arrowhead = none ];
2063 -> 181;

2064 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
180 -> 2064 [arrowhead = none ];
2064 -> 182;

2065 [label="ONLY EVAL with clause\nquot(0, s(X1041), s(X1042), 0).\nand substitution\nX1041 -> 0\nX1042 -> s(0)\nX1030 -> 0", fontsize=14, style = filled, fillcolor = white];
181 -> 2065 [arrowhead = none ];
2065 -> 183;

2066 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
182 -> 2066 [arrowhead = none ];
2066 -> 185;

2067 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
183 -> 2067 [arrowhead = none ];
2067 -> 184;

2068 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
185 -> 2068 [arrowhead = none ];
2068 -> 186;

2069 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
190 -> 2069 [arrowhead = none ];
2069 -> 192;

2070 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
191 -> 2070 [arrowhead = none ];
2070 -> 211;

2071 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
192 -> 2071 [arrowhead = none ];
2071 -> 193;

2072 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
192 -> 2072 [arrowhead = none ];
2072 -> 194;

2073 [label="EVAL with clause\ntimes(0, X1067, 0).\nand substitution\nT22 -> 0\nT20 -> T194\nX1067 -> s(s(T194))\nX39 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
193 -> 2073 [arrowhead = none ];
2073 -> 195;

2074 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
193 -> 2074 [arrowhead = none ];
2074 -> 196;

2075 [label="EVAL with clause\ntimes(s(X1078), X1079, X1080) :- ','(times(X1078, X1079, X1081), add(X1081, X1079, X1080)).\nand substitution\nX1078 -> T199\nT22 -> s(T199)\nT20 -> T200\nX1079 -> s(s(T200))\nX39 -> X1082\nX1080 -> X1082", fontsize=14, style = filled, fillcolor = lightblue];
194 -> 2075 [arrowhead = none ];
2075 -> 198;

2076 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
194 -> 2076 [arrowhead = none ];
2076 -> 199;

2077 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
195 -> 2077 [arrowhead = none ];
2077 -> 197;

2078 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
198 -> 2078 [arrowhead = none ];
2078 -> 200;

2079 [label="SPLIT 2\nnew knowledge:\nT203 is ground\nreplacements:\nX1081 -> T203", fontsize=14, style = filled, fillcolor = violet];
198 -> 2079 [arrowhead = none ];
2079 -> 201;

2080 [label="INSTANCE with matching:\nT22 -> T199\nT20 -> T200\nX39 -> X1081", fontsize=14, style = filled, fillcolor = lightgrey];
200 -> 2080 [arrowhead = none , style=dashed];
2080 -> 190[style=dashed];

2081 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
201 -> 2081 [arrowhead = none ];
2081 -> 202;

2082 [label="BACKTRACK\nfor clause: add(X, 0, X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
202 -> 2082 [arrowhead = none ];
2082 -> 203;

2083 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
203 -> 2083 [arrowhead = none ];
2083 -> 204;

2084 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
203 -> 2084 [arrowhead = none ];
2084 -> 205;

2085 [label="EVAL with clause\nadd(0, X1099, X1099).\nand substitution\nT203 -> 0\nT200 -> T215\nX1099 -> s(s(T215))\nX1082 -> s(s(T215))", fontsize=14, style = filled, fillcolor = lightblue];
204 -> 2085 [arrowhead = none ];
2085 -> 206;

2086 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
204 -> 2086 [arrowhead = none ];
2086 -> 207;

2087 [label="EVAL with clause\nadd(s(X1109), X1110, s(X1111)) :- add(X1109, X1110, X1111).\nand substitution\nX1109 -> T220\nT203 -> s(T220)\nT200 -> T221\nX1110 -> s(s(T221))\nX1111 -> X1112\nX1082 -> s(X1112)", fontsize=14, style = filled, fillcolor = lightblue];
205 -> 2087 [arrowhead = none ];
2087 -> 209;

2088 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
205 -> 2088 [arrowhead = none ];
2088 -> 210;

2089 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
206 -> 2089 [arrowhead = none ];
2089 -> 208;

2090 [label="INSTANCE with matching:\nT203 -> T220\nT200 -> T221\nX1082 -> X1112", fontsize=14, style = filled, fillcolor = lightgrey];
209 -> 2090 [arrowhead = none , style=dashed];
2090 -> 201[style=dashed];

2091 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
211 -> 2091 [arrowhead = none ];
2091 -> 212;

2092 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
211 -> 2092 [arrowhead = none ];
2092 -> 213;

2093 [label="EVAL with clause\nneq(s(X1126), 0).\nand substitution\nT20 -> T232\nX1126 -> s(s(T232))\nT187 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
212 -> 2093 [arrowhead = none ];
2093 -> 214;

2094 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
212 -> 2094 [arrowhead = none ];
2094 -> 215;

2095 [label="BACKTRACK\nfor clause: neq(0, s(X))because of non-unification", fontsize=14, style = filled, fillcolor = white];
213 -> 2095 [arrowhead = none ];
2095 -> 217;

2096 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
214 -> 2096 [arrowhead = none ];
2096 -> 216;

2097 [label="EVAL with clause\nneq(s(X1133), s(X1134)) :- neq(X1133, X1134).\nand substitution\nT20 -> T237\nX1133 -> s(s(T237))\nX1134 -> T238\nT187 -> s(T238)", fontsize=14, style = filled, fillcolor = lightblue];
217 -> 2097 [arrowhead = none ];
2097 -> 218;

2098 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
217 -> 2098 [arrowhead = none ];
2098 -> 219;

2099 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
218 -> 2099 [arrowhead = none ];
2099 -> 220;

2100 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
220 -> 2100 [arrowhead = none ];
2100 -> 221;

2101 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
220 -> 2101 [arrowhead = none ];
2101 -> 222;

2102 [label="EVAL with clause\nneq(s(X1143), 0).\nand substitution\nT237 -> T245\nX1143 -> s(T245)\nT238 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
221 -> 2102 [arrowhead = none ];
2102 -> 223;

2103 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
221 -> 2103 [arrowhead = none ];
2103 -> 224;

2104 [label="BACKTRACK\nfor clause: neq(0, s(X))because of non-unification", fontsize=14, style = filled, fillcolor = white];
222 -> 2104 [arrowhead = none ];
2104 -> 226;

2105 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
223 -> 2105 [arrowhead = none ];
2105 -> 225;

2106 [label="EVAL with clause\nneq(s(X1150), s(X1151)) :- neq(X1150, X1151).\nand substitution\nT237 -> T250\nX1150 -> s(T250)\nX1151 -> T251\nT238 -> s(T251)", fontsize=14, style = filled, fillcolor = lightblue];
226 -> 2106 [arrowhead = none ];
2106 -> 227;

2107 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
226 -> 2107 [arrowhead = none ];
2107 -> 228;

2108 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
227 -> 2108 [arrowhead = none ];
2108 -> 229;

2109 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
229 -> 2109 [arrowhead = none ];
2109 -> 230;

2110 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
229 -> 2110 [arrowhead = none ];
2110 -> 231;

2111 [label="EVAL with clause\nneq(s(X1160), 0).\nand substitution\nT250 -> T258\nX1160 -> T258\nT251 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
230 -> 2111 [arrowhead = none ];
2111 -> 232;

2112 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
230 -> 2112 [arrowhead = none ];
2112 -> 233;

2113 [label="BACKTRACK\nfor clause: neq(0, s(X))because of non-unification", fontsize=14, style = filled, fillcolor = white];
231 -> 2113 [arrowhead = none ];
2113 -> 235;

2114 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
232 -> 2114 [arrowhead = none ];
2114 -> 234;

2115 [label="EVAL with clause\nneq(s(X1167), s(X1168)) :- neq(X1167, X1168).\nand substitution\nT250 -> T263\nX1167 -> T263\nX1168 -> T264\nT251 -> s(T264)", fontsize=14, style = filled, fillcolor = lightblue];
235 -> 2115 [arrowhead = none ];
2115 -> 236;

2116 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
235 -> 2116 [arrowhead = none ];
2116 -> 237;

2117 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
236 -> 2117 [arrowhead = none ];
2117 -> 238;

2118 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
238 -> 2118 [arrowhead = none ];
2118 -> 239;

2119 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
238 -> 2119 [arrowhead = none ];
2119 -> 240;

2120 [label="EVAL with clause\nneq(s(X1177), 0).\nand substitution\nX1177 -> T271\nT263 -> s(T271)\nT264 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
239 -> 2120 [arrowhead = none ];
2120 -> 241;

2121 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
239 -> 2121 [arrowhead = none ];
2121 -> 242;

2122 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
240 -> 2122 [arrowhead = none ];
2122 -> 244;

2123 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
240 -> 2123 [arrowhead = none ];
2123 -> 245;

2124 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
241 -> 2124 [arrowhead = none ];
2124 -> 243;

2125 [label="EVAL with clause\nneq(0, s(X1183)).\nand substitution\nT263 -> 0\nX1183 -> T276\nT264 -> s(T276)", fontsize=14, style = filled, fillcolor = lightblue];
244 -> 2125 [arrowhead = none ];
2125 -> 246;

2126 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
244 -> 2126 [arrowhead = none ];
2126 -> 247;

2127 [label="EVAL with clause\nneq(s(X1189), s(X1190)) :- neq(X1189, X1190).\nand substitution\nX1189 -> T281\nT263 -> s(T281)\nX1190 -> T282\nT264 -> s(T282)", fontsize=14, style = filled, fillcolor = lightblue];
245 -> 2127 [arrowhead = none ];
2127 -> 249;

2128 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
245 -> 2128 [arrowhead = none ];
2128 -> 250;

2129 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
246 -> 2129 [arrowhead = none ];
2129 -> 248;

2130 [label="INSTANCE with matching:\nT263 -> T281\nT264 -> T282", fontsize=14, style = filled, fillcolor = lightgrey];
249 -> 2130 [arrowhead = none , style=dashed];
2130 -> 236[style=dashed];

2131 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
251 -> 2131 [arrowhead = none ];
2131 -> 252;

2132 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
251 -> 2132 [arrowhead = none ];
2132 -> 253;

2133 [label="EVAL with clause\npr(X1201, s(0)).\nand substitution\nT14 -> 0\nX1201 -> s(s(s(0)))\nT291 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
252 -> 2133 [arrowhead = none ];
2133 -> 254;

2134 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
252 -> 2134 [arrowhead = none ];
2134 -> 255;

2135 [label="EVAL with clause\npr(X1207, s(s(X1208))) :- ','(not_divides(s(s(X1208)), X1207), pr(X1207, s(X1208))).\nand substitution\nT14 -> s(T297)\nX1207 -> s(s(s(s(T297))))\nX1208 -> T297\nT296 -> s(T297)", fontsize=14, style = filled, fillcolor = lightblue];
253 -> 2135 [arrowhead = none ];
2135 -> 257;

2136 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
253 -> 2136 [arrowhead = none ];
2136 -> 258;

2137 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
254 -> 2137 [arrowhead = none ];
2137 -> 256;

2138 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
257 -> 2138 [arrowhead = none ];
2138 -> 259;

2139 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
257 -> 2139 [arrowhead = none ];
2139 -> 260;

2140 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
259 -> 2140 [arrowhead = none ];
2140 -> 261;

2141 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
260 -> 2141 [arrowhead = none ];
2141 -> 489;

2142 [label="ONLY EVAL with clause\nnot_divides(X1229, X1230) :- ','(div(X1230, X1229, X1231), ','(times(X1231, X1229, X1232), neq(X1230, X1232))).\nand substitution\nT297 -> T303\nX1229 -> s(s(T303))\nX1230 -> s(s(s(s(T303))))", fontsize=14, style = filled, fillcolor = white];
261 -> 2142 [arrowhead = none ];
2142 -> 262;

2143 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
262 -> 2143 [arrowhead = none ];
2143 -> 263;

2144 [label="SPLIT 2\nnew knowledge:\nT305 is ground\nreplacements:\nX1231 -> T305", fontsize=14, style = filled, fillcolor = violet];
262 -> 2144 [arrowhead = none ];
2144 -> 264;

2145 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
263 -> 2145 [arrowhead = none ];
2145 -> 265;

2146 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
264 -> 2146 [arrowhead = none ];
2146 -> 487;

2147 [label="SPLIT 2\nnew knowledge:\nT474 is ground\nreplacements:\nX1232 -> T474", fontsize=14, style = filled, fillcolor = violet];
264 -> 2147 [arrowhead = none ];
2147 -> 488;

2148 [label="ONLY EVAL with clause\ndiv(X1258, X1259, X1260) :- quot(X1258, X1259, X1259, X1260).\nand substitution\nT303 -> T310\nX1258 -> s(s(s(s(T310))))\nX1259 -> s(s(T310))\nX1231 -> X1261\nX1260 -> X1261", fontsize=14, style = filled, fillcolor = white];
265 -> 2148 [arrowhead = none ];
2148 -> 266;

2149 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
266 -> 2149 [arrowhead = none ];
2149 -> 267;

2150 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
267 -> 2150 [arrowhead = none ];
2150 -> 268;

2151 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
268 -> 2151 [arrowhead = none ];
2151 -> 269;

2152 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
268 -> 2152 [arrowhead = none ];
2152 -> 270;

2153 [label="ONLY EVAL with clause\nquot(s(X1311), s(X1312), X1313, X1314) :- quot(X1311, X1312, X1313, X1314).\nand substitution\nT310 -> T318\nX1311 -> s(s(s(T318)))\nX1312 -> s(T318)\nX1313 -> s(s(T318))\nX1261 -> X1315\nX1314 -> X1315", fontsize=14, style = filled, fillcolor = white];
269 -> 2153 [arrowhead = none ];
2153 -> 271;

2154 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
270 -> 2154 [arrowhead = none ];
2154 -> 486;

2155 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
271 -> 2155 [arrowhead = none ];
2155 -> 272;

2156 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
272 -> 2156 [arrowhead = none ];
2156 -> 273;

2157 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
273 -> 2157 [arrowhead = none ];
2157 -> 274;

2158 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
273 -> 2158 [arrowhead = none ];
2158 -> 275;

2159 [label="ONLY EVAL with clause\nquot(s(X1365), s(X1366), X1367, X1368) :- quot(X1365, X1366, X1367, X1368).\nand substitution\nT318 -> T328\nX1365 -> s(s(T328))\nX1366 -> T328\nX1367 -> s(s(T328))\nX1315 -> X1369\nX1368 -> X1369", fontsize=14, style = filled, fillcolor = white];
274 -> 2159 [arrowhead = none ];
2159 -> 276;

2160 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
275 -> 2160 [arrowhead = none ];
2160 -> 485;

2161 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
276 -> 2161 [arrowhead = none ];
2161 -> 277;

2162 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
277 -> 2162 [arrowhead = none ];
2162 -> 278;

2163 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
278 -> 2163 [arrowhead = none ];
2163 -> 279;

2164 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
278 -> 2164 [arrowhead = none ];
2164 -> 280;

2165 [label="EVAL with clause\nquot(s(X1401), s(X1402), X1403, X1404) :- quot(X1401, X1402, X1403, X1404).\nand substitution\nT328 -> s(T340)\nX1401 -> s(s(T340))\nX1402 -> T340\nT339 -> s(T340)\nX1403 -> s(s(s(T340)))\nX1369 -> X1405\nX1404 -> X1405", fontsize=14, style = filled, fillcolor = lightblue];
279 -> 2165 [arrowhead = none ];
2165 -> 281;

2166 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
279 -> 2166 [arrowhead = none ];
2166 -> 282;

2167 [label="EVAL with clause\nquot(X2624, 0, s(X2625), s(X2626)) :- quot(X2624, s(X2625), s(X2625), X2626).\nand substitution\nT328 -> 0\nX2624 -> s(s(0))\nT469 -> 0\nX2625 -> s(0)\nX2626 -> X2627\nX1369 -> s(X2627)", fontsize=14, style = filled, fillcolor = lightblue];
280 -> 2167 [arrowhead = none ];
2167 -> 467;

2168 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
280 -> 2168 [arrowhead = none ];
2168 -> 468;

2169 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
281 -> 2169 [arrowhead = none ];
2169 -> 283;

2170 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
283 -> 2170 [arrowhead = none ];
2170 -> 284;

2171 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
284 -> 2171 [arrowhead = none ];
2171 -> 285;

2172 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
284 -> 2172 [arrowhead = none ];
2172 -> 286;

2173 [label="EVAL with clause\nquot(s(X1441), s(X1442), X1443, X1444) :- quot(X1441, X1442, X1443, X1444).\nand substitution\nT340 -> s(T352)\nX1441 -> s(s(T352))\nX1442 -> T352\nT351 -> s(T352)\nX1443 -> s(s(s(s(T352))))\nX1405 -> X1445\nX1444 -> X1445", fontsize=14, style = filled, fillcolor = lightblue];
285 -> 2173 [arrowhead = none ];
2173 -> 287;

2174 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
285 -> 2174 [arrowhead = none ];
2174 -> 288;

2175 [label="EVAL with clause\nquot(X2490, 0, s(X2491), s(X2492)) :- quot(X2490, s(X2491), s(X2491), X2492).\nand substitution\nT340 -> 0\nX2490 -> s(s(0))\nT466 -> 0\nX2491 -> s(s(0))\nX2492 -> X2493\nX1405 -> s(X2493)", fontsize=14, style = filled, fillcolor = lightblue];
286 -> 2175 [arrowhead = none ];
2175 -> 446;

2176 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
286 -> 2176 [arrowhead = none ];
2176 -> 447;

2177 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
287 -> 2177 [arrowhead = none ];
2177 -> 289;

2178 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
289 -> 2178 [arrowhead = none ];
2178 -> 290;

2179 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
290 -> 2179 [arrowhead = none ];
2179 -> 291;

2180 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
290 -> 2180 [arrowhead = none ];
2180 -> 292;

2181 [label="EVAL with clause\nquot(s(X1481), s(X1482), X1483, X1484) :- quot(X1481, X1482, X1483, X1484).\nand substitution\nT352 -> s(T364)\nX1481 -> s(s(T364))\nX1482 -> T364\nT363 -> s(T364)\nX1483 -> s(s(s(s(s(T364)))))\nX1445 -> X1485\nX1484 -> X1485", fontsize=14, style = filled, fillcolor = lightblue];
291 -> 2181 [arrowhead = none ];
2181 -> 293;

2182 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
291 -> 2182 [arrowhead = none ];
2182 -> 294;

2183 [label="EVAL with clause\nquot(X2356, 0, s(X2357), s(X2358)) :- quot(X2356, s(X2357), s(X2357), X2358).\nand substitution\nT352 -> 0\nX2356 -> s(s(0))\nT463 -> 0\nX2357 -> s(s(s(0)))\nX2358 -> X2359\nX1445 -> s(X2359)", fontsize=14, style = filled, fillcolor = lightblue];
292 -> 2183 [arrowhead = none ];
2183 -> 425;

2184 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
292 -> 2184 [arrowhead = none ];
2184 -> 426;

2185 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
293 -> 2185 [arrowhead = none ];
2185 -> 295;

2186 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
295 -> 2186 [arrowhead = none ];
2186 -> 296;

2187 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
296 -> 2187 [arrowhead = none ];
2187 -> 297;

2188 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
296 -> 2188 [arrowhead = none ];
2188 -> 298;

2189 [label="EVAL with clause\nquot(s(X1521), s(X1522), X1523, X1524) :- quot(X1521, X1522, X1523, X1524).\nand substitution\nT364 -> s(T376)\nX1521 -> s(s(T376))\nX1522 -> T376\nT375 -> s(T376)\nX1523 -> s(s(s(s(s(s(T376))))))\nX1485 -> X1525\nX1524 -> X1525", fontsize=14, style = filled, fillcolor = lightblue];
297 -> 2189 [arrowhead = none ];
2189 -> 299;

2190 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
297 -> 2190 [arrowhead = none ];
2190 -> 300;

2191 [label="EVAL with clause\nquot(X2222, 0, s(X2223), s(X2224)) :- quot(X2222, s(X2223), s(X2223), X2224).\nand substitution\nT364 -> 0\nX2222 -> s(s(0))\nT460 -> 0\nX2223 -> s(s(s(s(0))))\nX2224 -> X2225\nX1485 -> s(X2225)", fontsize=14, style = filled, fillcolor = lightblue];
298 -> 2191 [arrowhead = none ];
2191 -> 404;

2192 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
298 -> 2192 [arrowhead = none ];
2192 -> 405;

2193 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
299 -> 2193 [arrowhead = none ];
2193 -> 301;

2194 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
301 -> 2194 [arrowhead = none ];
2194 -> 302;

2195 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
302 -> 2195 [arrowhead = none ];
2195 -> 303;

2196 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
302 -> 2196 [arrowhead = none ];
2196 -> 304;

2197 [label="EVAL with clause\nquot(s(X1561), s(X1562), X1563, X1564) :- quot(X1561, X1562, X1563, X1564).\nand substitution\nT376 -> s(T388)\nX1561 -> s(s(T388))\nX1562 -> T388\nT387 -> s(T388)\nX1563 -> s(s(s(s(s(s(s(T388)))))))\nX1525 -> X1565\nX1564 -> X1565", fontsize=14, style = filled, fillcolor = lightblue];
303 -> 2197 [arrowhead = none ];
2197 -> 305;

2198 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
303 -> 2198 [arrowhead = none ];
2198 -> 306;

2199 [label="EVAL with clause\nquot(X2088, 0, s(X2089), s(X2090)) :- quot(X2088, s(X2089), s(X2089), X2090).\nand substitution\nT376 -> 0\nX2088 -> s(s(0))\nT457 -> 0\nX2089 -> s(s(s(s(s(0)))))\nX2090 -> X2091\nX1525 -> s(X2091)", fontsize=14, style = filled, fillcolor = lightblue];
304 -> 2199 [arrowhead = none ];
2199 -> 383;

2200 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
304 -> 2200 [arrowhead = none ];
2200 -> 384;

2201 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
305 -> 2201 [arrowhead = none ];
2201 -> 307;

2202 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
307 -> 2202 [arrowhead = none ];
2202 -> 308;

2203 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
308 -> 2203 [arrowhead = none ];
2203 -> 309;

2204 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
308 -> 2204 [arrowhead = none ];
2204 -> 310;

2205 [label="EVAL with clause\nquot(s(X1601), s(X1602), X1603, X1604) :- quot(X1601, X1602, X1603, X1604).\nand substitution\nT388 -> s(T400)\nX1601 -> s(s(T400))\nX1602 -> T400\nT399 -> s(T400)\nX1603 -> s(s(s(s(s(s(s(s(T400))))))))\nX1565 -> X1605\nX1604 -> X1605", fontsize=14, style = filled, fillcolor = lightblue];
309 -> 2205 [arrowhead = none ];
2205 -> 311;

2206 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
309 -> 2206 [arrowhead = none ];
2206 -> 312;

2207 [label="EVAL with clause\nquot(X1954, 0, s(X1955), s(X1956)) :- quot(X1954, s(X1955), s(X1955), X1956).\nand substitution\nT388 -> 0\nX1954 -> s(s(0))\nT454 -> 0\nX1955 -> s(s(s(s(s(s(0))))))\nX1956 -> X1957\nX1565 -> s(X1957)", fontsize=14, style = filled, fillcolor = lightblue];
310 -> 2207 [arrowhead = none ];
2207 -> 362;

2208 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
310 -> 2208 [arrowhead = none ];
2208 -> 363;

2209 [label="GENERALIZATION\nT403 <-- s(s(s(s(s(s(s(T400)))))))\n\nNew Knowledge:\nT403 is ground", fontsize=14, style = filled, fillcolor = violet];
311 -> 2209 [arrowhead = none ];
2209 -> 313;

2210 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
313 -> 2210 [arrowhead = none ];
2210 -> 314;

2211 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
314 -> 2211 [arrowhead = none ];
2211 -> 315;

2212 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
315 -> 2212 [arrowhead = none ];
2212 -> 316;

2213 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
315 -> 2213 [arrowhead = none ];
2213 -> 317;

2214 [label="EVAL with clause\nquot(s(X1650), s(X1651), X1652, X1653) :- quot(X1650, X1651, X1652, X1653).\nand substitution\nT400 -> s(T420)\nX1650 -> s(s(T420))\nX1651 -> T420\nT419 -> s(T420)\nT403 -> T421\nX1652 -> s(T421)\nX1605 -> X1654\nX1653 -> X1654", fontsize=14, style = filled, fillcolor = lightblue];
316 -> 2214 [arrowhead = none ];
2214 -> 318;

2215 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
316 -> 2215 [arrowhead = none ];
2215 -> 319;

2216 [label="EVAL with clause\nquot(X1676, 0, s(X1677), s(X1678)) :- quot(X1676, s(X1677), s(X1677), X1678).\nand substitution\nT400 -> 0\nX1676 -> s(s(0))\nT429 -> 0\nT403 -> T430\nX1677 -> T430\nX1678 -> X1679\nX1605 -> s(X1679)", fontsize=14, style = filled, fillcolor = lightblue];
317 -> 2216 [arrowhead = none ];
2216 -> 320;

2217 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
317 -> 2217 [arrowhead = none ];
2217 -> 321;

2218 [label="INSTANCE with matching:\nT400 -> T420\nT403 -> T421\nX1605 -> X1654", fontsize=14, style = filled, fillcolor = lightgrey];
318 -> 2218 [arrowhead = none , style=dashed];
2218 -> 313[style=dashed];

2219 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
320 -> 2219 [arrowhead = none ];
2219 -> 322;

2220 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
322 -> 2220 [arrowhead = none ];
2220 -> 323;

2221 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
323 -> 2221 [arrowhead = none ];
2221 -> 324;

2222 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
323 -> 2222 [arrowhead = none ];
2222 -> 325;

2223 [label="ONLY EVAL with clause\nquot(s(X1732), s(X1733), X1734, X1735) :- quot(X1732, X1733, X1734, X1735).\nand substitution\nX1732 -> s(0)\nT430 -> T438\nX1733 -> T438\nX1734 -> s(T438)\nX1679 -> X1736\nX1735 -> X1736", fontsize=14, style = filled, fillcolor = white];
324 -> 2223 [arrowhead = none ];
2223 -> 326;

2224 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
325 -> 2224 [arrowhead = none ];
2224 -> 361;

2225 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
326 -> 2225 [arrowhead = none ];
2225 -> 327;

2226 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
327 -> 2226 [arrowhead = none ];
2226 -> 328;

2227 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
328 -> 2227 [arrowhead = none ];
2227 -> 329;

2228 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
328 -> 2228 [arrowhead = none ];
2228 -> 330;

2229 [label="EVAL with clause\nquot(s(X1768), s(X1769), X1770, X1771) :- quot(X1768, X1769, X1770, X1771).\nand substitution\nX1768 -> 0\nX1769 -> T444\nT438 -> s(T444)\nX1770 -> s(s(T444))\nX1736 -> X1772\nX1771 -> X1772", fontsize=14, style = filled, fillcolor = lightblue];
329 -> 2229 [arrowhead = none ];
2229 -> 331;

2230 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
329 -> 2230 [arrowhead = none ];
2230 -> 332;

2231 [label="EVAL with clause\nquot(X1839, 0, s(X1840), s(X1841)) :- quot(X1839, s(X1840), s(X1840), X1841).\nand substitution\nX1839 -> s(0)\nT438 -> 0\nX1840 -> 0\nX1841 -> X1842\nX1736 -> s(X1842)", fontsize=14, style = filled, fillcolor = lightblue];
330 -> 2231 [arrowhead = none ];
2231 -> 349;

2232 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
330 -> 2232 [arrowhead = none ];
2232 -> 350;

2233 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
331 -> 2233 [arrowhead = none ];
2233 -> 333;

2234 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
333 -> 2234 [arrowhead = none ];
2234 -> 334;

2235 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
333 -> 2235 [arrowhead = none ];
2235 -> 335;

2236 [label="EVAL with clause\nquot(0, s(X1789), s(X1790), 0).\nand substitution\nX1789 -> T451\nT444 -> s(T451)\nX1790 -> s(s(T451))\nX1772 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
334 -> 2236 [arrowhead = none ];
2236 -> 336;

2237 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
334 -> 2237 [arrowhead = none ];
2237 -> 337;

2238 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
335 -> 2238 [arrowhead = none ];
2238 -> 339;

2239 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
336 -> 2239 [arrowhead = none ];
2239 -> 338;

2240 [label="EVAL with clause\nquot(X1805, 0, s(X1806), s(X1807)) :- quot(X1805, s(X1806), s(X1806), X1807).\nand substitution\nX1805 -> 0\nT444 -> 0\nX1806 -> s(0)\nX1807 -> X1808\nX1772 -> s(X1808)", fontsize=14, style = filled, fillcolor = lightblue];
339 -> 2240 [arrowhead = none ];
2240 -> 340;

2241 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
339 -> 2241 [arrowhead = none ];
2241 -> 341;

2242 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
340 -> 2242 [arrowhead = none ];
2242 -> 342;

2243 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
342 -> 2243 [arrowhead = none ];
2243 -> 343;

2244 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
342 -> 2244 [arrowhead = none ];
2244 -> 344;

2245 [label="ONLY EVAL with clause\nquot(0, s(X1822), s(X1823), 0).\nand substitution\nX1822 -> s(0)\nX1823 -> s(0)\nX1808 -> 0", fontsize=14, style = filled, fillcolor = white];
343 -> 2245 [arrowhead = none ];
2245 -> 345;

2246 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
344 -> 2246 [arrowhead = none ];
2246 -> 347;

2247 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
345 -> 2247 [arrowhead = none ];
2247 -> 346;

2248 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
347 -> 2248 [arrowhead = none ];
2248 -> 348;

2249 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
349 -> 2249 [arrowhead = none ];
2249 -> 351;

2250 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
351 -> 2250 [arrowhead = none ];
2250 -> 352;

2251 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
352 -> 2251 [arrowhead = none ];
2251 -> 353;

2252 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
352 -> 2252 [arrowhead = none ];
2252 -> 354;

2253 [label="ONLY EVAL with clause\nquot(s(X1901), s(X1902), X1903, X1904) :- quot(X1901, X1902, X1903, X1904).\nand substitution\nX1901 -> 0\nX1902 -> 0\nX1903 -> s(0)\nX1842 -> X1905\nX1904 -> X1905", fontsize=14, style = filled, fillcolor = white];
353 -> 2253 [arrowhead = none ];
2253 -> 355;

2254 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
354 -> 2254 [arrowhead = none ];
2254 -> 360;

2255 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
355 -> 2255 [arrowhead = none ];
2255 -> 356;

2256 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
356 -> 2256 [arrowhead = none ];
2256 -> 357;

2257 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
357 -> 2257 [arrowhead = none ];
2257 -> 358;

2258 [label="ONLY EVAL with clause\nquot(X1934, 0, s(X1935), s(X1936)) :- quot(X1934, s(X1935), s(X1935), X1936).\nand substitution\nX1934 -> 0\nX1935 -> 0\nX1936 -> X1937\nX1905 -> s(X1937)", fontsize=14, style = filled, fillcolor = white];
358 -> 2258 [arrowhead = none ];
2258 -> 359;

2259 [label="INSTANCE with matching:\nX565 -> X1937", fontsize=14, style = filled, fillcolor = lightgrey];
359 -> 2259 [arrowhead = none , style=dashed];
2259 -> 88[style=dashed];

2260 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
362 -> 2260 [arrowhead = none ];
2260 -> 364;

2261 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
364 -> 2261 [arrowhead = none ];
2261 -> 365;

2262 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
365 -> 2262 [arrowhead = none ];
2262 -> 366;

2263 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
365 -> 2263 [arrowhead = none ];
2263 -> 367;

2264 [label="ONLY EVAL with clause\nquot(s(X2010), s(X2011), X2012, X2013) :- quot(X2010, X2011, X2012, X2013).\nand substitution\nX2010 -> s(0)\nX2011 -> s(s(s(s(s(s(0))))))\nX2012 -> s(s(s(s(s(s(s(0)))))))\nX1957 -> X2014\nX2013 -> X2014", fontsize=14, style = filled, fillcolor = white];
366 -> 2264 [arrowhead = none ];
2264 -> 368;

2265 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
367 -> 2265 [arrowhead = none ];
2265 -> 382;

2266 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
368 -> 2266 [arrowhead = none ];
2266 -> 369;

2267 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
369 -> 2267 [arrowhead = none ];
2267 -> 370;

2268 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
370 -> 2268 [arrowhead = none ];
2268 -> 371;

2269 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
370 -> 2269 [arrowhead = none ];
2269 -> 372;

2270 [label="ONLY EVAL with clause\nquot(s(X2050), s(X2051), X2052, X2053) :- quot(X2050, X2051, X2052, X2053).\nand substitution\nX2050 -> 0\nX2051 -> s(s(s(s(s(0)))))\nX2052 -> s(s(s(s(s(s(s(0)))))))\nX2014 -> X2054\nX2053 -> X2054", fontsize=14, style = filled, fillcolor = white];
371 -> 2270 [arrowhead = none ];
2270 -> 373;

2271 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
372 -> 2271 [arrowhead = none ];
2271 -> 381;

2272 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
373 -> 2272 [arrowhead = none ];
2272 -> 374;

2273 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
374 -> 2273 [arrowhead = none ];
2273 -> 375;

2274 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
374 -> 2274 [arrowhead = none ];
2274 -> 376;

2275 [label="ONLY EVAL with clause\nquot(0, s(X2065), s(X2066), 0).\nand substitution\nX2065 -> s(s(s(s(0))))\nX2066 -> s(s(s(s(s(s(0))))))\nX2054 -> 0", fontsize=14, style = filled, fillcolor = white];
375 -> 2275 [arrowhead = none ];
2275 -> 377;

2276 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
376 -> 2276 [arrowhead = none ];
2276 -> 379;

2277 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
377 -> 2277 [arrowhead = none ];
2277 -> 378;

2278 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
379 -> 2278 [arrowhead = none ];
2278 -> 380;

2279 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
383 -> 2279 [arrowhead = none ];
2279 -> 385;

2280 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
385 -> 2280 [arrowhead = none ];
2280 -> 386;

2281 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
386 -> 2281 [arrowhead = none ];
2281 -> 387;

2282 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
386 -> 2282 [arrowhead = none ];
2282 -> 388;

2283 [label="ONLY EVAL with clause\nquot(s(X2144), s(X2145), X2146, X2147) :- quot(X2144, X2145, X2146, X2147).\nand substitution\nX2144 -> s(0)\nX2145 -> s(s(s(s(s(0)))))\nX2146 -> s(s(s(s(s(s(0))))))\nX2091 -> X2148\nX2147 -> X2148", fontsize=14, style = filled, fillcolor = white];
387 -> 2283 [arrowhead = none ];
2283 -> 389;

2284 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
388 -> 2284 [arrowhead = none ];
2284 -> 403;

2285 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
389 -> 2285 [arrowhead = none ];
2285 -> 390;

2286 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
390 -> 2286 [arrowhead = none ];
2286 -> 391;

2287 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
391 -> 2287 [arrowhead = none ];
2287 -> 392;

2288 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
391 -> 2288 [arrowhead = none ];
2288 -> 393;

2289 [label="ONLY EVAL with clause\nquot(s(X2184), s(X2185), X2186, X2187) :- quot(X2184, X2185, X2186, X2187).\nand substitution\nX2184 -> 0\nX2185 -> s(s(s(s(0))))\nX2186 -> s(s(s(s(s(s(0))))))\nX2148 -> X2188\nX2187 -> X2188", fontsize=14, style = filled, fillcolor = white];
392 -> 2289 [arrowhead = none ];
2289 -> 394;

2290 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
393 -> 2290 [arrowhead = none ];
2290 -> 402;

2291 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
394 -> 2291 [arrowhead = none ];
2291 -> 395;

2292 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
395 -> 2292 [arrowhead = none ];
2292 -> 396;

2293 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
395 -> 2293 [arrowhead = none ];
2293 -> 397;

2294 [label="ONLY EVAL with clause\nquot(0, s(X2199), s(X2200), 0).\nand substitution\nX2199 -> s(s(s(0)))\nX2200 -> s(s(s(s(s(0)))))\nX2188 -> 0", fontsize=14, style = filled, fillcolor = white];
396 -> 2294 [arrowhead = none ];
2294 -> 398;

2295 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
397 -> 2295 [arrowhead = none ];
2295 -> 400;

2296 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
398 -> 2296 [arrowhead = none ];
2296 -> 399;

2297 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
400 -> 2297 [arrowhead = none ];
2297 -> 401;

2298 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
404 -> 2298 [arrowhead = none ];
2298 -> 406;

2299 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
406 -> 2299 [arrowhead = none ];
2299 -> 407;

2300 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
407 -> 2300 [arrowhead = none ];
2300 -> 408;

2301 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
407 -> 2301 [arrowhead = none ];
2301 -> 409;

2302 [label="ONLY EVAL with clause\nquot(s(X2278), s(X2279), X2280, X2281) :- quot(X2278, X2279, X2280, X2281).\nand substitution\nX2278 -> s(0)\nX2279 -> s(s(s(s(0))))\nX2280 -> s(s(s(s(s(0)))))\nX2225 -> X2282\nX2281 -> X2282", fontsize=14, style = filled, fillcolor = white];
408 -> 2302 [arrowhead = none ];
2302 -> 410;

2303 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
409 -> 2303 [arrowhead = none ];
2303 -> 424;

2304 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
410 -> 2304 [arrowhead = none ];
2304 -> 411;

2305 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
411 -> 2305 [arrowhead = none ];
2305 -> 412;

2306 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
412 -> 2306 [arrowhead = none ];
2306 -> 413;

2307 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
412 -> 2307 [arrowhead = none ];
2307 -> 414;

2308 [label="ONLY EVAL with clause\nquot(s(X2318), s(X2319), X2320, X2321) :- quot(X2318, X2319, X2320, X2321).\nand substitution\nX2318 -> 0\nX2319 -> s(s(s(0)))\nX2320 -> s(s(s(s(s(0)))))\nX2282 -> X2322\nX2321 -> X2322", fontsize=14, style = filled, fillcolor = white];
413 -> 2308 [arrowhead = none ];
2308 -> 415;

2309 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
414 -> 2309 [arrowhead = none ];
2309 -> 423;

2310 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
415 -> 2310 [arrowhead = none ];
2310 -> 416;

2311 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
416 -> 2311 [arrowhead = none ];
2311 -> 417;

2312 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
416 -> 2312 [arrowhead = none ];
2312 -> 418;

2313 [label="ONLY EVAL with clause\nquot(0, s(X2333), s(X2334), 0).\nand substitution\nX2333 -> s(s(0))\nX2334 -> s(s(s(s(0))))\nX2322 -> 0", fontsize=14, style = filled, fillcolor = white];
417 -> 2313 [arrowhead = none ];
2313 -> 419;

2314 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
418 -> 2314 [arrowhead = none ];
2314 -> 421;

2315 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
419 -> 2315 [arrowhead = none ];
2315 -> 420;

2316 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
421 -> 2316 [arrowhead = none ];
2316 -> 422;

2317 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
425 -> 2317 [arrowhead = none ];
2317 -> 427;

2318 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
427 -> 2318 [arrowhead = none ];
2318 -> 428;

2319 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
428 -> 2319 [arrowhead = none ];
2319 -> 429;

2320 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
428 -> 2320 [arrowhead = none ];
2320 -> 430;

2321 [label="ONLY EVAL with clause\nquot(s(X2412), s(X2413), X2414, X2415) :- quot(X2412, X2413, X2414, X2415).\nand substitution\nX2412 -> s(0)\nX2413 -> s(s(s(0)))\nX2414 -> s(s(s(s(0))))\nX2359 -> X2416\nX2415 -> X2416", fontsize=14, style = filled, fillcolor = white];
429 -> 2321 [arrowhead = none ];
2321 -> 431;

2322 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
430 -> 2322 [arrowhead = none ];
2322 -> 445;

2323 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
431 -> 2323 [arrowhead = none ];
2323 -> 432;

2324 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
432 -> 2324 [arrowhead = none ];
2324 -> 433;

2325 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
433 -> 2325 [arrowhead = none ];
2325 -> 434;

2326 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
433 -> 2326 [arrowhead = none ];
2326 -> 435;

2327 [label="ONLY EVAL with clause\nquot(s(X2452), s(X2453), X2454, X2455) :- quot(X2452, X2453, X2454, X2455).\nand substitution\nX2452 -> 0\nX2453 -> s(s(0))\nX2454 -> s(s(s(s(0))))\nX2416 -> X2456\nX2455 -> X2456", fontsize=14, style = filled, fillcolor = white];
434 -> 2327 [arrowhead = none ];
2327 -> 436;

2328 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
435 -> 2328 [arrowhead = none ];
2328 -> 444;

2329 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
436 -> 2329 [arrowhead = none ];
2329 -> 437;

2330 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
437 -> 2330 [arrowhead = none ];
2330 -> 438;

2331 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
437 -> 2331 [arrowhead = none ];
2331 -> 439;

2332 [label="ONLY EVAL with clause\nquot(0, s(X2467), s(X2468), 0).\nand substitution\nX2467 -> s(0)\nX2468 -> s(s(s(0)))\nX2456 -> 0", fontsize=14, style = filled, fillcolor = white];
438 -> 2332 [arrowhead = none ];
2332 -> 440;

2333 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
439 -> 2333 [arrowhead = none ];
2333 -> 442;

2334 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
440 -> 2334 [arrowhead = none ];
2334 -> 441;

2335 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
442 -> 2335 [arrowhead = none ];
2335 -> 443;

2336 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
446 -> 2336 [arrowhead = none ];
2336 -> 448;

2337 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
448 -> 2337 [arrowhead = none ];
2337 -> 449;

2338 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
449 -> 2338 [arrowhead = none ];
2338 -> 450;

2339 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
449 -> 2339 [arrowhead = none ];
2339 -> 451;

2340 [label="ONLY EVAL with clause\nquot(s(X2546), s(X2547), X2548, X2549) :- quot(X2546, X2547, X2548, X2549).\nand substitution\nX2546 -> s(0)\nX2547 -> s(s(0))\nX2548 -> s(s(s(0)))\nX2493 -> X2550\nX2549 -> X2550", fontsize=14, style = filled, fillcolor = white];
450 -> 2340 [arrowhead = none ];
2340 -> 452;

2341 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
451 -> 2341 [arrowhead = none ];
2341 -> 466;

2342 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
452 -> 2342 [arrowhead = none ];
2342 -> 453;

2343 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
453 -> 2343 [arrowhead = none ];
2343 -> 454;

2344 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
454 -> 2344 [arrowhead = none ];
2344 -> 455;

2345 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
454 -> 2345 [arrowhead = none ];
2345 -> 456;

2346 [label="ONLY EVAL with clause\nquot(s(X2586), s(X2587), X2588, X2589) :- quot(X2586, X2587, X2588, X2589).\nand substitution\nX2586 -> 0\nX2587 -> s(0)\nX2588 -> s(s(s(0)))\nX2550 -> X2590\nX2589 -> X2590", fontsize=14, style = filled, fillcolor = white];
455 -> 2346 [arrowhead = none ];
2346 -> 457;

2347 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
456 -> 2347 [arrowhead = none ];
2347 -> 465;

2348 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
457 -> 2348 [arrowhead = none ];
2348 -> 458;

2349 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
458 -> 2349 [arrowhead = none ];
2349 -> 459;

2350 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
458 -> 2350 [arrowhead = none ];
2350 -> 460;

2351 [label="ONLY EVAL with clause\nquot(0, s(X2601), s(X2602), 0).\nand substitution\nX2601 -> 0\nX2602 -> s(s(0))\nX2590 -> 0", fontsize=14, style = filled, fillcolor = white];
459 -> 2351 [arrowhead = none ];
2351 -> 461;

2352 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
460 -> 2352 [arrowhead = none ];
2352 -> 463;

2353 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
461 -> 2353 [arrowhead = none ];
2353 -> 462;

2354 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
463 -> 2354 [arrowhead = none ];
2354 -> 464;

2355 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
467 -> 2355 [arrowhead = none ];
2355 -> 469;

2356 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
469 -> 2356 [arrowhead = none ];
2356 -> 470;

2357 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
470 -> 2357 [arrowhead = none ];
2357 -> 471;

2358 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
470 -> 2358 [arrowhead = none ];
2358 -> 472;

2359 [label="ONLY EVAL with clause\nquot(s(X2680), s(X2681), X2682, X2683) :- quot(X2680, X2681, X2682, X2683).\nand substitution\nX2680 -> s(0)\nX2681 -> s(0)\nX2682 -> s(s(0))\nX2627 -> X2684\nX2683 -> X2684", fontsize=14, style = filled, fillcolor = white];
471 -> 2359 [arrowhead = none ];
2359 -> 473;

2360 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
472 -> 2360 [arrowhead = none ];
2360 -> 484;

2361 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
473 -> 2361 [arrowhead = none ];
2361 -> 474;

2362 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
474 -> 2362 [arrowhead = none ];
2362 -> 475;

2363 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
475 -> 2363 [arrowhead = none ];
2363 -> 476;

2364 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
475 -> 2364 [arrowhead = none ];
2364 -> 477;

2365 [label="ONLY EVAL with clause\nquot(s(X2740), s(X2741), X2742, X2743) :- quot(X2740, X2741, X2742, X2743).\nand substitution\nX2740 -> 0\nX2741 -> 0\nX2742 -> s(s(0))\nX2684 -> X2744\nX2743 -> X2744", fontsize=14, style = filled, fillcolor = white];
476 -> 2365 [arrowhead = none ];
2365 -> 478;

2366 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
477 -> 2366 [arrowhead = none ];
2366 -> 483;

2367 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
478 -> 2367 [arrowhead = none ];
2367 -> 479;

2368 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
479 -> 2368 [arrowhead = none ];
2368 -> 480;

2369 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
480 -> 2369 [arrowhead = none ];
2369 -> 481;

2370 [label="ONLY EVAL with clause\nquot(X2773, 0, s(X2774), s(X2775)) :- quot(X2773, s(X2774), s(X2774), X2775).\nand substitution\nX2773 -> 0\nX2774 -> s(0)\nX2775 -> X2776\nX2744 -> s(X2776)", fontsize=14, style = filled, fillcolor = white];
481 -> 2370 [arrowhead = none ];
2370 -> 482;

2371 [label="INSTANCE with matching:\nX1808 -> X2776", fontsize=14, style = filled, fillcolor = lightgrey];
482 -> 2371 [arrowhead = none , style=dashed];
2371 -> 340[style=dashed];

2372 [label="INSTANCE with matching:\nT22 -> T305\nT20 -> T303\nX39 -> X1232", fontsize=14, style = filled, fillcolor = lightgrey];
487 -> 2372 [arrowhead = none , style=dashed];
2372 -> 190[style=dashed];

2373 [label="INSTANCE with matching:\nT20 -> s(T303)\nT187 -> T474", fontsize=14, style = filled, fillcolor = lightgrey];
488 -> 2373 [arrowhead = none , style=dashed];
2373 -> 191[style=dashed];

2374 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
489 -> 2374 [arrowhead = none ];
2374 -> 490;

2375 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
489 -> 2375 [arrowhead = none ];
2375 -> 491;

2376 [label="EVAL with clause\npr(X2803, s(0)).\nand substitution\nT297 -> 0\nX2803 -> s(s(s(s(0))))\nT485 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
490 -> 2376 [arrowhead = none ];
2376 -> 492;

2377 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
490 -> 2377 [arrowhead = none ];
2377 -> 493;

2378 [label="EVAL with clause\npr(X2809, s(s(X2810))) :- ','(not_divides(s(s(X2810)), X2809), pr(X2809, s(X2810))).\nand substitution\nT297 -> s(T491)\nX2809 -> s(s(s(s(s(T491)))))\nX2810 -> T491\nT490 -> s(T491)", fontsize=14, style = filled, fillcolor = lightblue];
491 -> 2378 [arrowhead = none ];
2378 -> 495;

2379 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
491 -> 2379 [arrowhead = none ];
2379 -> 496;

2380 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
492 -> 2380 [arrowhead = none ];
2380 -> 494;

2381 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
495 -> 2381 [arrowhead = none ];
2381 -> 497;

2382 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
495 -> 2382 [arrowhead = none ];
2382 -> 498;

2383 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
497 -> 2383 [arrowhead = none ];
2383 -> 499;

2384 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
498 -> 2384 [arrowhead = none ];
2384 -> 762;

2385 [label="ONLY EVAL with clause\nnot_divides(X2831, X2832) :- ','(div(X2832, X2831, X2833), ','(times(X2833, X2831, X2834), neq(X2832, X2834))).\nand substitution\nT491 -> T497\nX2831 -> s(s(T497))\nX2832 -> s(s(s(s(s(T497)))))", fontsize=14, style = filled, fillcolor = white];
499 -> 2385 [arrowhead = none ];
2385 -> 500;

2386 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
500 -> 2386 [arrowhead = none ];
2386 -> 501;

2387 [label="SPLIT 2\nnew knowledge:\nT499 is ground\nreplacements:\nX2833 -> T499", fontsize=14, style = filled, fillcolor = violet];
500 -> 2387 [arrowhead = none ];
2387 -> 502;

2388 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
501 -> 2388 [arrowhead = none ];
2388 -> 503;

2389 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
502 -> 2389 [arrowhead = none ];
2389 -> 760;

2390 [label="SPLIT 2\nnew knowledge:\nT674 is ground\nreplacements:\nX2834 -> T674", fontsize=14, style = filled, fillcolor = violet];
502 -> 2390 [arrowhead = none ];
2390 -> 761;

2391 [label="ONLY EVAL with clause\ndiv(X2860, X2861, X2862) :- quot(X2860, X2861, X2861, X2862).\nand substitution\nT497 -> T504\nX2860 -> s(s(s(s(s(T504)))))\nX2861 -> s(s(T504))\nX2833 -> X2863\nX2862 -> X2863", fontsize=14, style = filled, fillcolor = white];
503 -> 2391 [arrowhead = none ];
2391 -> 504;

2392 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
504 -> 2392 [arrowhead = none ];
2392 -> 505;

2393 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
505 -> 2393 [arrowhead = none ];
2393 -> 506;

2394 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
506 -> 2394 [arrowhead = none ];
2394 -> 507;

2395 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
506 -> 2395 [arrowhead = none ];
2395 -> 508;

2396 [label="ONLY EVAL with clause\nquot(s(X2913), s(X2914), X2915, X2916) :- quot(X2913, X2914, X2915, X2916).\nand substitution\nT504 -> T512\nX2913 -> s(s(s(s(T512))))\nX2914 -> s(T512)\nX2915 -> s(s(T512))\nX2863 -> X2917\nX2916 -> X2917", fontsize=14, style = filled, fillcolor = white];
507 -> 2396 [arrowhead = none ];
2396 -> 509;

2397 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
508 -> 2397 [arrowhead = none ];
2397 -> 759;

2398 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
509 -> 2398 [arrowhead = none ];
2398 -> 510;

2399 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
510 -> 2399 [arrowhead = none ];
2399 -> 511;

2400 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
511 -> 2400 [arrowhead = none ];
2400 -> 512;

2401 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
511 -> 2401 [arrowhead = none ];
2401 -> 513;

2402 [label="ONLY EVAL with clause\nquot(s(X2967), s(X2968), X2969, X2970) :- quot(X2967, X2968, X2969, X2970).\nand substitution\nT512 -> T522\nX2967 -> s(s(s(T522)))\nX2968 -> T522\nX2969 -> s(s(T522))\nX2917 -> X2971\nX2970 -> X2971", fontsize=14, style = filled, fillcolor = white];
512 -> 2402 [arrowhead = none ];
2402 -> 514;

2403 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
513 -> 2403 [arrowhead = none ];
2403 -> 758;

2404 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
514 -> 2404 [arrowhead = none ];
2404 -> 515;

2405 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
515 -> 2405 [arrowhead = none ];
2405 -> 516;

2406 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
516 -> 2406 [arrowhead = none ];
2406 -> 517;

2407 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
516 -> 2407 [arrowhead = none ];
2407 -> 518;

2408 [label="EVAL with clause\nquot(s(X3003), s(X3004), X3005, X3006) :- quot(X3003, X3004, X3005, X3006).\nand substitution\nT522 -> s(T534)\nX3003 -> s(s(s(T534)))\nX3004 -> T534\nT533 -> s(T534)\nX3005 -> s(s(s(T534)))\nX2971 -> X3007\nX3006 -> X3007", fontsize=14, style = filled, fillcolor = lightblue];
517 -> 2408 [arrowhead = none ];
2408 -> 519;

2409 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
517 -> 2409 [arrowhead = none ];
2409 -> 520;

2410 [label="EVAL with clause\nquot(X4624, 0, s(X4625), s(X4626)) :- quot(X4624, s(X4625), s(X4625), X4626).\nand substitution\nT522 -> 0\nX4624 -> s(s(s(0)))\nT669 -> 0\nX4625 -> s(0)\nX4626 -> X4627\nX2971 -> s(X4627)", fontsize=14, style = filled, fillcolor = lightblue];
518 -> 2410 [arrowhead = none ];
2410 -> 740;

2411 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
518 -> 2411 [arrowhead = none ];
2411 -> 741;

2412 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
519 -> 2412 [arrowhead = none ];
2412 -> 521;

2413 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
521 -> 2413 [arrowhead = none ];
2413 -> 522;

2414 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
522 -> 2414 [arrowhead = none ];
2414 -> 523;

2415 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
522 -> 2415 [arrowhead = none ];
2415 -> 524;

2416 [label="EVAL with clause\nquot(s(X3043), s(X3044), X3045, X3046) :- quot(X3043, X3044, X3045, X3046).\nand substitution\nT534 -> s(T546)\nX3043 -> s(s(s(T546)))\nX3044 -> T546\nT545 -> s(T546)\nX3045 -> s(s(s(s(T546))))\nX3007 -> X3047\nX3046 -> X3047", fontsize=14, style = filled, fillcolor = lightblue];
523 -> 2416 [arrowhead = none ];
2416 -> 525;

2417 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
523 -> 2417 [arrowhead = none ];
2417 -> 526;

2418 [label="EVAL with clause\nquot(X4398, 0, s(X4399), s(X4400)) :- quot(X4398, s(X4399), s(X4399), X4400).\nand substitution\nT534 -> 0\nX4398 -> s(s(s(0)))\nT666 -> 0\nX4399 -> s(s(0))\nX4400 -> X4401\nX3007 -> s(X4401)", fontsize=14, style = filled, fillcolor = lightblue];
524 -> 2418 [arrowhead = none ];
2418 -> 716;

2419 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
524 -> 2419 [arrowhead = none ];
2419 -> 717;

2420 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
525 -> 2420 [arrowhead = none ];
2420 -> 527;

2421 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
527 -> 2421 [arrowhead = none ];
2421 -> 528;

2422 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
528 -> 2422 [arrowhead = none ];
2422 -> 529;

2423 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
528 -> 2423 [arrowhead = none ];
2423 -> 530;

2424 [label="EVAL with clause\nquot(s(X3083), s(X3084), X3085, X3086) :- quot(X3083, X3084, X3085, X3086).\nand substitution\nT546 -> s(T558)\nX3083 -> s(s(s(T558)))\nX3084 -> T558\nT557 -> s(T558)\nX3085 -> s(s(s(s(s(T558)))))\nX3047 -> X3087\nX3086 -> X3087", fontsize=14, style = filled, fillcolor = lightblue];
529 -> 2424 [arrowhead = none ];
2424 -> 531;

2425 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
529 -> 2425 [arrowhead = none ];
2425 -> 532;

2426 [label="EVAL with clause\nquot(X4207, 0, s(X4208), s(X4209)) :- quot(X4207, s(X4208), s(X4208), X4209).\nand substitution\nT546 -> 0\nX4207 -> s(s(s(0)))\nT663 -> 0\nX4208 -> s(s(s(0)))\nX4209 -> X4210\nX3047 -> s(X4210)", fontsize=14, style = filled, fillcolor = lightblue];
530 -> 2426 [arrowhead = none ];
2426 -> 689;

2427 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
530 -> 2427 [arrowhead = none ];
2427 -> 690;

2428 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
531 -> 2428 [arrowhead = none ];
2428 -> 533;

2429 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
533 -> 2429 [arrowhead = none ];
2429 -> 534;

2430 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
534 -> 2430 [arrowhead = none ];
2430 -> 535;

2431 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
534 -> 2431 [arrowhead = none ];
2431 -> 536;

2432 [label="EVAL with clause\nquot(s(X3123), s(X3124), X3125, X3126) :- quot(X3123, X3124, X3125, X3126).\nand substitution\nT558 -> s(T570)\nX3123 -> s(s(s(T570)))\nX3124 -> T570\nT569 -> s(T570)\nX3125 -> s(s(s(s(s(s(T570))))))\nX3087 -> X3127\nX3126 -> X3127", fontsize=14, style = filled, fillcolor = lightblue];
535 -> 2432 [arrowhead = none ];
2432 -> 537;

2433 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
535 -> 2433 [arrowhead = none ];
2433 -> 538;

2434 [label="EVAL with clause\nquot(X4016, 0, s(X4017), s(X4018)) :- quot(X4016, s(X4017), s(X4017), X4018).\nand substitution\nT558 -> 0\nX4016 -> s(s(s(0)))\nT660 -> 0\nX4017 -> s(s(s(s(0))))\nX4018 -> X4019\nX3087 -> s(X4019)", fontsize=14, style = filled, fillcolor = lightblue];
536 -> 2434 [arrowhead = none ];
2434 -> 662;

2435 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
536 -> 2435 [arrowhead = none ];
2435 -> 663;

2436 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
537 -> 2436 [arrowhead = none ];
2436 -> 539;

2437 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
539 -> 2437 [arrowhead = none ];
2437 -> 540;

2438 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
540 -> 2438 [arrowhead = none ];
2438 -> 541;

2439 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
540 -> 2439 [arrowhead = none ];
2439 -> 542;

2440 [label="EVAL with clause\nquot(s(X3163), s(X3164), X3165, X3166) :- quot(X3163, X3164, X3165, X3166).\nand substitution\nT570 -> s(T582)\nX3163 -> s(s(s(T582)))\nX3164 -> T582\nT581 -> s(T582)\nX3165 -> s(s(s(s(s(s(s(T582)))))))\nX3127 -> X3167\nX3166 -> X3167", fontsize=14, style = filled, fillcolor = lightblue];
541 -> 2440 [arrowhead = none ];
2440 -> 543;

2441 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
541 -> 2441 [arrowhead = none ];
2441 -> 544;

2442 [label="EVAL with clause\nquot(X3825, 0, s(X3826), s(X3827)) :- quot(X3825, s(X3826), s(X3826), X3827).\nand substitution\nT570 -> 0\nX3825 -> s(s(s(0)))\nT657 -> 0\nX3826 -> s(s(s(s(s(0)))))\nX3827 -> X3828\nX3127 -> s(X3828)", fontsize=14, style = filled, fillcolor = lightblue];
542 -> 2442 [arrowhead = none ];
2442 -> 635;

2443 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
542 -> 2443 [arrowhead = none ];
2443 -> 636;

2444 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
543 -> 2444 [arrowhead = none ];
2444 -> 545;

2445 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
545 -> 2445 [arrowhead = none ];
2445 -> 546;

2446 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
546 -> 2446 [arrowhead = none ];
2446 -> 547;

2447 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
546 -> 2447 [arrowhead = none ];
2447 -> 548;

2448 [label="EVAL with clause\nquot(s(X3203), s(X3204), X3205, X3206) :- quot(X3203, X3204, X3205, X3206).\nand substitution\nT582 -> s(T594)\nX3203 -> s(s(s(T594)))\nX3204 -> T594\nT593 -> s(T594)\nX3205 -> s(s(s(s(s(s(s(s(T594))))))))\nX3167 -> X3207\nX3206 -> X3207", fontsize=14, style = filled, fillcolor = lightblue];
547 -> 2448 [arrowhead = none ];
2448 -> 549;

2449 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
547 -> 2449 [arrowhead = none ];
2449 -> 550;

2450 [label="EVAL with clause\nquot(X3634, 0, s(X3635), s(X3636)) :- quot(X3634, s(X3635), s(X3635), X3636).\nand substitution\nT582 -> 0\nX3634 -> s(s(s(0)))\nT654 -> 0\nX3635 -> s(s(s(s(s(s(0))))))\nX3636 -> X3637\nX3167 -> s(X3637)", fontsize=14, style = filled, fillcolor = lightblue];
548 -> 2450 [arrowhead = none ];
2450 -> 608;

2451 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
548 -> 2451 [arrowhead = none ];
2451 -> 609;

2452 [label="GENERALIZATION\nT597 <-- s(s(s(s(s(s(s(T594)))))))\n\nNew Knowledge:\nT597 is ground", fontsize=14, style = filled, fillcolor = violet];
549 -> 2452 [arrowhead = none ];
2452 -> 551;

2453 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
551 -> 2453 [arrowhead = none ];
2453 -> 552;

2454 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
552 -> 2454 [arrowhead = none ];
2454 -> 553;

2455 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
553 -> 2455 [arrowhead = none ];
2455 -> 554;

2456 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
553 -> 2456 [arrowhead = none ];
2456 -> 555;

2457 [label="EVAL with clause\nquot(s(X3252), s(X3253), X3254, X3255) :- quot(X3252, X3253, X3254, X3255).\nand substitution\nT594 -> s(T614)\nX3252 -> s(s(s(T614)))\nX3253 -> T614\nT613 -> s(T614)\nT597 -> T615\nX3254 -> s(T615)\nX3207 -> X3256\nX3255 -> X3256", fontsize=14, style = filled, fillcolor = lightblue];
554 -> 2457 [arrowhead = none ];
2457 -> 556;

2458 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
554 -> 2458 [arrowhead = none ];
2458 -> 557;

2459 [label="EVAL with clause\nquot(X3278, 0, s(X3279), s(X3280)) :- quot(X3278, s(X3279), s(X3279), X3280).\nand substitution\nT594 -> 0\nX3278 -> s(s(s(0)))\nT623 -> 0\nT597 -> T624\nX3279 -> T624\nX3280 -> X3281\nX3207 -> s(X3281)", fontsize=14, style = filled, fillcolor = lightblue];
555 -> 2459 [arrowhead = none ];
2459 -> 558;

2460 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
555 -> 2460 [arrowhead = none ];
2460 -> 559;

2461 [label="INSTANCE with matching:\nT594 -> T614\nT597 -> T615\nX3207 -> X3256", fontsize=14, style = filled, fillcolor = lightgrey];
556 -> 2461 [arrowhead = none , style=dashed];
2461 -> 551[style=dashed];

2462 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
558 -> 2462 [arrowhead = none ];
2462 -> 560;

2463 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
560 -> 2463 [arrowhead = none ];
2463 -> 561;

2464 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
561 -> 2464 [arrowhead = none ];
2464 -> 562;

2465 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
561 -> 2465 [arrowhead = none ];
2465 -> 563;

2466 [label="ONLY EVAL with clause\nquot(s(X3334), s(X3335), X3336, X3337) :- quot(X3334, X3335, X3336, X3337).\nand substitution\nX3334 -> s(s(0))\nT624 -> T632\nX3335 -> T632\nX3336 -> s(T632)\nX3281 -> X3338\nX3337 -> X3338", fontsize=14, style = filled, fillcolor = white];
562 -> 2466 [arrowhead = none ];
2466 -> 564;

2467 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
563 -> 2467 [arrowhead = none ];
2467 -> 607;

2468 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
564 -> 2468 [arrowhead = none ];
2468 -> 565;

2469 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
565 -> 2469 [arrowhead = none ];
2469 -> 566;

2470 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
566 -> 2470 [arrowhead = none ];
2470 -> 567;

2471 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
566 -> 2471 [arrowhead = none ];
2471 -> 568;

2472 [label="EVAL with clause\nquot(s(X3370), s(X3371), X3372, X3373) :- quot(X3370, X3371, X3372, X3373).\nand substitution\nX3370 -> s(0)\nX3371 -> T638\nT632 -> s(T638)\nX3372 -> s(s(T638))\nX3338 -> X3374\nX3373 -> X3374", fontsize=14, style = filled, fillcolor = lightblue];
567 -> 2472 [arrowhead = none ];
2472 -> 569;

2473 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
567 -> 2473 [arrowhead = none ];
2473 -> 570;

2474 [label="EVAL with clause\nquot(X3505, 0, s(X3506), s(X3507)) :- quot(X3505, s(X3506), s(X3506), X3507).\nand substitution\nX3505 -> s(s(0))\nT632 -> 0\nX3506 -> 0\nX3507 -> X3508\nX3338 -> s(X3508)", fontsize=14, style = filled, fillcolor = lightblue];
568 -> 2474 [arrowhead = none ];
2474 -> 595;

2475 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
568 -> 2475 [arrowhead = none ];
2475 -> 596;

2476 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
569 -> 2476 [arrowhead = none ];
2476 -> 571;

2477 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
571 -> 2477 [arrowhead = none ];
2477 -> 572;

2478 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
572 -> 2478 [arrowhead = none ];
2478 -> 573;

2479 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
572 -> 2479 [arrowhead = none ];
2479 -> 574;

2480 [label="EVAL with clause\nquot(s(X3410), s(X3411), X3412, X3413) :- quot(X3410, X3411, X3412, X3413).\nand substitution\nX3410 -> 0\nX3411 -> T644\nT638 -> s(T644)\nX3412 -> s(s(s(T644)))\nX3374 -> X3414\nX3413 -> X3414", fontsize=14, style = filled, fillcolor = lightblue];
573 -> 2480 [arrowhead = none ];
2480 -> 575;

2481 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
573 -> 2481 [arrowhead = none ];
2481 -> 576;

2482 [label="EVAL with clause\nquot(X3481, 0, s(X3482), s(X3483)) :- quot(X3481, s(X3482), s(X3482), X3483).\nand substitution\nX3481 -> s(0)\nT638 -> 0\nX3482 -> s(0)\nX3483 -> X3484\nX3374 -> s(X3484)", fontsize=14, style = filled, fillcolor = lightblue];
574 -> 2482 [arrowhead = none ];
2482 -> 593;

2483 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
574 -> 2483 [arrowhead = none ];
2483 -> 594;

2484 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
575 -> 2484 [arrowhead = none ];
2484 -> 577;

2485 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
577 -> 2485 [arrowhead = none ];
2485 -> 578;

2486 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
577 -> 2486 [arrowhead = none ];
2486 -> 579;

2487 [label="EVAL with clause\nquot(0, s(X3431), s(X3432), 0).\nand substitution\nX3431 -> T651\nT644 -> s(T651)\nX3432 -> s(s(s(T651)))\nX3414 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
578 -> 2487 [arrowhead = none ];
2487 -> 580;

2488 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
578 -> 2488 [arrowhead = none ];
2488 -> 581;

2489 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
579 -> 2489 [arrowhead = none ];
2489 -> 583;

2490 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
580 -> 2490 [arrowhead = none ];
2490 -> 582;

2491 [label="EVAL with clause\nquot(X3447, 0, s(X3448), s(X3449)) :- quot(X3447, s(X3448), s(X3448), X3449).\nand substitution\nX3447 -> 0\nT644 -> 0\nX3448 -> s(s(0))\nX3449 -> X3450\nX3414 -> s(X3450)", fontsize=14, style = filled, fillcolor = lightblue];
583 -> 2491 [arrowhead = none ];
2491 -> 584;

2492 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
583 -> 2492 [arrowhead = none ];
2492 -> 585;

2493 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
584 -> 2493 [arrowhead = none ];
2493 -> 586;

2494 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
586 -> 2494 [arrowhead = none ];
2494 -> 587;

2495 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
586 -> 2495 [arrowhead = none ];
2495 -> 588;

2496 [label="ONLY EVAL with clause\nquot(0, s(X3464), s(X3465), 0).\nand substitution\nX3464 -> s(s(0))\nX3465 -> s(s(0))\nX3450 -> 0", fontsize=14, style = filled, fillcolor = white];
587 -> 2496 [arrowhead = none ];
2496 -> 589;

2497 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
588 -> 2497 [arrowhead = none ];
2497 -> 591;

2498 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
589 -> 2498 [arrowhead = none ];
2498 -> 590;

2499 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
591 -> 2499 [arrowhead = none ];
2499 -> 592;

2500 [label="INSTANCE with matching:\nX987 -> X3484", fontsize=14, style = filled, fillcolor = lightgrey];
593 -> 2500 [arrowhead = none , style=dashed];
2500 -> 173[style=dashed];

2501 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
595 -> 2501 [arrowhead = none ];
2501 -> 597;

2502 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
597 -> 2502 [arrowhead = none ];
2502 -> 598;

2503 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
598 -> 2503 [arrowhead = none ];
2503 -> 599;

2504 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
598 -> 2504 [arrowhead = none ];
2504 -> 600;

2505 [label="ONLY EVAL with clause\nquot(s(X3567), s(X3568), X3569, X3570) :- quot(X3567, X3568, X3569, X3570).\nand substitution\nX3567 -> s(0)\nX3568 -> 0\nX3569 -> s(0)\nX3508 -> X3571\nX3570 -> X3571", fontsize=14, style = filled, fillcolor = white];
599 -> 2505 [arrowhead = none ];
2505 -> 601;

2506 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
600 -> 2506 [arrowhead = none ];
2506 -> 606;

2507 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
601 -> 2507 [arrowhead = none ];
2507 -> 602;

2508 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
602 -> 2508 [arrowhead = none ];
2508 -> 603;

2509 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
603 -> 2509 [arrowhead = none ];
2509 -> 604;

2510 [label="ONLY EVAL with clause\nquot(X3607, 0, s(X3608), s(X3609)) :- quot(X3607, s(X3608), s(X3608), X3609).\nand substitution\nX3607 -> s(0)\nX3608 -> 0\nX3609 -> X3610\nX3571 -> s(X3610)", fontsize=14, style = filled, fillcolor = white];
604 -> 2510 [arrowhead = none ];
2510 -> 605;

2511 [label="INSTANCE with matching:\nX1842 -> X3610", fontsize=14, style = filled, fillcolor = lightgrey];
605 -> 2511 [arrowhead = none , style=dashed];
2511 -> 349[style=dashed];

2512 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
608 -> 2512 [arrowhead = none ];
2512 -> 610;

2513 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
610 -> 2513 [arrowhead = none ];
2513 -> 611;

2514 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
611 -> 2514 [arrowhead = none ];
2514 -> 612;

2515 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
611 -> 2515 [arrowhead = none ];
2515 -> 613;

2516 [label="ONLY EVAL with clause\nquot(s(X3690), s(X3691), X3692, X3693) :- quot(X3690, X3691, X3692, X3693).\nand substitution\nX3690 -> s(s(0))\nX3691 -> s(s(s(s(s(s(0))))))\nX3692 -> s(s(s(s(s(s(s(0)))))))\nX3637 -> X3694\nX3693 -> X3694", fontsize=14, style = filled, fillcolor = white];
612 -> 2516 [arrowhead = none ];
2516 -> 614;

2517 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
613 -> 2517 [arrowhead = none ];
2517 -> 634;

2518 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
614 -> 2518 [arrowhead = none ];
2518 -> 615;

2519 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
615 -> 2519 [arrowhead = none ];
2519 -> 616;

2520 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
616 -> 2520 [arrowhead = none ];
2520 -> 617;

2521 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
616 -> 2521 [arrowhead = none ];
2521 -> 618;

2522 [label="ONLY EVAL with clause\nquot(s(X3744), s(X3745), X3746, X3747) :- quot(X3744, X3745, X3746, X3747).\nand substitution\nX3744 -> s(0)\nX3745 -> s(s(s(s(s(0)))))\nX3746 -> s(s(s(s(s(s(s(0)))))))\nX3694 -> X3748\nX3747 -> X3748", fontsize=14, style = filled, fillcolor = white];
617 -> 2522 [arrowhead = none ];
2522 -> 619;

2523 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
618 -> 2523 [arrowhead = none ];
2523 -> 633;

2524 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
619 -> 2524 [arrowhead = none ];
2524 -> 620;

2525 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
620 -> 2525 [arrowhead = none ];
2525 -> 621;

2526 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
621 -> 2526 [arrowhead = none ];
2526 -> 622;

2527 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
621 -> 2527 [arrowhead = none ];
2527 -> 623;

2528 [label="ONLY EVAL with clause\nquot(s(X3784), s(X3785), X3786, X3787) :- quot(X3784, X3785, X3786, X3787).\nand substitution\nX3784 -> 0\nX3785 -> s(s(s(s(0))))\nX3786 -> s(s(s(s(s(s(s(0)))))))\nX3748 -> X3788\nX3787 -> X3788", fontsize=14, style = filled, fillcolor = white];
622 -> 2528 [arrowhead = none ];
2528 -> 624;

2529 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
623 -> 2529 [arrowhead = none ];
2529 -> 632;

2530 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
624 -> 2530 [arrowhead = none ];
2530 -> 625;

2531 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
625 -> 2531 [arrowhead = none ];
2531 -> 626;

2532 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
625 -> 2532 [arrowhead = none ];
2532 -> 627;

2533 [label="ONLY EVAL with clause\nquot(0, s(X3799), s(X3800), 0).\nand substitution\nX3799 -> s(s(s(0)))\nX3800 -> s(s(s(s(s(s(0))))))\nX3788 -> 0", fontsize=14, style = filled, fillcolor = white];
626 -> 2533 [arrowhead = none ];
2533 -> 628;

2534 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
627 -> 2534 [arrowhead = none ];
2534 -> 630;

2535 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
628 -> 2535 [arrowhead = none ];
2535 -> 629;

2536 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
630 -> 2536 [arrowhead = none ];
2536 -> 631;

2537 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
635 -> 2537 [arrowhead = none ];
2537 -> 637;

2538 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
637 -> 2538 [arrowhead = none ];
2538 -> 638;

2539 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
638 -> 2539 [arrowhead = none ];
2539 -> 639;

2540 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
638 -> 2540 [arrowhead = none ];
2540 -> 640;

2541 [label="ONLY EVAL with clause\nquot(s(X3881), s(X3882), X3883, X3884) :- quot(X3881, X3882, X3883, X3884).\nand substitution\nX3881 -> s(s(0))\nX3882 -> s(s(s(s(s(0)))))\nX3883 -> s(s(s(s(s(s(0))))))\nX3828 -> X3885\nX3884 -> X3885", fontsize=14, style = filled, fillcolor = white];
639 -> 2541 [arrowhead = none ];
2541 -> 641;

2542 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
640 -> 2542 [arrowhead = none ];
2542 -> 661;

2543 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
641 -> 2543 [arrowhead = none ];
2543 -> 642;

2544 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
642 -> 2544 [arrowhead = none ];
2544 -> 643;

2545 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
643 -> 2545 [arrowhead = none ];
2545 -> 644;

2546 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
643 -> 2546 [arrowhead = none ];
2546 -> 645;

2547 [label="ONLY EVAL with clause\nquot(s(X3935), s(X3936), X3937, X3938) :- quot(X3935, X3936, X3937, X3938).\nand substitution\nX3935 -> s(0)\nX3936 -> s(s(s(s(0))))\nX3937 -> s(s(s(s(s(s(0))))))\nX3885 -> X3939\nX3938 -> X3939", fontsize=14, style = filled, fillcolor = white];
644 -> 2547 [arrowhead = none ];
2547 -> 646;

2548 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
645 -> 2548 [arrowhead = none ];
2548 -> 660;

2549 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
646 -> 2549 [arrowhead = none ];
2549 -> 647;

2550 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
647 -> 2550 [arrowhead = none ];
2550 -> 648;

2551 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
648 -> 2551 [arrowhead = none ];
2551 -> 649;

2552 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
648 -> 2552 [arrowhead = none ];
2552 -> 650;

2553 [label="ONLY EVAL with clause\nquot(s(X3975), s(X3976), X3977, X3978) :- quot(X3975, X3976, X3977, X3978).\nand substitution\nX3975 -> 0\nX3976 -> s(s(s(0)))\nX3977 -> s(s(s(s(s(s(0))))))\nX3939 -> X3979\nX3978 -> X3979", fontsize=14, style = filled, fillcolor = white];
649 -> 2553 [arrowhead = none ];
2553 -> 651;

2554 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
650 -> 2554 [arrowhead = none ];
2554 -> 659;

2555 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
651 -> 2555 [arrowhead = none ];
2555 -> 652;

2556 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
652 -> 2556 [arrowhead = none ];
2556 -> 653;

2557 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
652 -> 2557 [arrowhead = none ];
2557 -> 654;

2558 [label="ONLY EVAL with clause\nquot(0, s(X3990), s(X3991), 0).\nand substitution\nX3990 -> s(s(0))\nX3991 -> s(s(s(s(s(0)))))\nX3979 -> 0", fontsize=14, style = filled, fillcolor = white];
653 -> 2558 [arrowhead = none ];
2558 -> 655;

2559 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
654 -> 2559 [arrowhead = none ];
2559 -> 657;

2560 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
655 -> 2560 [arrowhead = none ];
2560 -> 656;

2561 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
657 -> 2561 [arrowhead = none ];
2561 -> 658;

2562 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
662 -> 2562 [arrowhead = none ];
2562 -> 664;

2563 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
664 -> 2563 [arrowhead = none ];
2563 -> 665;

2564 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
665 -> 2564 [arrowhead = none ];
2564 -> 666;

2565 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
665 -> 2565 [arrowhead = none ];
2565 -> 667;

2566 [label="ONLY EVAL with clause\nquot(s(X4072), s(X4073), X4074, X4075) :- quot(X4072, X4073, X4074, X4075).\nand substitution\nX4072 -> s(s(0))\nX4073 -> s(s(s(s(0))))\nX4074 -> s(s(s(s(s(0)))))\nX4019 -> X4076\nX4075 -> X4076", fontsize=14, style = filled, fillcolor = white];
666 -> 2566 [arrowhead = none ];
2566 -> 668;

2567 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
667 -> 2567 [arrowhead = none ];
2567 -> 688;

2568 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
668 -> 2568 [arrowhead = none ];
2568 -> 669;

2569 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
669 -> 2569 [arrowhead = none ];
2569 -> 670;

2570 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
670 -> 2570 [arrowhead = none ];
2570 -> 671;

2571 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
670 -> 2571 [arrowhead = none ];
2571 -> 672;

2572 [label="ONLY EVAL with clause\nquot(s(X4126), s(X4127), X4128, X4129) :- quot(X4126, X4127, X4128, X4129).\nand substitution\nX4126 -> s(0)\nX4127 -> s(s(s(0)))\nX4128 -> s(s(s(s(s(0)))))\nX4076 -> X4130\nX4129 -> X4130", fontsize=14, style = filled, fillcolor = white];
671 -> 2572 [arrowhead = none ];
2572 -> 673;

2573 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
672 -> 2573 [arrowhead = none ];
2573 -> 687;

2574 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
673 -> 2574 [arrowhead = none ];
2574 -> 674;

2575 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
674 -> 2575 [arrowhead = none ];
2575 -> 675;

2576 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
675 -> 2576 [arrowhead = none ];
2576 -> 676;

2577 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
675 -> 2577 [arrowhead = none ];
2577 -> 677;

2578 [label="ONLY EVAL with clause\nquot(s(X4166), s(X4167), X4168, X4169) :- quot(X4166, X4167, X4168, X4169).\nand substitution\nX4166 -> 0\nX4167 -> s(s(0))\nX4168 -> s(s(s(s(s(0)))))\nX4130 -> X4170\nX4169 -> X4170", fontsize=14, style = filled, fillcolor = white];
676 -> 2578 [arrowhead = none ];
2578 -> 678;

2579 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
677 -> 2579 [arrowhead = none ];
2579 -> 686;

2580 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
678 -> 2580 [arrowhead = none ];
2580 -> 679;

2581 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
679 -> 2581 [arrowhead = none ];
2581 -> 680;

2582 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
679 -> 2582 [arrowhead = none ];
2582 -> 681;

2583 [label="ONLY EVAL with clause\nquot(0, s(X4181), s(X4182), 0).\nand substitution\nX4181 -> s(0)\nX4182 -> s(s(s(s(0))))\nX4170 -> 0", fontsize=14, style = filled, fillcolor = white];
680 -> 2583 [arrowhead = none ];
2583 -> 682;

2584 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
681 -> 2584 [arrowhead = none ];
2584 -> 684;

2585 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
682 -> 2585 [arrowhead = none ];
2585 -> 683;

2586 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
684 -> 2586 [arrowhead = none ];
2586 -> 685;

2587 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
689 -> 2587 [arrowhead = none ];
2587 -> 691;

2588 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
691 -> 2588 [arrowhead = none ];
2588 -> 692;

2589 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
692 -> 2589 [arrowhead = none ];
2589 -> 693;

2590 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
692 -> 2590 [arrowhead = none ];
2590 -> 694;

2591 [label="ONLY EVAL with clause\nquot(s(X4263), s(X4264), X4265, X4266) :- quot(X4263, X4264, X4265, X4266).\nand substitution\nX4263 -> s(s(0))\nX4264 -> s(s(s(0)))\nX4265 -> s(s(s(s(0))))\nX4210 -> X4267\nX4266 -> X4267", fontsize=14, style = filled, fillcolor = white];
693 -> 2591 [arrowhead = none ];
2591 -> 695;

2592 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
694 -> 2592 [arrowhead = none ];
2592 -> 715;

2593 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
695 -> 2593 [arrowhead = none ];
2593 -> 696;

2594 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
696 -> 2594 [arrowhead = none ];
2594 -> 697;

2595 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
697 -> 2595 [arrowhead = none ];
2595 -> 698;

2596 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
697 -> 2596 [arrowhead = none ];
2596 -> 699;

2597 [label="ONLY EVAL with clause\nquot(s(X4317), s(X4318), X4319, X4320) :- quot(X4317, X4318, X4319, X4320).\nand substitution\nX4317 -> s(0)\nX4318 -> s(s(0))\nX4319 -> s(s(s(s(0))))\nX4267 -> X4321\nX4320 -> X4321", fontsize=14, style = filled, fillcolor = white];
698 -> 2597 [arrowhead = none ];
2597 -> 700;

2598 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
699 -> 2598 [arrowhead = none ];
2598 -> 714;

2599 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
700 -> 2599 [arrowhead = none ];
2599 -> 701;

2600 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
701 -> 2600 [arrowhead = none ];
2600 -> 702;

2601 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
702 -> 2601 [arrowhead = none ];
2601 -> 703;

2602 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
702 -> 2602 [arrowhead = none ];
2602 -> 704;

2603 [label="ONLY EVAL with clause\nquot(s(X4357), s(X4358), X4359, X4360) :- quot(X4357, X4358, X4359, X4360).\nand substitution\nX4357 -> 0\nX4358 -> s(0)\nX4359 -> s(s(s(s(0))))\nX4321 -> X4361\nX4360 -> X4361", fontsize=14, style = filled, fillcolor = white];
703 -> 2603 [arrowhead = none ];
2603 -> 705;

2604 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
704 -> 2604 [arrowhead = none ];
2604 -> 713;

2605 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
705 -> 2605 [arrowhead = none ];
2605 -> 706;

2606 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
706 -> 2606 [arrowhead = none ];
2606 -> 707;

2607 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
706 -> 2607 [arrowhead = none ];
2607 -> 708;

2608 [label="ONLY EVAL with clause\nquot(0, s(X4372), s(X4373), 0).\nand substitution\nX4372 -> 0\nX4373 -> s(s(s(0)))\nX4361 -> 0", fontsize=14, style = filled, fillcolor = white];
707 -> 2608 [arrowhead = none ];
2608 -> 709;

2609 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
708 -> 2609 [arrowhead = none ];
2609 -> 711;

2610 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
709 -> 2610 [arrowhead = none ];
2610 -> 710;

2611 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
711 -> 2611 [arrowhead = none ];
2611 -> 712;

2612 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
716 -> 2612 [arrowhead = none ];
2612 -> 718;

2613 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
718 -> 2613 [arrowhead = none ];
2613 -> 719;

2614 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
719 -> 2614 [arrowhead = none ];
2614 -> 720;

2615 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
719 -> 2615 [arrowhead = none ];
2615 -> 721;

2616 [label="ONLY EVAL with clause\nquot(s(X4454), s(X4455), X4456, X4457) :- quot(X4454, X4455, X4456, X4457).\nand substitution\nX4454 -> s(s(0))\nX4455 -> s(s(0))\nX4456 -> s(s(s(0)))\nX4401 -> X4458\nX4457 -> X4458", fontsize=14, style = filled, fillcolor = white];
720 -> 2616 [arrowhead = none ];
2616 -> 722;

2617 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
721 -> 2617 [arrowhead = none ];
2617 -> 739;

2618 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
722 -> 2618 [arrowhead = none ];
2618 -> 723;

2619 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
723 -> 2619 [arrowhead = none ];
2619 -> 724;

2620 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
724 -> 2620 [arrowhead = none ];
2620 -> 725;

2621 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
724 -> 2621 [arrowhead = none ];
2621 -> 726;

2622 [label="ONLY EVAL with clause\nquot(s(X4508), s(X4509), X4510, X4511) :- quot(X4508, X4509, X4510, X4511).\nand substitution\nX4508 -> s(0)\nX4509 -> s(0)\nX4510 -> s(s(s(0)))\nX4458 -> X4512\nX4511 -> X4512", fontsize=14, style = filled, fillcolor = white];
725 -> 2622 [arrowhead = none ];
2622 -> 727;

2623 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
726 -> 2623 [arrowhead = none ];
2623 -> 738;

2624 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
727 -> 2624 [arrowhead = none ];
2624 -> 728;

2625 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
728 -> 2625 [arrowhead = none ];
2625 -> 729;

2626 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
729 -> 2626 [arrowhead = none ];
2626 -> 730;

2627 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
729 -> 2627 [arrowhead = none ];
2627 -> 731;

2628 [label="ONLY EVAL with clause\nquot(s(X4568), s(X4569), X4570, X4571) :- quot(X4568, X4569, X4570, X4571).\nand substitution\nX4568 -> 0\nX4569 -> 0\nX4570 -> s(s(s(0)))\nX4512 -> X4572\nX4571 -> X4572", fontsize=14, style = filled, fillcolor = white];
730 -> 2628 [arrowhead = none ];
2628 -> 732;

2629 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
731 -> 2629 [arrowhead = none ];
2629 -> 737;

2630 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
732 -> 2630 [arrowhead = none ];
2630 -> 733;

2631 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
733 -> 2631 [arrowhead = none ];
2631 -> 734;

2632 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
734 -> 2632 [arrowhead = none ];
2632 -> 735;

2633 [label="ONLY EVAL with clause\nquot(X4601, 0, s(X4602), s(X4603)) :- quot(X4601, s(X4602), s(X4602), X4603).\nand substitution\nX4601 -> 0\nX4602 -> s(s(0))\nX4603 -> X4604\nX4572 -> s(X4604)", fontsize=14, style = filled, fillcolor = white];
735 -> 2633 [arrowhead = none ];
2633 -> 736;

2634 [label="INSTANCE with matching:\nX3450 -> X4604", fontsize=14, style = filled, fillcolor = lightgrey];
736 -> 2634 [arrowhead = none , style=dashed];
2634 -> 584[style=dashed];

2635 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
740 -> 2635 [arrowhead = none ];
2635 -> 742;

2636 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
742 -> 2636 [arrowhead = none ];
2636 -> 743;

2637 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
743 -> 2637 [arrowhead = none ];
2637 -> 744;

2638 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
743 -> 2638 [arrowhead = none ];
2638 -> 745;

2639 [label="ONLY EVAL with clause\nquot(s(X4680), s(X4681), X4682, X4683) :- quot(X4680, X4681, X4682, X4683).\nand substitution\nX4680 -> s(s(0))\nX4681 -> s(0)\nX4682 -> s(s(0))\nX4627 -> X4684\nX4683 -> X4684", fontsize=14, style = filled, fillcolor = white];
744 -> 2639 [arrowhead = none ];
2639 -> 746;

2640 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
745 -> 2640 [arrowhead = none ];
2640 -> 757;

2641 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
746 -> 2641 [arrowhead = none ];
2641 -> 747;

2642 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
747 -> 2642 [arrowhead = none ];
2642 -> 748;

2643 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
748 -> 2643 [arrowhead = none ];
2643 -> 749;

2644 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
748 -> 2644 [arrowhead = none ];
2644 -> 750;

2645 [label="ONLY EVAL with clause\nquot(s(X4740), s(X4741), X4742, X4743) :- quot(X4740, X4741, X4742, X4743).\nand substitution\nX4740 -> s(0)\nX4741 -> 0\nX4742 -> s(s(0))\nX4684 -> X4744\nX4743 -> X4744", fontsize=14, style = filled, fillcolor = white];
749 -> 2645 [arrowhead = none ];
2645 -> 751;

2646 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
750 -> 2646 [arrowhead = none ];
2646 -> 756;

2647 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
751 -> 2647 [arrowhead = none ];
2647 -> 752;

2648 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
752 -> 2648 [arrowhead = none ];
2648 -> 753;

2649 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
753 -> 2649 [arrowhead = none ];
2649 -> 754;

2650 [label="ONLY EVAL with clause\nquot(X4780, 0, s(X4781), s(X4782)) :- quot(X4780, s(X4781), s(X4781), X4782).\nand substitution\nX4780 -> s(0)\nX4781 -> s(0)\nX4782 -> X4783\nX4744 -> s(X4783)", fontsize=14, style = filled, fillcolor = white];
754 -> 2650 [arrowhead = none ];
2650 -> 755;

2651 [label="INSTANCE with matching:\nX987 -> X4783", fontsize=14, style = filled, fillcolor = lightgrey];
755 -> 2651 [arrowhead = none , style=dashed];
2651 -> 173[style=dashed];

2652 [label="INSTANCE with matching:\nT22 -> T499\nT20 -> T497\nX39 -> X2834", fontsize=14, style = filled, fillcolor = lightgrey];
760 -> 2652 [arrowhead = none , style=dashed];
2652 -> 190[style=dashed];

2653 [label="INSTANCE with matching:\nT20 -> s(s(T497))\nT187 -> T674", fontsize=14, style = filled, fillcolor = lightgrey];
761 -> 2653 [arrowhead = none , style=dashed];
2653 -> 191[style=dashed];

2654 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
762 -> 2654 [arrowhead = none ];
2654 -> 763;

2655 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
762 -> 2655 [arrowhead = none ];
2655 -> 764;

2656 [label="EVAL with clause\npr(X4817, s(0)).\nand substitution\nT491 -> 0\nX4817 -> s(s(s(s(s(0)))))\nT685 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
763 -> 2656 [arrowhead = none ];
2656 -> 765;

2657 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
763 -> 2657 [arrowhead = none ];
2657 -> 766;

2658 [label="EVAL with clause\npr(X4823, s(s(X4824))) :- ','(not_divides(s(s(X4824)), X4823), pr(X4823, s(X4824))).\nand substitution\nT491 -> s(T691)\nX4823 -> s(s(s(s(s(s(T691))))))\nX4824 -> T691\nT690 -> s(T691)", fontsize=14, style = filled, fillcolor = lightblue];
764 -> 2658 [arrowhead = none ];
2658 -> 768;

2659 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
764 -> 2659 [arrowhead = none ];
2659 -> 769;

2660 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
765 -> 2660 [arrowhead = none ];
2660 -> 767;

2661 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
768 -> 2661 [arrowhead = none ];
2661 -> 770;

2662 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
768 -> 2662 [arrowhead = none ];
2662 -> 771;

2663 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
770 -> 2663 [arrowhead = none ];
2663 -> 772;

2664 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
771 -> 2664 [arrowhead = none ];
2664 -> 1064;

2665 [label="ONLY EVAL with clause\nnot_divides(X4845, X4846) :- ','(div(X4846, X4845, X4847), ','(times(X4847, X4845, X4848), neq(X4846, X4848))).\nand substitution\nT691 -> T697\nX4845 -> s(s(T697))\nX4846 -> s(s(s(s(s(s(T697))))))", fontsize=14, style = filled, fillcolor = white];
772 -> 2665 [arrowhead = none ];
2665 -> 773;

2666 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
773 -> 2666 [arrowhead = none ];
2666 -> 774;

2667 [label="SPLIT 2\nnew knowledge:\nT699 is ground\nreplacements:\nX4847 -> T699", fontsize=14, style = filled, fillcolor = violet];
773 -> 2667 [arrowhead = none ];
2667 -> 775;

2668 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
774 -> 2668 [arrowhead = none ];
2668 -> 776;

2669 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
775 -> 2669 [arrowhead = none ];
2669 -> 1062;

2670 [label="SPLIT 2\nnew knowledge:\nT880 is ground\nreplacements:\nX4848 -> T880", fontsize=14, style = filled, fillcolor = violet];
775 -> 2670 [arrowhead = none ];
2670 -> 1063;

2671 [label="ONLY EVAL with clause\ndiv(X4874, X4875, X4876) :- quot(X4874, X4875, X4875, X4876).\nand substitution\nT697 -> T704\nX4874 -> s(s(s(s(s(s(T704))))))\nX4875 -> s(s(T704))\nX4847 -> X4877\nX4876 -> X4877", fontsize=14, style = filled, fillcolor = white];
776 -> 2671 [arrowhead = none ];
2671 -> 777;

2672 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
777 -> 2672 [arrowhead = none ];
2672 -> 778;

2673 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
778 -> 2673 [arrowhead = none ];
2673 -> 779;

2674 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
779 -> 2674 [arrowhead = none ];
2674 -> 780;

2675 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
779 -> 2675 [arrowhead = none ];
2675 -> 781;

2676 [label="ONLY EVAL with clause\nquot(s(X4927), s(X4928), X4929, X4930) :- quot(X4927, X4928, X4929, X4930).\nand substitution\nT704 -> T712\nX4927 -> s(s(s(s(s(T712)))))\nX4928 -> s(T712)\nX4929 -> s(s(T712))\nX4877 -> X4931\nX4930 -> X4931", fontsize=14, style = filled, fillcolor = white];
780 -> 2676 [arrowhead = none ];
2676 -> 782;

2677 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
781 -> 2677 [arrowhead = none ];
2677 -> 1061;

2678 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
782 -> 2678 [arrowhead = none ];
2678 -> 783;

2679 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
783 -> 2679 [arrowhead = none ];
2679 -> 784;

2680 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
784 -> 2680 [arrowhead = none ];
2680 -> 785;

2681 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
784 -> 2681 [arrowhead = none ];
2681 -> 786;

2682 [label="ONLY EVAL with clause\nquot(s(X4981), s(X4982), X4983, X4984) :- quot(X4981, X4982, X4983, X4984).\nand substitution\nT712 -> T722\nX4981 -> s(s(s(s(T722))))\nX4982 -> T722\nX4983 -> s(s(T722))\nX4931 -> X4985\nX4984 -> X4985", fontsize=14, style = filled, fillcolor = white];
785 -> 2682 [arrowhead = none ];
2682 -> 787;

2683 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
786 -> 2683 [arrowhead = none ];
2683 -> 1060;

2684 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
787 -> 2684 [arrowhead = none ];
2684 -> 788;

2685 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
788 -> 2685 [arrowhead = none ];
2685 -> 789;

2686 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
789 -> 2686 [arrowhead = none ];
2686 -> 790;

2687 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
789 -> 2687 [arrowhead = none ];
2687 -> 791;

2688 [label="EVAL with clause\nquot(s(X5017), s(X5018), X5019, X5020) :- quot(X5017, X5018, X5019, X5020).\nand substitution\nT722 -> s(T734)\nX5017 -> s(s(s(s(T734))))\nX5018 -> T734\nT733 -> s(T734)\nX5019 -> s(s(s(T734)))\nX4985 -> X5021\nX5020 -> X5021", fontsize=14, style = filled, fillcolor = lightblue];
790 -> 2688 [arrowhead = none ];
2688 -> 792;

2689 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
790 -> 2689 [arrowhead = none ];
2689 -> 793;

2690 [label="EVAL with clause\nquot(X6979, 0, s(X6980), s(X6981)) :- quot(X6979, s(X6980), s(X6980), X6981).\nand substitution\nT722 -> 0\nX6979 -> s(s(s(s(0))))\nT875 -> 0\nX6980 -> s(0)\nX6981 -> X6982\nX4985 -> s(X6982)", fontsize=14, style = filled, fillcolor = lightblue];
791 -> 2690 [arrowhead = none ];
2690 -> 1042;

2691 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
791 -> 2691 [arrowhead = none ];
2691 -> 1043;

2692 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
792 -> 2692 [arrowhead = none ];
2692 -> 794;

2693 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
794 -> 2693 [arrowhead = none ];
2693 -> 795;

2694 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
795 -> 2694 [arrowhead = none ];
2694 -> 796;

2695 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
795 -> 2695 [arrowhead = none ];
2695 -> 797;

2696 [label="EVAL with clause\nquot(s(X5057), s(X5058), X5059, X5060) :- quot(X5057, X5058, X5059, X5060).\nand substitution\nT734 -> s(T746)\nX5057 -> s(s(s(s(T746))))\nX5058 -> T746\nT745 -> s(T746)\nX5059 -> s(s(s(s(T746))))\nX5021 -> X5061\nX5060 -> X5061", fontsize=14, style = filled, fillcolor = lightblue];
796 -> 2696 [arrowhead = none ];
2696 -> 798;

2697 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
796 -> 2697 [arrowhead = none ];
2697 -> 799;

2698 [label="EVAL with clause\nquot(X6739, 0, s(X6740), s(X6741)) :- quot(X6739, s(X6740), s(X6740), X6741).\nand substitution\nT734 -> 0\nX6739 -> s(s(s(s(0))))\nT872 -> 0\nX6740 -> s(s(0))\nX6741 -> X6742\nX5021 -> s(X6742)", fontsize=14, style = filled, fillcolor = lightblue];
797 -> 2698 [arrowhead = none ];
2698 -> 1018;

2699 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
797 -> 2699 [arrowhead = none ];
2699 -> 1019;

2700 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
798 -> 2700 [arrowhead = none ];
2700 -> 800;

2701 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
800 -> 2701 [arrowhead = none ];
2701 -> 801;

2702 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
801 -> 2702 [arrowhead = none ];
2702 -> 802;

2703 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
801 -> 2703 [arrowhead = none ];
2703 -> 803;

2704 [label="EVAL with clause\nquot(s(X5097), s(X5098), X5099, X5100) :- quot(X5097, X5098, X5099, X5100).\nand substitution\nT746 -> s(T758)\nX5097 -> s(s(s(s(T758))))\nX5098 -> T758\nT757 -> s(T758)\nX5099 -> s(s(s(s(s(T758)))))\nX5061 -> X5101\nX5100 -> X5101", fontsize=14, style = filled, fillcolor = lightblue];
802 -> 2704 [arrowhead = none ];
2704 -> 804;

2705 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
802 -> 2705 [arrowhead = none ];
2705 -> 805;

2706 [label="EVAL with clause\nquot(X6456, 0, s(X6457), s(X6458)) :- quot(X6456, s(X6457), s(X6457), X6458).\nand substitution\nT746 -> 0\nX6456 -> s(s(s(s(0))))\nT869 -> 0\nX6457 -> s(s(s(0)))\nX6458 -> X6459\nX5061 -> s(X6459)", fontsize=14, style = filled, fillcolor = lightblue];
803 -> 2706 [arrowhead = none ];
2706 -> 988;

2707 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
803 -> 2707 [arrowhead = none ];
2707 -> 989;

2708 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
804 -> 2708 [arrowhead = none ];
2708 -> 806;

2709 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
806 -> 2709 [arrowhead = none ];
2709 -> 807;

2710 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
807 -> 2710 [arrowhead = none ];
2710 -> 808;

2711 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
807 -> 2711 [arrowhead = none ];
2711 -> 809;

2712 [label="EVAL with clause\nquot(s(X5137), s(X5138), X5139, X5140) :- quot(X5137, X5138, X5139, X5140).\nand substitution\nT758 -> s(T770)\nX5137 -> s(s(s(s(T770))))\nX5138 -> T770\nT769 -> s(T770)\nX5139 -> s(s(s(s(s(s(T770))))))\nX5101 -> X5141\nX5140 -> X5141", fontsize=14, style = filled, fillcolor = lightblue];
808 -> 2712 [arrowhead = none ];
2712 -> 810;

2713 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
808 -> 2713 [arrowhead = none ];
2713 -> 811;

2714 [label="EVAL with clause\nquot(X6208, 0, s(X6209), s(X6210)) :- quot(X6208, s(X6209), s(X6209), X6210).\nand substitution\nT758 -> 0\nX6208 -> s(s(s(s(0))))\nT866 -> 0\nX6209 -> s(s(s(s(0))))\nX6210 -> X6211\nX5101 -> s(X6211)", fontsize=14, style = filled, fillcolor = lightblue];
809 -> 2714 [arrowhead = none ];
2714 -> 955;

2715 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
809 -> 2715 [arrowhead = none ];
2715 -> 956;

2716 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
810 -> 2716 [arrowhead = none ];
2716 -> 812;

2717 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
812 -> 2717 [arrowhead = none ];
2717 -> 813;

2718 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
813 -> 2718 [arrowhead = none ];
2718 -> 814;

2719 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
813 -> 2719 [arrowhead = none ];
2719 -> 815;

2720 [label="EVAL with clause\nquot(s(X5177), s(X5178), X5179, X5180) :- quot(X5177, X5178, X5179, X5180).\nand substitution\nT770 -> s(T782)\nX5177 -> s(s(s(s(T782))))\nX5178 -> T782\nT781 -> s(T782)\nX5179 -> s(s(s(s(s(s(s(T782)))))))\nX5141 -> X5181\nX5180 -> X5181", fontsize=14, style = filled, fillcolor = lightblue];
814 -> 2720 [arrowhead = none ];
2720 -> 816;

2721 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
814 -> 2721 [arrowhead = none ];
2721 -> 817;

2722 [label="EVAL with clause\nquot(X5960, 0, s(X5961), s(X5962)) :- quot(X5960, s(X5961), s(X5961), X5962).\nand substitution\nT770 -> 0\nX5960 -> s(s(s(s(0))))\nT863 -> 0\nX5961 -> s(s(s(s(s(0)))))\nX5962 -> X5963\nX5141 -> s(X5963)", fontsize=14, style = filled, fillcolor = lightblue];
815 -> 2722 [arrowhead = none ];
2722 -> 922;

2723 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
815 -> 2723 [arrowhead = none ];
2723 -> 923;

2724 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
816 -> 2724 [arrowhead = none ];
2724 -> 818;

2725 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
818 -> 2725 [arrowhead = none ];
2725 -> 819;

2726 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
819 -> 2726 [arrowhead = none ];
2726 -> 820;

2727 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
819 -> 2727 [arrowhead = none ];
2727 -> 821;

2728 [label="EVAL with clause\nquot(s(X5217), s(X5218), X5219, X5220) :- quot(X5217, X5218, X5219, X5220).\nand substitution\nT782 -> s(T794)\nX5217 -> s(s(s(s(T794))))\nX5218 -> T794\nT793 -> s(T794)\nX5219 -> s(s(s(s(s(s(s(s(T794))))))))\nX5181 -> X5221\nX5220 -> X5221", fontsize=14, style = filled, fillcolor = lightblue];
820 -> 2728 [arrowhead = none ];
2728 -> 822;

2729 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
820 -> 2729 [arrowhead = none ];
2729 -> 823;

2730 [label="EVAL with clause\nquot(X5712, 0, s(X5713), s(X5714)) :- quot(X5712, s(X5713), s(X5713), X5714).\nand substitution\nT782 -> 0\nX5712 -> s(s(s(s(0))))\nT860 -> 0\nX5713 -> s(s(s(s(s(s(0))))))\nX5714 -> X5715\nX5181 -> s(X5715)", fontsize=14, style = filled, fillcolor = lightblue];
821 -> 2730 [arrowhead = none ];
2730 -> 889;

2731 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
821 -> 2731 [arrowhead = none ];
2731 -> 890;

2732 [label="GENERALIZATION\nT797 <-- s(s(s(s(s(s(s(T794)))))))\n\nNew Knowledge:\nT797 is ground", fontsize=14, style = filled, fillcolor = violet];
822 -> 2732 [arrowhead = none ];
2732 -> 824;

2733 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
824 -> 2733 [arrowhead = none ];
2733 -> 825;

2734 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
825 -> 2734 [arrowhead = none ];
2734 -> 826;

2735 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
826 -> 2735 [arrowhead = none ];
2735 -> 827;

2736 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
826 -> 2736 [arrowhead = none ];
2736 -> 828;

2737 [label="EVAL with clause\nquot(s(X5266), s(X5267), X5268, X5269) :- quot(X5266, X5267, X5268, X5269).\nand substitution\nT794 -> s(T814)\nX5266 -> s(s(s(s(T814))))\nX5267 -> T814\nT813 -> s(T814)\nT797 -> T815\nX5268 -> s(T815)\nX5221 -> X5270\nX5269 -> X5270", fontsize=14, style = filled, fillcolor = lightblue];
827 -> 2737 [arrowhead = none ];
2737 -> 829;

2738 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
827 -> 2738 [arrowhead = none ];
2738 -> 830;

2739 [label="EVAL with clause\nquot(X5292, 0, s(X5293), s(X5294)) :- quot(X5292, s(X5293), s(X5293), X5294).\nand substitution\nT794 -> 0\nX5292 -> s(s(s(s(0))))\nT823 -> 0\nT797 -> T824\nX5293 -> T824\nX5294 -> X5295\nX5221 -> s(X5295)", fontsize=14, style = filled, fillcolor = lightblue];
828 -> 2739 [arrowhead = none ];
2739 -> 831;

2740 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
828 -> 2740 [arrowhead = none ];
2740 -> 832;

2741 [label="INSTANCE with matching:\nT794 -> T814\nT797 -> T815\nX5221 -> X5270", fontsize=14, style = filled, fillcolor = lightgrey];
829 -> 2741 [arrowhead = none , style=dashed];
2741 -> 824[style=dashed];

2742 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
831 -> 2742 [arrowhead = none ];
2742 -> 833;

2743 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
833 -> 2743 [arrowhead = none ];
2743 -> 834;

2744 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
834 -> 2744 [arrowhead = none ];
2744 -> 835;

2745 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
834 -> 2745 [arrowhead = none ];
2745 -> 836;

2746 [label="ONLY EVAL with clause\nquot(s(X5348), s(X5349), X5350, X5351) :- quot(X5348, X5349, X5350, X5351).\nand substitution\nX5348 -> s(s(s(0)))\nT824 -> T832\nX5349 -> T832\nX5350 -> s(T832)\nX5295 -> X5352\nX5351 -> X5352", fontsize=14, style = filled, fillcolor = white];
835 -> 2746 [arrowhead = none ];
2746 -> 837;

2747 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
836 -> 2747 [arrowhead = none ];
2747 -> 888;

2748 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
837 -> 2748 [arrowhead = none ];
2748 -> 838;

2749 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
838 -> 2749 [arrowhead = none ];
2749 -> 839;

2750 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
839 -> 2750 [arrowhead = none ];
2750 -> 840;

2751 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
839 -> 2751 [arrowhead = none ];
2751 -> 841;

2752 [label="EVAL with clause\nquot(s(X5384), s(X5385), X5386, X5387) :- quot(X5384, X5385, X5386, X5387).\nand substitution\nX5384 -> s(s(0))\nX5385 -> T838\nT832 -> s(T838)\nX5386 -> s(s(T838))\nX5352 -> X5388\nX5387 -> X5388", fontsize=14, style = filled, fillcolor = lightblue];
840 -> 2752 [arrowhead = none ];
2752 -> 842;

2753 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
840 -> 2753 [arrowhead = none ];
2753 -> 843;

2754 [label="EVAL with clause\nquot(X5583, 0, s(X5584), s(X5585)) :- quot(X5583, s(X5584), s(X5584), X5585).\nand substitution\nX5583 -> s(s(s(0)))\nT832 -> 0\nX5584 -> 0\nX5585 -> X5586\nX5352 -> s(X5586)", fontsize=14, style = filled, fillcolor = lightblue];
841 -> 2754 [arrowhead = none ];
2754 -> 876;

2755 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
841 -> 2755 [arrowhead = none ];
2755 -> 877;

2756 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
842 -> 2756 [arrowhead = none ];
2756 -> 844;

2757 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
844 -> 2757 [arrowhead = none ];
2757 -> 845;

2758 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
845 -> 2758 [arrowhead = none ];
2758 -> 846;

2759 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
845 -> 2759 [arrowhead = none ];
2759 -> 847;

2760 [label="EVAL with clause\nquot(s(X5424), s(X5425), X5426, X5427) :- quot(X5424, X5425, X5426, X5427).\nand substitution\nX5424 -> s(0)\nX5425 -> T844\nT838 -> s(T844)\nX5426 -> s(s(s(T844)))\nX5388 -> X5428\nX5427 -> X5428", fontsize=14, style = filled, fillcolor = lightblue];
846 -> 2760 [arrowhead = none ];
2760 -> 848;

2761 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
846 -> 2761 [arrowhead = none ];
2761 -> 849;

2762 [label="EVAL with clause\nquot(X5559, 0, s(X5560), s(X5561)) :- quot(X5559, s(X5560), s(X5560), X5561).\nand substitution\nX5559 -> s(s(0))\nT838 -> 0\nX5560 -> s(0)\nX5561 -> X5562\nX5388 -> s(X5562)", fontsize=14, style = filled, fillcolor = lightblue];
847 -> 2762 [arrowhead = none ];
2762 -> 874;

2763 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
847 -> 2763 [arrowhead = none ];
2763 -> 875;

2764 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
848 -> 2764 [arrowhead = none ];
2764 -> 850;

2765 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
850 -> 2765 [arrowhead = none ];
2765 -> 851;

2766 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
851 -> 2766 [arrowhead = none ];
2766 -> 852;

2767 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
851 -> 2767 [arrowhead = none ];
2767 -> 853;

2768 [label="EVAL with clause\nquot(s(X5464), s(X5465), X5466, X5467) :- quot(X5464, X5465, X5466, X5467).\nand substitution\nX5464 -> 0\nX5465 -> T850\nT844 -> s(T850)\nX5466 -> s(s(s(s(T850))))\nX5428 -> X5468\nX5467 -> X5468", fontsize=14, style = filled, fillcolor = lightblue];
852 -> 2768 [arrowhead = none ];
2768 -> 854;

2769 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
852 -> 2769 [arrowhead = none ];
2769 -> 855;

2770 [label="EVAL with clause\nquot(X5535, 0, s(X5536), s(X5537)) :- quot(X5535, s(X5536), s(X5536), X5537).\nand substitution\nX5535 -> s(0)\nT844 -> 0\nX5536 -> s(s(0))\nX5537 -> X5538\nX5428 -> s(X5538)", fontsize=14, style = filled, fillcolor = lightblue];
853 -> 2770 [arrowhead = none ];
2770 -> 872;

2771 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
853 -> 2771 [arrowhead = none ];
2771 -> 873;

2772 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
854 -> 2772 [arrowhead = none ];
2772 -> 856;

2773 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
856 -> 2773 [arrowhead = none ];
2773 -> 857;

2774 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
856 -> 2774 [arrowhead = none ];
2774 -> 858;

2775 [label="EVAL with clause\nquot(0, s(X5485), s(X5486), 0).\nand substitution\nX5485 -> T857\nT850 -> s(T857)\nX5486 -> s(s(s(s(T857))))\nX5468 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
857 -> 2775 [arrowhead = none ];
2775 -> 859;

2776 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
857 -> 2776 [arrowhead = none ];
2776 -> 860;

2777 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
858 -> 2777 [arrowhead = none ];
2777 -> 862;

2778 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
859 -> 2778 [arrowhead = none ];
2778 -> 861;

2779 [label="EVAL with clause\nquot(X5501, 0, s(X5502), s(X5503)) :- quot(X5501, s(X5502), s(X5502), X5503).\nand substitution\nX5501 -> 0\nT850 -> 0\nX5502 -> s(s(s(0)))\nX5503 -> X5504\nX5468 -> s(X5504)", fontsize=14, style = filled, fillcolor = lightblue];
862 -> 2779 [arrowhead = none ];
2779 -> 863;

2780 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
862 -> 2780 [arrowhead = none ];
2780 -> 864;

2781 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
863 -> 2781 [arrowhead = none ];
2781 -> 865;

2782 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
865 -> 2782 [arrowhead = none ];
2782 -> 866;

2783 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
865 -> 2783 [arrowhead = none ];
2783 -> 867;

2784 [label="ONLY EVAL with clause\nquot(0, s(X5518), s(X5519), 0).\nand substitution\nX5518 -> s(s(s(0)))\nX5519 -> s(s(s(0)))\nX5504 -> 0", fontsize=14, style = filled, fillcolor = white];
866 -> 2784 [arrowhead = none ];
2784 -> 868;

2785 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
867 -> 2785 [arrowhead = none ];
2785 -> 870;

2786 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
868 -> 2786 [arrowhead = none ];
2786 -> 869;

2787 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
870 -> 2787 [arrowhead = none ];
2787 -> 871;

2788 [label="INSTANCE with matching:\nX910 -> X5538", fontsize=14, style = filled, fillcolor = lightgrey];
872 -> 2788 [arrowhead = none , style=dashed];
2788 -> 158[style=dashed];

2789 [label="INSTANCE with matching:\nX2627 -> X5562", fontsize=14, style = filled, fillcolor = lightgrey];
874 -> 2789 [arrowhead = none , style=dashed];
2789 -> 467[style=dashed];

2790 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
876 -> 2790 [arrowhead = none ];
2790 -> 878;

2791 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
878 -> 2791 [arrowhead = none ];
2791 -> 879;

2792 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
879 -> 2792 [arrowhead = none ];
2792 -> 880;

2793 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
879 -> 2793 [arrowhead = none ];
2793 -> 881;

2794 [label="ONLY EVAL with clause\nquot(s(X5645), s(X5646), X5647, X5648) :- quot(X5645, X5646, X5647, X5648).\nand substitution\nX5645 -> s(s(0))\nX5646 -> 0\nX5647 -> s(0)\nX5586 -> X5649\nX5648 -> X5649", fontsize=14, style = filled, fillcolor = white];
880 -> 2794 [arrowhead = none ];
2794 -> 882;

2795 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
881 -> 2795 [arrowhead = none ];
2795 -> 887;

2796 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
882 -> 2796 [arrowhead = none ];
2796 -> 883;

2797 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
883 -> 2797 [arrowhead = none ];
2797 -> 884;

2798 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
884 -> 2798 [arrowhead = none ];
2798 -> 885;

2799 [label="ONLY EVAL with clause\nquot(X5685, 0, s(X5686), s(X5687)) :- quot(X5685, s(X5686), s(X5686), X5687).\nand substitution\nX5685 -> s(s(0))\nX5686 -> 0\nX5687 -> X5688\nX5649 -> s(X5688)", fontsize=14, style = filled, fillcolor = white];
885 -> 2799 [arrowhead = none ];
2799 -> 886;

2800 [label="INSTANCE with matching:\nX3508 -> X5688", fontsize=14, style = filled, fillcolor = lightgrey];
886 -> 2800 [arrowhead = none , style=dashed];
2800 -> 595[style=dashed];

2801 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
889 -> 2801 [arrowhead = none ];
2801 -> 891;

2802 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
891 -> 2802 [arrowhead = none ];
2802 -> 892;

2803 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
892 -> 2803 [arrowhead = none ];
2803 -> 893;

2804 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
892 -> 2804 [arrowhead = none ];
2804 -> 894;

2805 [label="ONLY EVAL with clause\nquot(s(X5768), s(X5769), X5770, X5771) :- quot(X5768, X5769, X5770, X5771).\nand substitution\nX5768 -> s(s(s(0)))\nX5769 -> s(s(s(s(s(s(0))))))\nX5770 -> s(s(s(s(s(s(s(0)))))))\nX5715 -> X5772\nX5771 -> X5772", fontsize=14, style = filled, fillcolor = white];
893 -> 2805 [arrowhead = none ];
2805 -> 895;

2806 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
894 -> 2806 [arrowhead = none ];
2806 -> 921;

2807 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
895 -> 2807 [arrowhead = none ];
2807 -> 896;

2808 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
896 -> 2808 [arrowhead = none ];
2808 -> 897;

2809 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
897 -> 2809 [arrowhead = none ];
2809 -> 898;

2810 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
897 -> 2810 [arrowhead = none ];
2810 -> 899;

2811 [label="ONLY EVAL with clause\nquot(s(X5822), s(X5823), X5824, X5825) :- quot(X5822, X5823, X5824, X5825).\nand substitution\nX5822 -> s(s(0))\nX5823 -> s(s(s(s(s(0)))))\nX5824 -> s(s(s(s(s(s(s(0)))))))\nX5772 -> X5826\nX5825 -> X5826", fontsize=14, style = filled, fillcolor = white];
898 -> 2811 [arrowhead = none ];
2811 -> 900;

2812 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
899 -> 2812 [arrowhead = none ];
2812 -> 920;

2813 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
900 -> 2813 [arrowhead = none ];
2813 -> 901;

2814 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
901 -> 2814 [arrowhead = none ];
2814 -> 902;

2815 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
902 -> 2815 [arrowhead = none ];
2815 -> 903;

2816 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
902 -> 2816 [arrowhead = none ];
2816 -> 904;

2817 [label="ONLY EVAL with clause\nquot(s(X5876), s(X5877), X5878, X5879) :- quot(X5876, X5877, X5878, X5879).\nand substitution\nX5876 -> s(0)\nX5877 -> s(s(s(s(0))))\nX5878 -> s(s(s(s(s(s(s(0)))))))\nX5826 -> X5880\nX5879 -> X5880", fontsize=14, style = filled, fillcolor = white];
903 -> 2817 [arrowhead = none ];
2817 -> 905;

2818 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
904 -> 2818 [arrowhead = none ];
2818 -> 919;

2819 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
905 -> 2819 [arrowhead = none ];
2819 -> 906;

2820 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
906 -> 2820 [arrowhead = none ];
2820 -> 907;

2821 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
907 -> 2821 [arrowhead = none ];
2821 -> 908;

2822 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
907 -> 2822 [arrowhead = none ];
2822 -> 909;

2823 [label="ONLY EVAL with clause\nquot(s(X5916), s(X5917), X5918, X5919) :- quot(X5916, X5917, X5918, X5919).\nand substitution\nX5916 -> 0\nX5917 -> s(s(s(0)))\nX5918 -> s(s(s(s(s(s(s(0)))))))\nX5880 -> X5920\nX5919 -> X5920", fontsize=14, style = filled, fillcolor = white];
908 -> 2823 [arrowhead = none ];
2823 -> 910;

2824 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
909 -> 2824 [arrowhead = none ];
2824 -> 918;

2825 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
910 -> 2825 [arrowhead = none ];
2825 -> 911;

2826 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
911 -> 2826 [arrowhead = none ];
2826 -> 912;

2827 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
911 -> 2827 [arrowhead = none ];
2827 -> 913;

2828 [label="ONLY EVAL with clause\nquot(0, s(X5931), s(X5932), 0).\nand substitution\nX5931 -> s(s(0))\nX5932 -> s(s(s(s(s(s(0))))))\nX5920 -> 0", fontsize=14, style = filled, fillcolor = white];
912 -> 2828 [arrowhead = none ];
2828 -> 914;

2829 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
913 -> 2829 [arrowhead = none ];
2829 -> 916;

2830 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
914 -> 2830 [arrowhead = none ];
2830 -> 915;

2831 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
916 -> 2831 [arrowhead = none ];
2831 -> 917;

2832 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
922 -> 2832 [arrowhead = none ];
2832 -> 924;

2833 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
924 -> 2833 [arrowhead = none ];
2833 -> 925;

2834 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
925 -> 2834 [arrowhead = none ];
2834 -> 926;

2835 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
925 -> 2835 [arrowhead = none ];
2835 -> 927;

2836 [label="ONLY EVAL with clause\nquot(s(X6016), s(X6017), X6018, X6019) :- quot(X6016, X6017, X6018, X6019).\nand substitution\nX6016 -> s(s(s(0)))\nX6017 -> s(s(s(s(s(0)))))\nX6018 -> s(s(s(s(s(s(0))))))\nX5963 -> X6020\nX6019 -> X6020", fontsize=14, style = filled, fillcolor = white];
926 -> 2836 [arrowhead = none ];
2836 -> 928;

2837 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
927 -> 2837 [arrowhead = none ];
2837 -> 954;

2838 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
928 -> 2838 [arrowhead = none ];
2838 -> 929;

2839 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
929 -> 2839 [arrowhead = none ];
2839 -> 930;

2840 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
930 -> 2840 [arrowhead = none ];
2840 -> 931;

2841 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
930 -> 2841 [arrowhead = none ];
2841 -> 932;

2842 [label="ONLY EVAL with clause\nquot(s(X6070), s(X6071), X6072, X6073) :- quot(X6070, X6071, X6072, X6073).\nand substitution\nX6070 -> s(s(0))\nX6071 -> s(s(s(s(0))))\nX6072 -> s(s(s(s(s(s(0))))))\nX6020 -> X6074\nX6073 -> X6074", fontsize=14, style = filled, fillcolor = white];
931 -> 2842 [arrowhead = none ];
2842 -> 933;

2843 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
932 -> 2843 [arrowhead = none ];
2843 -> 953;

2844 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
933 -> 2844 [arrowhead = none ];
2844 -> 934;

2845 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
934 -> 2845 [arrowhead = none ];
2845 -> 935;

2846 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
935 -> 2846 [arrowhead = none ];
2846 -> 936;

2847 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
935 -> 2847 [arrowhead = none ];
2847 -> 937;

2848 [label="ONLY EVAL with clause\nquot(s(X6124), s(X6125), X6126, X6127) :- quot(X6124, X6125, X6126, X6127).\nand substitution\nX6124 -> s(0)\nX6125 -> s(s(s(0)))\nX6126 -> s(s(s(s(s(s(0))))))\nX6074 -> X6128\nX6127 -> X6128", fontsize=14, style = filled, fillcolor = white];
936 -> 2848 [arrowhead = none ];
2848 -> 938;

2849 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
937 -> 2849 [arrowhead = none ];
2849 -> 952;

2850 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
938 -> 2850 [arrowhead = none ];
2850 -> 939;

2851 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
939 -> 2851 [arrowhead = none ];
2851 -> 940;

2852 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
940 -> 2852 [arrowhead = none ];
2852 -> 941;

2853 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
940 -> 2853 [arrowhead = none ];
2853 -> 942;

2854 [label="ONLY EVAL with clause\nquot(s(X6164), s(X6165), X6166, X6167) :- quot(X6164, X6165, X6166, X6167).\nand substitution\nX6164 -> 0\nX6165 -> s(s(0))\nX6166 -> s(s(s(s(s(s(0))))))\nX6128 -> X6168\nX6167 -> X6168", fontsize=14, style = filled, fillcolor = white];
941 -> 2854 [arrowhead = none ];
2854 -> 943;

2855 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
942 -> 2855 [arrowhead = none ];
2855 -> 951;

2856 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
943 -> 2856 [arrowhead = none ];
2856 -> 944;

2857 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
944 -> 2857 [arrowhead = none ];
2857 -> 945;

2858 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
944 -> 2858 [arrowhead = none ];
2858 -> 946;

2859 [label="ONLY EVAL with clause\nquot(0, s(X6179), s(X6180), 0).\nand substitution\nX6179 -> s(0)\nX6180 -> s(s(s(s(s(0)))))\nX6168 -> 0", fontsize=14, style = filled, fillcolor = white];
945 -> 2859 [arrowhead = none ];
2859 -> 947;

2860 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
946 -> 2860 [arrowhead = none ];
2860 -> 949;

2861 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
947 -> 2861 [arrowhead = none ];
2861 -> 948;

2862 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
949 -> 2862 [arrowhead = none ];
2862 -> 950;

2863 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
955 -> 2863 [arrowhead = none ];
2863 -> 957;

2864 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
957 -> 2864 [arrowhead = none ];
2864 -> 958;

2865 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
958 -> 2865 [arrowhead = none ];
2865 -> 959;

2866 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
958 -> 2866 [arrowhead = none ];
2866 -> 960;

2867 [label="ONLY EVAL with clause\nquot(s(X6264), s(X6265), X6266, X6267) :- quot(X6264, X6265, X6266, X6267).\nand substitution\nX6264 -> s(s(s(0)))\nX6265 -> s(s(s(s(0))))\nX6266 -> s(s(s(s(s(0)))))\nX6211 -> X6268\nX6267 -> X6268", fontsize=14, style = filled, fillcolor = white];
959 -> 2867 [arrowhead = none ];
2867 -> 961;

2868 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
960 -> 2868 [arrowhead = none ];
2868 -> 987;

2869 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
961 -> 2869 [arrowhead = none ];
2869 -> 962;

2870 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
962 -> 2870 [arrowhead = none ];
2870 -> 963;

2871 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
963 -> 2871 [arrowhead = none ];
2871 -> 964;

2872 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
963 -> 2872 [arrowhead = none ];
2872 -> 965;

2873 [label="ONLY EVAL with clause\nquot(s(X6318), s(X6319), X6320, X6321) :- quot(X6318, X6319, X6320, X6321).\nand substitution\nX6318 -> s(s(0))\nX6319 -> s(s(s(0)))\nX6320 -> s(s(s(s(s(0)))))\nX6268 -> X6322\nX6321 -> X6322", fontsize=14, style = filled, fillcolor = white];
964 -> 2873 [arrowhead = none ];
2873 -> 966;

2874 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
965 -> 2874 [arrowhead = none ];
2874 -> 986;

2875 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
966 -> 2875 [arrowhead = none ];
2875 -> 967;

2876 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
967 -> 2876 [arrowhead = none ];
2876 -> 968;

2877 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
968 -> 2877 [arrowhead = none ];
2877 -> 969;

2878 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
968 -> 2878 [arrowhead = none ];
2878 -> 970;

2879 [label="ONLY EVAL with clause\nquot(s(X6372), s(X6373), X6374, X6375) :- quot(X6372, X6373, X6374, X6375).\nand substitution\nX6372 -> s(0)\nX6373 -> s(s(0))\nX6374 -> s(s(s(s(s(0)))))\nX6322 -> X6376\nX6375 -> X6376", fontsize=14, style = filled, fillcolor = white];
969 -> 2879 [arrowhead = none ];
2879 -> 971;

2880 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
970 -> 2880 [arrowhead = none ];
2880 -> 985;

2881 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
971 -> 2881 [arrowhead = none ];
2881 -> 972;

2882 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
972 -> 2882 [arrowhead = none ];
2882 -> 973;

2883 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
973 -> 2883 [arrowhead = none ];
2883 -> 974;

2884 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
973 -> 2884 [arrowhead = none ];
2884 -> 975;

2885 [label="ONLY EVAL with clause\nquot(s(X6412), s(X6413), X6414, X6415) :- quot(X6412, X6413, X6414, X6415).\nand substitution\nX6412 -> 0\nX6413 -> s(0)\nX6414 -> s(s(s(s(s(0)))))\nX6376 -> X6416\nX6415 -> X6416", fontsize=14, style = filled, fillcolor = white];
974 -> 2885 [arrowhead = none ];
2885 -> 976;

2886 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
975 -> 2886 [arrowhead = none ];
2886 -> 984;

2887 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
976 -> 2887 [arrowhead = none ];
2887 -> 977;

2888 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
977 -> 2888 [arrowhead = none ];
2888 -> 978;

2889 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
977 -> 2889 [arrowhead = none ];
2889 -> 979;

2890 [label="ONLY EVAL with clause\nquot(0, s(X6427), s(X6428), 0).\nand substitution\nX6427 -> 0\nX6428 -> s(s(s(s(0))))\nX6416 -> 0", fontsize=14, style = filled, fillcolor = white];
978 -> 2890 [arrowhead = none ];
2890 -> 980;

2891 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
979 -> 2891 [arrowhead = none ];
2891 -> 982;

2892 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
980 -> 2892 [arrowhead = none ];
2892 -> 981;

2893 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
982 -> 2893 [arrowhead = none ];
2893 -> 983;

2894 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
988 -> 2894 [arrowhead = none ];
2894 -> 990;

2895 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
990 -> 2895 [arrowhead = none ];
2895 -> 991;

2896 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
991 -> 2896 [arrowhead = none ];
2896 -> 992;

2897 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
991 -> 2897 [arrowhead = none ];
2897 -> 993;

2898 [label="ONLY EVAL with clause\nquot(s(X6512), s(X6513), X6514, X6515) :- quot(X6512, X6513, X6514, X6515).\nand substitution\nX6512 -> s(s(s(0)))\nX6513 -> s(s(s(0)))\nX6514 -> s(s(s(s(0))))\nX6459 -> X6516\nX6515 -> X6516", fontsize=14, style = filled, fillcolor = white];
992 -> 2898 [arrowhead = none ];
2898 -> 994;

2899 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
993 -> 2899 [arrowhead = none ];
2899 -> 1017;

2900 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
994 -> 2900 [arrowhead = none ];
2900 -> 995;

2901 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
995 -> 2901 [arrowhead = none ];
2901 -> 996;

2902 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
996 -> 2902 [arrowhead = none ];
2902 -> 997;

2903 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
996 -> 2903 [arrowhead = none ];
2903 -> 998;

2904 [label="ONLY EVAL with clause\nquot(s(X6566), s(X6567), X6568, X6569) :- quot(X6566, X6567, X6568, X6569).\nand substitution\nX6566 -> s(s(0))\nX6567 -> s(s(0))\nX6568 -> s(s(s(s(0))))\nX6516 -> X6570\nX6569 -> X6570", fontsize=14, style = filled, fillcolor = white];
997 -> 2904 [arrowhead = none ];
2904 -> 999;

2905 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
998 -> 2905 [arrowhead = none ];
2905 -> 1016;

2906 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
999 -> 2906 [arrowhead = none ];
2906 -> 1000;

2907 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1000 -> 2907 [arrowhead = none ];
2907 -> 1001;

2908 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1001 -> 2908 [arrowhead = none ];
2908 -> 1002;

2909 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1001 -> 2909 [arrowhead = none ];
2909 -> 1003;

2910 [label="ONLY EVAL with clause\nquot(s(X6620), s(X6621), X6622, X6623) :- quot(X6620, X6621, X6622, X6623).\nand substitution\nX6620 -> s(0)\nX6621 -> s(0)\nX6622 -> s(s(s(s(0))))\nX6570 -> X6624\nX6623 -> X6624", fontsize=14, style = filled, fillcolor = white];
1002 -> 2910 [arrowhead = none ];
2910 -> 1004;

2911 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1003 -> 2911 [arrowhead = none ];
2911 -> 1015;

2912 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1004 -> 2912 [arrowhead = none ];
2912 -> 1005;

2913 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1005 -> 2913 [arrowhead = none ];
2913 -> 1006;

2914 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1006 -> 2914 [arrowhead = none ];
2914 -> 1007;

2915 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1006 -> 2915 [arrowhead = none ];
2915 -> 1008;

2916 [label="ONLY EVAL with clause\nquot(s(X6680), s(X6681), X6682, X6683) :- quot(X6680, X6681, X6682, X6683).\nand substitution\nX6680 -> 0\nX6681 -> 0\nX6682 -> s(s(s(s(0))))\nX6624 -> X6684\nX6683 -> X6684", fontsize=14, style = filled, fillcolor = white];
1007 -> 2916 [arrowhead = none ];
2916 -> 1009;

2917 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1008 -> 2917 [arrowhead = none ];
2917 -> 1014;

2918 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1009 -> 2918 [arrowhead = none ];
2918 -> 1010;

2919 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1010 -> 2919 [arrowhead = none ];
2919 -> 1011;

2920 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1011 -> 2920 [arrowhead = none ];
2920 -> 1012;

2921 [label="ONLY EVAL with clause\nquot(X6713, 0, s(X6714), s(X6715)) :- quot(X6713, s(X6714), s(X6714), X6715).\nand substitution\nX6713 -> 0\nX6714 -> s(s(s(0)))\nX6715 -> X6716\nX6684 -> s(X6716)", fontsize=14, style = filled, fillcolor = white];
1012 -> 2921 [arrowhead = none ];
2921 -> 1013;

2922 [label="INSTANCE with matching:\nX5504 -> X6716", fontsize=14, style = filled, fillcolor = lightgrey];
1013 -> 2922 [arrowhead = none , style=dashed];
2922 -> 863[style=dashed];

2923 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1018 -> 2923 [arrowhead = none ];
2923 -> 1020;

2924 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1020 -> 2924 [arrowhead = none ];
2924 -> 1021;

2925 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1021 -> 2925 [arrowhead = none ];
2925 -> 1022;

2926 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1021 -> 2926 [arrowhead = none ];
2926 -> 1023;

2927 [label="ONLY EVAL with clause\nquot(s(X6795), s(X6796), X6797, X6798) :- quot(X6795, X6796, X6797, X6798).\nand substitution\nX6795 -> s(s(s(0)))\nX6796 -> s(s(0))\nX6797 -> s(s(s(0)))\nX6742 -> X6799\nX6798 -> X6799", fontsize=14, style = filled, fillcolor = white];
1022 -> 2927 [arrowhead = none ];
2927 -> 1024;

2928 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1023 -> 2928 [arrowhead = none ];
2928 -> 1041;

2929 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1024 -> 2929 [arrowhead = none ];
2929 -> 1025;

2930 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1025 -> 2930 [arrowhead = none ];
2930 -> 1026;

2931 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1026 -> 2931 [arrowhead = none ];
2931 -> 1027;

2932 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1026 -> 2932 [arrowhead = none ];
2932 -> 1028;

2933 [label="ONLY EVAL with clause\nquot(s(X6849), s(X6850), X6851, X6852) :- quot(X6849, X6850, X6851, X6852).\nand substitution\nX6849 -> s(s(0))\nX6850 -> s(0)\nX6851 -> s(s(s(0)))\nX6799 -> X6853\nX6852 -> X6853", fontsize=14, style = filled, fillcolor = white];
1027 -> 2933 [arrowhead = none ];
2933 -> 1029;

2934 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1028 -> 2934 [arrowhead = none ];
2934 -> 1040;

2935 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1029 -> 2935 [arrowhead = none ];
2935 -> 1030;

2936 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1030 -> 2936 [arrowhead = none ];
2936 -> 1031;

2937 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1031 -> 2937 [arrowhead = none ];
2937 -> 1032;

2938 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1031 -> 2938 [arrowhead = none ];
2938 -> 1033;

2939 [label="ONLY EVAL with clause\nquot(s(X6909), s(X6910), X6911, X6912) :- quot(X6909, X6910, X6911, X6912).\nand substitution\nX6909 -> s(0)\nX6910 -> 0\nX6911 -> s(s(s(0)))\nX6853 -> X6913\nX6912 -> X6913", fontsize=14, style = filled, fillcolor = white];
1032 -> 2939 [arrowhead = none ];
2939 -> 1034;

2940 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1033 -> 2940 [arrowhead = none ];
2940 -> 1039;

2941 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1034 -> 2941 [arrowhead = none ];
2941 -> 1035;

2942 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1035 -> 2942 [arrowhead = none ];
2942 -> 1036;

2943 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1036 -> 2943 [arrowhead = none ];
2943 -> 1037;

2944 [label="ONLY EVAL with clause\nquot(X6949, 0, s(X6950), s(X6951)) :- quot(X6949, s(X6950), s(X6950), X6951).\nand substitution\nX6949 -> s(0)\nX6950 -> s(s(0))\nX6951 -> X6952\nX6913 -> s(X6952)", fontsize=14, style = filled, fillcolor = white];
1037 -> 2944 [arrowhead = none ];
2944 -> 1038;

2945 [label="INSTANCE with matching:\nX910 -> X6952", fontsize=14, style = filled, fillcolor = lightgrey];
1038 -> 2945 [arrowhead = none , style=dashed];
2945 -> 158[style=dashed];

2946 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1042 -> 2946 [arrowhead = none ];
2946 -> 1044;

2947 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1044 -> 2947 [arrowhead = none ];
2947 -> 1045;

2948 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1045 -> 2948 [arrowhead = none ];
2948 -> 1046;

2949 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1045 -> 2949 [arrowhead = none ];
2949 -> 1047;

2950 [label="ONLY EVAL with clause\nquot(s(X7035), s(X7036), X7037, X7038) :- quot(X7035, X7036, X7037, X7038).\nand substitution\nX7035 -> s(s(s(0)))\nX7036 -> s(0)\nX7037 -> s(s(0))\nX6982 -> X7039\nX7038 -> X7039", fontsize=14, style = filled, fillcolor = white];
1046 -> 2950 [arrowhead = none ];
2950 -> 1048;

2951 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1047 -> 2951 [arrowhead = none ];
2951 -> 1059;

2952 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1048 -> 2952 [arrowhead = none ];
2952 -> 1049;

2953 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1049 -> 2953 [arrowhead = none ];
2953 -> 1050;

2954 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1050 -> 2954 [arrowhead = none ];
2954 -> 1051;

2955 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1050 -> 2955 [arrowhead = none ];
2955 -> 1052;

2956 [label="ONLY EVAL with clause\nquot(s(X7095), s(X7096), X7097, X7098) :- quot(X7095, X7096, X7097, X7098).\nand substitution\nX7095 -> s(s(0))\nX7096 -> 0\nX7097 -> s(s(0))\nX7039 -> X7099\nX7098 -> X7099", fontsize=14, style = filled, fillcolor = white];
1051 -> 2956 [arrowhead = none ];
2956 -> 1053;

2957 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1052 -> 2957 [arrowhead = none ];
2957 -> 1058;

2958 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1053 -> 2958 [arrowhead = none ];
2958 -> 1054;

2959 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1054 -> 2959 [arrowhead = none ];
2959 -> 1055;

2960 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1055 -> 2960 [arrowhead = none ];
2960 -> 1056;

2961 [label="ONLY EVAL with clause\nquot(X7135, 0, s(X7136), s(X7137)) :- quot(X7135, s(X7136), s(X7136), X7137).\nand substitution\nX7135 -> s(s(0))\nX7136 -> s(0)\nX7137 -> X7138\nX7099 -> s(X7138)", fontsize=14, style = filled, fillcolor = white];
1056 -> 2961 [arrowhead = none ];
2961 -> 1057;

2962 [label="INSTANCE with matching:\nX2627 -> X7138", fontsize=14, style = filled, fillcolor = lightgrey];
1057 -> 2962 [arrowhead = none , style=dashed];
2962 -> 467[style=dashed];

2963 [label="INSTANCE with matching:\nT22 -> T699\nT20 -> T697\nX39 -> X4848", fontsize=14, style = filled, fillcolor = lightgrey];
1062 -> 2963 [arrowhead = none , style=dashed];
2963 -> 190[style=dashed];

2964 [label="INSTANCE with matching:\nT20 -> s(s(s(T697)))\nT187 -> T880", fontsize=14, style = filled, fillcolor = lightgrey];
1063 -> 2964 [arrowhead = none , style=dashed];
2964 -> 191[style=dashed];

2965 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1064 -> 2965 [arrowhead = none ];
2965 -> 1065;

2966 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1064 -> 2966 [arrowhead = none ];
2966 -> 1066;

2967 [label="EVAL with clause\npr(X7172, s(0)).\nand substitution\nT691 -> 0\nX7172 -> s(s(s(s(s(s(0))))))\nT891 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1065 -> 2967 [arrowhead = none ];
2967 -> 1067;

2968 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1065 -> 2968 [arrowhead = none ];
2968 -> 1068;

2969 [label="EVAL with clause\npr(X7178, s(s(X7179))) :- ','(not_divides(s(s(X7179)), X7178), pr(X7178, s(X7179))).\nand substitution\nT691 -> s(T897)\nX7178 -> s(s(s(s(s(s(s(T897)))))))\nX7179 -> T897\nT896 -> s(T897)", fontsize=14, style = filled, fillcolor = lightblue];
1066 -> 2969 [arrowhead = none ];
2969 -> 1070;

2970 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1066 -> 2970 [arrowhead = none ];
2970 -> 1071;

2971 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1067 -> 2971 [arrowhead = none ];
2971 -> 1069;

2972 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
1070 -> 2972 [arrowhead = none ];
2972 -> 1072;

2973 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
1070 -> 2973 [arrowhead = none ];
2973 -> 1073;

2974 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1072 -> 2974 [arrowhead = none ];
2974 -> 1074;

2975 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1073 -> 2975 [arrowhead = none ];
2975 -> 1389;

2976 [label="ONLY EVAL with clause\nnot_divides(X7200, X7201) :- ','(div(X7201, X7200, X7202), ','(times(X7202, X7200, X7203), neq(X7201, X7203))).\nand substitution\nT897 -> T903\nX7200 -> s(s(T903))\nX7201 -> s(s(s(s(s(s(s(T903)))))))", fontsize=14, style = filled, fillcolor = white];
1074 -> 2976 [arrowhead = none ];
2976 -> 1075;

2977 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
1075 -> 2977 [arrowhead = none ];
2977 -> 1076;

2978 [label="SPLIT 2\nnew knowledge:\nT905 is ground\nreplacements:\nX7202 -> T905", fontsize=14, style = filled, fillcolor = violet];
1075 -> 2978 [arrowhead = none ];
2978 -> 1077;

2979 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1076 -> 2979 [arrowhead = none ];
2979 -> 1078;

2980 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
1077 -> 2980 [arrowhead = none ];
2980 -> 1387;

2981 [label="SPLIT 2\nnew knowledge:\nT1092 is ground\nreplacements:\nX7203 -> T1092", fontsize=14, style = filled, fillcolor = violet];
1077 -> 2981 [arrowhead = none ];
2981 -> 1388;

2982 [label="ONLY EVAL with clause\ndiv(X7229, X7230, X7231) :- quot(X7229, X7230, X7230, X7231).\nand substitution\nT903 -> T910\nX7229 -> s(s(s(s(s(s(s(T910)))))))\nX7230 -> s(s(T910))\nX7202 -> X7232\nX7231 -> X7232", fontsize=14, style = filled, fillcolor = white];
1078 -> 2982 [arrowhead = none ];
2982 -> 1079;

2983 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1079 -> 2983 [arrowhead = none ];
2983 -> 1080;

2984 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1080 -> 2984 [arrowhead = none ];
2984 -> 1081;

2985 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1081 -> 2985 [arrowhead = none ];
2985 -> 1082;

2986 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1081 -> 2986 [arrowhead = none ];
2986 -> 1083;

2987 [label="ONLY EVAL with clause\nquot(s(X7282), s(X7283), X7284, X7285) :- quot(X7282, X7283, X7284, X7285).\nand substitution\nT910 -> T918\nX7282 -> s(s(s(s(s(s(T918))))))\nX7283 -> s(T918)\nX7284 -> s(s(T918))\nX7232 -> X7286\nX7285 -> X7286", fontsize=14, style = filled, fillcolor = white];
1082 -> 2987 [arrowhead = none ];
2987 -> 1084;

2988 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1083 -> 2988 [arrowhead = none ];
2988 -> 1386;

2989 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1084 -> 2989 [arrowhead = none ];
2989 -> 1085;

2990 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1085 -> 2990 [arrowhead = none ];
2990 -> 1086;

2991 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1086 -> 2991 [arrowhead = none ];
2991 -> 1087;

2992 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1086 -> 2992 [arrowhead = none ];
2992 -> 1088;

2993 [label="ONLY EVAL with clause\nquot(s(X7336), s(X7337), X7338, X7339) :- quot(X7336, X7337, X7338, X7339).\nand substitution\nT918 -> T928\nX7336 -> s(s(s(s(s(T928)))))\nX7337 -> T928\nX7338 -> s(s(T928))\nX7286 -> X7340\nX7339 -> X7340", fontsize=14, style = filled, fillcolor = white];
1087 -> 2993 [arrowhead = none ];
2993 -> 1089;

2994 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1088 -> 2994 [arrowhead = none ];
2994 -> 1385;

2995 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1089 -> 2995 [arrowhead = none ];
2995 -> 1090;

2996 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1090 -> 2996 [arrowhead = none ];
2996 -> 1091;

2997 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1091 -> 2997 [arrowhead = none ];
2997 -> 1092;

2998 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1091 -> 2998 [arrowhead = none ];
2998 -> 1093;

2999 [label="EVAL with clause\nquot(s(X7372), s(X7373), X7374, X7375) :- quot(X7372, X7373, X7374, X7375).\nand substitution\nT928 -> s(T940)\nX7372 -> s(s(s(s(s(T940)))))\nX7373 -> T940\nT939 -> s(T940)\nX7374 -> s(s(s(T940)))\nX7340 -> X7376\nX7375 -> X7376", fontsize=14, style = filled, fillcolor = lightblue];
1092 -> 2999 [arrowhead = none ];
2999 -> 1094;

3000 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1092 -> 3000 [arrowhead = none ];
3000 -> 1095;

3001 [label="EVAL with clause\nquot(X9618, 0, s(X9619), s(X9620)) :- quot(X9618, s(X9619), s(X9619), X9620).\nand substitution\nT928 -> 0\nX9618 -> s(s(s(s(s(0)))))\nT1087 -> 0\nX9619 -> s(0)\nX9620 -> X9621\nX7340 -> s(X9621)", fontsize=14, style = filled, fillcolor = lightblue];
1093 -> 3001 [arrowhead = none ];
3001 -> 1367;

3002 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1093 -> 3002 [arrowhead = none ];
3002 -> 1368;

3003 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1094 -> 3003 [arrowhead = none ];
3003 -> 1096;

3004 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1096 -> 3004 [arrowhead = none ];
3004 -> 1097;

3005 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1097 -> 3005 [arrowhead = none ];
3005 -> 1098;

3006 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1097 -> 3006 [arrowhead = none ];
3006 -> 1099;

3007 [label="EVAL with clause\nquot(s(X7412), s(X7413), X7414, X7415) :- quot(X7412, X7413, X7414, X7415).\nand substitution\nT940 -> s(T952)\nX7412 -> s(s(s(s(s(T952)))))\nX7413 -> T952\nT951 -> s(T952)\nX7414 -> s(s(s(s(T952))))\nX7376 -> X7416\nX7415 -> X7416", fontsize=14, style = filled, fillcolor = lightblue];
1098 -> 3007 [arrowhead = none ];
3007 -> 1100;

3008 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1098 -> 3008 [arrowhead = none ];
3008 -> 1101;

3009 [label="EVAL with clause\nquot(X9378, 0, s(X9379), s(X9380)) :- quot(X9378, s(X9379), s(X9379), X9380).\nand substitution\nT940 -> 0\nX9378 -> s(s(s(s(s(0)))))\nT1084 -> 0\nX9379 -> s(s(0))\nX9380 -> X9381\nX7376 -> s(X9381)", fontsize=14, style = filled, fillcolor = lightblue];
1099 -> 3009 [arrowhead = none ];
3009 -> 1343;

3010 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1099 -> 3010 [arrowhead = none ];
3010 -> 1344;

3011 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1100 -> 3011 [arrowhead = none ];
3011 -> 1102;

3012 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1102 -> 3012 [arrowhead = none ];
3012 -> 1103;

3013 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1103 -> 3013 [arrowhead = none ];
3013 -> 1104;

3014 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1103 -> 3014 [arrowhead = none ];
3014 -> 1105;

3015 [label="EVAL with clause\nquot(s(X7452), s(X7453), X7454, X7455) :- quot(X7452, X7453, X7454, X7455).\nand substitution\nT952 -> s(T964)\nX7452 -> s(s(s(s(s(T964)))))\nX7453 -> T964\nT963 -> s(T964)\nX7454 -> s(s(s(s(s(T964)))))\nX7416 -> X7456\nX7455 -> X7456", fontsize=14, style = filled, fillcolor = lightblue];
1104 -> 3015 [arrowhead = none ];
3015 -> 1106;

3016 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1104 -> 3016 [arrowhead = none ];
3016 -> 1107;

3017 [label="EVAL with clause\nquot(X9081, 0, s(X9082), s(X9083)) :- quot(X9081, s(X9082), s(X9082), X9083).\nand substitution\nT952 -> 0\nX9081 -> s(s(s(s(s(0)))))\nT1081 -> 0\nX9082 -> s(s(s(0)))\nX9083 -> X9084\nX7416 -> s(X9084)", fontsize=14, style = filled, fillcolor = lightblue];
1105 -> 3017 [arrowhead = none ];
3017 -> 1313;

3018 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1105 -> 3018 [arrowhead = none ];
3018 -> 1314;

3019 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1106 -> 3019 [arrowhead = none ];
3019 -> 1108;

3020 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1108 -> 3020 [arrowhead = none ];
3020 -> 1109;

3021 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1109 -> 3021 [arrowhead = none ];
3021 -> 1110;

3022 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1109 -> 3022 [arrowhead = none ];
3022 -> 1111;

3023 [label="EVAL with clause\nquot(s(X7492), s(X7493), X7494, X7495) :- quot(X7492, X7493, X7494, X7495).\nand substitution\nT964 -> s(T976)\nX7492 -> s(s(s(s(s(T976)))))\nX7493 -> T976\nT975 -> s(T976)\nX7494 -> s(s(s(s(s(s(T976))))))\nX7456 -> X7496\nX7495 -> X7496", fontsize=14, style = filled, fillcolor = lightblue];
1110 -> 3023 [arrowhead = none ];
3023 -> 1112;

3024 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1110 -> 3024 [arrowhead = none ];
3024 -> 1113;

3025 [label="EVAL with clause\nquot(X8741, 0, s(X8742), s(X8743)) :- quot(X8741, s(X8742), s(X8742), X8743).\nand substitution\nT964 -> 0\nX8741 -> s(s(s(s(s(0)))))\nT1078 -> 0\nX8742 -> s(s(s(s(0))))\nX8743 -> X8744\nX7456 -> s(X8744)", fontsize=14, style = filled, fillcolor = lightblue];
1111 -> 3025 [arrowhead = none ];
3025 -> 1277;

3026 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1111 -> 3026 [arrowhead = none ];
3026 -> 1278;

3027 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1112 -> 3027 [arrowhead = none ];
3027 -> 1114;

3028 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1114 -> 3028 [arrowhead = none ];
3028 -> 1115;

3029 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1115 -> 3029 [arrowhead = none ];
3029 -> 1116;

3030 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1115 -> 3030 [arrowhead = none ];
3030 -> 1117;

3031 [label="EVAL with clause\nquot(s(X7532), s(X7533), X7534, X7535) :- quot(X7532, X7533, X7534, X7535).\nand substitution\nT976 -> s(T988)\nX7532 -> s(s(s(s(s(T988)))))\nX7533 -> T988\nT987 -> s(T988)\nX7534 -> s(s(s(s(s(s(s(T988)))))))\nX7496 -> X7536\nX7535 -> X7536", fontsize=14, style = filled, fillcolor = lightblue];
1116 -> 3031 [arrowhead = none ];
3031 -> 1118;

3032 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1116 -> 3032 [arrowhead = none ];
3032 -> 1119;

3033 [label="EVAL with clause\nquot(X8436, 0, s(X8437), s(X8438)) :- quot(X8436, s(X8437), s(X8437), X8438).\nand substitution\nT976 -> 0\nX8436 -> s(s(s(s(s(0)))))\nT1075 -> 0\nX8437 -> s(s(s(s(s(0)))))\nX8438 -> X8439\nX7496 -> s(X8439)", fontsize=14, style = filled, fillcolor = lightblue];
1117 -> 3033 [arrowhead = none ];
3033 -> 1238;

3034 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1117 -> 3034 [arrowhead = none ];
3034 -> 1239;

3035 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1118 -> 3035 [arrowhead = none ];
3035 -> 1120;

3036 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1120 -> 3036 [arrowhead = none ];
3036 -> 1121;

3037 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1121 -> 3037 [arrowhead = none ];
3037 -> 1122;

3038 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1121 -> 3038 [arrowhead = none ];
3038 -> 1123;

3039 [label="EVAL with clause\nquot(s(X7572), s(X7573), X7574, X7575) :- quot(X7572, X7573, X7574, X7575).\nand substitution\nT988 -> s(T1000)\nX7572 -> s(s(s(s(s(T1000)))))\nX7573 -> T1000\nT999 -> s(T1000)\nX7574 -> s(s(s(s(s(s(s(s(T1000))))))))\nX7536 -> X7576\nX7575 -> X7576", fontsize=14, style = filled, fillcolor = lightblue];
1122 -> 3039 [arrowhead = none ];
3039 -> 1124;

3040 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1122 -> 3040 [arrowhead = none ];
3040 -> 1125;

3041 [label="EVAL with clause\nquot(X8131, 0, s(X8132), s(X8133)) :- quot(X8131, s(X8132), s(X8132), X8133).\nand substitution\nT988 -> 0\nX8131 -> s(s(s(s(s(0)))))\nT1072 -> 0\nX8132 -> s(s(s(s(s(s(0))))))\nX8133 -> X8134\nX7536 -> s(X8134)", fontsize=14, style = filled, fillcolor = lightblue];
1123 -> 3041 [arrowhead = none ];
3041 -> 1199;

3042 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1123 -> 3042 [arrowhead = none ];
3042 -> 1200;

3043 [label="GENERALIZATION\nT1003 <-- s(s(s(s(s(s(s(T1000)))))))\n\nNew Knowledge:\nT1003 is ground", fontsize=14, style = filled, fillcolor = violet];
1124 -> 3043 [arrowhead = none ];
3043 -> 1126;

3044 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1126 -> 3044 [arrowhead = none ];
3044 -> 1127;

3045 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1127 -> 3045 [arrowhead = none ];
3045 -> 1128;

3046 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1128 -> 3046 [arrowhead = none ];
3046 -> 1129;

3047 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1128 -> 3047 [arrowhead = none ];
3047 -> 1130;

3048 [label="EVAL with clause\nquot(s(X7621), s(X7622), X7623, X7624) :- quot(X7621, X7622, X7623, X7624).\nand substitution\nT1000 -> s(T1020)\nX7621 -> s(s(s(s(s(T1020)))))\nX7622 -> T1020\nT1019 -> s(T1020)\nT1003 -> T1021\nX7623 -> s(T1021)\nX7576 -> X7625\nX7624 -> X7625", fontsize=14, style = filled, fillcolor = lightblue];
1129 -> 3048 [arrowhead = none ];
3048 -> 1131;

3049 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1129 -> 3049 [arrowhead = none ];
3049 -> 1132;

3050 [label="EVAL with clause\nquot(X7647, 0, s(X7648), s(X7649)) :- quot(X7647, s(X7648), s(X7648), X7649).\nand substitution\nT1000 -> 0\nX7647 -> s(s(s(s(s(0)))))\nT1029 -> 0\nT1003 -> T1030\nX7648 -> T1030\nX7649 -> X7650\nX7576 -> s(X7650)", fontsize=14, style = filled, fillcolor = lightblue];
1130 -> 3050 [arrowhead = none ];
3050 -> 1133;

3051 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1130 -> 3051 [arrowhead = none ];
3051 -> 1134;

3052 [label="INSTANCE with matching:\nT1000 -> T1020\nT1003 -> T1021\nX7576 -> X7625", fontsize=14, style = filled, fillcolor = lightgrey];
1131 -> 3052 [arrowhead = none , style=dashed];
3052 -> 1126[style=dashed];

3053 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1133 -> 3053 [arrowhead = none ];
3053 -> 1135;

3054 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1135 -> 3054 [arrowhead = none ];
3054 -> 1136;

3055 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1136 -> 3055 [arrowhead = none ];
3055 -> 1137;

3056 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1136 -> 3056 [arrowhead = none ];
3056 -> 1138;

3057 [label="ONLY EVAL with clause\nquot(s(X7703), s(X7704), X7705, X7706) :- quot(X7703, X7704, X7705, X7706).\nand substitution\nX7703 -> s(s(s(s(0))))\nT1030 -> T1038\nX7704 -> T1038\nX7705 -> s(T1038)\nX7650 -> X7707\nX7706 -> X7707", fontsize=14, style = filled, fillcolor = white];
1137 -> 3057 [arrowhead = none ];
3057 -> 1139;

3058 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1138 -> 3058 [arrowhead = none ];
3058 -> 1198;

3059 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1139 -> 3059 [arrowhead = none ];
3059 -> 1140;

3060 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1140 -> 3060 [arrowhead = none ];
3060 -> 1141;

3061 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1141 -> 3061 [arrowhead = none ];
3061 -> 1142;

3062 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1141 -> 3062 [arrowhead = none ];
3062 -> 1143;

3063 [label="EVAL with clause\nquot(s(X7739), s(X7740), X7741, X7742) :- quot(X7739, X7740, X7741, X7742).\nand substitution\nX7739 -> s(s(s(0)))\nX7740 -> T1044\nT1038 -> s(T1044)\nX7741 -> s(s(T1044))\nX7707 -> X7743\nX7742 -> X7743", fontsize=14, style = filled, fillcolor = lightblue];
1142 -> 3063 [arrowhead = none ];
3063 -> 1144;

3064 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1142 -> 3064 [arrowhead = none ];
3064 -> 1145;

3065 [label="EVAL with clause\nquot(X8002, 0, s(X8003), s(X8004)) :- quot(X8002, s(X8003), s(X8003), X8004).\nand substitution\nX8002 -> s(s(s(s(0))))\nT1038 -> 0\nX8003 -> 0\nX8004 -> X8005\nX7707 -> s(X8005)", fontsize=14, style = filled, fillcolor = lightblue];
1143 -> 3065 [arrowhead = none ];
3065 -> 1186;

3066 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1143 -> 3066 [arrowhead = none ];
3066 -> 1187;

3067 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1144 -> 3067 [arrowhead = none ];
3067 -> 1146;

3068 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1146 -> 3068 [arrowhead = none ];
3068 -> 1147;

3069 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1147 -> 3069 [arrowhead = none ];
3069 -> 1148;

3070 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1147 -> 3070 [arrowhead = none ];
3070 -> 1149;

3071 [label="EVAL with clause\nquot(s(X7779), s(X7780), X7781, X7782) :- quot(X7779, X7780, X7781, X7782).\nand substitution\nX7779 -> s(s(0))\nX7780 -> T1050\nT1044 -> s(T1050)\nX7781 -> s(s(s(T1050)))\nX7743 -> X7783\nX7782 -> X7783", fontsize=14, style = filled, fillcolor = lightblue];
1148 -> 3071 [arrowhead = none ];
3071 -> 1150;

3072 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1148 -> 3072 [arrowhead = none ];
3072 -> 1151;

3073 [label="EVAL with clause\nquot(X7978, 0, s(X7979), s(X7980)) :- quot(X7978, s(X7979), s(X7979), X7980).\nand substitution\nX7978 -> s(s(s(0)))\nT1044 -> 0\nX7979 -> s(0)\nX7980 -> X7981\nX7743 -> s(X7981)", fontsize=14, style = filled, fillcolor = lightblue];
1149 -> 3073 [arrowhead = none ];
3073 -> 1184;

3074 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1149 -> 3074 [arrowhead = none ];
3074 -> 1185;

3075 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1150 -> 3075 [arrowhead = none ];
3075 -> 1152;

3076 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1152 -> 3076 [arrowhead = none ];
3076 -> 1153;

3077 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1153 -> 3077 [arrowhead = none ];
3077 -> 1154;

3078 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1153 -> 3078 [arrowhead = none ];
3078 -> 1155;

3079 [label="EVAL with clause\nquot(s(X7819), s(X7820), X7821, X7822) :- quot(X7819, X7820, X7821, X7822).\nand substitution\nX7819 -> s(0)\nX7820 -> T1056\nT1050 -> s(T1056)\nX7821 -> s(s(s(s(T1056))))\nX7783 -> X7823\nX7822 -> X7823", fontsize=14, style = filled, fillcolor = lightblue];
1154 -> 3079 [arrowhead = none ];
3079 -> 1156;

3080 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1154 -> 3080 [arrowhead = none ];
3080 -> 1157;

3081 [label="EVAL with clause\nquot(X7954, 0, s(X7955), s(X7956)) :- quot(X7954, s(X7955), s(X7955), X7956).\nand substitution\nX7954 -> s(s(0))\nT1050 -> 0\nX7955 -> s(s(0))\nX7956 -> X7957\nX7783 -> s(X7957)", fontsize=14, style = filled, fillcolor = lightblue];
1155 -> 3081 [arrowhead = none ];
3081 -> 1182;

3082 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1155 -> 3082 [arrowhead = none ];
3082 -> 1183;

3083 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1156 -> 3083 [arrowhead = none ];
3083 -> 1158;

3084 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1158 -> 3084 [arrowhead = none ];
3084 -> 1159;

3085 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1159 -> 3085 [arrowhead = none ];
3085 -> 1160;

3086 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1159 -> 3086 [arrowhead = none ];
3086 -> 1161;

3087 [label="EVAL with clause\nquot(s(X7859), s(X7860), X7861, X7862) :- quot(X7859, X7860, X7861, X7862).\nand substitution\nX7859 -> 0\nX7860 -> T1062\nT1056 -> s(T1062)\nX7861 -> s(s(s(s(s(T1062)))))\nX7823 -> X7863\nX7862 -> X7863", fontsize=14, style = filled, fillcolor = lightblue];
1160 -> 3087 [arrowhead = none ];
3087 -> 1162;

3088 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1160 -> 3088 [arrowhead = none ];
3088 -> 1163;

3089 [label="EVAL with clause\nquot(X7930, 0, s(X7931), s(X7932)) :- quot(X7930, s(X7931), s(X7931), X7932).\nand substitution\nX7930 -> s(0)\nT1056 -> 0\nX7931 -> s(s(s(0)))\nX7932 -> X7933\nX7823 -> s(X7933)", fontsize=14, style = filled, fillcolor = lightblue];
1161 -> 3089 [arrowhead = none ];
3089 -> 1180;

3090 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1161 -> 3090 [arrowhead = none ];
3090 -> 1181;

3091 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1162 -> 3091 [arrowhead = none ];
3091 -> 1164;

3092 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1164 -> 3092 [arrowhead = none ];
3092 -> 1165;

3093 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1164 -> 3093 [arrowhead = none ];
3093 -> 1166;

3094 [label="EVAL with clause\nquot(0, s(X7880), s(X7881), 0).\nand substitution\nX7880 -> T1069\nT1062 -> s(T1069)\nX7881 -> s(s(s(s(s(T1069)))))\nX7863 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1165 -> 3094 [arrowhead = none ];
3094 -> 1167;

3095 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1165 -> 3095 [arrowhead = none ];
3095 -> 1168;

3096 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1166 -> 3096 [arrowhead = none ];
3096 -> 1170;

3097 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1167 -> 3097 [arrowhead = none ];
3097 -> 1169;

3098 [label="EVAL with clause\nquot(X7896, 0, s(X7897), s(X7898)) :- quot(X7896, s(X7897), s(X7897), X7898).\nand substitution\nX7896 -> 0\nT1062 -> 0\nX7897 -> s(s(s(s(0))))\nX7898 -> X7899\nX7863 -> s(X7899)", fontsize=14, style = filled, fillcolor = lightblue];
1170 -> 3098 [arrowhead = none ];
3098 -> 1171;

3099 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1170 -> 3099 [arrowhead = none ];
3099 -> 1172;

3100 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1171 -> 3100 [arrowhead = none ];
3100 -> 1173;

3101 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1173 -> 3101 [arrowhead = none ];
3101 -> 1174;

3102 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1173 -> 3102 [arrowhead = none ];
3102 -> 1175;

3103 [label="ONLY EVAL with clause\nquot(0, s(X7913), s(X7914), 0).\nand substitution\nX7913 -> s(s(s(s(0))))\nX7914 -> s(s(s(s(0))))\nX7899 -> 0", fontsize=14, style = filled, fillcolor = white];
1174 -> 3103 [arrowhead = none ];
3103 -> 1176;

3104 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1175 -> 3104 [arrowhead = none ];
3104 -> 1178;

3105 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1176 -> 3105 [arrowhead = none ];
3105 -> 1177;

3106 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1178 -> 3106 [arrowhead = none ];
3106 -> 1179;

3107 [label="INSTANCE with matching:\nX833 -> X7933", fontsize=14, style = filled, fillcolor = lightgrey];
1180 -> 3107 [arrowhead = none , style=dashed];
3107 -> 143[style=dashed];

3108 [label="INSTANCE with matching:\nX2493 -> X7957", fontsize=14, style = filled, fillcolor = lightgrey];
1182 -> 3108 [arrowhead = none , style=dashed];
3108 -> 446[style=dashed];

3109 [label="INSTANCE with matching:\nX4627 -> X7981", fontsize=14, style = filled, fillcolor = lightgrey];
1184 -> 3109 [arrowhead = none , style=dashed];
3109 -> 740[style=dashed];

3110 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1186 -> 3110 [arrowhead = none ];
3110 -> 1188;

3111 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1188 -> 3111 [arrowhead = none ];
3111 -> 1189;

3112 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1189 -> 3112 [arrowhead = none ];
3112 -> 1190;

3113 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1189 -> 3113 [arrowhead = none ];
3113 -> 1191;

3114 [label="ONLY EVAL with clause\nquot(s(X8064), s(X8065), X8066, X8067) :- quot(X8064, X8065, X8066, X8067).\nand substitution\nX8064 -> s(s(s(0)))\nX8065 -> 0\nX8066 -> s(0)\nX8005 -> X8068\nX8067 -> X8068", fontsize=14, style = filled, fillcolor = white];
1190 -> 3114 [arrowhead = none ];
3114 -> 1192;

3115 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1191 -> 3115 [arrowhead = none ];
3115 -> 1197;

3116 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1192 -> 3116 [arrowhead = none ];
3116 -> 1193;

3117 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1193 -> 3117 [arrowhead = none ];
3117 -> 1194;

3118 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1194 -> 3118 [arrowhead = none ];
3118 -> 1195;

3119 [label="ONLY EVAL with clause\nquot(X8104, 0, s(X8105), s(X8106)) :- quot(X8104, s(X8105), s(X8105), X8106).\nand substitution\nX8104 -> s(s(s(0)))\nX8105 -> 0\nX8106 -> X8107\nX8068 -> s(X8107)", fontsize=14, style = filled, fillcolor = white];
1195 -> 3119 [arrowhead = none ];
3119 -> 1196;

3120 [label="INSTANCE with matching:\nX5586 -> X8107", fontsize=14, style = filled, fillcolor = lightgrey];
1196 -> 3120 [arrowhead = none , style=dashed];
3120 -> 876[style=dashed];

3121 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1199 -> 3121 [arrowhead = none ];
3121 -> 1201;

3122 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1201 -> 3122 [arrowhead = none ];
3122 -> 1202;

3123 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1202 -> 3123 [arrowhead = none ];
3123 -> 1203;

3124 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1202 -> 3124 [arrowhead = none ];
3124 -> 1204;

3125 [label="ONLY EVAL with clause\nquot(s(X8187), s(X8188), X8189, X8190) :- quot(X8187, X8188, X8189, X8190).\nand substitution\nX8187 -> s(s(s(s(0))))\nX8188 -> s(s(s(s(s(s(0))))))\nX8189 -> s(s(s(s(s(s(s(0)))))))\nX8134 -> X8191\nX8190 -> X8191", fontsize=14, style = filled, fillcolor = white];
1203 -> 3125 [arrowhead = none ];
3125 -> 1205;

3126 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1204 -> 3126 [arrowhead = none ];
3126 -> 1237;

3127 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1205 -> 3127 [arrowhead = none ];
3127 -> 1206;

3128 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1206 -> 3128 [arrowhead = none ];
3128 -> 1207;

3129 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1207 -> 3129 [arrowhead = none ];
3129 -> 1208;

3130 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1207 -> 3130 [arrowhead = none ];
3130 -> 1209;

3131 [label="ONLY EVAL with clause\nquot(s(X8241), s(X8242), X8243, X8244) :- quot(X8241, X8242, X8243, X8244).\nand substitution\nX8241 -> s(s(s(0)))\nX8242 -> s(s(s(s(s(0)))))\nX8243 -> s(s(s(s(s(s(s(0)))))))\nX8191 -> X8245\nX8244 -> X8245", fontsize=14, style = filled, fillcolor = white];
1208 -> 3131 [arrowhead = none ];
3131 -> 1210;

3132 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1209 -> 3132 [arrowhead = none ];
3132 -> 1236;

3133 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1210 -> 3133 [arrowhead = none ];
3133 -> 1211;

3134 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1211 -> 3134 [arrowhead = none ];
3134 -> 1212;

3135 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1212 -> 3135 [arrowhead = none ];
3135 -> 1213;

3136 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1212 -> 3136 [arrowhead = none ];
3136 -> 1214;

3137 [label="ONLY EVAL with clause\nquot(s(X8295), s(X8296), X8297, X8298) :- quot(X8295, X8296, X8297, X8298).\nand substitution\nX8295 -> s(s(0))\nX8296 -> s(s(s(s(0))))\nX8297 -> s(s(s(s(s(s(s(0)))))))\nX8245 -> X8299\nX8298 -> X8299", fontsize=14, style = filled, fillcolor = white];
1213 -> 3137 [arrowhead = none ];
3137 -> 1215;

3138 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1214 -> 3138 [arrowhead = none ];
3138 -> 1235;

3139 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1215 -> 3139 [arrowhead = none ];
3139 -> 1216;

3140 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1216 -> 3140 [arrowhead = none ];
3140 -> 1217;

3141 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1217 -> 3141 [arrowhead = none ];
3141 -> 1218;

3142 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1217 -> 3142 [arrowhead = none ];
3142 -> 1219;

3143 [label="ONLY EVAL with clause\nquot(s(X8349), s(X8350), X8351, X8352) :- quot(X8349, X8350, X8351, X8352).\nand substitution\nX8349 -> s(0)\nX8350 -> s(s(s(0)))\nX8351 -> s(s(s(s(s(s(s(0)))))))\nX8299 -> X8353\nX8352 -> X8353", fontsize=14, style = filled, fillcolor = white];
1218 -> 3143 [arrowhead = none ];
3143 -> 1220;

3144 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1219 -> 3144 [arrowhead = none ];
3144 -> 1234;

3145 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1220 -> 3145 [arrowhead = none ];
3145 -> 1221;

3146 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1221 -> 3146 [arrowhead = none ];
3146 -> 1222;

3147 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1222 -> 3147 [arrowhead = none ];
3147 -> 1223;

3148 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1222 -> 3148 [arrowhead = none ];
3148 -> 1224;

3149 [label="ONLY EVAL with clause\nquot(s(X8389), s(X8390), X8391, X8392) :- quot(X8389, X8390, X8391, X8392).\nand substitution\nX8389 -> 0\nX8390 -> s(s(0))\nX8391 -> s(s(s(s(s(s(s(0)))))))\nX8353 -> X8393\nX8392 -> X8393", fontsize=14, style = filled, fillcolor = white];
1223 -> 3149 [arrowhead = none ];
3149 -> 1225;

3150 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1224 -> 3150 [arrowhead = none ];
3150 -> 1233;

3151 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1225 -> 3151 [arrowhead = none ];
3151 -> 1226;

3152 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1226 -> 3152 [arrowhead = none ];
3152 -> 1227;

3153 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1226 -> 3153 [arrowhead = none ];
3153 -> 1228;

3154 [label="ONLY EVAL with clause\nquot(0, s(X8404), s(X8405), 0).\nand substitution\nX8404 -> s(0)\nX8405 -> s(s(s(s(s(s(0))))))\nX8393 -> 0", fontsize=14, style = filled, fillcolor = white];
1227 -> 3154 [arrowhead = none ];
3154 -> 1229;

3155 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1228 -> 3155 [arrowhead = none ];
3155 -> 1231;

3156 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1229 -> 3156 [arrowhead = none ];
3156 -> 1230;

3157 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1231 -> 3157 [arrowhead = none ];
3157 -> 1232;

3158 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1238 -> 3158 [arrowhead = none ];
3158 -> 1240;

3159 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1240 -> 3159 [arrowhead = none ];
3159 -> 1241;

3160 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1241 -> 3160 [arrowhead = none ];
3160 -> 1242;

3161 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1241 -> 3161 [arrowhead = none ];
3161 -> 1243;

3162 [label="ONLY EVAL with clause\nquot(s(X8492), s(X8493), X8494, X8495) :- quot(X8492, X8493, X8494, X8495).\nand substitution\nX8492 -> s(s(s(s(0))))\nX8493 -> s(s(s(s(s(0)))))\nX8494 -> s(s(s(s(s(s(0))))))\nX8439 -> X8496\nX8495 -> X8496", fontsize=14, style = filled, fillcolor = white];
1242 -> 3162 [arrowhead = none ];
3162 -> 1244;

3163 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1243 -> 3163 [arrowhead = none ];
3163 -> 1276;

3164 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1244 -> 3164 [arrowhead = none ];
3164 -> 1245;

3165 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1245 -> 3165 [arrowhead = none ];
3165 -> 1246;

3166 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1246 -> 3166 [arrowhead = none ];
3166 -> 1247;

3167 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1246 -> 3167 [arrowhead = none ];
3167 -> 1248;

3168 [label="ONLY EVAL with clause\nquot(s(X8546), s(X8547), X8548, X8549) :- quot(X8546, X8547, X8548, X8549).\nand substitution\nX8546 -> s(s(s(0)))\nX8547 -> s(s(s(s(0))))\nX8548 -> s(s(s(s(s(s(0))))))\nX8496 -> X8550\nX8549 -> X8550", fontsize=14, style = filled, fillcolor = white];
1247 -> 3168 [arrowhead = none ];
3168 -> 1249;

3169 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1248 -> 3169 [arrowhead = none ];
3169 -> 1275;

3170 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1249 -> 3170 [arrowhead = none ];
3170 -> 1250;

3171 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1250 -> 3171 [arrowhead = none ];
3171 -> 1251;

3172 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1251 -> 3172 [arrowhead = none ];
3172 -> 1252;

3173 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1251 -> 3173 [arrowhead = none ];
3173 -> 1253;

3174 [label="ONLY EVAL with clause\nquot(s(X8600), s(X8601), X8602, X8603) :- quot(X8600, X8601, X8602, X8603).\nand substitution\nX8600 -> s(s(0))\nX8601 -> s(s(s(0)))\nX8602 -> s(s(s(s(s(s(0))))))\nX8550 -> X8604\nX8603 -> X8604", fontsize=14, style = filled, fillcolor = white];
1252 -> 3174 [arrowhead = none ];
3174 -> 1254;

3175 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1253 -> 3175 [arrowhead = none ];
3175 -> 1274;

3176 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1254 -> 3176 [arrowhead = none ];
3176 -> 1255;

3177 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1255 -> 3177 [arrowhead = none ];
3177 -> 1256;

3178 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1256 -> 3178 [arrowhead = none ];
3178 -> 1257;

3179 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1256 -> 3179 [arrowhead = none ];
3179 -> 1258;

3180 [label="ONLY EVAL with clause\nquot(s(X8654), s(X8655), X8656, X8657) :- quot(X8654, X8655, X8656, X8657).\nand substitution\nX8654 -> s(0)\nX8655 -> s(s(0))\nX8656 -> s(s(s(s(s(s(0))))))\nX8604 -> X8658\nX8657 -> X8658", fontsize=14, style = filled, fillcolor = white];
1257 -> 3180 [arrowhead = none ];
3180 -> 1259;

3181 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1258 -> 3181 [arrowhead = none ];
3181 -> 1273;

3182 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1259 -> 3182 [arrowhead = none ];
3182 -> 1260;

3183 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1260 -> 3183 [arrowhead = none ];
3183 -> 1261;

3184 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1261 -> 3184 [arrowhead = none ];
3184 -> 1262;

3185 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1261 -> 3185 [arrowhead = none ];
3185 -> 1263;

3186 [label="ONLY EVAL with clause\nquot(s(X8694), s(X8695), X8696, X8697) :- quot(X8694, X8695, X8696, X8697).\nand substitution\nX8694 -> 0\nX8695 -> s(0)\nX8696 -> s(s(s(s(s(s(0))))))\nX8658 -> X8698\nX8697 -> X8698", fontsize=14, style = filled, fillcolor = white];
1262 -> 3186 [arrowhead = none ];
3186 -> 1264;

3187 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1263 -> 3187 [arrowhead = none ];
3187 -> 1272;

3188 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1264 -> 3188 [arrowhead = none ];
3188 -> 1265;

3189 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1265 -> 3189 [arrowhead = none ];
3189 -> 1266;

3190 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1265 -> 3190 [arrowhead = none ];
3190 -> 1267;

3191 [label="ONLY EVAL with clause\nquot(0, s(X8709), s(X8710), 0).\nand substitution\nX8709 -> 0\nX8710 -> s(s(s(s(s(0)))))\nX8698 -> 0", fontsize=14, style = filled, fillcolor = white];
1266 -> 3191 [arrowhead = none ];
3191 -> 1268;

3192 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1267 -> 3192 [arrowhead = none ];
3192 -> 1270;

3193 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1268 -> 3193 [arrowhead = none ];
3193 -> 1269;

3194 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1270 -> 3194 [arrowhead = none ];
3194 -> 1271;

3195 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1277 -> 3195 [arrowhead = none ];
3195 -> 1279;

3196 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1279 -> 3196 [arrowhead = none ];
3196 -> 1280;

3197 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1280 -> 3197 [arrowhead = none ];
3197 -> 1281;

3198 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1280 -> 3198 [arrowhead = none ];
3198 -> 1282;

3199 [label="ONLY EVAL with clause\nquot(s(X8797), s(X8798), X8799, X8800) :- quot(X8797, X8798, X8799, X8800).\nand substitution\nX8797 -> s(s(s(s(0))))\nX8798 -> s(s(s(s(0))))\nX8799 -> s(s(s(s(s(0)))))\nX8744 -> X8801\nX8800 -> X8801", fontsize=14, style = filled, fillcolor = white];
1281 -> 3199 [arrowhead = none ];
3199 -> 1283;

3200 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1282 -> 3200 [arrowhead = none ];
3200 -> 1312;

3201 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1283 -> 3201 [arrowhead = none ];
3201 -> 1284;

3202 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1284 -> 3202 [arrowhead = none ];
3202 -> 1285;

3203 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1285 -> 3203 [arrowhead = none ];
3203 -> 1286;

3204 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1285 -> 3204 [arrowhead = none ];
3204 -> 1287;

3205 [label="ONLY EVAL with clause\nquot(s(X8851), s(X8852), X8853, X8854) :- quot(X8851, X8852, X8853, X8854).\nand substitution\nX8851 -> s(s(s(0)))\nX8852 -> s(s(s(0)))\nX8853 -> s(s(s(s(s(0)))))\nX8801 -> X8855\nX8854 -> X8855", fontsize=14, style = filled, fillcolor = white];
1286 -> 3205 [arrowhead = none ];
3205 -> 1288;

3206 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1287 -> 3206 [arrowhead = none ];
3206 -> 1311;

3207 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1288 -> 3207 [arrowhead = none ];
3207 -> 1289;

3208 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1289 -> 3208 [arrowhead = none ];
3208 -> 1290;

3209 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1290 -> 3209 [arrowhead = none ];
3209 -> 1291;

3210 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1290 -> 3210 [arrowhead = none ];
3210 -> 1292;

3211 [label="ONLY EVAL with clause\nquot(s(X8905), s(X8906), X8907, X8908) :- quot(X8905, X8906, X8907, X8908).\nand substitution\nX8905 -> s(s(0))\nX8906 -> s(s(0))\nX8907 -> s(s(s(s(s(0)))))\nX8855 -> X8909\nX8908 -> X8909", fontsize=14, style = filled, fillcolor = white];
1291 -> 3211 [arrowhead = none ];
3211 -> 1293;

3212 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1292 -> 3212 [arrowhead = none ];
3212 -> 1310;

3213 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1293 -> 3213 [arrowhead = none ];
3213 -> 1294;

3214 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1294 -> 3214 [arrowhead = none ];
3214 -> 1295;

3215 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1295 -> 3215 [arrowhead = none ];
3215 -> 1296;

3216 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1295 -> 3216 [arrowhead = none ];
3216 -> 1297;

3217 [label="ONLY EVAL with clause\nquot(s(X8959), s(X8960), X8961, X8962) :- quot(X8959, X8960, X8961, X8962).\nand substitution\nX8959 -> s(0)\nX8960 -> s(0)\nX8961 -> s(s(s(s(s(0)))))\nX8909 -> X8963\nX8962 -> X8963", fontsize=14, style = filled, fillcolor = white];
1296 -> 3217 [arrowhead = none ];
3217 -> 1298;

3218 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1297 -> 3218 [arrowhead = none ];
3218 -> 1309;

3219 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1298 -> 3219 [arrowhead = none ];
3219 -> 1299;

3220 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1299 -> 3220 [arrowhead = none ];
3220 -> 1300;

3221 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1300 -> 3221 [arrowhead = none ];
3221 -> 1301;

3222 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1300 -> 3222 [arrowhead = none ];
3222 -> 1302;

3223 [label="ONLY EVAL with clause\nquot(s(X9019), s(X9020), X9021, X9022) :- quot(X9019, X9020, X9021, X9022).\nand substitution\nX9019 -> 0\nX9020 -> 0\nX9021 -> s(s(s(s(s(0)))))\nX8963 -> X9023\nX9022 -> X9023", fontsize=14, style = filled, fillcolor = white];
1301 -> 3223 [arrowhead = none ];
3223 -> 1303;

3224 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1302 -> 3224 [arrowhead = none ];
3224 -> 1308;

3225 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1303 -> 3225 [arrowhead = none ];
3225 -> 1304;

3226 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1304 -> 3226 [arrowhead = none ];
3226 -> 1305;

3227 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1305 -> 3227 [arrowhead = none ];
3227 -> 1306;

3228 [label="ONLY EVAL with clause\nquot(X9052, 0, s(X9053), s(X9054)) :- quot(X9052, s(X9053), s(X9053), X9054).\nand substitution\nX9052 -> 0\nX9053 -> s(s(s(s(0))))\nX9054 -> X9055\nX9023 -> s(X9055)", fontsize=14, style = filled, fillcolor = white];
1306 -> 3228 [arrowhead = none ];
3228 -> 1307;

3229 [label="INSTANCE with matching:\nX7899 -> X9055", fontsize=14, style = filled, fillcolor = lightgrey];
1307 -> 3229 [arrowhead = none , style=dashed];
3229 -> 1171[style=dashed];

3230 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1313 -> 3230 [arrowhead = none ];
3230 -> 1315;

3231 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1315 -> 3231 [arrowhead = none ];
3231 -> 1316;

3232 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1316 -> 3232 [arrowhead = none ];
3232 -> 1317;

3233 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1316 -> 3233 [arrowhead = none ];
3233 -> 1318;

3234 [label="ONLY EVAL with clause\nquot(s(X9137), s(X9138), X9139, X9140) :- quot(X9137, X9138, X9139, X9140).\nand substitution\nX9137 -> s(s(s(s(0))))\nX9138 -> s(s(s(0)))\nX9139 -> s(s(s(s(0))))\nX9084 -> X9141\nX9140 -> X9141", fontsize=14, style = filled, fillcolor = white];
1317 -> 3234 [arrowhead = none ];
3234 -> 1319;

3235 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1318 -> 3235 [arrowhead = none ];
3235 -> 1342;

3236 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1319 -> 3236 [arrowhead = none ];
3236 -> 1320;

3237 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1320 -> 3237 [arrowhead = none ];
3237 -> 1321;

3238 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1321 -> 3238 [arrowhead = none ];
3238 -> 1322;

3239 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1321 -> 3239 [arrowhead = none ];
3239 -> 1323;

3240 [label="ONLY EVAL with clause\nquot(s(X9191), s(X9192), X9193, X9194) :- quot(X9191, X9192, X9193, X9194).\nand substitution\nX9191 -> s(s(s(0)))\nX9192 -> s(s(0))\nX9193 -> s(s(s(s(0))))\nX9141 -> X9195\nX9194 -> X9195", fontsize=14, style = filled, fillcolor = white];
1322 -> 3240 [arrowhead = none ];
3240 -> 1324;

3241 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1323 -> 3241 [arrowhead = none ];
3241 -> 1341;

3242 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1324 -> 3242 [arrowhead = none ];
3242 -> 1325;

3243 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1325 -> 3243 [arrowhead = none ];
3243 -> 1326;

3244 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1326 -> 3244 [arrowhead = none ];
3244 -> 1327;

3245 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1326 -> 3245 [arrowhead = none ];
3245 -> 1328;

3246 [label="ONLY EVAL with clause\nquot(s(X9245), s(X9246), X9247, X9248) :- quot(X9245, X9246, X9247, X9248).\nand substitution\nX9245 -> s(s(0))\nX9246 -> s(0)\nX9247 -> s(s(s(s(0))))\nX9195 -> X9249\nX9248 -> X9249", fontsize=14, style = filled, fillcolor = white];
1327 -> 3246 [arrowhead = none ];
3246 -> 1329;

3247 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1328 -> 3247 [arrowhead = none ];
3247 -> 1340;

3248 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1329 -> 3248 [arrowhead = none ];
3248 -> 1330;

3249 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1330 -> 3249 [arrowhead = none ];
3249 -> 1331;

3250 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1331 -> 3250 [arrowhead = none ];
3250 -> 1332;

3251 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1331 -> 3251 [arrowhead = none ];
3251 -> 1333;

3252 [label="ONLY EVAL with clause\nquot(s(X9305), s(X9306), X9307, X9308) :- quot(X9305, X9306, X9307, X9308).\nand substitution\nX9305 -> s(0)\nX9306 -> 0\nX9307 -> s(s(s(s(0))))\nX9249 -> X9309\nX9308 -> X9309", fontsize=14, style = filled, fillcolor = white];
1332 -> 3252 [arrowhead = none ];
3252 -> 1334;

3253 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1333 -> 3253 [arrowhead = none ];
3253 -> 1339;

3254 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1334 -> 3254 [arrowhead = none ];
3254 -> 1335;

3255 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1335 -> 3255 [arrowhead = none ];
3255 -> 1336;

3256 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1336 -> 3256 [arrowhead = none ];
3256 -> 1337;

3257 [label="ONLY EVAL with clause\nquot(X9345, 0, s(X9346), s(X9347)) :- quot(X9345, s(X9346), s(X9346), X9347).\nand substitution\nX9345 -> s(0)\nX9346 -> s(s(s(0)))\nX9347 -> X9348\nX9309 -> s(X9348)", fontsize=14, style = filled, fillcolor = white];
1337 -> 3257 [arrowhead = none ];
3257 -> 1338;

3258 [label="INSTANCE with matching:\nX833 -> X9348", fontsize=14, style = filled, fillcolor = lightgrey];
1338 -> 3258 [arrowhead = none , style=dashed];
3258 -> 143[style=dashed];

3259 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1343 -> 3259 [arrowhead = none ];
3259 -> 1345;

3260 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1345 -> 3260 [arrowhead = none ];
3260 -> 1346;

3261 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1346 -> 3261 [arrowhead = none ];
3261 -> 1347;

3262 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1346 -> 3262 [arrowhead = none ];
3262 -> 1348;

3263 [label="ONLY EVAL with clause\nquot(s(X9434), s(X9435), X9436, X9437) :- quot(X9434, X9435, X9436, X9437).\nand substitution\nX9434 -> s(s(s(s(0))))\nX9435 -> s(s(0))\nX9436 -> s(s(s(0)))\nX9381 -> X9438\nX9437 -> X9438", fontsize=14, style = filled, fillcolor = white];
1347 -> 3263 [arrowhead = none ];
3263 -> 1349;

3264 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1348 -> 3264 [arrowhead = none ];
3264 -> 1366;

3265 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1349 -> 3265 [arrowhead = none ];
3265 -> 1350;

3266 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1350 -> 3266 [arrowhead = none ];
3266 -> 1351;

3267 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1351 -> 3267 [arrowhead = none ];
3267 -> 1352;

3268 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1351 -> 3268 [arrowhead = none ];
3268 -> 1353;

3269 [label="ONLY EVAL with clause\nquot(s(X9488), s(X9489), X9490, X9491) :- quot(X9488, X9489, X9490, X9491).\nand substitution\nX9488 -> s(s(s(0)))\nX9489 -> s(0)\nX9490 -> s(s(s(0)))\nX9438 -> X9492\nX9491 -> X9492", fontsize=14, style = filled, fillcolor = white];
1352 -> 3269 [arrowhead = none ];
3269 -> 1354;

3270 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1353 -> 3270 [arrowhead = none ];
3270 -> 1365;

3271 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1354 -> 3271 [arrowhead = none ];
3271 -> 1355;

3272 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1355 -> 3272 [arrowhead = none ];
3272 -> 1356;

3273 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1356 -> 3273 [arrowhead = none ];
3273 -> 1357;

3274 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1356 -> 3274 [arrowhead = none ];
3274 -> 1358;

3275 [label="ONLY EVAL with clause\nquot(s(X9548), s(X9549), X9550, X9551) :- quot(X9548, X9549, X9550, X9551).\nand substitution\nX9548 -> s(s(0))\nX9549 -> 0\nX9550 -> s(s(s(0)))\nX9492 -> X9552\nX9551 -> X9552", fontsize=14, style = filled, fillcolor = white];
1357 -> 3275 [arrowhead = none ];
3275 -> 1359;

3276 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1358 -> 3276 [arrowhead = none ];
3276 -> 1364;

3277 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1359 -> 3277 [arrowhead = none ];
3277 -> 1360;

3278 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1360 -> 3278 [arrowhead = none ];
3278 -> 1361;

3279 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1361 -> 3279 [arrowhead = none ];
3279 -> 1362;

3280 [label="ONLY EVAL with clause\nquot(X9588, 0, s(X9589), s(X9590)) :- quot(X9588, s(X9589), s(X9589), X9590).\nand substitution\nX9588 -> s(s(0))\nX9589 -> s(s(0))\nX9590 -> X9591\nX9552 -> s(X9591)", fontsize=14, style = filled, fillcolor = white];
1362 -> 3280 [arrowhead = none ];
3280 -> 1363;

3281 [label="INSTANCE with matching:\nX2493 -> X9591", fontsize=14, style = filled, fillcolor = lightgrey];
1363 -> 3281 [arrowhead = none , style=dashed];
3281 -> 446[style=dashed];

3282 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1367 -> 3282 [arrowhead = none ];
3282 -> 1369;

3283 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1369 -> 3283 [arrowhead = none ];
3283 -> 1370;

3284 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1370 -> 3284 [arrowhead = none ];
3284 -> 1371;

3285 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1370 -> 3285 [arrowhead = none ];
3285 -> 1372;

3286 [label="ONLY EVAL with clause\nquot(s(X9674), s(X9675), X9676, X9677) :- quot(X9674, X9675, X9676, X9677).\nand substitution\nX9674 -> s(s(s(s(0))))\nX9675 -> s(0)\nX9676 -> s(s(0))\nX9621 -> X9678\nX9677 -> X9678", fontsize=14, style = filled, fillcolor = white];
1371 -> 3286 [arrowhead = none ];
3286 -> 1373;

3287 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1372 -> 3287 [arrowhead = none ];
3287 -> 1384;

3288 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1373 -> 3288 [arrowhead = none ];
3288 -> 1374;

3289 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1374 -> 3289 [arrowhead = none ];
3289 -> 1375;

3290 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1375 -> 3290 [arrowhead = none ];
3290 -> 1376;

3291 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1375 -> 3291 [arrowhead = none ];
3291 -> 1377;

3292 [label="ONLY EVAL with clause\nquot(s(X9734), s(X9735), X9736, X9737) :- quot(X9734, X9735, X9736, X9737).\nand substitution\nX9734 -> s(s(s(0)))\nX9735 -> 0\nX9736 -> s(s(0))\nX9678 -> X9738\nX9737 -> X9738", fontsize=14, style = filled, fillcolor = white];
1376 -> 3292 [arrowhead = none ];
3292 -> 1378;

3293 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1377 -> 3293 [arrowhead = none ];
3293 -> 1383;

3294 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1378 -> 3294 [arrowhead = none ];
3294 -> 1379;

3295 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1379 -> 3295 [arrowhead = none ];
3295 -> 1380;

3296 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1380 -> 3296 [arrowhead = none ];
3296 -> 1381;

3297 [label="ONLY EVAL with clause\nquot(X9774, 0, s(X9775), s(X9776)) :- quot(X9774, s(X9775), s(X9775), X9776).\nand substitution\nX9774 -> s(s(s(0)))\nX9775 -> s(0)\nX9776 -> X9777\nX9738 -> s(X9777)", fontsize=14, style = filled, fillcolor = white];
1381 -> 3297 [arrowhead = none ];
3297 -> 1382;

3298 [label="INSTANCE with matching:\nX4627 -> X9777", fontsize=14, style = filled, fillcolor = lightgrey];
1382 -> 3298 [arrowhead = none , style=dashed];
3298 -> 740[style=dashed];

3299 [label="INSTANCE with matching:\nT22 -> T905\nT20 -> T903\nX39 -> X7203", fontsize=14, style = filled, fillcolor = lightgrey];
1387 -> 3299 [arrowhead = none , style=dashed];
3299 -> 190[style=dashed];

3300 [label="INSTANCE with matching:\nT20 -> s(s(s(s(T903))))\nT187 -> T1092", fontsize=14, style = filled, fillcolor = lightgrey];
1388 -> 3300 [arrowhead = none , style=dashed];
3300 -> 191[style=dashed];

3301 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1389 -> 3301 [arrowhead = none ];
3301 -> 1390;

3302 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1389 -> 3302 [arrowhead = none ];
3302 -> 1391;

3303 [label="EVAL with clause\npr(X9811, s(0)).\nand substitution\nT897 -> 0\nX9811 -> s(s(s(s(s(s(s(0)))))))\nT1103 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1390 -> 3303 [arrowhead = none ];
3303 -> 1392;

3304 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1390 -> 3304 [arrowhead = none ];
3304 -> 1393;

3305 [label="EVAL with clause\npr(X9817, s(s(X9818))) :- ','(not_divides(s(s(X9818)), X9817), pr(X9817, s(X9818))).\nand substitution\nT897 -> s(T1109)\nX9817 -> s(s(s(s(s(s(s(s(T1109))))))))\nX9818 -> T1109\nT1108 -> s(T1109)", fontsize=14, style = filled, fillcolor = lightblue];
1391 -> 3305 [arrowhead = none ];
3305 -> 1395;

3306 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1391 -> 3306 [arrowhead = none ];
3306 -> 1396;

3307 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1392 -> 3307 [arrowhead = none ];
3307 -> 1394;

3308 [label="GENERALIZATION\nT1111 <-- s(s(s(s(s(s(s(T1109)))))))\n\nNew Knowledge:\nT1111 is ground", fontsize=14, style = filled, fillcolor = violet];
1395 -> 3308 [arrowhead = none ];
3308 -> 1397;

3309 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
1397 -> 3309 [arrowhead = none ];
3309 -> 1398;

3310 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
1397 -> 3310 [arrowhead = none ];
3310 -> 1399;

3311 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1398 -> 3311 [arrowhead = none ];
3311 -> 1400;

3312 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1399 -> 3312 [arrowhead = none ];
3312 -> 1869;

3313 [label="ONLY EVAL with clause\nnot_divides(X9843, X9844) :- ','(div(X9844, X9843, X9845), ','(times(X9845, X9843, X9846), neq(X9844, X9846))).\nand substitution\nT1109 -> T1122\nX9843 -> s(s(T1122))\nT1111 -> T1123\nX9844 -> s(T1123)", fontsize=14, style = filled, fillcolor = white];
1400 -> 3313 [arrowhead = none ];
3313 -> 1401;

3314 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
1401 -> 3314 [arrowhead = none ];
3314 -> 1402;

3315 [label="SPLIT 2\nnew knowledge:\nT1126 is ground\nreplacements:\nX9845 -> T1126", fontsize=14, style = filled, fillcolor = violet];
1401 -> 3315 [arrowhead = none ];
3315 -> 1403;

3316 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1402 -> 3316 [arrowhead = none ];
3316 -> 1404;

3317 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
1403 -> 3317 [arrowhead = none ];
3317 -> 1867;

3318 [label="SPLIT 2\nnew knowledge:\nT1586 is ground\nreplacements:\nX9846 -> T1586", fontsize=14, style = filled, fillcolor = violet];
1403 -> 3318 [arrowhead = none ];
3318 -> 1868;

3319 [label="ONLY EVAL with clause\ndiv(X9872, X9873, X9874) :- quot(X9872, X9873, X9873, X9874).\nand substitution\nT1123 -> T1135\nX9872 -> s(T1135)\nT1122 -> T1136\nX9873 -> s(s(T1136))\nX9845 -> X9875\nX9874 -> X9875", fontsize=14, style = filled, fillcolor = white];
1404 -> 3319 [arrowhead = none ];
3319 -> 1405;

3320 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1405 -> 3320 [arrowhead = none ];
3320 -> 1406;

3321 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1406 -> 3321 [arrowhead = none ];
3321 -> 1407;

3322 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1407 -> 3322 [arrowhead = none ];
3322 -> 1408;

3323 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1407 -> 3323 [arrowhead = none ];
3323 -> 1409;

3324 [label="ONLY EVAL with clause\nquot(s(X9915), s(X9916), X9917, X9918) :- quot(X9915, X9916, X9917, X9918).\nand substitution\nT1135 -> T1151\nX9915 -> T1151\nT1136 -> T1152\nX9916 -> s(T1152)\nX9917 -> s(s(T1152))\nX9875 -> X9919\nX9918 -> X9919", fontsize=14, style = filled, fillcolor = white];
1408 -> 3324 [arrowhead = none ];
3324 -> 1410;

3325 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1409 -> 3325 [arrowhead = none ];
3325 -> 1866;

3326 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1410 -> 3326 [arrowhead = none ];
3326 -> 1411;

3327 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1411 -> 3327 [arrowhead = none ];
3327 -> 1412;

3328 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1411 -> 3328 [arrowhead = none ];
3328 -> 1413;

3329 [label="EVAL with clause\nquot(0, s(X9932), s(X9933), 0).\nand substitution\nT1151 -> 0\nT1152 -> T1159\nX9932 -> T1159\nX9933 -> s(T1159)\nX9919 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1412 -> 3329 [arrowhead = none ];
3329 -> 1414;

3330 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1412 -> 3330 [arrowhead = none ];
3330 -> 1415;

3331 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1413 -> 3331 [arrowhead = none ];
3331 -> 1417;

3332 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1413 -> 3332 [arrowhead = none ];
3332 -> 1418;

3333 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1414 -> 3333 [arrowhead = none ];
3333 -> 1416;

3334 [label="EVAL with clause\nquot(s(X9956), s(X9957), X9958, X9959) :- quot(X9956, X9957, X9958, X9959).\nand substitution\nX9956 -> T1168\nT1151 -> s(T1168)\nT1152 -> T1169\nX9957 -> T1169\nX9958 -> s(s(T1169))\nX9919 -> X9960\nX9959 -> X9960", fontsize=14, style = filled, fillcolor = lightblue];
1417 -> 3334 [arrowhead = none ];
3334 -> 1419;

3335 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1417 -> 3335 [arrowhead = none ];
3335 -> 1420;

3336 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1418 -> 3336 [arrowhead = none ];
3336 -> 1865;

3337 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1419 -> 3337 [arrowhead = none ];
3337 -> 1421;

3338 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1421 -> 3338 [arrowhead = none ];
3338 -> 1422;

3339 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1421 -> 3339 [arrowhead = none ];
3339 -> 1423;

3340 [label="EVAL with clause\nquot(0, s(X9977), s(X9978), 0).\nand substitution\nT1168 -> 0\nX9977 -> T1176\nT1169 -> s(T1176)\nX9978 -> s(s(T1176))\nX9960 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1422 -> 3340 [arrowhead = none ];
3340 -> 1424;

3341 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1422 -> 3341 [arrowhead = none ];
3341 -> 1425;

3342 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1423 -> 3342 [arrowhead = none ];
3342 -> 1427;

3343 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1423 -> 3343 [arrowhead = none ];
3343 -> 1428;

3344 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1424 -> 3344 [arrowhead = none ];
3344 -> 1426;

3345 [label="EVAL with clause\nquot(s(X10001), s(X10002), X10003, X10004) :- quot(X10001, X10002, X10003, X10004).\nand substitution\nX10001 -> T1185\nT1168 -> s(T1185)\nX10002 -> T1186\nT1169 -> s(T1186)\nX10003 -> s(s(s(T1186)))\nX9960 -> X10005\nX10004 -> X10005", fontsize=14, style = filled, fillcolor = lightblue];
1427 -> 3345 [arrowhead = none ];
3345 -> 1429;

3346 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1427 -> 3346 [arrowhead = none ];
3346 -> 1430;

3347 [label="EVAL with clause\nquot(X11974, 0, s(X11975), s(X11976)) :- quot(X11974, s(X11975), s(X11975), X11976).\nand substitution\nT1168 -> T1563\nX11974 -> T1563\nT1169 -> 0\nX11975 -> s(0)\nX11976 -> X11977\nX9960 -> s(X11977)", fontsize=14, style = filled, fillcolor = lightblue];
1428 -> 3347 [arrowhead = none ];
3347 -> 1837;

3348 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1428 -> 3348 [arrowhead = none ];
3348 -> 1838;

3349 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1429 -> 3349 [arrowhead = none ];
3349 -> 1431;

3350 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1431 -> 3350 [arrowhead = none ];
3350 -> 1432;

3351 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1431 -> 3351 [arrowhead = none ];
3351 -> 1433;

3352 [label="EVAL with clause\nquot(0, s(X10022), s(X10023), 0).\nand substitution\nT1185 -> 0\nX10022 -> T1193\nT1186 -> s(T1193)\nX10023 -> s(s(s(T1193)))\nX10005 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1432 -> 3352 [arrowhead = none ];
3352 -> 1434;

3353 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1432 -> 3353 [arrowhead = none ];
3353 -> 1435;

3354 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1433 -> 3354 [arrowhead = none ];
3354 -> 1437;

3355 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1433 -> 3355 [arrowhead = none ];
3355 -> 1438;

3356 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1434 -> 3356 [arrowhead = none ];
3356 -> 1436;

3357 [label="EVAL with clause\nquot(s(X10046), s(X10047), X10048, X10049) :- quot(X10046, X10047, X10048, X10049).\nand substitution\nX10046 -> T1202\nT1185 -> s(T1202)\nX10047 -> T1203\nT1186 -> s(T1203)\nX10048 -> s(s(s(s(T1203))))\nX10005 -> X10050\nX10049 -> X10050", fontsize=14, style = filled, fillcolor = lightblue];
1437 -> 3357 [arrowhead = none ];
3357 -> 1439;

3358 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1437 -> 3358 [arrowhead = none ];
3358 -> 1440;

3359 [label="EVAL with clause\nquot(X11777, 0, s(X11778), s(X11779)) :- quot(X11777, s(X11778), s(X11778), X11779).\nand substitution\nT1185 -> T1536\nX11777 -> T1536\nT1186 -> 0\nX11778 -> s(s(0))\nX11779 -> X11780\nX10005 -> s(X11780)", fontsize=14, style = filled, fillcolor = lightblue];
1438 -> 3359 [arrowhead = none ];
3359 -> 1798;

3360 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1438 -> 3360 [arrowhead = none ];
3360 -> 1799;

3361 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1439 -> 3361 [arrowhead = none ];
3361 -> 1441;

3362 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1441 -> 3362 [arrowhead = none ];
3362 -> 1442;

3363 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1441 -> 3363 [arrowhead = none ];
3363 -> 1443;

3364 [label="EVAL with clause\nquot(0, s(X10067), s(X10068), 0).\nand substitution\nT1202 -> 0\nX10067 -> T1210\nT1203 -> s(T1210)\nX10068 -> s(s(s(s(T1210))))\nX10050 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1442 -> 3364 [arrowhead = none ];
3364 -> 1444;

3365 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1442 -> 3365 [arrowhead = none ];
3365 -> 1445;

3366 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1443 -> 3366 [arrowhead = none ];
3366 -> 1447;

3367 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1443 -> 3367 [arrowhead = none ];
3367 -> 1448;

3368 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1444 -> 3368 [arrowhead = none ];
3368 -> 1446;

3369 [label="EVAL with clause\nquot(s(X10091), s(X10092), X10093, X10094) :- quot(X10091, X10092, X10093, X10094).\nand substitution\nX10091 -> T1219\nT1202 -> s(T1219)\nX10092 -> T1220\nT1203 -> s(T1220)\nX10093 -> s(s(s(s(s(T1220)))))\nX10050 -> X10095\nX10094 -> X10095", fontsize=14, style = filled, fillcolor = lightblue];
1447 -> 3369 [arrowhead = none ];
3369 -> 1449;

3370 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1447 -> 3370 [arrowhead = none ];
3370 -> 1450;

3371 [label="EVAL with clause\nquot(X11532, 0, s(X11533), s(X11534)) :- quot(X11532, s(X11533), s(X11533), X11534).\nand substitution\nT1202 -> T1503\nX11532 -> T1503\nT1203 -> 0\nX11533 -> s(s(s(0)))\nX11534 -> X11535\nX10050 -> s(X11535)", fontsize=14, style = filled, fillcolor = lightblue];
1448 -> 3371 [arrowhead = none ];
3371 -> 1748;

3372 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1448 -> 3372 [arrowhead = none ];
3372 -> 1749;

3373 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1449 -> 3373 [arrowhead = none ];
3373 -> 1451;

3374 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1451 -> 3374 [arrowhead = none ];
3374 -> 1452;

3375 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1451 -> 3375 [arrowhead = none ];
3375 -> 1453;

3376 [label="EVAL with clause\nquot(0, s(X10112), s(X10113), 0).\nand substitution\nT1219 -> 0\nX10112 -> T1227\nT1220 -> s(T1227)\nX10113 -> s(s(s(s(s(T1227)))))\nX10095 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1452 -> 3376 [arrowhead = none ];
3376 -> 1454;

3377 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1452 -> 3377 [arrowhead = none ];
3377 -> 1455;

3378 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1453 -> 3378 [arrowhead = none ];
3378 -> 1457;

3379 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1453 -> 3379 [arrowhead = none ];
3379 -> 1458;

3380 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1454 -> 3380 [arrowhead = none ];
3380 -> 1456;

3381 [label="EVAL with clause\nquot(s(X10136), s(X10137), X10138, X10139) :- quot(X10136, X10137, X10138, X10139).\nand substitution\nX10136 -> T1236\nT1219 -> s(T1236)\nX10137 -> T1237\nT1220 -> s(T1237)\nX10138 -> s(s(s(s(s(s(T1237))))))\nX10095 -> X10140\nX10139 -> X10140", fontsize=14, style = filled, fillcolor = lightblue];
1457 -> 3381 [arrowhead = none ];
3381 -> 1459;

3382 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1457 -> 3382 [arrowhead = none ];
3382 -> 1460;

3383 [label="EVAL with clause\nquot(X11239, 0, s(X11240), s(X11241)) :- quot(X11239, s(X11240), s(X11240), X11241).\nand substitution\nT1219 -> T1464\nX11239 -> T1464\nT1220 -> 0\nX11240 -> s(s(s(s(0))))\nX11241 -> X11242\nX10095 -> s(X11242)", fontsize=14, style = filled, fillcolor = lightblue];
1458 -> 3383 [arrowhead = none ];
3383 -> 1687;

3384 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1458 -> 3384 [arrowhead = none ];
3384 -> 1688;

3385 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1459 -> 3385 [arrowhead = none ];
3385 -> 1461;

3386 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1461 -> 3386 [arrowhead = none ];
3386 -> 1462;

3387 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1461 -> 3387 [arrowhead = none ];
3387 -> 1463;

3388 [label="EVAL with clause\nquot(0, s(X10157), s(X10158), 0).\nand substitution\nT1236 -> 0\nX10157 -> T1244\nT1237 -> s(T1244)\nX10158 -> s(s(s(s(s(s(T1244))))))\nX10140 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1462 -> 3388 [arrowhead = none ];
3388 -> 1464;

3389 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1462 -> 3389 [arrowhead = none ];
3389 -> 1465;

3390 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1463 -> 3390 [arrowhead = none ];
3390 -> 1467;

3391 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1463 -> 3391 [arrowhead = none ];
3391 -> 1468;

3392 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1464 -> 3392 [arrowhead = none ];
3392 -> 1466;

3393 [label="EVAL with clause\nquot(s(X10181), s(X10182), X10183, X10184) :- quot(X10181, X10182, X10183, X10184).\nand substitution\nX10181 -> T1253\nT1236 -> s(T1253)\nX10182 -> T1254\nT1237 -> s(T1254)\nX10183 -> s(s(s(s(s(s(s(T1254)))))))\nX10140 -> X10185\nX10184 -> X10185", fontsize=14, style = filled, fillcolor = lightblue];
1467 -> 3393 [arrowhead = none ];
3393 -> 1469;

3394 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1467 -> 3394 [arrowhead = none ];
3394 -> 1470;

3395 [label="EVAL with clause\nquot(X10898, 0, s(X10899), s(X10900)) :- quot(X10898, s(X10899), s(X10899), X10900).\nand substitution\nT1236 -> T1419\nX10898 -> T1419\nT1237 -> 0\nX10899 -> s(s(s(s(s(0)))))\nX10900 -> X10901\nX10140 -> s(X10901)", fontsize=14, style = filled, fillcolor = lightblue];
1468 -> 3395 [arrowhead = none ];
3395 -> 1615;

3396 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1468 -> 3396 [arrowhead = none ];
3396 -> 1616;

3397 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1469 -> 3397 [arrowhead = none ];
3397 -> 1471;

3398 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1471 -> 3398 [arrowhead = none ];
3398 -> 1472;

3399 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1471 -> 3399 [arrowhead = none ];
3399 -> 1473;

3400 [label="EVAL with clause\nquot(0, s(X10202), s(X10203), 0).\nand substitution\nT1253 -> 0\nX10202 -> T1261\nT1254 -> s(T1261)\nX10203 -> s(s(s(s(s(s(s(T1261)))))))\nX10185 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1472 -> 3400 [arrowhead = none ];
3400 -> 1474;

3401 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1472 -> 3401 [arrowhead = none ];
3401 -> 1475;

3402 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1473 -> 3402 [arrowhead = none ];
3402 -> 1477;

3403 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1473 -> 3403 [arrowhead = none ];
3403 -> 1478;

3404 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1474 -> 3404 [arrowhead = none ];
3404 -> 1476;

3405 [label="EVAL with clause\nquot(s(X10226), s(X10227), X10228, X10229) :- quot(X10226, X10227, X10228, X10229).\nand substitution\nX10226 -> T1270\nT1253 -> s(T1270)\nX10227 -> T1271\nT1254 -> s(T1271)\nX10228 -> s(s(s(s(s(s(s(s(T1271))))))))\nX10185 -> X10230\nX10229 -> X10230", fontsize=14, style = filled, fillcolor = lightblue];
1477 -> 3405 [arrowhead = none ];
3405 -> 1479;

3406 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1477 -> 3406 [arrowhead = none ];
3406 -> 1480;

3407 [label="EVAL with clause\nquot(X10509, 0, s(X10510), s(X10511)) :- quot(X10509, s(X10510), s(X10510), X10511).\nand substitution\nT1253 -> T1368\nX10509 -> T1368\nT1254 -> 0\nX10510 -> s(s(s(s(s(s(0))))))\nX10511 -> X10512\nX10185 -> s(X10512)", fontsize=14, style = filled, fillcolor = lightblue];
1478 -> 3407 [arrowhead = none ];
3407 -> 1532;

3408 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1478 -> 3408 [arrowhead = none ];
3408 -> 1533;

3409 [label="GENERALIZATION\nT1274 <-- s(s(s(s(s(s(s(T1271)))))))\n\nNew Knowledge:\nT1274 is ground", fontsize=14, style = filled, fillcolor = violet];
1479 -> 3409 [arrowhead = none ];
3409 -> 1481;

3410 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1481 -> 3410 [arrowhead = none ];
3410 -> 1482;

3411 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1482 -> 3411 [arrowhead = none ];
3411 -> 1483;

3412 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1482 -> 3412 [arrowhead = none ];
3412 -> 1484;

3413 [label="EVAL with clause\nquot(0, s(X10251), s(X10252), 0).\nand substitution\nT1270 -> 0\nX10251 -> T1287\nT1271 -> s(T1287)\nT1274 -> T1288\nX10252 -> T1288\nX10230 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1483 -> 3413 [arrowhead = none ];
3413 -> 1485;

3414 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1483 -> 3414 [arrowhead = none ];
3414 -> 1486;

3415 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1484 -> 3415 [arrowhead = none ];
3415 -> 1488;

3416 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1484 -> 3416 [arrowhead = none ];
3416 -> 1489;

3417 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1485 -> 3417 [arrowhead = none ];
3417 -> 1487;

3418 [label="EVAL with clause\nquot(s(X10275), s(X10276), X10277, X10278) :- quot(X10275, X10276, X10277, X10278).\nand substitution\nX10275 -> T1301\nT1270 -> s(T1301)\nX10276 -> T1302\nT1271 -> s(T1302)\nT1274 -> T1303\nX10277 -> s(T1303)\nX10230 -> X10279\nX10278 -> X10279", fontsize=14, style = filled, fillcolor = lightblue];
1488 -> 3418 [arrowhead = none ];
3418 -> 1490;

3419 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1488 -> 3419 [arrowhead = none ];
3419 -> 1491;

3420 [label="EVAL with clause\nquot(X10296, 0, s(X10297), s(X10298)) :- quot(X10296, s(X10297), s(X10297), X10298).\nand substitution\nT1270 -> T1312\nX10296 -> T1312\nT1271 -> 0\nT1274 -> T1313\nX10297 -> T1313\nX10298 -> X10299\nX10230 -> s(X10299)", fontsize=14, style = filled, fillcolor = lightblue];
1489 -> 3420 [arrowhead = none ];
3420 -> 1492;

3421 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1489 -> 3421 [arrowhead = none ];
3421 -> 1493;

3422 [label="INSTANCE with matching:\nT1270 -> T1301\nT1271 -> T1302\nT1274 -> T1303\nX10230 -> X10279", fontsize=14, style = filled, fillcolor = lightgrey];
1490 -> 3422 [arrowhead = none , style=dashed];
3422 -> 1481[style=dashed];

3423 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1492 -> 3423 [arrowhead = none ];
3423 -> 1494;

3424 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1494 -> 3424 [arrowhead = none ];
3424 -> 1495;

3425 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1494 -> 3425 [arrowhead = none ];
3425 -> 1496;

3426 [label="EVAL with clause\nquot(0, s(X10315), s(X10316), 0).\nand substitution\nT1312 -> 0\nT1313 -> T1320\nX10315 -> T1320\nX10316 -> T1320\nX10299 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1495 -> 3426 [arrowhead = none ];
3426 -> 1497;

3427 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1495 -> 3427 [arrowhead = none ];
3427 -> 1498;

3428 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1496 -> 3428 [arrowhead = none ];
3428 -> 1500;

3429 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1496 -> 3429 [arrowhead = none ];
3429 -> 1501;

3430 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1497 -> 3430 [arrowhead = none ];
3430 -> 1499;

3431 [label="EVAL with clause\nquot(s(X10339), s(X10340), X10341, X10342) :- quot(X10339, X10340, X10341, X10342).\nand substitution\nX10339 -> T1329\nT1312 -> s(T1329)\nT1313 -> T1330\nX10340 -> T1330\nX10341 -> s(T1330)\nX10299 -> X10343\nX10342 -> X10343", fontsize=14, style = filled, fillcolor = lightblue];
1500 -> 3431 [arrowhead = none ];
3431 -> 1502;

3432 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1500 -> 3432 [arrowhead = none ];
3432 -> 1503;

3433 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1501 -> 3433 [arrowhead = none ];
3433 -> 1531;

3434 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1502 -> 3434 [arrowhead = none ];
3434 -> 1504;

3435 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1504 -> 3435 [arrowhead = none ];
3435 -> 1505;

3436 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1504 -> 3436 [arrowhead = none ];
3436 -> 1506;

3437 [label="EVAL with clause\nquot(0, s(X10360), s(X10361), 0).\nand substitution\nT1329 -> 0\nX10360 -> T1337\nT1330 -> s(T1337)\nX10361 -> s(T1337)\nX10343 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1505 -> 3437 [arrowhead = none ];
3437 -> 1507;

3438 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1505 -> 3438 [arrowhead = none ];
3438 -> 1508;

3439 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1506 -> 3439 [arrowhead = none ];
3439 -> 1510;

3440 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1506 -> 3440 [arrowhead = none ];
3440 -> 1511;

3441 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1507 -> 3441 [arrowhead = none ];
3441 -> 1509;

3442 [label="EVAL with clause\nquot(s(X10384), s(X10385), X10386, X10387) :- quot(X10384, X10385, X10386, X10387).\nand substitution\nX10384 -> T1346\nT1329 -> s(T1346)\nX10385 -> T1347\nT1330 -> s(T1347)\nX10386 -> s(s(T1347))\nX10343 -> X10388\nX10387 -> X10388", fontsize=14, style = filled, fillcolor = lightblue];
1510 -> 3442 [arrowhead = none ];
3442 -> 1512;

3443 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1510 -> 3443 [arrowhead = none ];
3443 -> 1513;

3444 [label="EVAL with clause\nquot(X10405, 0, s(X10406), s(X10407)) :- quot(X10405, s(X10406), s(X10406), X10407).\nand substitution\nT1329 -> T1352\nX10405 -> T1352\nT1330 -> 0\nX10406 -> 0\nX10407 -> X10408\nX10343 -> s(X10408)", fontsize=14, style = filled, fillcolor = lightblue];
1511 -> 3444 [arrowhead = none ];
3444 -> 1514;

3445 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1511 -> 3445 [arrowhead = none ];
3445 -> 1515;

3446 [label="INSTANCE with matching:\nT1168 -> T1346\nT1169 -> T1347\nX9960 -> X10388", fontsize=14, style = filled, fillcolor = lightgrey];
1512 -> 3446 [arrowhead = none , style=dashed];
3446 -> 1419[style=dashed];

3447 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1514 -> 3447 [arrowhead = none ];
3447 -> 1516;

3448 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1516 -> 3448 [arrowhead = none ];
3448 -> 1517;

3449 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1516 -> 3449 [arrowhead = none ];
3449 -> 1518;

3450 [label="EVAL with clause\nquot(0, s(X10424), s(X10425), 0).\nand substitution\nT1352 -> 0\nX10424 -> 0\nX10425 -> 0\nX10408 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1517 -> 3450 [arrowhead = none ];
3450 -> 1519;

3451 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1517 -> 3451 [arrowhead = none ];
3451 -> 1520;

3452 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1518 -> 3452 [arrowhead = none ];
3452 -> 1522;

3453 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1518 -> 3453 [arrowhead = none ];
3453 -> 1523;

3454 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1519 -> 3454 [arrowhead = none ];
3454 -> 1521;

3455 [label="EVAL with clause\nquot(s(X10448), s(X10449), X10450, X10451) :- quot(X10448, X10449, X10450, X10451).\nand substitution\nX10448 -> T1357\nT1352 -> s(T1357)\nX10449 -> 0\nX10450 -> s(0)\nX10408 -> X10452\nX10451 -> X10452", fontsize=14, style = filled, fillcolor = lightblue];
1522 -> 3455 [arrowhead = none ];
3455 -> 1524;

3456 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1522 -> 3456 [arrowhead = none ];
3456 -> 1525;

3457 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1523 -> 3457 [arrowhead = none ];
3457 -> 1530;

3458 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1524 -> 3458 [arrowhead = none ];
3458 -> 1526;

3459 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1526 -> 3459 [arrowhead = none ];
3459 -> 1527;

3460 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1527 -> 3460 [arrowhead = none ];
3460 -> 1528;

3461 [label="ONLY EVAL with clause\nquot(X10487, 0, s(X10488), s(X10489)) :- quot(X10487, s(X10488), s(X10488), X10489).\nand substitution\nT1357 -> T1363\nX10487 -> T1363\nX10488 -> 0\nX10489 -> X10490\nX10452 -> s(X10490)", fontsize=14, style = filled, fillcolor = white];
1528 -> 3461 [arrowhead = none ];
3461 -> 1529;

3462 [label="INSTANCE with matching:\nT1352 -> T1363\nX10408 -> X10490", fontsize=14, style = filled, fillcolor = lightgrey];
1529 -> 3462 [arrowhead = none , style=dashed];
3462 -> 1514[style=dashed];

3463 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1532 -> 3463 [arrowhead = none ];
3463 -> 1534;

3464 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1534 -> 3464 [arrowhead = none ];
3464 -> 1535;

3465 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1534 -> 3465 [arrowhead = none ];
3465 -> 1536;

3466 [label="EVAL with clause\nquot(0, s(X10528), s(X10529), 0).\nand substitution\nT1368 -> 0\nX10528 -> s(s(s(s(s(s(0))))))\nX10529 -> s(s(s(s(s(s(0))))))\nX10512 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1535 -> 3466 [arrowhead = none ];
3466 -> 1537;

3467 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1535 -> 3467 [arrowhead = none ];
3467 -> 1538;

3468 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1536 -> 3468 [arrowhead = none ];
3468 -> 1540;

3469 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1536 -> 3469 [arrowhead = none ];
3469 -> 1541;

3470 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1537 -> 3470 [arrowhead = none ];
3470 -> 1539;

3471 [label="EVAL with clause\nquot(s(X10552), s(X10553), X10554, X10555) :- quot(X10552, X10553, X10554, X10555).\nand substitution\nX10552 -> T1373\nT1368 -> s(T1373)\nX10553 -> s(s(s(s(s(s(0))))))\nX10554 -> s(s(s(s(s(s(s(0)))))))\nX10512 -> X10556\nX10555 -> X10556", fontsize=14, style = filled, fillcolor = lightblue];
1540 -> 3471 [arrowhead = none ];
3471 -> 1542;

3472 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1540 -> 3472 [arrowhead = none ];
3472 -> 1543;

3473 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1541 -> 3473 [arrowhead = none ];
3473 -> 1614;

3474 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1542 -> 3474 [arrowhead = none ];
3474 -> 1544;

3475 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1544 -> 3475 [arrowhead = none ];
3475 -> 1545;

3476 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1544 -> 3476 [arrowhead = none ];
3476 -> 1546;

3477 [label="EVAL with clause\nquot(0, s(X10573), s(X10574), 0).\nand substitution\nT1373 -> 0\nX10573 -> s(s(s(s(s(0)))))\nX10574 -> s(s(s(s(s(s(0))))))\nX10556 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1545 -> 3477 [arrowhead = none ];
3477 -> 1547;

3478 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1545 -> 3478 [arrowhead = none ];
3478 -> 1548;

3479 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1546 -> 3479 [arrowhead = none ];
3479 -> 1550;

3480 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1546 -> 3480 [arrowhead = none ];
3480 -> 1551;

3481 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1547 -> 3481 [arrowhead = none ];
3481 -> 1549;

3482 [label="EVAL with clause\nquot(s(X10597), s(X10598), X10599, X10600) :- quot(X10597, X10598, X10599, X10600).\nand substitution\nX10597 -> T1378\nT1373 -> s(T1378)\nX10598 -> s(s(s(s(s(0)))))\nX10599 -> s(s(s(s(s(s(s(0)))))))\nX10556 -> X10601\nX10600 -> X10601", fontsize=14, style = filled, fillcolor = lightblue];
1550 -> 3482 [arrowhead = none ];
3482 -> 1552;

3483 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1550 -> 3483 [arrowhead = none ];
3483 -> 1553;

3484 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1551 -> 3484 [arrowhead = none ];
3484 -> 1613;

3485 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1552 -> 3485 [arrowhead = none ];
3485 -> 1554;

3486 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1554 -> 3486 [arrowhead = none ];
3486 -> 1555;

3487 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1554 -> 3487 [arrowhead = none ];
3487 -> 1556;

3488 [label="EVAL with clause\nquot(0, s(X10618), s(X10619), 0).\nand substitution\nT1378 -> 0\nX10618 -> s(s(s(s(0))))\nX10619 -> s(s(s(s(s(s(0))))))\nX10601 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1555 -> 3488 [arrowhead = none ];
3488 -> 1557;

3489 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1555 -> 3489 [arrowhead = none ];
3489 -> 1558;

3490 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1556 -> 3490 [arrowhead = none ];
3490 -> 1560;

3491 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1556 -> 3491 [arrowhead = none ];
3491 -> 1561;

3492 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1557 -> 3492 [arrowhead = none ];
3492 -> 1559;

3493 [label="EVAL with clause\nquot(s(X10642), s(X10643), X10644, X10645) :- quot(X10642, X10643, X10644, X10645).\nand substitution\nX10642 -> T1383\nT1378 -> s(T1383)\nX10643 -> s(s(s(s(0))))\nX10644 -> s(s(s(s(s(s(s(0)))))))\nX10601 -> X10646\nX10645 -> X10646", fontsize=14, style = filled, fillcolor = lightblue];
1560 -> 3493 [arrowhead = none ];
3493 -> 1562;

3494 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1560 -> 3494 [arrowhead = none ];
3494 -> 1563;

3495 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1561 -> 3495 [arrowhead = none ];
3495 -> 1612;

3496 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1562 -> 3496 [arrowhead = none ];
3496 -> 1564;

3497 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1564 -> 3497 [arrowhead = none ];
3497 -> 1565;

3498 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1564 -> 3498 [arrowhead = none ];
3498 -> 1566;

3499 [label="EVAL with clause\nquot(0, s(X10663), s(X10664), 0).\nand substitution\nT1383 -> 0\nX10663 -> s(s(s(0)))\nX10664 -> s(s(s(s(s(s(0))))))\nX10646 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1565 -> 3499 [arrowhead = none ];
3499 -> 1567;

3500 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1565 -> 3500 [arrowhead = none ];
3500 -> 1568;

3501 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1566 -> 3501 [arrowhead = none ];
3501 -> 1570;

3502 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1566 -> 3502 [arrowhead = none ];
3502 -> 1571;

3503 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1567 -> 3503 [arrowhead = none ];
3503 -> 1569;

3504 [label="EVAL with clause\nquot(s(X10687), s(X10688), X10689, X10690) :- quot(X10687, X10688, X10689, X10690).\nand substitution\nX10687 -> T1388\nT1383 -> s(T1388)\nX10688 -> s(s(s(0)))\nX10689 -> s(s(s(s(s(s(s(0)))))))\nX10646 -> X10691\nX10690 -> X10691", fontsize=14, style = filled, fillcolor = lightblue];
1570 -> 3504 [arrowhead = none ];
3504 -> 1572;

3505 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1570 -> 3505 [arrowhead = none ];
3505 -> 1573;

3506 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1571 -> 3506 [arrowhead = none ];
3506 -> 1611;

3507 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1572 -> 3507 [arrowhead = none ];
3507 -> 1574;

3508 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1574 -> 3508 [arrowhead = none ];
3508 -> 1575;

3509 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1574 -> 3509 [arrowhead = none ];
3509 -> 1576;

3510 [label="EVAL with clause\nquot(0, s(X10708), s(X10709), 0).\nand substitution\nT1388 -> 0\nX10708 -> s(s(0))\nX10709 -> s(s(s(s(s(s(0))))))\nX10691 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1575 -> 3510 [arrowhead = none ];
3510 -> 1577;

3511 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1575 -> 3511 [arrowhead = none ];
3511 -> 1578;

3512 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1576 -> 3512 [arrowhead = none ];
3512 -> 1580;

3513 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1576 -> 3513 [arrowhead = none ];
3513 -> 1581;

3514 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1577 -> 3514 [arrowhead = none ];
3514 -> 1579;

3515 [label="EVAL with clause\nquot(s(X10732), s(X10733), X10734, X10735) :- quot(X10732, X10733, X10734, X10735).\nand substitution\nX10732 -> T1393\nT1388 -> s(T1393)\nX10733 -> s(s(0))\nX10734 -> s(s(s(s(s(s(s(0)))))))\nX10691 -> X10736\nX10735 -> X10736", fontsize=14, style = filled, fillcolor = lightblue];
1580 -> 3515 [arrowhead = none ];
3515 -> 1582;

3516 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1580 -> 3516 [arrowhead = none ];
3516 -> 1583;

3517 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1581 -> 3517 [arrowhead = none ];
3517 -> 1610;

3518 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1582 -> 3518 [arrowhead = none ];
3518 -> 1584;

3519 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1584 -> 3519 [arrowhead = none ];
3519 -> 1585;

3520 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1584 -> 3520 [arrowhead = none ];
3520 -> 1586;

3521 [label="EVAL with clause\nquot(0, s(X10753), s(X10754), 0).\nand substitution\nT1393 -> 0\nX10753 -> s(0)\nX10754 -> s(s(s(s(s(s(0))))))\nX10736 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1585 -> 3521 [arrowhead = none ];
3521 -> 1587;

3522 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1585 -> 3522 [arrowhead = none ];
3522 -> 1588;

3523 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1586 -> 3523 [arrowhead = none ];
3523 -> 1590;

3524 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1586 -> 3524 [arrowhead = none ];
3524 -> 1591;

3525 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1587 -> 3525 [arrowhead = none ];
3525 -> 1589;

3526 [label="EVAL with clause\nquot(s(X10777), s(X10778), X10779, X10780) :- quot(X10777, X10778, X10779, X10780).\nand substitution\nX10777 -> T1398\nT1393 -> s(T1398)\nX10778 -> s(0)\nX10779 -> s(s(s(s(s(s(s(0)))))))\nX10736 -> X10781\nX10780 -> X10781", fontsize=14, style = filled, fillcolor = lightblue];
1590 -> 3526 [arrowhead = none ];
3526 -> 1592;

3527 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1590 -> 3527 [arrowhead = none ];
3527 -> 1593;

3528 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1591 -> 3528 [arrowhead = none ];
3528 -> 1609;

3529 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1592 -> 3529 [arrowhead = none ];
3529 -> 1594;

3530 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1594 -> 3530 [arrowhead = none ];
3530 -> 1595;

3531 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1594 -> 3531 [arrowhead = none ];
3531 -> 1596;

3532 [label="EVAL with clause\nquot(0, s(X10798), s(X10799), 0).\nand substitution\nT1398 -> 0\nX10798 -> 0\nX10799 -> s(s(s(s(s(s(0))))))\nX10781 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1595 -> 3532 [arrowhead = none ];
3532 -> 1597;

3533 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1595 -> 3533 [arrowhead = none ];
3533 -> 1598;

3534 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1596 -> 3534 [arrowhead = none ];
3534 -> 1600;

3535 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1596 -> 3535 [arrowhead = none ];
3535 -> 1601;

3536 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1597 -> 3536 [arrowhead = none ];
3536 -> 1599;

3537 [label="EVAL with clause\nquot(s(X10822), s(X10823), X10824, X10825) :- quot(X10822, X10823, X10824, X10825).\nand substitution\nX10822 -> T1403\nT1398 -> s(T1403)\nX10823 -> 0\nX10824 -> s(s(s(s(s(s(s(0)))))))\nX10781 -> X10826\nX10825 -> X10826", fontsize=14, style = filled, fillcolor = lightblue];
1600 -> 3537 [arrowhead = none ];
3537 -> 1602;

3538 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1600 -> 3538 [arrowhead = none ];
3538 -> 1603;

3539 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1601 -> 3539 [arrowhead = none ];
3539 -> 1608;

3540 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1602 -> 3540 [arrowhead = none ];
3540 -> 1604;

3541 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1604 -> 3541 [arrowhead = none ];
3541 -> 1605;

3542 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1605 -> 3542 [arrowhead = none ];
3542 -> 1606;

3543 [label="ONLY EVAL with clause\nquot(X10861, 0, s(X10862), s(X10863)) :- quot(X10861, s(X10862), s(X10862), X10863).\nand substitution\nT1403 -> T1409\nX10861 -> T1409\nX10862 -> s(s(s(s(s(s(0))))))\nX10863 -> X10864\nX10826 -> s(X10864)", fontsize=14, style = filled, fillcolor = white];
1606 -> 3543 [arrowhead = none ];
3543 -> 1607;

3544 [label="INSTANCE with matching:\nT1368 -> T1409\nX10512 -> X10864", fontsize=14, style = filled, fillcolor = lightgrey];
1607 -> 3544 [arrowhead = none , style=dashed];
3544 -> 1532[style=dashed];

3545 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1615 -> 3545 [arrowhead = none ];
3545 -> 1617;

3546 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1617 -> 3546 [arrowhead = none ];
3546 -> 1618;

3547 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1617 -> 3547 [arrowhead = none ];
3547 -> 1619;

3548 [label="EVAL with clause\nquot(0, s(X10917), s(X10918), 0).\nand substitution\nT1419 -> 0\nX10917 -> s(s(s(s(s(0)))))\nX10918 -> s(s(s(s(s(0)))))\nX10901 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1618 -> 3548 [arrowhead = none ];
3548 -> 1620;

3549 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1618 -> 3549 [arrowhead = none ];
3549 -> 1621;

3550 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1619 -> 3550 [arrowhead = none ];
3550 -> 1623;

3551 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1619 -> 3551 [arrowhead = none ];
3551 -> 1624;

3552 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1620 -> 3552 [arrowhead = none ];
3552 -> 1622;

3553 [label="EVAL with clause\nquot(s(X10941), s(X10942), X10943, X10944) :- quot(X10941, X10942, X10943, X10944).\nand substitution\nX10941 -> T1424\nT1419 -> s(T1424)\nX10942 -> s(s(s(s(s(0)))))\nX10943 -> s(s(s(s(s(s(0))))))\nX10901 -> X10945\nX10944 -> X10945", fontsize=14, style = filled, fillcolor = lightblue];
1623 -> 3553 [arrowhead = none ];
3553 -> 1625;

3554 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1623 -> 3554 [arrowhead = none ];
3554 -> 1626;

3555 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1624 -> 3555 [arrowhead = none ];
3555 -> 1686;

3556 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1625 -> 3556 [arrowhead = none ];
3556 -> 1627;

3557 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1627 -> 3557 [arrowhead = none ];
3557 -> 1628;

3558 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1627 -> 3558 [arrowhead = none ];
3558 -> 1629;

3559 [label="EVAL with clause\nquot(0, s(X10962), s(X10963), 0).\nand substitution\nT1424 -> 0\nX10962 -> s(s(s(s(0))))\nX10963 -> s(s(s(s(s(0)))))\nX10945 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1628 -> 3559 [arrowhead = none ];
3559 -> 1630;

3560 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1628 -> 3560 [arrowhead = none ];
3560 -> 1631;

3561 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1629 -> 3561 [arrowhead = none ];
3561 -> 1633;

3562 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1629 -> 3562 [arrowhead = none ];
3562 -> 1634;

3563 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1630 -> 3563 [arrowhead = none ];
3563 -> 1632;

3564 [label="EVAL with clause\nquot(s(X10986), s(X10987), X10988, X10989) :- quot(X10986, X10987, X10988, X10989).\nand substitution\nX10986 -> T1429\nT1424 -> s(T1429)\nX10987 -> s(s(s(s(0))))\nX10988 -> s(s(s(s(s(s(0))))))\nX10945 -> X10990\nX10989 -> X10990", fontsize=14, style = filled, fillcolor = lightblue];
1633 -> 3564 [arrowhead = none ];
3564 -> 1635;

3565 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1633 -> 3565 [arrowhead = none ];
3565 -> 1636;

3566 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1634 -> 3566 [arrowhead = none ];
3566 -> 1685;

3567 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1635 -> 3567 [arrowhead = none ];
3567 -> 1637;

3568 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1637 -> 3568 [arrowhead = none ];
3568 -> 1638;

3569 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1637 -> 3569 [arrowhead = none ];
3569 -> 1639;

3570 [label="EVAL with clause\nquot(0, s(X11007), s(X11008), 0).\nand substitution\nT1429 -> 0\nX11007 -> s(s(s(0)))\nX11008 -> s(s(s(s(s(0)))))\nX10990 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1638 -> 3570 [arrowhead = none ];
3570 -> 1640;

3571 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1638 -> 3571 [arrowhead = none ];
3571 -> 1641;

3572 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1639 -> 3572 [arrowhead = none ];
3572 -> 1643;

3573 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1639 -> 3573 [arrowhead = none ];
3573 -> 1644;

3574 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1640 -> 3574 [arrowhead = none ];
3574 -> 1642;

3575 [label="EVAL with clause\nquot(s(X11031), s(X11032), X11033, X11034) :- quot(X11031, X11032, X11033, X11034).\nand substitution\nX11031 -> T1434\nT1429 -> s(T1434)\nX11032 -> s(s(s(0)))\nX11033 -> s(s(s(s(s(s(0))))))\nX10990 -> X11035\nX11034 -> X11035", fontsize=14, style = filled, fillcolor = lightblue];
1643 -> 3575 [arrowhead = none ];
3575 -> 1645;

3576 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1643 -> 3576 [arrowhead = none ];
3576 -> 1646;

3577 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1644 -> 3577 [arrowhead = none ];
3577 -> 1684;

3578 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1645 -> 3578 [arrowhead = none ];
3578 -> 1647;

3579 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1647 -> 3579 [arrowhead = none ];
3579 -> 1648;

3580 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1647 -> 3580 [arrowhead = none ];
3580 -> 1649;

3581 [label="EVAL with clause\nquot(0, s(X11052), s(X11053), 0).\nand substitution\nT1434 -> 0\nX11052 -> s(s(0))\nX11053 -> s(s(s(s(s(0)))))\nX11035 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1648 -> 3581 [arrowhead = none ];
3581 -> 1650;

3582 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1648 -> 3582 [arrowhead = none ];
3582 -> 1651;

3583 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1649 -> 3583 [arrowhead = none ];
3583 -> 1653;

3584 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1649 -> 3584 [arrowhead = none ];
3584 -> 1654;

3585 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1650 -> 3585 [arrowhead = none ];
3585 -> 1652;

3586 [label="EVAL with clause\nquot(s(X11076), s(X11077), X11078, X11079) :- quot(X11076, X11077, X11078, X11079).\nand substitution\nX11076 -> T1439\nT1434 -> s(T1439)\nX11077 -> s(s(0))\nX11078 -> s(s(s(s(s(s(0))))))\nX11035 -> X11080\nX11079 -> X11080", fontsize=14, style = filled, fillcolor = lightblue];
1653 -> 3586 [arrowhead = none ];
3586 -> 1655;

3587 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1653 -> 3587 [arrowhead = none ];
3587 -> 1656;

3588 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1654 -> 3588 [arrowhead = none ];
3588 -> 1683;

3589 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1655 -> 3589 [arrowhead = none ];
3589 -> 1657;

3590 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1657 -> 3590 [arrowhead = none ];
3590 -> 1658;

3591 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1657 -> 3591 [arrowhead = none ];
3591 -> 1659;

3592 [label="EVAL with clause\nquot(0, s(X11097), s(X11098), 0).\nand substitution\nT1439 -> 0\nX11097 -> s(0)\nX11098 -> s(s(s(s(s(0)))))\nX11080 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1658 -> 3592 [arrowhead = none ];
3592 -> 1660;

3593 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1658 -> 3593 [arrowhead = none ];
3593 -> 1661;

3594 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1659 -> 3594 [arrowhead = none ];
3594 -> 1663;

3595 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1659 -> 3595 [arrowhead = none ];
3595 -> 1664;

3596 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1660 -> 3596 [arrowhead = none ];
3596 -> 1662;

3597 [label="EVAL with clause\nquot(s(X11121), s(X11122), X11123, X11124) :- quot(X11121, X11122, X11123, X11124).\nand substitution\nX11121 -> T1444\nT1439 -> s(T1444)\nX11122 -> s(0)\nX11123 -> s(s(s(s(s(s(0))))))\nX11080 -> X11125\nX11124 -> X11125", fontsize=14, style = filled, fillcolor = lightblue];
1663 -> 3597 [arrowhead = none ];
3597 -> 1665;

3598 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1663 -> 3598 [arrowhead = none ];
3598 -> 1666;

3599 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1664 -> 3599 [arrowhead = none ];
3599 -> 1682;

3600 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1665 -> 3600 [arrowhead = none ];
3600 -> 1667;

3601 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1667 -> 3601 [arrowhead = none ];
3601 -> 1668;

3602 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1667 -> 3602 [arrowhead = none ];
3602 -> 1669;

3603 [label="EVAL with clause\nquot(0, s(X11142), s(X11143), 0).\nand substitution\nT1444 -> 0\nX11142 -> 0\nX11143 -> s(s(s(s(s(0)))))\nX11125 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1668 -> 3603 [arrowhead = none ];
3603 -> 1670;

3604 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1668 -> 3604 [arrowhead = none ];
3604 -> 1671;

3605 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1669 -> 3605 [arrowhead = none ];
3605 -> 1673;

3606 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1669 -> 3606 [arrowhead = none ];
3606 -> 1674;

3607 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1670 -> 3607 [arrowhead = none ];
3607 -> 1672;

3608 [label="EVAL with clause\nquot(s(X11166), s(X11167), X11168, X11169) :- quot(X11166, X11167, X11168, X11169).\nand substitution\nX11166 -> T1449\nT1444 -> s(T1449)\nX11167 -> 0\nX11168 -> s(s(s(s(s(s(0))))))\nX11125 -> X11170\nX11169 -> X11170", fontsize=14, style = filled, fillcolor = lightblue];
1673 -> 3608 [arrowhead = none ];
3608 -> 1675;

3609 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1673 -> 3609 [arrowhead = none ];
3609 -> 1676;

3610 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1674 -> 3610 [arrowhead = none ];
3610 -> 1681;

3611 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1675 -> 3611 [arrowhead = none ];
3611 -> 1677;

3612 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1677 -> 3612 [arrowhead = none ];
3612 -> 1678;

3613 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1678 -> 3613 [arrowhead = none ];
3613 -> 1679;

3614 [label="ONLY EVAL with clause\nquot(X11205, 0, s(X11206), s(X11207)) :- quot(X11205, s(X11206), s(X11206), X11207).\nand substitution\nT1449 -> T1455\nX11205 -> T1455\nX11206 -> s(s(s(s(s(0)))))\nX11207 -> X11208\nX11170 -> s(X11208)", fontsize=14, style = filled, fillcolor = white];
1679 -> 3614 [arrowhead = none ];
3614 -> 1680;

3615 [label="INSTANCE with matching:\nT1419 -> T1455\nX10901 -> X11208", fontsize=14, style = filled, fillcolor = lightgrey];
1680 -> 3615 [arrowhead = none , style=dashed];
3615 -> 1615[style=dashed];

3616 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1687 -> 3616 [arrowhead = none ];
3616 -> 1689;

3617 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1689 -> 3617 [arrowhead = none ];
3617 -> 1690;

3618 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1689 -> 3618 [arrowhead = none ];
3618 -> 1691;

3619 [label="EVAL with clause\nquot(0, s(X11258), s(X11259), 0).\nand substitution\nT1464 -> 0\nX11258 -> s(s(s(s(0))))\nX11259 -> s(s(s(s(0))))\nX11242 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1690 -> 3619 [arrowhead = none ];
3619 -> 1692;

3620 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1690 -> 3620 [arrowhead = none ];
3620 -> 1693;

3621 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1691 -> 3621 [arrowhead = none ];
3621 -> 1695;

3622 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1691 -> 3622 [arrowhead = none ];
3622 -> 1696;

3623 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1692 -> 3623 [arrowhead = none ];
3623 -> 1694;

3624 [label="EVAL with clause\nquot(s(X11282), s(X11283), X11284, X11285) :- quot(X11282, X11283, X11284, X11285).\nand substitution\nX11282 -> T1469\nT1464 -> s(T1469)\nX11283 -> s(s(s(s(0))))\nX11284 -> s(s(s(s(s(0)))))\nX11242 -> X11286\nX11285 -> X11286", fontsize=14, style = filled, fillcolor = lightblue];
1695 -> 3624 [arrowhead = none ];
3624 -> 1697;

3625 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1695 -> 3625 [arrowhead = none ];
3625 -> 1698;

3626 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1696 -> 3626 [arrowhead = none ];
3626 -> 1747;

3627 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1697 -> 3627 [arrowhead = none ];
3627 -> 1699;

3628 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1699 -> 3628 [arrowhead = none ];
3628 -> 1700;

3629 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1699 -> 3629 [arrowhead = none ];
3629 -> 1701;

3630 [label="EVAL with clause\nquot(0, s(X11303), s(X11304), 0).\nand substitution\nT1469 -> 0\nX11303 -> s(s(s(0)))\nX11304 -> s(s(s(s(0))))\nX11286 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1700 -> 3630 [arrowhead = none ];
3630 -> 1702;

3631 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1700 -> 3631 [arrowhead = none ];
3631 -> 1703;

3632 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1701 -> 3632 [arrowhead = none ];
3632 -> 1705;

3633 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1701 -> 3633 [arrowhead = none ];
3633 -> 1706;

3634 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1702 -> 3634 [arrowhead = none ];
3634 -> 1704;

3635 [label="EVAL with clause\nquot(s(X11327), s(X11328), X11329, X11330) :- quot(X11327, X11328, X11329, X11330).\nand substitution\nX11327 -> T1474\nT1469 -> s(T1474)\nX11328 -> s(s(s(0)))\nX11329 -> s(s(s(s(s(0)))))\nX11286 -> X11331\nX11330 -> X11331", fontsize=14, style = filled, fillcolor = lightblue];
1705 -> 3635 [arrowhead = none ];
3635 -> 1707;

3636 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1705 -> 3636 [arrowhead = none ];
3636 -> 1708;

3637 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1706 -> 3637 [arrowhead = none ];
3637 -> 1746;

3638 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1707 -> 3638 [arrowhead = none ];
3638 -> 1709;

3639 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1709 -> 3639 [arrowhead = none ];
3639 -> 1710;

3640 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1709 -> 3640 [arrowhead = none ];
3640 -> 1711;

3641 [label="EVAL with clause\nquot(0, s(X11348), s(X11349), 0).\nand substitution\nT1474 -> 0\nX11348 -> s(s(0))\nX11349 -> s(s(s(s(0))))\nX11331 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1710 -> 3641 [arrowhead = none ];
3641 -> 1712;

3642 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1710 -> 3642 [arrowhead = none ];
3642 -> 1713;

3643 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1711 -> 3643 [arrowhead = none ];
3643 -> 1715;

3644 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1711 -> 3644 [arrowhead = none ];
3644 -> 1716;

3645 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1712 -> 3645 [arrowhead = none ];
3645 -> 1714;

3646 [label="EVAL with clause\nquot(s(X11372), s(X11373), X11374, X11375) :- quot(X11372, X11373, X11374, X11375).\nand substitution\nX11372 -> T1479\nT1474 -> s(T1479)\nX11373 -> s(s(0))\nX11374 -> s(s(s(s(s(0)))))\nX11331 -> X11376\nX11375 -> X11376", fontsize=14, style = filled, fillcolor = lightblue];
1715 -> 3646 [arrowhead = none ];
3646 -> 1717;

3647 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1715 -> 3647 [arrowhead = none ];
3647 -> 1718;

3648 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1716 -> 3648 [arrowhead = none ];
3648 -> 1745;

3649 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1717 -> 3649 [arrowhead = none ];
3649 -> 1719;

3650 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1719 -> 3650 [arrowhead = none ];
3650 -> 1720;

3651 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1719 -> 3651 [arrowhead = none ];
3651 -> 1721;

3652 [label="EVAL with clause\nquot(0, s(X11393), s(X11394), 0).\nand substitution\nT1479 -> 0\nX11393 -> s(0)\nX11394 -> s(s(s(s(0))))\nX11376 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1720 -> 3652 [arrowhead = none ];
3652 -> 1722;

3653 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1720 -> 3653 [arrowhead = none ];
3653 -> 1723;

3654 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1721 -> 3654 [arrowhead = none ];
3654 -> 1725;

3655 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1721 -> 3655 [arrowhead = none ];
3655 -> 1726;

3656 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1722 -> 3656 [arrowhead = none ];
3656 -> 1724;

3657 [label="EVAL with clause\nquot(s(X11417), s(X11418), X11419, X11420) :- quot(X11417, X11418, X11419, X11420).\nand substitution\nX11417 -> T1484\nT1479 -> s(T1484)\nX11418 -> s(0)\nX11419 -> s(s(s(s(s(0)))))\nX11376 -> X11421\nX11420 -> X11421", fontsize=14, style = filled, fillcolor = lightblue];
1725 -> 3657 [arrowhead = none ];
3657 -> 1727;

3658 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1725 -> 3658 [arrowhead = none ];
3658 -> 1728;

3659 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1726 -> 3659 [arrowhead = none ];
3659 -> 1744;

3660 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1727 -> 3660 [arrowhead = none ];
3660 -> 1729;

3661 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1729 -> 3661 [arrowhead = none ];
3661 -> 1730;

3662 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1729 -> 3662 [arrowhead = none ];
3662 -> 1731;

3663 [label="EVAL with clause\nquot(0, s(X11438), s(X11439), 0).\nand substitution\nT1484 -> 0\nX11438 -> 0\nX11439 -> s(s(s(s(0))))\nX11421 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1730 -> 3663 [arrowhead = none ];
3663 -> 1732;

3664 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1730 -> 3664 [arrowhead = none ];
3664 -> 1733;

3665 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1731 -> 3665 [arrowhead = none ];
3665 -> 1735;

3666 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1731 -> 3666 [arrowhead = none ];
3666 -> 1736;

3667 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1732 -> 3667 [arrowhead = none ];
3667 -> 1734;

3668 [label="EVAL with clause\nquot(s(X11462), s(X11463), X11464, X11465) :- quot(X11462, X11463, X11464, X11465).\nand substitution\nX11462 -> T1489\nT1484 -> s(T1489)\nX11463 -> 0\nX11464 -> s(s(s(s(s(0)))))\nX11421 -> X11466\nX11465 -> X11466", fontsize=14, style = filled, fillcolor = lightblue];
1735 -> 3668 [arrowhead = none ];
3668 -> 1737;

3669 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1735 -> 3669 [arrowhead = none ];
3669 -> 1738;

3670 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1736 -> 3670 [arrowhead = none ];
3670 -> 1743;

3671 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1737 -> 3671 [arrowhead = none ];
3671 -> 1739;

3672 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1739 -> 3672 [arrowhead = none ];
3672 -> 1740;

3673 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1740 -> 3673 [arrowhead = none ];
3673 -> 1741;

3674 [label="ONLY EVAL with clause\nquot(X11501, 0, s(X11502), s(X11503)) :- quot(X11501, s(X11502), s(X11502), X11503).\nand substitution\nT1489 -> T1495\nX11501 -> T1495\nX11502 -> s(s(s(s(0))))\nX11503 -> X11504\nX11466 -> s(X11504)", fontsize=14, style = filled, fillcolor = white];
1741 -> 3674 [arrowhead = none ];
3674 -> 1742;

3675 [label="INSTANCE with matching:\nT1464 -> T1495\nX11242 -> X11504", fontsize=14, style = filled, fillcolor = lightgrey];
1742 -> 3675 [arrowhead = none , style=dashed];
3675 -> 1687[style=dashed];

3676 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1748 -> 3676 [arrowhead = none ];
3676 -> 1750;

3677 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1750 -> 3677 [arrowhead = none ];
3677 -> 1751;

3678 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1750 -> 3678 [arrowhead = none ];
3678 -> 1752;

3679 [label="EVAL with clause\nquot(0, s(X11551), s(X11552), 0).\nand substitution\nT1503 -> 0\nX11551 -> s(s(s(0)))\nX11552 -> s(s(s(0)))\nX11535 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1751 -> 3679 [arrowhead = none ];
3679 -> 1753;

3680 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1751 -> 3680 [arrowhead = none ];
3680 -> 1754;

3681 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1752 -> 3681 [arrowhead = none ];
3681 -> 1756;

3682 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1752 -> 3682 [arrowhead = none ];
3682 -> 1757;

3683 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1753 -> 3683 [arrowhead = none ];
3683 -> 1755;

3684 [label="EVAL with clause\nquot(s(X11575), s(X11576), X11577, X11578) :- quot(X11575, X11576, X11577, X11578).\nand substitution\nX11575 -> T1508\nT1503 -> s(T1508)\nX11576 -> s(s(s(0)))\nX11577 -> s(s(s(s(0))))\nX11535 -> X11579\nX11578 -> X11579", fontsize=14, style = filled, fillcolor = lightblue];
1756 -> 3684 [arrowhead = none ];
3684 -> 1758;

3685 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1756 -> 3685 [arrowhead = none ];
3685 -> 1759;

3686 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1757 -> 3686 [arrowhead = none ];
3686 -> 1797;

3687 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1758 -> 3687 [arrowhead = none ];
3687 -> 1760;

3688 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1760 -> 3688 [arrowhead = none ];
3688 -> 1761;

3689 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1760 -> 3689 [arrowhead = none ];
3689 -> 1762;

3690 [label="EVAL with clause\nquot(0, s(X11596), s(X11597), 0).\nand substitution\nT1508 -> 0\nX11596 -> s(s(0))\nX11597 -> s(s(s(0)))\nX11579 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1761 -> 3690 [arrowhead = none ];
3690 -> 1763;

3691 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1761 -> 3691 [arrowhead = none ];
3691 -> 1764;

3692 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1762 -> 3692 [arrowhead = none ];
3692 -> 1766;

3693 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1762 -> 3693 [arrowhead = none ];
3693 -> 1767;

3694 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1763 -> 3694 [arrowhead = none ];
3694 -> 1765;

3695 [label="EVAL with clause\nquot(s(X11620), s(X11621), X11622, X11623) :- quot(X11620, X11621, X11622, X11623).\nand substitution\nX11620 -> T1513\nT1508 -> s(T1513)\nX11621 -> s(s(0))\nX11622 -> s(s(s(s(0))))\nX11579 -> X11624\nX11623 -> X11624", fontsize=14, style = filled, fillcolor = lightblue];
1766 -> 3695 [arrowhead = none ];
3695 -> 1768;

3696 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1766 -> 3696 [arrowhead = none ];
3696 -> 1769;

3697 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1767 -> 3697 [arrowhead = none ];
3697 -> 1796;

3698 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1768 -> 3698 [arrowhead = none ];
3698 -> 1770;

3699 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1770 -> 3699 [arrowhead = none ];
3699 -> 1771;

3700 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1770 -> 3700 [arrowhead = none ];
3700 -> 1772;

3701 [label="EVAL with clause\nquot(0, s(X11641), s(X11642), 0).\nand substitution\nT1513 -> 0\nX11641 -> s(0)\nX11642 -> s(s(s(0)))\nX11624 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1771 -> 3701 [arrowhead = none ];
3701 -> 1773;

3702 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1771 -> 3702 [arrowhead = none ];
3702 -> 1774;

3703 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1772 -> 3703 [arrowhead = none ];
3703 -> 1776;

3704 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1772 -> 3704 [arrowhead = none ];
3704 -> 1777;

3705 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1773 -> 3705 [arrowhead = none ];
3705 -> 1775;

3706 [label="EVAL with clause\nquot(s(X11665), s(X11666), X11667, X11668) :- quot(X11665, X11666, X11667, X11668).\nand substitution\nX11665 -> T1518\nT1513 -> s(T1518)\nX11666 -> s(0)\nX11667 -> s(s(s(s(0))))\nX11624 -> X11669\nX11668 -> X11669", fontsize=14, style = filled, fillcolor = lightblue];
1776 -> 3706 [arrowhead = none ];
3706 -> 1778;

3707 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1776 -> 3707 [arrowhead = none ];
3707 -> 1779;

3708 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1777 -> 3708 [arrowhead = none ];
3708 -> 1795;

3709 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1778 -> 3709 [arrowhead = none ];
3709 -> 1780;

3710 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1780 -> 3710 [arrowhead = none ];
3710 -> 1781;

3711 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1780 -> 3711 [arrowhead = none ];
3711 -> 1782;

3712 [label="EVAL with clause\nquot(0, s(X11686), s(X11687), 0).\nand substitution\nT1518 -> 0\nX11686 -> 0\nX11687 -> s(s(s(0)))\nX11669 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1781 -> 3712 [arrowhead = none ];
3712 -> 1783;

3713 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1781 -> 3713 [arrowhead = none ];
3713 -> 1784;

3714 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1782 -> 3714 [arrowhead = none ];
3714 -> 1786;

3715 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1782 -> 3715 [arrowhead = none ];
3715 -> 1787;

3716 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1783 -> 3716 [arrowhead = none ];
3716 -> 1785;

3717 [label="EVAL with clause\nquot(s(X11710), s(X11711), X11712, X11713) :- quot(X11710, X11711, X11712, X11713).\nand substitution\nX11710 -> T1523\nT1518 -> s(T1523)\nX11711 -> 0\nX11712 -> s(s(s(s(0))))\nX11669 -> X11714\nX11713 -> X11714", fontsize=14, style = filled, fillcolor = lightblue];
1786 -> 3717 [arrowhead = none ];
3717 -> 1788;

3718 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1786 -> 3718 [arrowhead = none ];
3718 -> 1789;

3719 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1787 -> 3719 [arrowhead = none ];
3719 -> 1794;

3720 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1788 -> 3720 [arrowhead = none ];
3720 -> 1790;

3721 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1790 -> 3721 [arrowhead = none ];
3721 -> 1791;

3722 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1791 -> 3722 [arrowhead = none ];
3722 -> 1792;

3723 [label="ONLY EVAL with clause\nquot(X11749, 0, s(X11750), s(X11751)) :- quot(X11749, s(X11750), s(X11750), X11751).\nand substitution\nT1523 -> T1529\nX11749 -> T1529\nX11750 -> s(s(s(0)))\nX11751 -> X11752\nX11714 -> s(X11752)", fontsize=14, style = filled, fillcolor = white];
1792 -> 3723 [arrowhead = none ];
3723 -> 1793;

3724 [label="INSTANCE with matching:\nT1503 -> T1529\nX11535 -> X11752", fontsize=14, style = filled, fillcolor = lightgrey];
1793 -> 3724 [arrowhead = none , style=dashed];
3724 -> 1748[style=dashed];

3725 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1798 -> 3725 [arrowhead = none ];
3725 -> 1800;

3726 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1800 -> 3726 [arrowhead = none ];
3726 -> 1801;

3727 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1800 -> 3727 [arrowhead = none ];
3727 -> 1802;

3728 [label="EVAL with clause\nquot(0, s(X11796), s(X11797), 0).\nand substitution\nT1536 -> 0\nX11796 -> s(s(0))\nX11797 -> s(s(0))\nX11780 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1801 -> 3728 [arrowhead = none ];
3728 -> 1803;

3729 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1801 -> 3729 [arrowhead = none ];
3729 -> 1804;

3730 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1802 -> 3730 [arrowhead = none ];
3730 -> 1806;

3731 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1802 -> 3731 [arrowhead = none ];
3731 -> 1807;

3732 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1803 -> 3732 [arrowhead = none ];
3732 -> 1805;

3733 [label="EVAL with clause\nquot(s(X11820), s(X11821), X11822, X11823) :- quot(X11820, X11821, X11822, X11823).\nand substitution\nX11820 -> T1541\nT1536 -> s(T1541)\nX11821 -> s(s(0))\nX11822 -> s(s(s(0)))\nX11780 -> X11824\nX11823 -> X11824", fontsize=14, style = filled, fillcolor = lightblue];
1806 -> 3733 [arrowhead = none ];
3733 -> 1808;

3734 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1806 -> 3734 [arrowhead = none ];
3734 -> 1809;

3735 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1807 -> 3735 [arrowhead = none ];
3735 -> 1836;

3736 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1808 -> 3736 [arrowhead = none ];
3736 -> 1810;

3737 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1810 -> 3737 [arrowhead = none ];
3737 -> 1811;

3738 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1810 -> 3738 [arrowhead = none ];
3738 -> 1812;

3739 [label="EVAL with clause\nquot(0, s(X11841), s(X11842), 0).\nand substitution\nT1541 -> 0\nX11841 -> s(0)\nX11842 -> s(s(0))\nX11824 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1811 -> 3739 [arrowhead = none ];
3739 -> 1813;

3740 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1811 -> 3740 [arrowhead = none ];
3740 -> 1814;

3741 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1812 -> 3741 [arrowhead = none ];
3741 -> 1816;

3742 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1812 -> 3742 [arrowhead = none ];
3742 -> 1817;

3743 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1813 -> 3743 [arrowhead = none ];
3743 -> 1815;

3744 [label="EVAL with clause\nquot(s(X11865), s(X11866), X11867, X11868) :- quot(X11865, X11866, X11867, X11868).\nand substitution\nX11865 -> T1546\nT1541 -> s(T1546)\nX11866 -> s(0)\nX11867 -> s(s(s(0)))\nX11824 -> X11869\nX11868 -> X11869", fontsize=14, style = filled, fillcolor = lightblue];
1816 -> 3744 [arrowhead = none ];
3744 -> 1818;

3745 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1816 -> 3745 [arrowhead = none ];
3745 -> 1819;

3746 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1817 -> 3746 [arrowhead = none ];
3746 -> 1835;

3747 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1818 -> 3747 [arrowhead = none ];
3747 -> 1820;

3748 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1820 -> 3748 [arrowhead = none ];
3748 -> 1821;

3749 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1820 -> 3749 [arrowhead = none ];
3749 -> 1822;

3750 [label="EVAL with clause\nquot(0, s(X11886), s(X11887), 0).\nand substitution\nT1546 -> 0\nX11886 -> 0\nX11887 -> s(s(0))\nX11869 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1821 -> 3750 [arrowhead = none ];
3750 -> 1823;

3751 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1821 -> 3751 [arrowhead = none ];
3751 -> 1824;

3752 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1822 -> 3752 [arrowhead = none ];
3752 -> 1826;

3753 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1822 -> 3753 [arrowhead = none ];
3753 -> 1827;

3754 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1823 -> 3754 [arrowhead = none ];
3754 -> 1825;

3755 [label="EVAL with clause\nquot(s(X11910), s(X11911), X11912, X11913) :- quot(X11910, X11911, X11912, X11913).\nand substitution\nX11910 -> T1551\nT1546 -> s(T1551)\nX11911 -> 0\nX11912 -> s(s(s(0)))\nX11869 -> X11914\nX11913 -> X11914", fontsize=14, style = filled, fillcolor = lightblue];
1826 -> 3755 [arrowhead = none ];
3755 -> 1828;

3756 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1826 -> 3756 [arrowhead = none ];
3756 -> 1829;

3757 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1827 -> 3757 [arrowhead = none ];
3757 -> 1834;

3758 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1828 -> 3758 [arrowhead = none ];
3758 -> 1830;

3759 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1830 -> 3759 [arrowhead = none ];
3759 -> 1831;

3760 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1831 -> 3760 [arrowhead = none ];
3760 -> 1832;

3761 [label="ONLY EVAL with clause\nquot(X11949, 0, s(X11950), s(X11951)) :- quot(X11949, s(X11950), s(X11950), X11951).\nand substitution\nT1551 -> T1557\nX11949 -> T1557\nX11950 -> s(s(0))\nX11951 -> X11952\nX11914 -> s(X11952)", fontsize=14, style = filled, fillcolor = white];
1832 -> 3761 [arrowhead = none ];
3761 -> 1833;

3762 [label="INSTANCE with matching:\nT1536 -> T1557\nX11780 -> X11952", fontsize=14, style = filled, fillcolor = lightgrey];
1833 -> 3762 [arrowhead = none , style=dashed];
3762 -> 1798[style=dashed];

3763 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1837 -> 3763 [arrowhead = none ];
3763 -> 1839;

3764 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1839 -> 3764 [arrowhead = none ];
3764 -> 1840;

3765 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1839 -> 3765 [arrowhead = none ];
3765 -> 1841;

3766 [label="EVAL with clause\nquot(0, s(X11993), s(X11994), 0).\nand substitution\nT1563 -> 0\nX11993 -> s(0)\nX11994 -> s(0)\nX11977 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1840 -> 3766 [arrowhead = none ];
3766 -> 1842;

3767 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1840 -> 3767 [arrowhead = none ];
3767 -> 1843;

3768 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1841 -> 3768 [arrowhead = none ];
3768 -> 1845;

3769 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1841 -> 3769 [arrowhead = none ];
3769 -> 1846;

3770 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1842 -> 3770 [arrowhead = none ];
3770 -> 1844;

3771 [label="EVAL with clause\nquot(s(X12017), s(X12018), X12019, X12020) :- quot(X12017, X12018, X12019, X12020).\nand substitution\nX12017 -> T1568\nT1563 -> s(T1568)\nX12018 -> s(0)\nX12019 -> s(s(0))\nX11977 -> X12021\nX12020 -> X12021", fontsize=14, style = filled, fillcolor = lightblue];
1845 -> 3771 [arrowhead = none ];
3771 -> 1847;

3772 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1845 -> 3772 [arrowhead = none ];
3772 -> 1848;

3773 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1846 -> 3773 [arrowhead = none ];
3773 -> 1864;

3774 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1847 -> 3774 [arrowhead = none ];
3774 -> 1849;

3775 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1849 -> 3775 [arrowhead = none ];
3775 -> 1850;

3776 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1849 -> 3776 [arrowhead = none ];
3776 -> 1851;

3777 [label="EVAL with clause\nquot(0, s(X12038), s(X12039), 0).\nand substitution\nT1568 -> 0\nX12038 -> 0\nX12039 -> s(0)\nX12021 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1850 -> 3777 [arrowhead = none ];
3777 -> 1852;

3778 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1850 -> 3778 [arrowhead = none ];
3778 -> 1853;

3779 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1851 -> 3779 [arrowhead = none ];
3779 -> 1855;

3780 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1851 -> 3780 [arrowhead = none ];
3780 -> 1856;

3781 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1852 -> 3781 [arrowhead = none ];
3781 -> 1854;

3782 [label="EVAL with clause\nquot(s(X12062), s(X12063), X12064, X12065) :- quot(X12062, X12063, X12064, X12065).\nand substitution\nX12062 -> T1573\nT1568 -> s(T1573)\nX12063 -> 0\nX12064 -> s(s(0))\nX12021 -> X12066\nX12065 -> X12066", fontsize=14, style = filled, fillcolor = lightblue];
1855 -> 3782 [arrowhead = none ];
3782 -> 1857;

3783 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1855 -> 3783 [arrowhead = none ];
3783 -> 1858;

3784 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1856 -> 3784 [arrowhead = none ];
3784 -> 1863;

3785 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1857 -> 3785 [arrowhead = none ];
3785 -> 1859;

3786 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1859 -> 3786 [arrowhead = none ];
3786 -> 1860;

3787 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = white];
1860 -> 3787 [arrowhead = none ];
3787 -> 1861;

3788 [label="ONLY EVAL with clause\nquot(X12101, 0, s(X12102), s(X12103)) :- quot(X12101, s(X12102), s(X12102), X12103).\nand substitution\nT1573 -> T1579\nX12101 -> T1579\nX12102 -> s(0)\nX12103 -> X12104\nX12066 -> s(X12104)", fontsize=14, style = filled, fillcolor = white];
1861 -> 3788 [arrowhead = none ];
3788 -> 1862;

3789 [label="INSTANCE with matching:\nT1563 -> T1579\nX11977 -> X12104", fontsize=14, style = filled, fillcolor = lightgrey];
1862 -> 3789 [arrowhead = none , style=dashed];
3789 -> 1837[style=dashed];

3790 [label="INSTANCE with matching:\nT22 -> T1126\nT20 -> T1122\nX39 -> X9846", fontsize=14, style = filled, fillcolor = lightgrey];
1867 -> 3790 [arrowhead = none , style=dashed];
3790 -> 190[style=dashed];

3791 [label="INSTANCE with matching:\nT250 -> T1123\nT251 -> T1586", fontsize=14, style = filled, fillcolor = lightgrey];
1868 -> 3791 [arrowhead = none , style=dashed];
3791 -> 227[style=dashed];

3792 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1869 -> 3792 [arrowhead = none ];
3792 -> 1870;

3793 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1869 -> 3793 [arrowhead = none ];
3793 -> 1871;

3794 [label="EVAL with clause\npr(X12133, s(0)).\nand substitution\nT1111 -> T1597\nX12133 -> s(T1597)\nT1109 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
1870 -> 3794 [arrowhead = none ];
3794 -> 1872;

3795 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1870 -> 3795 [arrowhead = none ];
3795 -> 1873;

3796 [label="EVAL with clause\npr(X12139, s(s(X12140))) :- ','(not_divides(s(s(X12140)), X12139), pr(X12139, s(X12140))).\nand substitution\nT1111 -> T1602\nX12139 -> s(T1602)\nX12140 -> T1603\nT1109 -> s(T1603)", fontsize=14, style = filled, fillcolor = lightblue];
1871 -> 3796 [arrowhead = none ];
3796 -> 1875;

3797 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
1871 -> 3797 [arrowhead = none ];
3797 -> 1876;

3798 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1872 -> 3798 [arrowhead = none ];
3798 -> 1874;

3799 [label="INSTANCE with matching:\nT1109 -> T1603\nT1111 -> T1602", fontsize=14, style = filled, fillcolor = lightgrey];
1875 -> 3799 [arrowhead = none , style=dashed];
3799 -> 1397[style=dashed];

}

(2) Obligation:

Clauses:

quot67(s(T137), T138, X461) :- quot67(T137, T138, X461).
quot67(0, s(T164), s(0)).
quot67(0, 0, s(s(X565))) :- quot88(X565).
times190(0, T194, 0).
times190(s(T199), T200, X1082) :- times190(T199, T200, X1081).
times190(s(T199), T200, X1082) :- ','(times190(T199, T200, T203), add201(T203, T200, X1082)).
add201(0, T215, s(s(T215))).
add201(s(T220), T221, s(X1112)) :- add201(T220, T221, X1112).
neq236(s(T271), 0).
neq236(0, s(T276)).
neq236(s(T281), s(T282)) :- neq236(T281, T282).
quot313(s(T420), T421, X1654) :- quot313(T420, T421, X1654).
quot313(0, s(s(T451)), s(0)).
quot313(0, s(0), s(s(X1808))) :- quot340(X1808).
quot313(0, 0, s(s(X1842))) :- quot349(X1842).
quot88(0).
quot340(0).
neq191(T232, 0).
neq191(T245, s(0)).
neq191(T250, s(s(T251))) :- neq227(T250, T251).
quot551(s(T614), T615, X3256) :- quot551(T614, T615, X3256).
quot551(0, s(s(s(T651))), s(0)).
quot551(0, s(s(0)), s(s(X3450))) :- quot584(X3450).
quot551(0, s(0), s(s(X3484))) :- quot173(X3484).
quot551(0, 0, s(s(X3508))) :- quot595(X3508).
quot173(0).
quot349(s(X1937)) :- quot88(X1937).
quot584(0).
quot824(s(T814), T815, X5270) :- quot824(T814, T815, X5270).
quot824(0, s(s(s(s(T857)))), s(0)).
quot824(0, s(s(s(0))), s(s(X5504))) :- quot863(X5504).
quot824(0, s(s(0)), s(s(X5538))) :- quot158(X5538).
quot824(0, s(0), s(s(X5562))) :- quot467(X5562).
quot824(0, 0, s(s(X5586))) :- quot876(X5586).
quot158(0).
quot467(s(X2776)) :- quot340(X2776).
quot595(s(X3610)) :- quot349(X3610).
quot863(0).
quot1126(s(T1020), T1021, X7625) :- quot1126(T1020, T1021, X7625).
quot1126(0, s(s(s(s(s(T1069))))), s(0)).
quot1126(0, s(s(s(s(0)))), s(s(X7899))) :- quot1171(X7899).
quot1126(0, s(s(s(0))), s(s(X7933))) :- quot143(X7933).
quot1126(0, s(s(0)), s(s(X7957))) :- quot446(X7957).
quot1126(0, s(0), s(s(X7981))) :- quot740(X7981).
quot1126(0, 0, s(s(s(X8107)))) :- quot876(X8107).
quot143(0).
quot446(0).
quot740(s(X4783)) :- quot173(X4783).
quot876(s(X5688)) :- quot595(X5688).
quot1171(0).
quot1481(0, s(T1287), T1288, 0).
quot1481(s(T1301), s(T1302), T1303, X10279) :- quot1481(T1301, T1302, T1303, X10279).
quot1481(0, 0, T1320, s(0)).
quot1481(s(0), 0, s(T1337), s(0)).
quot1481(s(s(T1346)), 0, s(T1347), s(X10388)) :- quot1419(T1346, T1347, X10388).
quot1481(s(T1352), 0, 0, s(s(X10408))) :- quot1514(T1352, X10408).
quot1419(0, s(T1176), 0).
quot1419(s(0), s(s(T1193)), 0).
quot1419(s(s(0)), s(s(s(T1210))), 0).
quot1419(s(s(s(0))), s(s(s(s(T1227)))), 0).
quot1419(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0).
quot1419(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0).
quot1419(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) :- quot1481(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230).
quot1419(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) :- quot1532(T1368, X10512).
quot1419(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) :- quot1615(T1419, X10901).
quot1419(s(s(s(T1464))), s(s(s(0))), s(X11242)) :- quot1687(T1464, X11242).
quot1419(s(s(T1503)), s(s(0)), s(X11535)) :- quot1748(T1503, X11535).
quot1419(s(T1536), s(0), s(X11780)) :- quot1798(T1536, X11780).
quot1419(T1563, 0, s(X11977)) :- quot1837(T1563, X11977).
quot1514(0, 0).
quot1514(s(T1363), s(X10490)) :- quot1514(T1363, X10490).
quot1532(0, 0).
quot1532(s(0), 0).
quot1532(s(s(0)), 0).
quot1532(s(s(s(0))), 0).
quot1532(s(s(s(s(0)))), 0).
quot1532(s(s(s(s(s(0))))), 0).
quot1532(s(s(s(s(s(s(0)))))), 0).
quot1532(s(s(s(s(s(s(s(T1409))))))), s(X10864)) :- quot1532(T1409, X10864).
quot1615(0, 0).
quot1615(s(0), 0).
quot1615(s(s(0)), 0).
quot1615(s(s(s(0))), 0).
quot1615(s(s(s(s(0)))), 0).
quot1615(s(s(s(s(s(0))))), 0).
quot1615(s(s(s(s(s(s(T1455)))))), s(X11208)) :- quot1615(T1455, X11208).
quot1687(0, 0).
quot1687(s(0), 0).
quot1687(s(s(0)), 0).
quot1687(s(s(s(0))), 0).
quot1687(s(s(s(s(0)))), 0).
quot1687(s(s(s(s(s(T1495))))), s(X11504)) :- quot1687(T1495, X11504).
quot1748(0, 0).
quot1748(s(0), 0).
quot1748(s(s(0)), 0).
quot1748(s(s(s(0))), 0).
quot1748(s(s(s(s(T1529)))), s(X11752)) :- quot1748(T1529, X11752).
quot1798(0, 0).
quot1798(s(0), 0).
quot1798(s(s(0)), 0).
quot1798(s(s(s(T1557))), s(X11952)) :- quot1798(T1557, X11952).
quot1837(0, 0).
quot1837(s(0), 0).
quot1837(s(s(T1579)), s(X12104)) :- quot1837(T1579, X12104).
neq227(T258, 0).
neq227(T263, s(T264)) :- neq236(T263, T264).
p1397(T1109, T1111) :- not_divides1398(T1109, T1111).
p1397(0, T1597) :- not_divides1398(0, T1597).
p1397(s(T1603), T1602) :- ','(not_divides1398(s(T1603), T1602), p1397(T1603, T1602)).
not_divides13(T20) :- div17(T20, X38).
not_divides13(T20) :- ','(div17(T20, T22), times190(T22, T20, X39)).
not_divides13(T20) :- ','(div17(T20, T22), ','(times190(T22, T20, T187), neq191(T20, T187))).
div17(s(s(s(s(s(s(T117)))))), X412) :- quot67(T117, s(s(s(s(s(s(s(T117))))))), X412).
div17(s(s(s(s(s(0))))), s(0)).
div17(s(s(s(s(0)))), s(0)).
div17(s(s(s(0))), s(0)).
div17(s(s(0)), s(X833)) :- quot143(X833).
div17(s(0), s(X910)) :- quot158(X910).
div17(0, s(X987)) :- quot173(X987).
not_divides259(T303) :- div263(T303, X1231).
not_divides259(T303) :- ','(div263(T303, T305), times190(T305, T303, X1232)).
not_divides259(T303) :- ','(div263(T303, T305), ','(times190(T305, T303, T474), neq191(s(T303), T474))).
div263(s(s(s(s(s(s(T400)))))), X1605) :- quot313(T400, s(s(s(s(s(s(s(T400))))))), X1605).
div263(s(s(s(s(s(0))))), s(0)).
div263(s(s(s(s(0)))), s(0)).
div263(s(s(s(0))), s(0)).
div263(s(s(0)), s(0)).
div263(s(0), s(X2493)) :- quot446(X2493).
div263(0, s(X2627)) :- quot467(X2627).
not_divides497(T497) :- div501(T497, X2833).
not_divides497(T497) :- ','(div501(T497, T499), times190(T499, T497, X2834)).
not_divides497(T497) :- ','(div501(T497, T499), ','(times190(T499, T497, T674), neq191(s(s(T497)), T674))).
div501(s(s(s(s(s(s(T594)))))), X3207) :- quot551(T594, s(s(s(s(s(s(s(T594))))))), X3207).
div501(s(s(s(s(s(0))))), s(0)).
div501(s(s(s(s(0)))), s(0)).
div501(s(s(s(0))), s(0)).
div501(s(s(0)), s(0)).
div501(s(0), s(s(X4604))) :- quot584(X4604).
div501(0, s(X4627)) :- quot740(X4627).
not_divides770(T697) :- div774(T697, X4847).
not_divides770(T697) :- ','(div774(T697, T699), times190(T699, T697, X4848)).
not_divides770(T697) :- ','(div774(T697, T699), ','(times190(T699, T697, T880), neq191(s(s(s(T697))), T880))).
div774(s(s(s(s(s(s(T794)))))), X5221) :- quot824(T794, s(s(s(s(s(s(s(T794))))))), X5221).
div774(s(s(s(s(s(0))))), s(0)).
div774(s(s(s(s(0)))), s(0)).
div774(s(s(s(0))), s(0)).
div774(s(s(0)), s(s(X6716))) :- quot863(X6716).
div774(s(0), s(s(X6952))) :- quot158(X6952).
div774(0, s(s(X7138))) :- quot467(X7138).
not_divides1072(T903) :- div1076(T903, X7202).
not_divides1072(T903) :- ','(div1076(T903, T905), times190(T905, T903, X7203)).
not_divides1072(T903) :- ','(div1076(T903, T905), ','(times190(T905, T903, T1092), neq191(s(s(s(s(T903)))), T1092))).
div1076(s(s(s(s(s(s(T1000)))))), X7576) :- quot1126(T1000, s(s(s(s(s(s(s(T1000))))))), X7576).
div1076(s(s(s(s(s(0))))), s(0)).
div1076(s(s(s(s(0)))), s(0)).
div1076(s(s(s(0))), s(s(X9055))) :- quot1171(X9055).
div1076(s(s(0)), s(s(X9348))) :- quot143(X9348).
div1076(s(0), s(s(X9591))) :- quot446(X9591).
div1076(0, s(s(X9777))) :- quot740(X9777).
not_divides1398(T1122, T1123) :- div1402(T1123, T1122, X9845).
not_divides1398(T1122, T1123) :- ','(div1402(T1123, T1122, T1126), times190(T1126, T1122, X9846)).
not_divides1398(T1122, T1123) :- ','(div1402(T1123, T1122, T1126), ','(times190(T1126, T1122, T1586), neq227(T1123, T1586))).
div1402(0, T1159, 0).
div1402(s(T1168), T1169, X9960) :- quot1419(T1168, T1169, X9960).
prime1(s(s(0))).
prime1(s(s(s(T14)))) :- not_divides13(T14).
prime1(s(s(s(0)))) :- not_divides13(0).
prime1(s(s(s(s(T297))))) :- ','(not_divides13(s(T297)), not_divides259(T297)).
prime1(s(s(s(s(0))))) :- ','(not_divides13(s(0)), not_divides259(0)).
prime1(s(s(s(s(s(T491)))))) :- ','(not_divides13(s(s(T491))), ','(not_divides259(s(T491)), not_divides497(T491))).
prime1(s(s(s(s(s(0)))))) :- ','(not_divides13(s(s(0))), ','(not_divides259(s(0)), not_divides497(0))).
prime1(s(s(s(s(s(s(T691))))))) :- ','(not_divides13(s(s(s(T691)))), ','(not_divides259(s(s(T691))), ','(not_divides497(s(T691)), not_divides770(T691)))).
prime1(s(s(s(s(s(s(0))))))) :- ','(not_divides13(s(s(s(0)))), ','(not_divides259(s(s(0))), ','(not_divides497(s(0)), not_divides770(0)))).
prime1(s(s(s(s(s(s(s(T897)))))))) :- ','(not_divides13(s(s(s(s(T897))))), ','(not_divides259(s(s(s(T897)))), ','(not_divides497(s(s(T897))), ','(not_divides770(s(T897)), not_divides1072(T897))))).
prime1(s(s(s(s(s(s(s(0)))))))) :- ','(not_divides13(s(s(s(s(0))))), ','(not_divides259(s(s(s(0)))), ','(not_divides497(s(s(0))), ','(not_divides770(s(0)), not_divides1072(0))))).
prime1(s(s(s(s(s(s(s(s(T1109))))))))) :- ','(not_divides13(s(s(s(s(s(T1109)))))), ','(not_divides259(s(s(s(s(T1109))))), ','(not_divides497(s(s(s(T1109)))), ','(not_divides770(s(s(T1109))), ','(not_divides1072(s(T1109)), p1397(T1109, s(s(s(s(s(s(s(T1109))))))))))))).

Queries:

prime1(g).

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
prime1_in: (b)
not_divides13_in: (b)
div17_in: (b,f)
quot67_in: (b,b,f)
times190_in: (b,b,f)
add201_in: (f,b,f)
neq191_in: (b,f)
neq227_in: (b,f)
neq236_in: (b,f)
not_divides259_in: (b)
div263_in: (b,f)
quot313_in: (b,b,f)
quot349_in: (f)
quot467_in: (f)
not_divides497_in: (b)
div501_in: (b,f)
quot551_in: (b,b,f)
quot595_in: (f)
quot740_in: (f)
not_divides770_in: (b)
div774_in: (b,f)
quot824_in: (b,b,f)
quot876_in: (f)
not_divides1072_in: (b)
div1076_in: (b,f)
quot1126_in: (b,b,f)
p1397_in: (b,b)
not_divides1398_in: (b,b)
div1402_in: (b,b,f)
quot1419_in: (b,b,f)
quot1481_in: (b,b,b,f)
quot1532_in: (b,f)
quot1615_in: (b,f)
quot1687_in: (b,f)
quot1748_in: (b,f)
quot1798_in: (b,f)
quot1837_in: (b,f)
quot1514_in: (b,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

Pi-finite rewrite system:
The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)

(5) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
Pi DP problem:
The TRS P consists of the following rules:

PRIME1_IN_G(s(s(s(T14)))) → U104_G(T14, not_divides13_in_g(T14))
PRIME1_IN_G(s(s(s(T14)))) → NOT_DIVIDES13_IN_G(T14)
NOT_DIVIDES13_IN_G(T20) → U54_G(T20, div17_in_ga(T20, X38))
NOT_DIVIDES13_IN_G(T20) → DIV17_IN_GA(T20, X38)
DIV17_IN_GA(s(s(s(s(s(s(T117)))))), X412) → U59_GA(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
DIV17_IN_GA(s(s(s(s(s(s(T117)))))), X412) → QUOT67_IN_GGA(T117, s(s(s(s(s(s(s(T117))))))), X412)
QUOT67_IN_GGA(s(T137), T138, X461) → U1_GGA(T137, T138, X461, quot67_in_gga(T137, T138, X461))
QUOT67_IN_GGA(s(T137), T138, X461) → QUOT67_IN_GGA(T137, T138, X461)
QUOT67_IN_GGA(0, 0, s(s(X565))) → U2_GGA(X565, quot88_in_a(X565))
QUOT67_IN_GGA(0, 0, s(s(X565))) → QUOT88_IN_A(X565)
DIV17_IN_GA(s(s(0)), s(X833)) → U60_GA(X833, quot143_in_a(X833))
DIV17_IN_GA(s(s(0)), s(X833)) → QUOT143_IN_A(X833)
DIV17_IN_GA(s(0), s(X910)) → U61_GA(X910, quot158_in_a(X910))
DIV17_IN_GA(s(0), s(X910)) → QUOT158_IN_A(X910)
DIV17_IN_GA(0, s(X987)) → U62_GA(X987, quot173_in_a(X987))
DIV17_IN_GA(0, s(X987)) → QUOT173_IN_A(X987)
NOT_DIVIDES13_IN_G(T20) → U55_G(T20, div17_in_ga(T20, T22))
U55_G(T20, div17_out_ga(T20, T22)) → U56_G(T20, times190_in_gga(T22, T20, X39))
U55_G(T20, div17_out_ga(T20, T22)) → TIMES190_IN_GGA(T22, T20, X39)
TIMES190_IN_GGA(s(T199), T200, X1082) → U3_GGA(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
TIMES190_IN_GGA(s(T199), T200, X1082) → TIMES190_IN_GGA(T199, T200, X1081)
TIMES190_IN_GGA(s(T199), T200, X1082) → U4_GGA(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_GGA(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_GGA(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
U4_GGA(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → ADD201_IN_AGA(T203, T200, X1082)
ADD201_IN_AGA(s(T220), T221, s(X1112)) → U6_AGA(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
ADD201_IN_AGA(s(T220), T221, s(X1112)) → ADD201_IN_AGA(T220, T221, X1112)
U55_G(T20, div17_out_ga(T20, T22)) → U57_G(T20, times190_in_gga(T22, T20, T187))
U57_G(T20, times190_out_gga(T22, T20, T187)) → U58_G(T20, neq191_in_ga(T20, T187))
U57_G(T20, times190_out_gga(T22, T20, T187)) → NEQ191_IN_GA(T20, T187)
NEQ191_IN_GA(T250, s(s(T251))) → U11_GA(T250, T251, neq227_in_ga(T250, T251))
NEQ191_IN_GA(T250, s(s(T251))) → NEQ227_IN_GA(T250, T251)
NEQ227_IN_GA(T263, s(T264)) → U49_GA(T263, T264, neq236_in_ga(T263, T264))
NEQ227_IN_GA(T263, s(T264)) → NEQ236_IN_GA(T263, T264)
NEQ236_IN_GA(s(T281), s(T282)) → U7_GA(T281, T282, neq236_in_ga(T281, T282))
NEQ236_IN_GA(s(T281), s(T282)) → NEQ236_IN_GA(T281, T282)
PRIME1_IN_G(s(s(s(0)))) → U105_G(not_divides13_in_g(0))
PRIME1_IN_G(s(s(s(0)))) → NOT_DIVIDES13_IN_G(0)
PRIME1_IN_G(s(s(s(s(T297))))) → U106_G(T297, not_divides13_in_g(s(T297)))
PRIME1_IN_G(s(s(s(s(T297))))) → NOT_DIVIDES13_IN_G(s(T297))
U106_G(T297, not_divides13_out_g(s(T297))) → U107_G(T297, not_divides259_in_g(T297))
U106_G(T297, not_divides13_out_g(s(T297))) → NOT_DIVIDES259_IN_G(T297)
NOT_DIVIDES259_IN_G(T303) → U63_G(T303, div263_in_ga(T303, X1231))
NOT_DIVIDES259_IN_G(T303) → DIV263_IN_GA(T303, X1231)
DIV263_IN_GA(s(s(s(s(s(s(T400)))))), X1605) → U68_GA(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
DIV263_IN_GA(s(s(s(s(s(s(T400)))))), X1605) → QUOT313_IN_GGA(T400, s(s(s(s(s(s(s(T400))))))), X1605)
QUOT313_IN_GGA(s(T420), T421, X1654) → U8_GGA(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
QUOT313_IN_GGA(s(T420), T421, X1654) → QUOT313_IN_GGA(T420, T421, X1654)
QUOT313_IN_GGA(0, s(0), s(s(X1808))) → U9_GGA(X1808, quot340_in_a(X1808))
QUOT313_IN_GGA(0, s(0), s(s(X1808))) → QUOT340_IN_A(X1808)
QUOT313_IN_GGA(0, 0, s(s(X1842))) → U10_GGA(X1842, quot349_in_a(X1842))
QUOT313_IN_GGA(0, 0, s(s(X1842))) → QUOT349_IN_A(X1842)
QUOT349_IN_A(s(X1937)) → U16_A(X1937, quot88_in_a(X1937))
QUOT349_IN_A(s(X1937)) → QUOT88_IN_A(X1937)
DIV263_IN_GA(s(0), s(X2493)) → U69_GA(X2493, quot446_in_a(X2493))
DIV263_IN_GA(s(0), s(X2493)) → QUOT446_IN_A(X2493)
DIV263_IN_GA(0, s(X2627)) → U70_GA(X2627, quot467_in_a(X2627))
DIV263_IN_GA(0, s(X2627)) → QUOT467_IN_A(X2627)
QUOT467_IN_A(s(X2776)) → U22_A(X2776, quot340_in_a(X2776))
QUOT467_IN_A(s(X2776)) → QUOT340_IN_A(X2776)
NOT_DIVIDES259_IN_G(T303) → U64_G(T303, div263_in_ga(T303, T305))
U64_G(T303, div263_out_ga(T303, T305)) → U65_G(T303, times190_in_gga(T305, T303, X1232))
U64_G(T303, div263_out_ga(T303, T305)) → TIMES190_IN_GGA(T305, T303, X1232)
U64_G(T303, div263_out_ga(T303, T305)) → U66_G(T303, times190_in_gga(T305, T303, T474))
U66_G(T303, times190_out_gga(T305, T303, T474)) → U67_G(T303, neq191_in_ga(s(T303), T474))
U66_G(T303, times190_out_gga(T305, T303, T474)) → NEQ191_IN_GA(s(T303), T474)
PRIME1_IN_G(s(s(s(s(0))))) → U108_G(not_divides13_in_g(s(0)))
PRIME1_IN_G(s(s(s(s(0))))) → NOT_DIVIDES13_IN_G(s(0))
U108_G(not_divides13_out_g(s(0))) → U109_G(not_divides259_in_g(0))
U108_G(not_divides13_out_g(s(0))) → NOT_DIVIDES259_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(T491)))))) → U110_G(T491, not_divides13_in_g(s(s(T491))))
PRIME1_IN_G(s(s(s(s(s(T491)))))) → NOT_DIVIDES13_IN_G(s(s(T491)))
U110_G(T491, not_divides13_out_g(s(s(T491)))) → U111_G(T491, not_divides259_in_g(s(T491)))
U110_G(T491, not_divides13_out_g(s(s(T491)))) → NOT_DIVIDES259_IN_G(s(T491))
U111_G(T491, not_divides259_out_g(s(T491))) → U112_G(T491, not_divides497_in_g(T491))
U111_G(T491, not_divides259_out_g(s(T491))) → NOT_DIVIDES497_IN_G(T491)
NOT_DIVIDES497_IN_G(T497) → U71_G(T497, div501_in_ga(T497, X2833))
NOT_DIVIDES497_IN_G(T497) → DIV501_IN_GA(T497, X2833)
DIV501_IN_GA(s(s(s(s(s(s(T594)))))), X3207) → U76_GA(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
DIV501_IN_GA(s(s(s(s(s(s(T594)))))), X3207) → QUOT551_IN_GGA(T594, s(s(s(s(s(s(s(T594))))))), X3207)
QUOT551_IN_GGA(s(T614), T615, X3256) → U12_GGA(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
QUOT551_IN_GGA(s(T614), T615, X3256) → QUOT551_IN_GGA(T614, T615, X3256)
QUOT551_IN_GGA(0, s(s(0)), s(s(X3450))) → U13_GGA(X3450, quot584_in_a(X3450))
QUOT551_IN_GGA(0, s(s(0)), s(s(X3450))) → QUOT584_IN_A(X3450)
QUOT551_IN_GGA(0, s(0), s(s(X3484))) → U14_GGA(X3484, quot173_in_a(X3484))
QUOT551_IN_GGA(0, s(0), s(s(X3484))) → QUOT173_IN_A(X3484)
QUOT551_IN_GGA(0, 0, s(s(X3508))) → U15_GGA(X3508, quot595_in_a(X3508))
QUOT551_IN_GGA(0, 0, s(s(X3508))) → QUOT595_IN_A(X3508)
QUOT595_IN_A(s(X3610)) → U23_A(X3610, quot349_in_a(X3610))
QUOT595_IN_A(s(X3610)) → QUOT349_IN_A(X3610)
DIV501_IN_GA(s(0), s(s(X4604))) → U77_GA(X4604, quot584_in_a(X4604))
DIV501_IN_GA(s(0), s(s(X4604))) → QUOT584_IN_A(X4604)
DIV501_IN_GA(0, s(X4627)) → U78_GA(X4627, quot740_in_a(X4627))
DIV501_IN_GA(0, s(X4627)) → QUOT740_IN_A(X4627)
QUOT740_IN_A(s(X4783)) → U30_A(X4783, quot173_in_a(X4783))
QUOT740_IN_A(s(X4783)) → QUOT173_IN_A(X4783)
NOT_DIVIDES497_IN_G(T497) → U72_G(T497, div501_in_ga(T497, T499))
U72_G(T497, div501_out_ga(T497, T499)) → U73_G(T497, times190_in_gga(T499, T497, X2834))
U72_G(T497, div501_out_ga(T497, T499)) → TIMES190_IN_GGA(T499, T497, X2834)
U72_G(T497, div501_out_ga(T497, T499)) → U74_G(T497, times190_in_gga(T499, T497, T674))
U74_G(T497, times190_out_gga(T499, T497, T674)) → U75_G(T497, neq191_in_ga(s(s(T497)), T674))
U74_G(T497, times190_out_gga(T499, T497, T674)) → NEQ191_IN_GA(s(s(T497)), T674)
PRIME1_IN_G(s(s(s(s(s(0)))))) → U113_G(not_divides13_in_g(s(s(0))))
PRIME1_IN_G(s(s(s(s(s(0)))))) → NOT_DIVIDES13_IN_G(s(s(0)))
U113_G(not_divides13_out_g(s(s(0)))) → U114_G(not_divides259_in_g(s(0)))
U113_G(not_divides13_out_g(s(s(0)))) → NOT_DIVIDES259_IN_G(s(0))
U114_G(not_divides259_out_g(s(0))) → U115_G(not_divides497_in_g(0))
U114_G(not_divides259_out_g(s(0))) → NOT_DIVIDES497_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(s(T691))))))) → U116_G(T691, not_divides13_in_g(s(s(s(T691)))))
PRIME1_IN_G(s(s(s(s(s(s(T691))))))) → NOT_DIVIDES13_IN_G(s(s(s(T691))))
U116_G(T691, not_divides13_out_g(s(s(s(T691))))) → U117_G(T691, not_divides259_in_g(s(s(T691))))
U116_G(T691, not_divides13_out_g(s(s(s(T691))))) → NOT_DIVIDES259_IN_G(s(s(T691)))
U117_G(T691, not_divides259_out_g(s(s(T691)))) → U118_G(T691, not_divides497_in_g(s(T691)))
U117_G(T691, not_divides259_out_g(s(s(T691)))) → NOT_DIVIDES497_IN_G(s(T691))
U118_G(T691, not_divides497_out_g(s(T691))) → U119_G(T691, not_divides770_in_g(T691))
U118_G(T691, not_divides497_out_g(s(T691))) → NOT_DIVIDES770_IN_G(T691)
NOT_DIVIDES770_IN_G(T697) → U79_G(T697, div774_in_ga(T697, X4847))
NOT_DIVIDES770_IN_G(T697) → DIV774_IN_GA(T697, X4847)
DIV774_IN_GA(s(s(s(s(s(s(T794)))))), X5221) → U84_GA(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
DIV774_IN_GA(s(s(s(s(s(s(T794)))))), X5221) → QUOT824_IN_GGA(T794, s(s(s(s(s(s(s(T794))))))), X5221)
QUOT824_IN_GGA(s(T814), T815, X5270) → U17_GGA(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
QUOT824_IN_GGA(s(T814), T815, X5270) → QUOT824_IN_GGA(T814, T815, X5270)
QUOT824_IN_GGA(0, s(s(s(0))), s(s(X5504))) → U18_GGA(X5504, quot863_in_a(X5504))
QUOT824_IN_GGA(0, s(s(s(0))), s(s(X5504))) → QUOT863_IN_A(X5504)
QUOT824_IN_GGA(0, s(s(0)), s(s(X5538))) → U19_GGA(X5538, quot158_in_a(X5538))
QUOT824_IN_GGA(0, s(s(0)), s(s(X5538))) → QUOT158_IN_A(X5538)
QUOT824_IN_GGA(0, s(0), s(s(X5562))) → U20_GGA(X5562, quot467_in_a(X5562))
QUOT824_IN_GGA(0, s(0), s(s(X5562))) → QUOT467_IN_A(X5562)
QUOT824_IN_GGA(0, 0, s(s(X5586))) → U21_GGA(X5586, quot876_in_a(X5586))
QUOT824_IN_GGA(0, 0, s(s(X5586))) → QUOT876_IN_A(X5586)
QUOT876_IN_A(s(X5688)) → U31_A(X5688, quot595_in_a(X5688))
QUOT876_IN_A(s(X5688)) → QUOT595_IN_A(X5688)
DIV774_IN_GA(s(s(0)), s(s(X6716))) → U85_GA(X6716, quot863_in_a(X6716))
DIV774_IN_GA(s(s(0)), s(s(X6716))) → QUOT863_IN_A(X6716)
DIV774_IN_GA(s(0), s(s(X6952))) → U86_GA(X6952, quot158_in_a(X6952))
DIV774_IN_GA(s(0), s(s(X6952))) → QUOT158_IN_A(X6952)
DIV774_IN_GA(0, s(s(X7138))) → U87_GA(X7138, quot467_in_a(X7138))
DIV774_IN_GA(0, s(s(X7138))) → QUOT467_IN_A(X7138)
NOT_DIVIDES770_IN_G(T697) → U80_G(T697, div774_in_ga(T697, T699))
U80_G(T697, div774_out_ga(T697, T699)) → U81_G(T697, times190_in_gga(T699, T697, X4848))
U80_G(T697, div774_out_ga(T697, T699)) → TIMES190_IN_GGA(T699, T697, X4848)
U80_G(T697, div774_out_ga(T697, T699)) → U82_G(T697, times190_in_gga(T699, T697, T880))
U82_G(T697, times190_out_gga(T699, T697, T880)) → U83_G(T697, neq191_in_ga(s(s(s(T697))), T880))
U82_G(T697, times190_out_gga(T699, T697, T880)) → NEQ191_IN_GA(s(s(s(T697))), T880)
PRIME1_IN_G(s(s(s(s(s(s(0))))))) → U120_G(not_divides13_in_g(s(s(s(0)))))
PRIME1_IN_G(s(s(s(s(s(s(0))))))) → NOT_DIVIDES13_IN_G(s(s(s(0))))
U120_G(not_divides13_out_g(s(s(s(0))))) → U121_G(not_divides259_in_g(s(s(0))))
U120_G(not_divides13_out_g(s(s(s(0))))) → NOT_DIVIDES259_IN_G(s(s(0)))
U121_G(not_divides259_out_g(s(s(0)))) → U122_G(not_divides497_in_g(s(0)))
U121_G(not_divides259_out_g(s(s(0)))) → NOT_DIVIDES497_IN_G(s(0))
U122_G(not_divides497_out_g(s(0))) → U123_G(not_divides770_in_g(0))
U122_G(not_divides497_out_g(s(0))) → NOT_DIVIDES770_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(s(s(T897)))))))) → U124_G(T897, not_divides13_in_g(s(s(s(s(T897))))))
PRIME1_IN_G(s(s(s(s(s(s(s(T897)))))))) → NOT_DIVIDES13_IN_G(s(s(s(s(T897)))))
U124_G(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_G(T897, not_divides259_in_g(s(s(s(T897)))))
U124_G(T897, not_divides13_out_g(s(s(s(s(T897)))))) → NOT_DIVIDES259_IN_G(s(s(s(T897))))
U125_G(T897, not_divides259_out_g(s(s(s(T897))))) → U126_G(T897, not_divides497_in_g(s(s(T897))))
U125_G(T897, not_divides259_out_g(s(s(s(T897))))) → NOT_DIVIDES497_IN_G(s(s(T897)))
U126_G(T897, not_divides497_out_g(s(s(T897)))) → U127_G(T897, not_divides770_in_g(s(T897)))
U126_G(T897, not_divides497_out_g(s(s(T897)))) → NOT_DIVIDES770_IN_G(s(T897))
U127_G(T897, not_divides770_out_g(s(T897))) → U128_G(T897, not_divides1072_in_g(T897))
U127_G(T897, not_divides770_out_g(s(T897))) → NOT_DIVIDES1072_IN_G(T897)
NOT_DIVIDES1072_IN_G(T903) → U88_G(T903, div1076_in_ga(T903, X7202))
NOT_DIVIDES1072_IN_G(T903) → DIV1076_IN_GA(T903, X7202)
DIV1076_IN_GA(s(s(s(s(s(s(T1000)))))), X7576) → U93_GA(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
DIV1076_IN_GA(s(s(s(s(s(s(T1000)))))), X7576) → QUOT1126_IN_GGA(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)
QUOT1126_IN_GGA(s(T1020), T1021, X7625) → U24_GGA(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
QUOT1126_IN_GGA(s(T1020), T1021, X7625) → QUOT1126_IN_GGA(T1020, T1021, X7625)
QUOT1126_IN_GGA(0, s(s(s(s(0)))), s(s(X7899))) → U25_GGA(X7899, quot1171_in_a(X7899))
QUOT1126_IN_GGA(0, s(s(s(s(0)))), s(s(X7899))) → QUOT1171_IN_A(X7899)
QUOT1126_IN_GGA(0, s(s(s(0))), s(s(X7933))) → U26_GGA(X7933, quot143_in_a(X7933))
QUOT1126_IN_GGA(0, s(s(s(0))), s(s(X7933))) → QUOT143_IN_A(X7933)
QUOT1126_IN_GGA(0, s(s(0)), s(s(X7957))) → U27_GGA(X7957, quot446_in_a(X7957))
QUOT1126_IN_GGA(0, s(s(0)), s(s(X7957))) → QUOT446_IN_A(X7957)
QUOT1126_IN_GGA(0, s(0), s(s(X7981))) → U28_GGA(X7981, quot740_in_a(X7981))
QUOT1126_IN_GGA(0, s(0), s(s(X7981))) → QUOT740_IN_A(X7981)
QUOT1126_IN_GGA(0, 0, s(s(s(X8107)))) → U29_GGA(X8107, quot876_in_a(X8107))
QUOT1126_IN_GGA(0, 0, s(s(s(X8107)))) → QUOT876_IN_A(X8107)
DIV1076_IN_GA(s(s(s(0))), s(s(X9055))) → U94_GA(X9055, quot1171_in_a(X9055))
DIV1076_IN_GA(s(s(s(0))), s(s(X9055))) → QUOT1171_IN_A(X9055)
DIV1076_IN_GA(s(s(0)), s(s(X9348))) → U95_GA(X9348, quot143_in_a(X9348))
DIV1076_IN_GA(s(s(0)), s(s(X9348))) → QUOT143_IN_A(X9348)
DIV1076_IN_GA(s(0), s(s(X9591))) → U96_GA(X9591, quot446_in_a(X9591))
DIV1076_IN_GA(s(0), s(s(X9591))) → QUOT446_IN_A(X9591)
DIV1076_IN_GA(0, s(s(X9777))) → U97_GA(X9777, quot740_in_a(X9777))
DIV1076_IN_GA(0, s(s(X9777))) → QUOT740_IN_A(X9777)
NOT_DIVIDES1072_IN_G(T903) → U89_G(T903, div1076_in_ga(T903, T905))
U89_G(T903, div1076_out_ga(T903, T905)) → U90_G(T903, times190_in_gga(T905, T903, X7203))
U89_G(T903, div1076_out_ga(T903, T905)) → TIMES190_IN_GGA(T905, T903, X7203)
U89_G(T903, div1076_out_ga(T903, T905)) → U91_G(T903, times190_in_gga(T905, T903, T1092))
U91_G(T903, times190_out_gga(T905, T903, T1092)) → U92_G(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U91_G(T903, times190_out_gga(T905, T903, T1092)) → NEQ191_IN_GA(s(s(s(s(T903)))), T1092)
PRIME1_IN_G(s(s(s(s(s(s(s(0)))))))) → U129_G(not_divides13_in_g(s(s(s(s(0))))))
PRIME1_IN_G(s(s(s(s(s(s(s(0)))))))) → NOT_DIVIDES13_IN_G(s(s(s(s(0)))))
U129_G(not_divides13_out_g(s(s(s(s(0)))))) → U130_G(not_divides259_in_g(s(s(s(0)))))
U129_G(not_divides13_out_g(s(s(s(s(0)))))) → NOT_DIVIDES259_IN_G(s(s(s(0))))
U130_G(not_divides259_out_g(s(s(s(0))))) → U131_G(not_divides497_in_g(s(s(0))))
U130_G(not_divides259_out_g(s(s(s(0))))) → NOT_DIVIDES497_IN_G(s(s(0)))
U131_G(not_divides497_out_g(s(s(0)))) → U132_G(not_divides770_in_g(s(0)))
U131_G(not_divides497_out_g(s(s(0)))) → NOT_DIVIDES770_IN_G(s(0))
U132_G(not_divides770_out_g(s(0))) → U133_G(not_divides1072_in_g(0))
U132_G(not_divides770_out_g(s(0))) → NOT_DIVIDES1072_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(s(s(s(T1109))))))))) → U134_G(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
PRIME1_IN_G(s(s(s(s(s(s(s(s(T1109))))))))) → NOT_DIVIDES13_IN_G(s(s(s(s(s(T1109))))))
U134_G(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_G(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U134_G(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → NOT_DIVIDES259_IN_G(s(s(s(s(T1109)))))
U135_G(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_G(T1109, not_divides497_in_g(s(s(s(T1109)))))
U135_G(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → NOT_DIVIDES497_IN_G(s(s(s(T1109))))
U136_G(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_G(T1109, not_divides770_in_g(s(s(T1109))))
U136_G(T1109, not_divides497_out_g(s(s(s(T1109))))) → NOT_DIVIDES770_IN_G(s(s(T1109)))
U137_G(T1109, not_divides770_out_g(s(s(T1109)))) → U138_G(T1109, not_divides1072_in_g(s(T1109)))
U137_G(T1109, not_divides770_out_g(s(s(T1109)))) → NOT_DIVIDES1072_IN_G(s(T1109))
U138_G(T1109, not_divides1072_out_g(s(T1109))) → U139_G(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
U138_G(T1109, not_divides1072_out_g(s(T1109))) → P1397_IN_GG(T1109, s(s(s(s(s(s(s(T1109))))))))
P1397_IN_GG(T1109, T1111) → U50_GG(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
P1397_IN_GG(T1109, T1111) → NOT_DIVIDES1398_IN_GG(T1109, T1111)
NOT_DIVIDES1398_IN_GG(T1122, T1123) → U98_GG(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
NOT_DIVIDES1398_IN_GG(T1122, T1123) → DIV1402_IN_GGA(T1123, T1122, X9845)
DIV1402_IN_GGA(s(T1168), T1169, X9960) → U103_GGA(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
DIV1402_IN_GGA(s(T1168), T1169, X9960) → QUOT1419_IN_GGA(T1168, T1169, X9960)
QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_GGA(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → QUOT1481_IN_GGGA(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)
QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303, X10279) → U32_GGGA(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303, X10279) → QUOT1481_IN_GGGA(T1301, T1302, T1303, X10279)
QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_GGGA(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347), s(X10388)) → QUOT1419_IN_GGA(T1346, T1347, X10388)
QUOT1419_IN_GGA(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_GGA(T1368, X10512, quot1532_in_ga(T1368, X10512))
QUOT1419_IN_GGA(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → QUOT1532_IN_GA(T1368, X10512)
QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_GA(T1409, X10864, quot1532_in_ga(T1409, X10864))
QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → QUOT1532_IN_GA(T1409, X10864)
QUOT1419_IN_GGA(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_GGA(T1419, X10901, quot1615_in_ga(T1419, X10901))
QUOT1419_IN_GGA(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → QUOT1615_IN_GA(T1419, X10901)
QUOT1615_IN_GA(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_GA(T1455, X11208, quot1615_in_ga(T1455, X11208))
QUOT1615_IN_GA(s(s(s(s(s(s(T1455)))))), s(X11208)) → QUOT1615_IN_GA(T1455, X11208)
QUOT1419_IN_GGA(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_GGA(T1464, X11242, quot1687_in_ga(T1464, X11242))
QUOT1419_IN_GGA(s(s(s(T1464))), s(s(s(0))), s(X11242)) → QUOT1687_IN_GA(T1464, X11242)
QUOT1687_IN_GA(s(s(s(s(s(T1495))))), s(X11504)) → U45_GA(T1495, X11504, quot1687_in_ga(T1495, X11504))
QUOT1687_IN_GA(s(s(s(s(s(T1495))))), s(X11504)) → QUOT1687_IN_GA(T1495, X11504)
QUOT1419_IN_GGA(s(s(T1503)), s(s(0)), s(X11535)) → U39_GGA(T1503, X11535, quot1748_in_ga(T1503, X11535))
QUOT1419_IN_GGA(s(s(T1503)), s(s(0)), s(X11535)) → QUOT1748_IN_GA(T1503, X11535)
QUOT1748_IN_GA(s(s(s(s(T1529)))), s(X11752)) → U46_GA(T1529, X11752, quot1748_in_ga(T1529, X11752))
QUOT1748_IN_GA(s(s(s(s(T1529)))), s(X11752)) → QUOT1748_IN_GA(T1529, X11752)
QUOT1419_IN_GGA(s(T1536), s(0), s(X11780)) → U40_GGA(T1536, X11780, quot1798_in_ga(T1536, X11780))
QUOT1419_IN_GGA(s(T1536), s(0), s(X11780)) → QUOT1798_IN_GA(T1536, X11780)
QUOT1798_IN_GA(s(s(s(T1557))), s(X11952)) → U47_GA(T1557, X11952, quot1798_in_ga(T1557, X11952))
QUOT1798_IN_GA(s(s(s(T1557))), s(X11952)) → QUOT1798_IN_GA(T1557, X11952)
QUOT1419_IN_GGA(T1563, 0, s(X11977)) → U41_GGA(T1563, X11977, quot1837_in_ga(T1563, X11977))
QUOT1419_IN_GGA(T1563, 0, s(X11977)) → QUOT1837_IN_GA(T1563, X11977)
QUOT1837_IN_GA(s(s(T1579)), s(X12104)) → U48_GA(T1579, X12104, quot1837_in_ga(T1579, X12104))
QUOT1837_IN_GA(s(s(T1579)), s(X12104)) → QUOT1837_IN_GA(T1579, X12104)
QUOT1481_IN_GGGA(s(T1352), 0, 0, s(s(X10408))) → U34_GGGA(T1352, X10408, quot1514_in_ga(T1352, X10408))
QUOT1481_IN_GGGA(s(T1352), 0, 0, s(s(X10408))) → QUOT1514_IN_GA(T1352, X10408)
QUOT1514_IN_GA(s(T1363), s(X10490)) → U42_GA(T1363, X10490, quot1514_in_ga(T1363, X10490))
QUOT1514_IN_GA(s(T1363), s(X10490)) → QUOT1514_IN_GA(T1363, X10490)
NOT_DIVIDES1398_IN_GG(T1122, T1123) → U99_GG(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_GG(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_GG(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U99_GG(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → TIMES190_IN_GGA(T1126, T1122, X9846)
U99_GG(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_GG(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_GG(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_GG(T1122, T1123, neq227_in_ga(T1123, T1586))
U101_GG(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → NEQ227_IN_GA(T1123, T1586)
P1397_IN_GG(0, T1597) → U51_GG(T1597, not_divides1398_in_gg(0, T1597))
P1397_IN_GG(0, T1597) → NOT_DIVIDES1398_IN_GG(0, T1597)
P1397_IN_GG(s(T1603), T1602) → U52_GG(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
P1397_IN_GG(s(T1603), T1602) → NOT_DIVIDES1398_IN_GG(s(T1603), T1602)
U52_GG(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_GG(T1603, T1602, p1397_in_gg(T1603, T1602))
U52_GG(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → P1397_IN_GG(T1603, T1602)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
PRIME1_IN_G(x1)  =  PRIME1_IN_G(x1)
U104_G(x1, x2)  =  U104_G(x1, x2)
NOT_DIVIDES13_IN_G(x1)  =  NOT_DIVIDES13_IN_G(x1)
U54_G(x1, x2)  =  U54_G(x1, x2)
DIV17_IN_GA(x1, x2)  =  DIV17_IN_GA(x1)
U59_GA(x1, x2, x3)  =  U59_GA(x1, x3)
QUOT67_IN_GGA(x1, x2, x3)  =  QUOT67_IN_GGA(x1, x2)
U1_GGA(x1, x2, x3, x4)  =  U1_GGA(x1, x2, x4)
U2_GGA(x1, x2)  =  U2_GGA(x2)
QUOT88_IN_A(x1)  =  QUOT88_IN_A
U60_GA(x1, x2)  =  U60_GA(x2)
QUOT143_IN_A(x1)  =  QUOT143_IN_A
U61_GA(x1, x2)  =  U61_GA(x2)
QUOT158_IN_A(x1)  =  QUOT158_IN_A
U62_GA(x1, x2)  =  U62_GA(x2)
QUOT173_IN_A(x1)  =  QUOT173_IN_A
U55_G(x1, x2)  =  U55_G(x1, x2)
U56_G(x1, x2)  =  U56_G(x1, x2)
TIMES190_IN_GGA(x1, x2, x3)  =  TIMES190_IN_GGA(x1, x2)
U3_GGA(x1, x2, x3, x4)  =  U3_GGA(x1, x2, x4)
U4_GGA(x1, x2, x3, x4)  =  U4_GGA(x1, x2, x4)
U5_GGA(x1, x2, x3, x4)  =  U5_GGA(x1, x2, x4)
ADD201_IN_AGA(x1, x2, x3)  =  ADD201_IN_AGA(x2)
U6_AGA(x1, x2, x3, x4)  =  U6_AGA(x2, x4)
U57_G(x1, x2)  =  U57_G(x1, x2)
U58_G(x1, x2)  =  U58_G(x1, x2)
NEQ191_IN_GA(x1, x2)  =  NEQ191_IN_GA(x1)
U11_GA(x1, x2, x3)  =  U11_GA(x1, x3)
NEQ227_IN_GA(x1, x2)  =  NEQ227_IN_GA(x1)
U49_GA(x1, x2, x3)  =  U49_GA(x1, x3)
NEQ236_IN_GA(x1, x2)  =  NEQ236_IN_GA(x1)
U7_GA(x1, x2, x3)  =  U7_GA(x1, x3)
U105_G(x1)  =  U105_G(x1)
U106_G(x1, x2)  =  U106_G(x1, x2)
U107_G(x1, x2)  =  U107_G(x1, x2)
NOT_DIVIDES259_IN_G(x1)  =  NOT_DIVIDES259_IN_G(x1)
U63_G(x1, x2)  =  U63_G(x1, x2)
DIV263_IN_GA(x1, x2)  =  DIV263_IN_GA(x1)
U68_GA(x1, x2, x3)  =  U68_GA(x1, x3)
QUOT313_IN_GGA(x1, x2, x3)  =  QUOT313_IN_GGA(x1, x2)
U8_GGA(x1, x2, x3, x4)  =  U8_GGA(x1, x2, x4)
U9_GGA(x1, x2)  =  U9_GGA(x2)
QUOT340_IN_A(x1)  =  QUOT340_IN_A
U10_GGA(x1, x2)  =  U10_GGA(x2)
QUOT349_IN_A(x1)  =  QUOT349_IN_A
U16_A(x1, x2)  =  U16_A(x2)
U69_GA(x1, x2)  =  U69_GA(x2)
QUOT446_IN_A(x1)  =  QUOT446_IN_A
U70_GA(x1, x2)  =  U70_GA(x2)
QUOT467_IN_A(x1)  =  QUOT467_IN_A
U22_A(x1, x2)  =  U22_A(x2)
U64_G(x1, x2)  =  U64_G(x1, x2)
U65_G(x1, x2)  =  U65_G(x1, x2)
U66_G(x1, x2)  =  U66_G(x1, x2)
U67_G(x1, x2)  =  U67_G(x1, x2)
U108_G(x1)  =  U108_G(x1)
U109_G(x1)  =  U109_G(x1)
U110_G(x1, x2)  =  U110_G(x1, x2)
U111_G(x1, x2)  =  U111_G(x1, x2)
U112_G(x1, x2)  =  U112_G(x1, x2)
NOT_DIVIDES497_IN_G(x1)  =  NOT_DIVIDES497_IN_G(x1)
U71_G(x1, x2)  =  U71_G(x1, x2)
DIV501_IN_GA(x1, x2)  =  DIV501_IN_GA(x1)
U76_GA(x1, x2, x3)  =  U76_GA(x1, x3)
QUOT551_IN_GGA(x1, x2, x3)  =  QUOT551_IN_GGA(x1, x2)
U12_GGA(x1, x2, x3, x4)  =  U12_GGA(x1, x2, x4)
U13_GGA(x1, x2)  =  U13_GGA(x2)
QUOT584_IN_A(x1)  =  QUOT584_IN_A
U14_GGA(x1, x2)  =  U14_GGA(x2)
U15_GGA(x1, x2)  =  U15_GGA(x2)
QUOT595_IN_A(x1)  =  QUOT595_IN_A
U23_A(x1, x2)  =  U23_A(x2)
U77_GA(x1, x2)  =  U77_GA(x2)
U78_GA(x1, x2)  =  U78_GA(x2)
QUOT740_IN_A(x1)  =  QUOT740_IN_A
U30_A(x1, x2)  =  U30_A(x2)
U72_G(x1, x2)  =  U72_G(x1, x2)
U73_G(x1, x2)  =  U73_G(x1, x2)
U74_G(x1, x2)  =  U74_G(x1, x2)
U75_G(x1, x2)  =  U75_G(x1, x2)
U113_G(x1)  =  U113_G(x1)
U114_G(x1)  =  U114_G(x1)
U115_G(x1)  =  U115_G(x1)
U116_G(x1, x2)  =  U116_G(x1, x2)
U117_G(x1, x2)  =  U117_G(x1, x2)
U118_G(x1, x2)  =  U118_G(x1, x2)
U119_G(x1, x2)  =  U119_G(x1, x2)
NOT_DIVIDES770_IN_G(x1)  =  NOT_DIVIDES770_IN_G(x1)
U79_G(x1, x2)  =  U79_G(x1, x2)
DIV774_IN_GA(x1, x2)  =  DIV774_IN_GA(x1)
U84_GA(x1, x2, x3)  =  U84_GA(x1, x3)
QUOT824_IN_GGA(x1, x2, x3)  =  QUOT824_IN_GGA(x1, x2)
U17_GGA(x1, x2, x3, x4)  =  U17_GGA(x1, x2, x4)
U18_GGA(x1, x2)  =  U18_GGA(x2)
QUOT863_IN_A(x1)  =  QUOT863_IN_A
U19_GGA(x1, x2)  =  U19_GGA(x2)
U20_GGA(x1, x2)  =  U20_GGA(x2)
U21_GGA(x1, x2)  =  U21_GGA(x2)
QUOT876_IN_A(x1)  =  QUOT876_IN_A
U31_A(x1, x2)  =  U31_A(x2)
U85_GA(x1, x2)  =  U85_GA(x2)
U86_GA(x1, x2)  =  U86_GA(x2)
U87_GA(x1, x2)  =  U87_GA(x2)
U80_G(x1, x2)  =  U80_G(x1, x2)
U81_G(x1, x2)  =  U81_G(x1, x2)
U82_G(x1, x2)  =  U82_G(x1, x2)
U83_G(x1, x2)  =  U83_G(x1, x2)
U120_G(x1)  =  U120_G(x1)
U121_G(x1)  =  U121_G(x1)
U122_G(x1)  =  U122_G(x1)
U123_G(x1)  =  U123_G(x1)
U124_G(x1, x2)  =  U124_G(x1, x2)
U125_G(x1, x2)  =  U125_G(x1, x2)
U126_G(x1, x2)  =  U126_G(x1, x2)
U127_G(x1, x2)  =  U127_G(x1, x2)
U128_G(x1, x2)  =  U128_G(x1, x2)
NOT_DIVIDES1072_IN_G(x1)  =  NOT_DIVIDES1072_IN_G(x1)
U88_G(x1, x2)  =  U88_G(x1, x2)
DIV1076_IN_GA(x1, x2)  =  DIV1076_IN_GA(x1)
U93_GA(x1, x2, x3)  =  U93_GA(x1, x3)
QUOT1126_IN_GGA(x1, x2, x3)  =  QUOT1126_IN_GGA(x1, x2)
U24_GGA(x1, x2, x3, x4)  =  U24_GGA(x1, x2, x4)
U25_GGA(x1, x2)  =  U25_GGA(x2)
QUOT1171_IN_A(x1)  =  QUOT1171_IN_A
U26_GGA(x1, x2)  =  U26_GGA(x2)
U27_GGA(x1, x2)  =  U27_GGA(x2)
U28_GGA(x1, x2)  =  U28_GGA(x2)
U29_GGA(x1, x2)  =  U29_GGA(x2)
U94_GA(x1, x2)  =  U94_GA(x2)
U95_GA(x1, x2)  =  U95_GA(x2)
U96_GA(x1, x2)  =  U96_GA(x2)
U97_GA(x1, x2)  =  U97_GA(x2)
U89_G(x1, x2)  =  U89_G(x1, x2)
U90_G(x1, x2)  =  U90_G(x1, x2)
U91_G(x1, x2)  =  U91_G(x1, x2)
U92_G(x1, x2)  =  U92_G(x1, x2)
U129_G(x1)  =  U129_G(x1)
U130_G(x1)  =  U130_G(x1)
U131_G(x1)  =  U131_G(x1)
U132_G(x1)  =  U132_G(x1)
U133_G(x1)  =  U133_G(x1)
U134_G(x1, x2)  =  U134_G(x1, x2)
U135_G(x1, x2)  =  U135_G(x1, x2)
U136_G(x1, x2)  =  U136_G(x1, x2)
U137_G(x1, x2)  =  U137_G(x1, x2)
U138_G(x1, x2)  =  U138_G(x1, x2)
U139_G(x1, x2)  =  U139_G(x1, x2)
P1397_IN_GG(x1, x2)  =  P1397_IN_GG(x1, x2)
U50_GG(x1, x2, x3)  =  U50_GG(x1, x2, x3)
NOT_DIVIDES1398_IN_GG(x1, x2)  =  NOT_DIVIDES1398_IN_GG(x1, x2)
U98_GG(x1, x2, x3)  =  U98_GG(x1, x2, x3)
DIV1402_IN_GGA(x1, x2, x3)  =  DIV1402_IN_GGA(x1, x2)
U103_GGA(x1, x2, x3, x4)  =  U103_GGA(x1, x2, x4)
QUOT1419_IN_GGA(x1, x2, x3)  =  QUOT1419_IN_GGA(x1, x2)
U35_GGA(x1, x2, x3, x4)  =  U35_GGA(x1, x2, x4)
QUOT1481_IN_GGGA(x1, x2, x3, x4)  =  QUOT1481_IN_GGGA(x1, x2, x3)
U32_GGGA(x1, x2, x3, x4, x5)  =  U32_GGGA(x1, x2, x3, x5)
U33_GGGA(x1, x2, x3, x4)  =  U33_GGGA(x1, x2, x4)
U36_GGA(x1, x2, x3)  =  U36_GGA(x1, x3)
QUOT1532_IN_GA(x1, x2)  =  QUOT1532_IN_GA(x1)
U43_GA(x1, x2, x3)  =  U43_GA(x1, x3)
U37_GGA(x1, x2, x3)  =  U37_GGA(x1, x3)
QUOT1615_IN_GA(x1, x2)  =  QUOT1615_IN_GA(x1)
U44_GA(x1, x2, x3)  =  U44_GA(x1, x3)
U38_GGA(x1, x2, x3)  =  U38_GGA(x1, x3)
QUOT1687_IN_GA(x1, x2)  =  QUOT1687_IN_GA(x1)
U45_GA(x1, x2, x3)  =  U45_GA(x1, x3)
U39_GGA(x1, x2, x3)  =  U39_GGA(x1, x3)
QUOT1748_IN_GA(x1, x2)  =  QUOT1748_IN_GA(x1)
U46_GA(x1, x2, x3)  =  U46_GA(x1, x3)
U40_GGA(x1, x2, x3)  =  U40_GGA(x1, x3)
QUOT1798_IN_GA(x1, x2)  =  QUOT1798_IN_GA(x1)
U47_GA(x1, x2, x3)  =  U47_GA(x1, x3)
U41_GGA(x1, x2, x3)  =  U41_GGA(x1, x3)
QUOT1837_IN_GA(x1, x2)  =  QUOT1837_IN_GA(x1)
U48_GA(x1, x2, x3)  =  U48_GA(x1, x3)
U34_GGGA(x1, x2, x3)  =  U34_GGGA(x1, x3)
QUOT1514_IN_GA(x1, x2)  =  QUOT1514_IN_GA(x1)
U42_GA(x1, x2, x3)  =  U42_GA(x1, x3)
U99_GG(x1, x2, x3)  =  U99_GG(x1, x2, x3)
U100_GG(x1, x2, x3)  =  U100_GG(x1, x2, x3)
U101_GG(x1, x2, x3)  =  U101_GG(x1, x2, x3)
U102_GG(x1, x2, x3)  =  U102_GG(x1, x2, x3)
U51_GG(x1, x2)  =  U51_GG(x1, x2)
U52_GG(x1, x2, x3)  =  U52_GG(x1, x2, x3)
U53_GG(x1, x2, x3)  =  U53_GG(x1, x2, x3)

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

(6) Obligation:

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

PRIME1_IN_G(s(s(s(T14)))) → U104_G(T14, not_divides13_in_g(T14))
PRIME1_IN_G(s(s(s(T14)))) → NOT_DIVIDES13_IN_G(T14)
NOT_DIVIDES13_IN_G(T20) → U54_G(T20, div17_in_ga(T20, X38))
NOT_DIVIDES13_IN_G(T20) → DIV17_IN_GA(T20, X38)
DIV17_IN_GA(s(s(s(s(s(s(T117)))))), X412) → U59_GA(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
DIV17_IN_GA(s(s(s(s(s(s(T117)))))), X412) → QUOT67_IN_GGA(T117, s(s(s(s(s(s(s(T117))))))), X412)
QUOT67_IN_GGA(s(T137), T138, X461) → U1_GGA(T137, T138, X461, quot67_in_gga(T137, T138, X461))
QUOT67_IN_GGA(s(T137), T138, X461) → QUOT67_IN_GGA(T137, T138, X461)
QUOT67_IN_GGA(0, 0, s(s(X565))) → U2_GGA(X565, quot88_in_a(X565))
QUOT67_IN_GGA(0, 0, s(s(X565))) → QUOT88_IN_A(X565)
DIV17_IN_GA(s(s(0)), s(X833)) → U60_GA(X833, quot143_in_a(X833))
DIV17_IN_GA(s(s(0)), s(X833)) → QUOT143_IN_A(X833)
DIV17_IN_GA(s(0), s(X910)) → U61_GA(X910, quot158_in_a(X910))
DIV17_IN_GA(s(0), s(X910)) → QUOT158_IN_A(X910)
DIV17_IN_GA(0, s(X987)) → U62_GA(X987, quot173_in_a(X987))
DIV17_IN_GA(0, s(X987)) → QUOT173_IN_A(X987)
NOT_DIVIDES13_IN_G(T20) → U55_G(T20, div17_in_ga(T20, T22))
U55_G(T20, div17_out_ga(T20, T22)) → U56_G(T20, times190_in_gga(T22, T20, X39))
U55_G(T20, div17_out_ga(T20, T22)) → TIMES190_IN_GGA(T22, T20, X39)
TIMES190_IN_GGA(s(T199), T200, X1082) → U3_GGA(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
TIMES190_IN_GGA(s(T199), T200, X1082) → TIMES190_IN_GGA(T199, T200, X1081)
TIMES190_IN_GGA(s(T199), T200, X1082) → U4_GGA(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_GGA(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_GGA(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
U4_GGA(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → ADD201_IN_AGA(T203, T200, X1082)
ADD201_IN_AGA(s(T220), T221, s(X1112)) → U6_AGA(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
ADD201_IN_AGA(s(T220), T221, s(X1112)) → ADD201_IN_AGA(T220, T221, X1112)
U55_G(T20, div17_out_ga(T20, T22)) → U57_G(T20, times190_in_gga(T22, T20, T187))
U57_G(T20, times190_out_gga(T22, T20, T187)) → U58_G(T20, neq191_in_ga(T20, T187))
U57_G(T20, times190_out_gga(T22, T20, T187)) → NEQ191_IN_GA(T20, T187)
NEQ191_IN_GA(T250, s(s(T251))) → U11_GA(T250, T251, neq227_in_ga(T250, T251))
NEQ191_IN_GA(T250, s(s(T251))) → NEQ227_IN_GA(T250, T251)
NEQ227_IN_GA(T263, s(T264)) → U49_GA(T263, T264, neq236_in_ga(T263, T264))
NEQ227_IN_GA(T263, s(T264)) → NEQ236_IN_GA(T263, T264)
NEQ236_IN_GA(s(T281), s(T282)) → U7_GA(T281, T282, neq236_in_ga(T281, T282))
NEQ236_IN_GA(s(T281), s(T282)) → NEQ236_IN_GA(T281, T282)
PRIME1_IN_G(s(s(s(0)))) → U105_G(not_divides13_in_g(0))
PRIME1_IN_G(s(s(s(0)))) → NOT_DIVIDES13_IN_G(0)
PRIME1_IN_G(s(s(s(s(T297))))) → U106_G(T297, not_divides13_in_g(s(T297)))
PRIME1_IN_G(s(s(s(s(T297))))) → NOT_DIVIDES13_IN_G(s(T297))
U106_G(T297, not_divides13_out_g(s(T297))) → U107_G(T297, not_divides259_in_g(T297))
U106_G(T297, not_divides13_out_g(s(T297))) → NOT_DIVIDES259_IN_G(T297)
NOT_DIVIDES259_IN_G(T303) → U63_G(T303, div263_in_ga(T303, X1231))
NOT_DIVIDES259_IN_G(T303) → DIV263_IN_GA(T303, X1231)
DIV263_IN_GA(s(s(s(s(s(s(T400)))))), X1605) → U68_GA(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
DIV263_IN_GA(s(s(s(s(s(s(T400)))))), X1605) → QUOT313_IN_GGA(T400, s(s(s(s(s(s(s(T400))))))), X1605)
QUOT313_IN_GGA(s(T420), T421, X1654) → U8_GGA(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
QUOT313_IN_GGA(s(T420), T421, X1654) → QUOT313_IN_GGA(T420, T421, X1654)
QUOT313_IN_GGA(0, s(0), s(s(X1808))) → U9_GGA(X1808, quot340_in_a(X1808))
QUOT313_IN_GGA(0, s(0), s(s(X1808))) → QUOT340_IN_A(X1808)
QUOT313_IN_GGA(0, 0, s(s(X1842))) → U10_GGA(X1842, quot349_in_a(X1842))
QUOT313_IN_GGA(0, 0, s(s(X1842))) → QUOT349_IN_A(X1842)
QUOT349_IN_A(s(X1937)) → U16_A(X1937, quot88_in_a(X1937))
QUOT349_IN_A(s(X1937)) → QUOT88_IN_A(X1937)
DIV263_IN_GA(s(0), s(X2493)) → U69_GA(X2493, quot446_in_a(X2493))
DIV263_IN_GA(s(0), s(X2493)) → QUOT446_IN_A(X2493)
DIV263_IN_GA(0, s(X2627)) → U70_GA(X2627, quot467_in_a(X2627))
DIV263_IN_GA(0, s(X2627)) → QUOT467_IN_A(X2627)
QUOT467_IN_A(s(X2776)) → U22_A(X2776, quot340_in_a(X2776))
QUOT467_IN_A(s(X2776)) → QUOT340_IN_A(X2776)
NOT_DIVIDES259_IN_G(T303) → U64_G(T303, div263_in_ga(T303, T305))
U64_G(T303, div263_out_ga(T303, T305)) → U65_G(T303, times190_in_gga(T305, T303, X1232))
U64_G(T303, div263_out_ga(T303, T305)) → TIMES190_IN_GGA(T305, T303, X1232)
U64_G(T303, div263_out_ga(T303, T305)) → U66_G(T303, times190_in_gga(T305, T303, T474))
U66_G(T303, times190_out_gga(T305, T303, T474)) → U67_G(T303, neq191_in_ga(s(T303), T474))
U66_G(T303, times190_out_gga(T305, T303, T474)) → NEQ191_IN_GA(s(T303), T474)
PRIME1_IN_G(s(s(s(s(0))))) → U108_G(not_divides13_in_g(s(0)))
PRIME1_IN_G(s(s(s(s(0))))) → NOT_DIVIDES13_IN_G(s(0))
U108_G(not_divides13_out_g(s(0))) → U109_G(not_divides259_in_g(0))
U108_G(not_divides13_out_g(s(0))) → NOT_DIVIDES259_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(T491)))))) → U110_G(T491, not_divides13_in_g(s(s(T491))))
PRIME1_IN_G(s(s(s(s(s(T491)))))) → NOT_DIVIDES13_IN_G(s(s(T491)))
U110_G(T491, not_divides13_out_g(s(s(T491)))) → U111_G(T491, not_divides259_in_g(s(T491)))
U110_G(T491, not_divides13_out_g(s(s(T491)))) → NOT_DIVIDES259_IN_G(s(T491))
U111_G(T491, not_divides259_out_g(s(T491))) → U112_G(T491, not_divides497_in_g(T491))
U111_G(T491, not_divides259_out_g(s(T491))) → NOT_DIVIDES497_IN_G(T491)
NOT_DIVIDES497_IN_G(T497) → U71_G(T497, div501_in_ga(T497, X2833))
NOT_DIVIDES497_IN_G(T497) → DIV501_IN_GA(T497, X2833)
DIV501_IN_GA(s(s(s(s(s(s(T594)))))), X3207) → U76_GA(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
DIV501_IN_GA(s(s(s(s(s(s(T594)))))), X3207) → QUOT551_IN_GGA(T594, s(s(s(s(s(s(s(T594))))))), X3207)
QUOT551_IN_GGA(s(T614), T615, X3256) → U12_GGA(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
QUOT551_IN_GGA(s(T614), T615, X3256) → QUOT551_IN_GGA(T614, T615, X3256)
QUOT551_IN_GGA(0, s(s(0)), s(s(X3450))) → U13_GGA(X3450, quot584_in_a(X3450))
QUOT551_IN_GGA(0, s(s(0)), s(s(X3450))) → QUOT584_IN_A(X3450)
QUOT551_IN_GGA(0, s(0), s(s(X3484))) → U14_GGA(X3484, quot173_in_a(X3484))
QUOT551_IN_GGA(0, s(0), s(s(X3484))) → QUOT173_IN_A(X3484)
QUOT551_IN_GGA(0, 0, s(s(X3508))) → U15_GGA(X3508, quot595_in_a(X3508))
QUOT551_IN_GGA(0, 0, s(s(X3508))) → QUOT595_IN_A(X3508)
QUOT595_IN_A(s(X3610)) → U23_A(X3610, quot349_in_a(X3610))
QUOT595_IN_A(s(X3610)) → QUOT349_IN_A(X3610)
DIV501_IN_GA(s(0), s(s(X4604))) → U77_GA(X4604, quot584_in_a(X4604))
DIV501_IN_GA(s(0), s(s(X4604))) → QUOT584_IN_A(X4604)
DIV501_IN_GA(0, s(X4627)) → U78_GA(X4627, quot740_in_a(X4627))
DIV501_IN_GA(0, s(X4627)) → QUOT740_IN_A(X4627)
QUOT740_IN_A(s(X4783)) → U30_A(X4783, quot173_in_a(X4783))
QUOT740_IN_A(s(X4783)) → QUOT173_IN_A(X4783)
NOT_DIVIDES497_IN_G(T497) → U72_G(T497, div501_in_ga(T497, T499))
U72_G(T497, div501_out_ga(T497, T499)) → U73_G(T497, times190_in_gga(T499, T497, X2834))
U72_G(T497, div501_out_ga(T497, T499)) → TIMES190_IN_GGA(T499, T497, X2834)
U72_G(T497, div501_out_ga(T497, T499)) → U74_G(T497, times190_in_gga(T499, T497, T674))
U74_G(T497, times190_out_gga(T499, T497, T674)) → U75_G(T497, neq191_in_ga(s(s(T497)), T674))
U74_G(T497, times190_out_gga(T499, T497, T674)) → NEQ191_IN_GA(s(s(T497)), T674)
PRIME1_IN_G(s(s(s(s(s(0)))))) → U113_G(not_divides13_in_g(s(s(0))))
PRIME1_IN_G(s(s(s(s(s(0)))))) → NOT_DIVIDES13_IN_G(s(s(0)))
U113_G(not_divides13_out_g(s(s(0)))) → U114_G(not_divides259_in_g(s(0)))
U113_G(not_divides13_out_g(s(s(0)))) → NOT_DIVIDES259_IN_G(s(0))
U114_G(not_divides259_out_g(s(0))) → U115_G(not_divides497_in_g(0))
U114_G(not_divides259_out_g(s(0))) → NOT_DIVIDES497_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(s(T691))))))) → U116_G(T691, not_divides13_in_g(s(s(s(T691)))))
PRIME1_IN_G(s(s(s(s(s(s(T691))))))) → NOT_DIVIDES13_IN_G(s(s(s(T691))))
U116_G(T691, not_divides13_out_g(s(s(s(T691))))) → U117_G(T691, not_divides259_in_g(s(s(T691))))
U116_G(T691, not_divides13_out_g(s(s(s(T691))))) → NOT_DIVIDES259_IN_G(s(s(T691)))
U117_G(T691, not_divides259_out_g(s(s(T691)))) → U118_G(T691, not_divides497_in_g(s(T691)))
U117_G(T691, not_divides259_out_g(s(s(T691)))) → NOT_DIVIDES497_IN_G(s(T691))
U118_G(T691, not_divides497_out_g(s(T691))) → U119_G(T691, not_divides770_in_g(T691))
U118_G(T691, not_divides497_out_g(s(T691))) → NOT_DIVIDES770_IN_G(T691)
NOT_DIVIDES770_IN_G(T697) → U79_G(T697, div774_in_ga(T697, X4847))
NOT_DIVIDES770_IN_G(T697) → DIV774_IN_GA(T697, X4847)
DIV774_IN_GA(s(s(s(s(s(s(T794)))))), X5221) → U84_GA(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
DIV774_IN_GA(s(s(s(s(s(s(T794)))))), X5221) → QUOT824_IN_GGA(T794, s(s(s(s(s(s(s(T794))))))), X5221)
QUOT824_IN_GGA(s(T814), T815, X5270) → U17_GGA(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
QUOT824_IN_GGA(s(T814), T815, X5270) → QUOT824_IN_GGA(T814, T815, X5270)
QUOT824_IN_GGA(0, s(s(s(0))), s(s(X5504))) → U18_GGA(X5504, quot863_in_a(X5504))
QUOT824_IN_GGA(0, s(s(s(0))), s(s(X5504))) → QUOT863_IN_A(X5504)
QUOT824_IN_GGA(0, s(s(0)), s(s(X5538))) → U19_GGA(X5538, quot158_in_a(X5538))
QUOT824_IN_GGA(0, s(s(0)), s(s(X5538))) → QUOT158_IN_A(X5538)
QUOT824_IN_GGA(0, s(0), s(s(X5562))) → U20_GGA(X5562, quot467_in_a(X5562))
QUOT824_IN_GGA(0, s(0), s(s(X5562))) → QUOT467_IN_A(X5562)
QUOT824_IN_GGA(0, 0, s(s(X5586))) → U21_GGA(X5586, quot876_in_a(X5586))
QUOT824_IN_GGA(0, 0, s(s(X5586))) → QUOT876_IN_A(X5586)
QUOT876_IN_A(s(X5688)) → U31_A(X5688, quot595_in_a(X5688))
QUOT876_IN_A(s(X5688)) → QUOT595_IN_A(X5688)
DIV774_IN_GA(s(s(0)), s(s(X6716))) → U85_GA(X6716, quot863_in_a(X6716))
DIV774_IN_GA(s(s(0)), s(s(X6716))) → QUOT863_IN_A(X6716)
DIV774_IN_GA(s(0), s(s(X6952))) → U86_GA(X6952, quot158_in_a(X6952))
DIV774_IN_GA(s(0), s(s(X6952))) → QUOT158_IN_A(X6952)
DIV774_IN_GA(0, s(s(X7138))) → U87_GA(X7138, quot467_in_a(X7138))
DIV774_IN_GA(0, s(s(X7138))) → QUOT467_IN_A(X7138)
NOT_DIVIDES770_IN_G(T697) → U80_G(T697, div774_in_ga(T697, T699))
U80_G(T697, div774_out_ga(T697, T699)) → U81_G(T697, times190_in_gga(T699, T697, X4848))
U80_G(T697, div774_out_ga(T697, T699)) → TIMES190_IN_GGA(T699, T697, X4848)
U80_G(T697, div774_out_ga(T697, T699)) → U82_G(T697, times190_in_gga(T699, T697, T880))
U82_G(T697, times190_out_gga(T699, T697, T880)) → U83_G(T697, neq191_in_ga(s(s(s(T697))), T880))
U82_G(T697, times190_out_gga(T699, T697, T880)) → NEQ191_IN_GA(s(s(s(T697))), T880)
PRIME1_IN_G(s(s(s(s(s(s(0))))))) → U120_G(not_divides13_in_g(s(s(s(0)))))
PRIME1_IN_G(s(s(s(s(s(s(0))))))) → NOT_DIVIDES13_IN_G(s(s(s(0))))
U120_G(not_divides13_out_g(s(s(s(0))))) → U121_G(not_divides259_in_g(s(s(0))))
U120_G(not_divides13_out_g(s(s(s(0))))) → NOT_DIVIDES259_IN_G(s(s(0)))
U121_G(not_divides259_out_g(s(s(0)))) → U122_G(not_divides497_in_g(s(0)))
U121_G(not_divides259_out_g(s(s(0)))) → NOT_DIVIDES497_IN_G(s(0))
U122_G(not_divides497_out_g(s(0))) → U123_G(not_divides770_in_g(0))
U122_G(not_divides497_out_g(s(0))) → NOT_DIVIDES770_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(s(s(T897)))))))) → U124_G(T897, not_divides13_in_g(s(s(s(s(T897))))))
PRIME1_IN_G(s(s(s(s(s(s(s(T897)))))))) → NOT_DIVIDES13_IN_G(s(s(s(s(T897)))))
U124_G(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_G(T897, not_divides259_in_g(s(s(s(T897)))))
U124_G(T897, not_divides13_out_g(s(s(s(s(T897)))))) → NOT_DIVIDES259_IN_G(s(s(s(T897))))
U125_G(T897, not_divides259_out_g(s(s(s(T897))))) → U126_G(T897, not_divides497_in_g(s(s(T897))))
U125_G(T897, not_divides259_out_g(s(s(s(T897))))) → NOT_DIVIDES497_IN_G(s(s(T897)))
U126_G(T897, not_divides497_out_g(s(s(T897)))) → U127_G(T897, not_divides770_in_g(s(T897)))
U126_G(T897, not_divides497_out_g(s(s(T897)))) → NOT_DIVIDES770_IN_G(s(T897))
U127_G(T897, not_divides770_out_g(s(T897))) → U128_G(T897, not_divides1072_in_g(T897))
U127_G(T897, not_divides770_out_g(s(T897))) → NOT_DIVIDES1072_IN_G(T897)
NOT_DIVIDES1072_IN_G(T903) → U88_G(T903, div1076_in_ga(T903, X7202))
NOT_DIVIDES1072_IN_G(T903) → DIV1076_IN_GA(T903, X7202)
DIV1076_IN_GA(s(s(s(s(s(s(T1000)))))), X7576) → U93_GA(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
DIV1076_IN_GA(s(s(s(s(s(s(T1000)))))), X7576) → QUOT1126_IN_GGA(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)
QUOT1126_IN_GGA(s(T1020), T1021, X7625) → U24_GGA(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
QUOT1126_IN_GGA(s(T1020), T1021, X7625) → QUOT1126_IN_GGA(T1020, T1021, X7625)
QUOT1126_IN_GGA(0, s(s(s(s(0)))), s(s(X7899))) → U25_GGA(X7899, quot1171_in_a(X7899))
QUOT1126_IN_GGA(0, s(s(s(s(0)))), s(s(X7899))) → QUOT1171_IN_A(X7899)
QUOT1126_IN_GGA(0, s(s(s(0))), s(s(X7933))) → U26_GGA(X7933, quot143_in_a(X7933))
QUOT1126_IN_GGA(0, s(s(s(0))), s(s(X7933))) → QUOT143_IN_A(X7933)
QUOT1126_IN_GGA(0, s(s(0)), s(s(X7957))) → U27_GGA(X7957, quot446_in_a(X7957))
QUOT1126_IN_GGA(0, s(s(0)), s(s(X7957))) → QUOT446_IN_A(X7957)
QUOT1126_IN_GGA(0, s(0), s(s(X7981))) → U28_GGA(X7981, quot740_in_a(X7981))
QUOT1126_IN_GGA(0, s(0), s(s(X7981))) → QUOT740_IN_A(X7981)
QUOT1126_IN_GGA(0, 0, s(s(s(X8107)))) → U29_GGA(X8107, quot876_in_a(X8107))
QUOT1126_IN_GGA(0, 0, s(s(s(X8107)))) → QUOT876_IN_A(X8107)
DIV1076_IN_GA(s(s(s(0))), s(s(X9055))) → U94_GA(X9055, quot1171_in_a(X9055))
DIV1076_IN_GA(s(s(s(0))), s(s(X9055))) → QUOT1171_IN_A(X9055)
DIV1076_IN_GA(s(s(0)), s(s(X9348))) → U95_GA(X9348, quot143_in_a(X9348))
DIV1076_IN_GA(s(s(0)), s(s(X9348))) → QUOT143_IN_A(X9348)
DIV1076_IN_GA(s(0), s(s(X9591))) → U96_GA(X9591, quot446_in_a(X9591))
DIV1076_IN_GA(s(0), s(s(X9591))) → QUOT446_IN_A(X9591)
DIV1076_IN_GA(0, s(s(X9777))) → U97_GA(X9777, quot740_in_a(X9777))
DIV1076_IN_GA(0, s(s(X9777))) → QUOT740_IN_A(X9777)
NOT_DIVIDES1072_IN_G(T903) → U89_G(T903, div1076_in_ga(T903, T905))
U89_G(T903, div1076_out_ga(T903, T905)) → U90_G(T903, times190_in_gga(T905, T903, X7203))
U89_G(T903, div1076_out_ga(T903, T905)) → TIMES190_IN_GGA(T905, T903, X7203)
U89_G(T903, div1076_out_ga(T903, T905)) → U91_G(T903, times190_in_gga(T905, T903, T1092))
U91_G(T903, times190_out_gga(T905, T903, T1092)) → U92_G(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U91_G(T903, times190_out_gga(T905, T903, T1092)) → NEQ191_IN_GA(s(s(s(s(T903)))), T1092)
PRIME1_IN_G(s(s(s(s(s(s(s(0)))))))) → U129_G(not_divides13_in_g(s(s(s(s(0))))))
PRIME1_IN_G(s(s(s(s(s(s(s(0)))))))) → NOT_DIVIDES13_IN_G(s(s(s(s(0)))))
U129_G(not_divides13_out_g(s(s(s(s(0)))))) → U130_G(not_divides259_in_g(s(s(s(0)))))
U129_G(not_divides13_out_g(s(s(s(s(0)))))) → NOT_DIVIDES259_IN_G(s(s(s(0))))
U130_G(not_divides259_out_g(s(s(s(0))))) → U131_G(not_divides497_in_g(s(s(0))))
U130_G(not_divides259_out_g(s(s(s(0))))) → NOT_DIVIDES497_IN_G(s(s(0)))
U131_G(not_divides497_out_g(s(s(0)))) → U132_G(not_divides770_in_g(s(0)))
U131_G(not_divides497_out_g(s(s(0)))) → NOT_DIVIDES770_IN_G(s(0))
U132_G(not_divides770_out_g(s(0))) → U133_G(not_divides1072_in_g(0))
U132_G(not_divides770_out_g(s(0))) → NOT_DIVIDES1072_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(s(s(s(T1109))))))))) → U134_G(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
PRIME1_IN_G(s(s(s(s(s(s(s(s(T1109))))))))) → NOT_DIVIDES13_IN_G(s(s(s(s(s(T1109))))))
U134_G(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_G(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U134_G(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → NOT_DIVIDES259_IN_G(s(s(s(s(T1109)))))
U135_G(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_G(T1109, not_divides497_in_g(s(s(s(T1109)))))
U135_G(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → NOT_DIVIDES497_IN_G(s(s(s(T1109))))
U136_G(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_G(T1109, not_divides770_in_g(s(s(T1109))))
U136_G(T1109, not_divides497_out_g(s(s(s(T1109))))) → NOT_DIVIDES770_IN_G(s(s(T1109)))
U137_G(T1109, not_divides770_out_g(s(s(T1109)))) → U138_G(T1109, not_divides1072_in_g(s(T1109)))
U137_G(T1109, not_divides770_out_g(s(s(T1109)))) → NOT_DIVIDES1072_IN_G(s(T1109))
U138_G(T1109, not_divides1072_out_g(s(T1109))) → U139_G(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
U138_G(T1109, not_divides1072_out_g(s(T1109))) → P1397_IN_GG(T1109, s(s(s(s(s(s(s(T1109))))))))
P1397_IN_GG(T1109, T1111) → U50_GG(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
P1397_IN_GG(T1109, T1111) → NOT_DIVIDES1398_IN_GG(T1109, T1111)
NOT_DIVIDES1398_IN_GG(T1122, T1123) → U98_GG(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
NOT_DIVIDES1398_IN_GG(T1122, T1123) → DIV1402_IN_GGA(T1123, T1122, X9845)
DIV1402_IN_GGA(s(T1168), T1169, X9960) → U103_GGA(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
DIV1402_IN_GGA(s(T1168), T1169, X9960) → QUOT1419_IN_GGA(T1168, T1169, X9960)
QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_GGA(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → QUOT1481_IN_GGGA(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)
QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303, X10279) → U32_GGGA(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303, X10279) → QUOT1481_IN_GGGA(T1301, T1302, T1303, X10279)
QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_GGGA(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347), s(X10388)) → QUOT1419_IN_GGA(T1346, T1347, X10388)
QUOT1419_IN_GGA(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_GGA(T1368, X10512, quot1532_in_ga(T1368, X10512))
QUOT1419_IN_GGA(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → QUOT1532_IN_GA(T1368, X10512)
QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_GA(T1409, X10864, quot1532_in_ga(T1409, X10864))
QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → QUOT1532_IN_GA(T1409, X10864)
QUOT1419_IN_GGA(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_GGA(T1419, X10901, quot1615_in_ga(T1419, X10901))
QUOT1419_IN_GGA(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → QUOT1615_IN_GA(T1419, X10901)
QUOT1615_IN_GA(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_GA(T1455, X11208, quot1615_in_ga(T1455, X11208))
QUOT1615_IN_GA(s(s(s(s(s(s(T1455)))))), s(X11208)) → QUOT1615_IN_GA(T1455, X11208)
QUOT1419_IN_GGA(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_GGA(T1464, X11242, quot1687_in_ga(T1464, X11242))
QUOT1419_IN_GGA(s(s(s(T1464))), s(s(s(0))), s(X11242)) → QUOT1687_IN_GA(T1464, X11242)
QUOT1687_IN_GA(s(s(s(s(s(T1495))))), s(X11504)) → U45_GA(T1495, X11504, quot1687_in_ga(T1495, X11504))
QUOT1687_IN_GA(s(s(s(s(s(T1495))))), s(X11504)) → QUOT1687_IN_GA(T1495, X11504)
QUOT1419_IN_GGA(s(s(T1503)), s(s(0)), s(X11535)) → U39_GGA(T1503, X11535, quot1748_in_ga(T1503, X11535))
QUOT1419_IN_GGA(s(s(T1503)), s(s(0)), s(X11535)) → QUOT1748_IN_GA(T1503, X11535)
QUOT1748_IN_GA(s(s(s(s(T1529)))), s(X11752)) → U46_GA(T1529, X11752, quot1748_in_ga(T1529, X11752))
QUOT1748_IN_GA(s(s(s(s(T1529)))), s(X11752)) → QUOT1748_IN_GA(T1529, X11752)
QUOT1419_IN_GGA(s(T1536), s(0), s(X11780)) → U40_GGA(T1536, X11780, quot1798_in_ga(T1536, X11780))
QUOT1419_IN_GGA(s(T1536), s(0), s(X11780)) → QUOT1798_IN_GA(T1536, X11780)
QUOT1798_IN_GA(s(s(s(T1557))), s(X11952)) → U47_GA(T1557, X11952, quot1798_in_ga(T1557, X11952))
QUOT1798_IN_GA(s(s(s(T1557))), s(X11952)) → QUOT1798_IN_GA(T1557, X11952)
QUOT1419_IN_GGA(T1563, 0, s(X11977)) → U41_GGA(T1563, X11977, quot1837_in_ga(T1563, X11977))
QUOT1419_IN_GGA(T1563, 0, s(X11977)) → QUOT1837_IN_GA(T1563, X11977)
QUOT1837_IN_GA(s(s(T1579)), s(X12104)) → U48_GA(T1579, X12104, quot1837_in_ga(T1579, X12104))
QUOT1837_IN_GA(s(s(T1579)), s(X12104)) → QUOT1837_IN_GA(T1579, X12104)
QUOT1481_IN_GGGA(s(T1352), 0, 0, s(s(X10408))) → U34_GGGA(T1352, X10408, quot1514_in_ga(T1352, X10408))
QUOT1481_IN_GGGA(s(T1352), 0, 0, s(s(X10408))) → QUOT1514_IN_GA(T1352, X10408)
QUOT1514_IN_GA(s(T1363), s(X10490)) → U42_GA(T1363, X10490, quot1514_in_ga(T1363, X10490))
QUOT1514_IN_GA(s(T1363), s(X10490)) → QUOT1514_IN_GA(T1363, X10490)
NOT_DIVIDES1398_IN_GG(T1122, T1123) → U99_GG(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_GG(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_GG(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U99_GG(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → TIMES190_IN_GGA(T1126, T1122, X9846)
U99_GG(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_GG(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_GG(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_GG(T1122, T1123, neq227_in_ga(T1123, T1586))
U101_GG(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → NEQ227_IN_GA(T1123, T1586)
P1397_IN_GG(0, T1597) → U51_GG(T1597, not_divides1398_in_gg(0, T1597))
P1397_IN_GG(0, T1597) → NOT_DIVIDES1398_IN_GG(0, T1597)
P1397_IN_GG(s(T1603), T1602) → U52_GG(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
P1397_IN_GG(s(T1603), T1602) → NOT_DIVIDES1398_IN_GG(s(T1603), T1602)
U52_GG(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_GG(T1603, T1602, p1397_in_gg(T1603, T1602))
U52_GG(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → P1397_IN_GG(T1603, T1602)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
PRIME1_IN_G(x1)  =  PRIME1_IN_G(x1)
U104_G(x1, x2)  =  U104_G(x1, x2)
NOT_DIVIDES13_IN_G(x1)  =  NOT_DIVIDES13_IN_G(x1)
U54_G(x1, x2)  =  U54_G(x1, x2)
DIV17_IN_GA(x1, x2)  =  DIV17_IN_GA(x1)
U59_GA(x1, x2, x3)  =  U59_GA(x1, x3)
QUOT67_IN_GGA(x1, x2, x3)  =  QUOT67_IN_GGA(x1, x2)
U1_GGA(x1, x2, x3, x4)  =  U1_GGA(x1, x2, x4)
U2_GGA(x1, x2)  =  U2_GGA(x2)
QUOT88_IN_A(x1)  =  QUOT88_IN_A
U60_GA(x1, x2)  =  U60_GA(x2)
QUOT143_IN_A(x1)  =  QUOT143_IN_A
U61_GA(x1, x2)  =  U61_GA(x2)
QUOT158_IN_A(x1)  =  QUOT158_IN_A
U62_GA(x1, x2)  =  U62_GA(x2)
QUOT173_IN_A(x1)  =  QUOT173_IN_A
U55_G(x1, x2)  =  U55_G(x1, x2)
U56_G(x1, x2)  =  U56_G(x1, x2)
TIMES190_IN_GGA(x1, x2, x3)  =  TIMES190_IN_GGA(x1, x2)
U3_GGA(x1, x2, x3, x4)  =  U3_GGA(x1, x2, x4)
U4_GGA(x1, x2, x3, x4)  =  U4_GGA(x1, x2, x4)
U5_GGA(x1, x2, x3, x4)  =  U5_GGA(x1, x2, x4)
ADD201_IN_AGA(x1, x2, x3)  =  ADD201_IN_AGA(x2)
U6_AGA(x1, x2, x3, x4)  =  U6_AGA(x2, x4)
U57_G(x1, x2)  =  U57_G(x1, x2)
U58_G(x1, x2)  =  U58_G(x1, x2)
NEQ191_IN_GA(x1, x2)  =  NEQ191_IN_GA(x1)
U11_GA(x1, x2, x3)  =  U11_GA(x1, x3)
NEQ227_IN_GA(x1, x2)  =  NEQ227_IN_GA(x1)
U49_GA(x1, x2, x3)  =  U49_GA(x1, x3)
NEQ236_IN_GA(x1, x2)  =  NEQ236_IN_GA(x1)
U7_GA(x1, x2, x3)  =  U7_GA(x1, x3)
U105_G(x1)  =  U105_G(x1)
U106_G(x1, x2)  =  U106_G(x1, x2)
U107_G(x1, x2)  =  U107_G(x1, x2)
NOT_DIVIDES259_IN_G(x1)  =  NOT_DIVIDES259_IN_G(x1)
U63_G(x1, x2)  =  U63_G(x1, x2)
DIV263_IN_GA(x1, x2)  =  DIV263_IN_GA(x1)
U68_GA(x1, x2, x3)  =  U68_GA(x1, x3)
QUOT313_IN_GGA(x1, x2, x3)  =  QUOT313_IN_GGA(x1, x2)
U8_GGA(x1, x2, x3, x4)  =  U8_GGA(x1, x2, x4)
U9_GGA(x1, x2)  =  U9_GGA(x2)
QUOT340_IN_A(x1)  =  QUOT340_IN_A
U10_GGA(x1, x2)  =  U10_GGA(x2)
QUOT349_IN_A(x1)  =  QUOT349_IN_A
U16_A(x1, x2)  =  U16_A(x2)
U69_GA(x1, x2)  =  U69_GA(x2)
QUOT446_IN_A(x1)  =  QUOT446_IN_A
U70_GA(x1, x2)  =  U70_GA(x2)
QUOT467_IN_A(x1)  =  QUOT467_IN_A
U22_A(x1, x2)  =  U22_A(x2)
U64_G(x1, x2)  =  U64_G(x1, x2)
U65_G(x1, x2)  =  U65_G(x1, x2)
U66_G(x1, x2)  =  U66_G(x1, x2)
U67_G(x1, x2)  =  U67_G(x1, x2)
U108_G(x1)  =  U108_G(x1)
U109_G(x1)  =  U109_G(x1)
U110_G(x1, x2)  =  U110_G(x1, x2)
U111_G(x1, x2)  =  U111_G(x1, x2)
U112_G(x1, x2)  =  U112_G(x1, x2)
NOT_DIVIDES497_IN_G(x1)  =  NOT_DIVIDES497_IN_G(x1)
U71_G(x1, x2)  =  U71_G(x1, x2)
DIV501_IN_GA(x1, x2)  =  DIV501_IN_GA(x1)
U76_GA(x1, x2, x3)  =  U76_GA(x1, x3)
QUOT551_IN_GGA(x1, x2, x3)  =  QUOT551_IN_GGA(x1, x2)
U12_GGA(x1, x2, x3, x4)  =  U12_GGA(x1, x2, x4)
U13_GGA(x1, x2)  =  U13_GGA(x2)
QUOT584_IN_A(x1)  =  QUOT584_IN_A
U14_GGA(x1, x2)  =  U14_GGA(x2)
U15_GGA(x1, x2)  =  U15_GGA(x2)
QUOT595_IN_A(x1)  =  QUOT595_IN_A
U23_A(x1, x2)  =  U23_A(x2)
U77_GA(x1, x2)  =  U77_GA(x2)
U78_GA(x1, x2)  =  U78_GA(x2)
QUOT740_IN_A(x1)  =  QUOT740_IN_A
U30_A(x1, x2)  =  U30_A(x2)
U72_G(x1, x2)  =  U72_G(x1, x2)
U73_G(x1, x2)  =  U73_G(x1, x2)
U74_G(x1, x2)  =  U74_G(x1, x2)
U75_G(x1, x2)  =  U75_G(x1, x2)
U113_G(x1)  =  U113_G(x1)
U114_G(x1)  =  U114_G(x1)
U115_G(x1)  =  U115_G(x1)
U116_G(x1, x2)  =  U116_G(x1, x2)
U117_G(x1, x2)  =  U117_G(x1, x2)
U118_G(x1, x2)  =  U118_G(x1, x2)
U119_G(x1, x2)  =  U119_G(x1, x2)
NOT_DIVIDES770_IN_G(x1)  =  NOT_DIVIDES770_IN_G(x1)
U79_G(x1, x2)  =  U79_G(x1, x2)
DIV774_IN_GA(x1, x2)  =  DIV774_IN_GA(x1)
U84_GA(x1, x2, x3)  =  U84_GA(x1, x3)
QUOT824_IN_GGA(x1, x2, x3)  =  QUOT824_IN_GGA(x1, x2)
U17_GGA(x1, x2, x3, x4)  =  U17_GGA(x1, x2, x4)
U18_GGA(x1, x2)  =  U18_GGA(x2)
QUOT863_IN_A(x1)  =  QUOT863_IN_A
U19_GGA(x1, x2)  =  U19_GGA(x2)
U20_GGA(x1, x2)  =  U20_GGA(x2)
U21_GGA(x1, x2)  =  U21_GGA(x2)
QUOT876_IN_A(x1)  =  QUOT876_IN_A
U31_A(x1, x2)  =  U31_A(x2)
U85_GA(x1, x2)  =  U85_GA(x2)
U86_GA(x1, x2)  =  U86_GA(x2)
U87_GA(x1, x2)  =  U87_GA(x2)
U80_G(x1, x2)  =  U80_G(x1, x2)
U81_G(x1, x2)  =  U81_G(x1, x2)
U82_G(x1, x2)  =  U82_G(x1, x2)
U83_G(x1, x2)  =  U83_G(x1, x2)
U120_G(x1)  =  U120_G(x1)
U121_G(x1)  =  U121_G(x1)
U122_G(x1)  =  U122_G(x1)
U123_G(x1)  =  U123_G(x1)
U124_G(x1, x2)  =  U124_G(x1, x2)
U125_G(x1, x2)  =  U125_G(x1, x2)
U126_G(x1, x2)  =  U126_G(x1, x2)
U127_G(x1, x2)  =  U127_G(x1, x2)
U128_G(x1, x2)  =  U128_G(x1, x2)
NOT_DIVIDES1072_IN_G(x1)  =  NOT_DIVIDES1072_IN_G(x1)
U88_G(x1, x2)  =  U88_G(x1, x2)
DIV1076_IN_GA(x1, x2)  =  DIV1076_IN_GA(x1)
U93_GA(x1, x2, x3)  =  U93_GA(x1, x3)
QUOT1126_IN_GGA(x1, x2, x3)  =  QUOT1126_IN_GGA(x1, x2)
U24_GGA(x1, x2, x3, x4)  =  U24_GGA(x1, x2, x4)
U25_GGA(x1, x2)  =  U25_GGA(x2)
QUOT1171_IN_A(x1)  =  QUOT1171_IN_A
U26_GGA(x1, x2)  =  U26_GGA(x2)
U27_GGA(x1, x2)  =  U27_GGA(x2)
U28_GGA(x1, x2)  =  U28_GGA(x2)
U29_GGA(x1, x2)  =  U29_GGA(x2)
U94_GA(x1, x2)  =  U94_GA(x2)
U95_GA(x1, x2)  =  U95_GA(x2)
U96_GA(x1, x2)  =  U96_GA(x2)
U97_GA(x1, x2)  =  U97_GA(x2)
U89_G(x1, x2)  =  U89_G(x1, x2)
U90_G(x1, x2)  =  U90_G(x1, x2)
U91_G(x1, x2)  =  U91_G(x1, x2)
U92_G(x1, x2)  =  U92_G(x1, x2)
U129_G(x1)  =  U129_G(x1)
U130_G(x1)  =  U130_G(x1)
U131_G(x1)  =  U131_G(x1)
U132_G(x1)  =  U132_G(x1)
U133_G(x1)  =  U133_G(x1)
U134_G(x1, x2)  =  U134_G(x1, x2)
U135_G(x1, x2)  =  U135_G(x1, x2)
U136_G(x1, x2)  =  U136_G(x1, x2)
U137_G(x1, x2)  =  U137_G(x1, x2)
U138_G(x1, x2)  =  U138_G(x1, x2)
U139_G(x1, x2)  =  U139_G(x1, x2)
P1397_IN_GG(x1, x2)  =  P1397_IN_GG(x1, x2)
U50_GG(x1, x2, x3)  =  U50_GG(x1, x2, x3)
NOT_DIVIDES1398_IN_GG(x1, x2)  =  NOT_DIVIDES1398_IN_GG(x1, x2)
U98_GG(x1, x2, x3)  =  U98_GG(x1, x2, x3)
DIV1402_IN_GGA(x1, x2, x3)  =  DIV1402_IN_GGA(x1, x2)
U103_GGA(x1, x2, x3, x4)  =  U103_GGA(x1, x2, x4)
QUOT1419_IN_GGA(x1, x2, x3)  =  QUOT1419_IN_GGA(x1, x2)
U35_GGA(x1, x2, x3, x4)  =  U35_GGA(x1, x2, x4)
QUOT1481_IN_GGGA(x1, x2, x3, x4)  =  QUOT1481_IN_GGGA(x1, x2, x3)
U32_GGGA(x1, x2, x3, x4, x5)  =  U32_GGGA(x1, x2, x3, x5)
U33_GGGA(x1, x2, x3, x4)  =  U33_GGGA(x1, x2, x4)
U36_GGA(x1, x2, x3)  =  U36_GGA(x1, x3)
QUOT1532_IN_GA(x1, x2)  =  QUOT1532_IN_GA(x1)
U43_GA(x1, x2, x3)  =  U43_GA(x1, x3)
U37_GGA(x1, x2, x3)  =  U37_GGA(x1, x3)
QUOT1615_IN_GA(x1, x2)  =  QUOT1615_IN_GA(x1)
U44_GA(x1, x2, x3)  =  U44_GA(x1, x3)
U38_GGA(x1, x2, x3)  =  U38_GGA(x1, x3)
QUOT1687_IN_GA(x1, x2)  =  QUOT1687_IN_GA(x1)
U45_GA(x1, x2, x3)  =  U45_GA(x1, x3)
U39_GGA(x1, x2, x3)  =  U39_GGA(x1, x3)
QUOT1748_IN_GA(x1, x2)  =  QUOT1748_IN_GA(x1)
U46_GA(x1, x2, x3)  =  U46_GA(x1, x3)
U40_GGA(x1, x2, x3)  =  U40_GGA(x1, x3)
QUOT1798_IN_GA(x1, x2)  =  QUOT1798_IN_GA(x1)
U47_GA(x1, x2, x3)  =  U47_GA(x1, x3)
U41_GGA(x1, x2, x3)  =  U41_GGA(x1, x3)
QUOT1837_IN_GA(x1, x2)  =  QUOT1837_IN_GA(x1)
U48_GA(x1, x2, x3)  =  U48_GA(x1, x3)
U34_GGGA(x1, x2, x3)  =  U34_GGGA(x1, x3)
QUOT1514_IN_GA(x1, x2)  =  QUOT1514_IN_GA(x1)
U42_GA(x1, x2, x3)  =  U42_GA(x1, x3)
U99_GG(x1, x2, x3)  =  U99_GG(x1, x2, x3)
U100_GG(x1, x2, x3)  =  U100_GG(x1, x2, x3)
U101_GG(x1, x2, x3)  =  U101_GG(x1, x2, x3)
U102_GG(x1, x2, x3)  =  U102_GG(x1, x2, x3)
U51_GG(x1, x2)  =  U51_GG(x1, x2)
U52_GG(x1, x2, x3)  =  U52_GG(x1, x2, x3)
U53_GG(x1, x2, x3)  =  U53_GG(x1, x2, x3)

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

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 17 SCCs with 245 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

QUOT1514_IN_GA(s(T1363), s(X10490)) → QUOT1514_IN_GA(T1363, X10490)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
QUOT1514_IN_GA(x1, x2)  =  QUOT1514_IN_GA(x1)

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

(10) UsableRulesProof (EQUIVALENT transformation)

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

(11) Obligation:

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

QUOT1514_IN_GA(s(T1363), s(X10490)) → QUOT1514_IN_GA(T1363, X10490)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1514_IN_GA(x1, x2)  =  QUOT1514_IN_GA(x1)

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

(12) PiDPToQDPProof (SOUND transformation)

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

(13) Obligation:

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

QUOT1514_IN_GA(s(T1363)) → QUOT1514_IN_GA(T1363)

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

(14) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1514_IN_GA(s(T1363)) → QUOT1514_IN_GA(T1363)
  The graph contains the following edges 1 > 1

(15) YES

(16) Obligation:

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

QUOT1837_IN_GA(s(s(T1579)), s(X12104)) → QUOT1837_IN_GA(T1579, X12104)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
QUOT1837_IN_GA(x1, x2)  =  QUOT1837_IN_GA(x1)

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

(17) UsableRulesProof (EQUIVALENT transformation)

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

(18) Obligation:

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

QUOT1837_IN_GA(s(s(T1579)), s(X12104)) → QUOT1837_IN_GA(T1579, X12104)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1837_IN_GA(x1, x2)  =  QUOT1837_IN_GA(x1)

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

(19) PiDPToQDPProof (SOUND transformation)

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

(20) Obligation:

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

QUOT1837_IN_GA(s(s(T1579))) → QUOT1837_IN_GA(T1579)

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

(21) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1837_IN_GA(s(s(T1579))) → QUOT1837_IN_GA(T1579)
  The graph contains the following edges 1 > 1

(22) YES

(23) Obligation:

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

QUOT1798_IN_GA(s(s(s(T1557))), s(X11952)) → QUOT1798_IN_GA(T1557, X11952)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
QUOT1798_IN_GA(x1, x2)  =  QUOT1798_IN_GA(x1)

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

(24) UsableRulesProof (EQUIVALENT transformation)

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

(25) Obligation:

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

QUOT1798_IN_GA(s(s(s(T1557))), s(X11952)) → QUOT1798_IN_GA(T1557, X11952)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1798_IN_GA(x1, x2)  =  QUOT1798_IN_GA(x1)

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

(26) PiDPToQDPProof (SOUND transformation)

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

(27) Obligation:

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

QUOT1798_IN_GA(s(s(s(T1557)))) → QUOT1798_IN_GA(T1557)

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

(28) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1798_IN_GA(s(s(s(T1557)))) → QUOT1798_IN_GA(T1557)
  The graph contains the following edges 1 > 1

(29) YES

(30) Obligation:

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

QUOT1748_IN_GA(s(s(s(s(T1529)))), s(X11752)) → QUOT1748_IN_GA(T1529, X11752)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
QUOT1748_IN_GA(x1, x2)  =  QUOT1748_IN_GA(x1)

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

(31) UsableRulesProof (EQUIVALENT transformation)

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

(32) Obligation:

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

QUOT1748_IN_GA(s(s(s(s(T1529)))), s(X11752)) → QUOT1748_IN_GA(T1529, X11752)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1748_IN_GA(x1, x2)  =  QUOT1748_IN_GA(x1)

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

(33) PiDPToQDPProof (SOUND transformation)

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

(34) Obligation:

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

QUOT1748_IN_GA(s(s(s(s(T1529))))) → QUOT1748_IN_GA(T1529)

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

(35) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1748_IN_GA(s(s(s(s(T1529))))) → QUOT1748_IN_GA(T1529)
  The graph contains the following edges 1 > 1

(36) YES

(37) Obligation:

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

QUOT1687_IN_GA(s(s(s(s(s(T1495))))), s(X11504)) → QUOT1687_IN_GA(T1495, X11504)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
QUOT1687_IN_GA(x1, x2)  =  QUOT1687_IN_GA(x1)

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

(38) UsableRulesProof (EQUIVALENT transformation)

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

(39) Obligation:

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

QUOT1687_IN_GA(s(s(s(s(s(T1495))))), s(X11504)) → QUOT1687_IN_GA(T1495, X11504)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1687_IN_GA(x1, x2)  =  QUOT1687_IN_GA(x1)

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

(40) PiDPToQDPProof (SOUND transformation)

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

(41) Obligation:

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

QUOT1687_IN_GA(s(s(s(s(s(T1495)))))) → QUOT1687_IN_GA(T1495)

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

(42) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1687_IN_GA(s(s(s(s(s(T1495)))))) → QUOT1687_IN_GA(T1495)
  The graph contains the following edges 1 > 1

(43) YES

(44) Obligation:

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

QUOT1615_IN_GA(s(s(s(s(s(s(T1455)))))), s(X11208)) → QUOT1615_IN_GA(T1455, X11208)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
QUOT1615_IN_GA(x1, x2)  =  QUOT1615_IN_GA(x1)

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

(45) UsableRulesProof (EQUIVALENT transformation)

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

(46) Obligation:

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

QUOT1615_IN_GA(s(s(s(s(s(s(T1455)))))), s(X11208)) → QUOT1615_IN_GA(T1455, X11208)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1615_IN_GA(x1, x2)  =  QUOT1615_IN_GA(x1)

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

(47) PiDPToQDPProof (SOUND transformation)

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

(48) Obligation:

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

QUOT1615_IN_GA(s(s(s(s(s(s(T1455))))))) → QUOT1615_IN_GA(T1455)

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

(49) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1615_IN_GA(s(s(s(s(s(s(T1455))))))) → QUOT1615_IN_GA(T1455)
  The graph contains the following edges 1 > 1

(50) YES

(51) Obligation:

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

QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → QUOT1532_IN_GA(T1409, X10864)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
QUOT1532_IN_GA(x1, x2)  =  QUOT1532_IN_GA(x1)

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

(52) UsableRulesProof (EQUIVALENT transformation)

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

(53) Obligation:

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

QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → QUOT1532_IN_GA(T1409, X10864)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1532_IN_GA(x1, x2)  =  QUOT1532_IN_GA(x1)

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

(54) PiDPToQDPProof (SOUND transformation)

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

(55) Obligation:

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

QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409)))))))) → QUOT1532_IN_GA(T1409)

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

(56) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409)))))))) → QUOT1532_IN_GA(T1409)
  The graph contains the following edges 1 > 1

(57) YES

(58) Obligation:

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

QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → QUOT1481_IN_GGGA(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)
QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303, X10279) → QUOT1481_IN_GGGA(T1301, T1302, T1303, X10279)
QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347), s(X10388)) → QUOT1419_IN_GGA(T1346, T1347, X10388)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
QUOT1419_IN_GGA(x1, x2, x3)  =  QUOT1419_IN_GGA(x1, x2)
QUOT1481_IN_GGGA(x1, x2, x3, x4)  =  QUOT1481_IN_GGGA(x1, x2, x3)

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

(59) UsableRulesProof (EQUIVALENT transformation)

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

(60) Obligation:

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

QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → QUOT1481_IN_GGGA(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)
QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303, X10279) → QUOT1481_IN_GGGA(T1301, T1302, T1303, X10279)
QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347), s(X10388)) → QUOT1419_IN_GGA(T1346, T1347, X10388)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
0  =  0
QUOT1419_IN_GGA(x1, x2, x3)  =  QUOT1419_IN_GGA(x1, x2)
QUOT1481_IN_GGGA(x1, x2, x3, x4)  =  QUOT1481_IN_GGGA(x1, x2, x3)

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

(61) PiDPToQDPProof (SOUND transformation)

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

(62) Obligation:

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

QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271))))))) → QUOT1481_IN_GGGA(T1270, T1271, s(s(s(s(s(s(s(T1271))))))))
QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303) → QUOT1481_IN_GGGA(T1301, T1302, T1303)
QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347)) → QUOT1419_IN_GGA(T1346, T1347)

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

(63) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347)) → QUOT1419_IN_GGA(T1346, T1347)
  The graph contains the following edges 1 > 1, 3 > 2

• QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303) → QUOT1481_IN_GGGA(T1301, T1302, T1303)
  The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3

• QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271))))))) → QUOT1481_IN_GGGA(T1270, T1271, s(s(s(s(s(s(s(T1271))))))))
  The graph contains the following edges 1 > 1, 2 > 2

(64) YES

(65) Obligation:

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

QUOT1126_IN_GGA(s(T1020), T1021, X7625) → QUOT1126_IN_GGA(T1020, T1021, X7625)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
QUOT1126_IN_GGA(x1, x2, x3)  =  QUOT1126_IN_GGA(x1, x2)

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

(66) UsableRulesProof (EQUIVALENT transformation)

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

(67) Obligation:

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

QUOT1126_IN_GGA(s(T1020), T1021, X7625) → QUOT1126_IN_GGA(T1020, T1021, X7625)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1126_IN_GGA(x1, x2, x3)  =  QUOT1126_IN_GGA(x1, x2)

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

(68) PiDPToQDPProof (SOUND transformation)

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

(69) Obligation:

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

QUOT1126_IN_GGA(s(T1020), T1021) → QUOT1126_IN_GGA(T1020, T1021)

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

(70) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1126_IN_GGA(s(T1020), T1021) → QUOT1126_IN_GGA(T1020, T1021)
  The graph contains the following edges 1 > 1, 2 >= 2

(71) YES

(72) Obligation:

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

QUOT824_IN_GGA(s(T814), T815, X5270) → QUOT824_IN_GGA(T814, T815, X5270)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
QUOT824_IN_GGA(x1, x2, x3)  =  QUOT824_IN_GGA(x1, x2)

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

(73) UsableRulesProof (EQUIVALENT transformation)

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

(74) Obligation:

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

QUOT824_IN_GGA(s(T814), T815, X5270) → QUOT824_IN_GGA(T814, T815, X5270)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT824_IN_GGA(x1, x2, x3)  =  QUOT824_IN_GGA(x1, x2)

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

(75) PiDPToQDPProof (SOUND transformation)

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

(76) Obligation:

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

QUOT824_IN_GGA(s(T814), T815) → QUOT824_IN_GGA(T814, T815)

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

(77) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT824_IN_GGA(s(T814), T815) → QUOT824_IN_GGA(T814, T815)
  The graph contains the following edges 1 > 1, 2 >= 2

(78) YES

(79) Obligation:

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

QUOT551_IN_GGA(s(T614), T615, X3256) → QUOT551_IN_GGA(T614, T615, X3256)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
QUOT551_IN_GGA(x1, x2, x3)  =  QUOT551_IN_GGA(x1, x2)

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

(80) UsableRulesProof (EQUIVALENT transformation)

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

(81) Obligation:

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

QUOT551_IN_GGA(s(T614), T615, X3256) → QUOT551_IN_GGA(T614, T615, X3256)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT551_IN_GGA(x1, x2, x3)  =  QUOT551_IN_GGA(x1, x2)

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

(82) PiDPToQDPProof (SOUND transformation)

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

(83) Obligation:

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

QUOT551_IN_GGA(s(T614), T615) → QUOT551_IN_GGA(T614, T615)

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

(84) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT551_IN_GGA(s(T614), T615) → QUOT551_IN_GGA(T614, T615)
  The graph contains the following edges 1 > 1, 2 >= 2

(85) YES

(86) Obligation:

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

QUOT313_IN_GGA(s(T420), T421, X1654) → QUOT313_IN_GGA(T420, T421, X1654)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
QUOT313_IN_GGA(x1, x2, x3)  =  QUOT313_IN_GGA(x1, x2)

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

(87) UsableRulesProof (EQUIVALENT transformation)

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

(88) Obligation:

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

QUOT313_IN_GGA(s(T420), T421, X1654) → QUOT313_IN_GGA(T420, T421, X1654)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT313_IN_GGA(x1, x2, x3)  =  QUOT313_IN_GGA(x1, x2)

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

(89) PiDPToQDPProof (SOUND transformation)

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

(90) Obligation:

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

QUOT313_IN_GGA(s(T420), T421) → QUOT313_IN_GGA(T420, T421)

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

(91) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT313_IN_GGA(s(T420), T421) → QUOT313_IN_GGA(T420, T421)
  The graph contains the following edges 1 > 1, 2 >= 2

(92) YES

(93) Obligation:

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

NEQ236_IN_GA(s(T281), s(T282)) → NEQ236_IN_GA(T281, T282)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
NEQ236_IN_GA(x1, x2)  =  NEQ236_IN_GA(x1)

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

(94) UsableRulesProof (EQUIVALENT transformation)

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

(95) Obligation:

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

NEQ236_IN_GA(s(T281), s(T282)) → NEQ236_IN_GA(T281, T282)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
NEQ236_IN_GA(x1, x2)  =  NEQ236_IN_GA(x1)

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

(96) PiDPToQDPProof (SOUND transformation)

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

(97) Obligation:

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

NEQ236_IN_GA(s(T281)) → NEQ236_IN_GA(T281)

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

(98) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• NEQ236_IN_GA(s(T281)) → NEQ236_IN_GA(T281)
  The graph contains the following edges 1 > 1

(99) YES

(100) Obligation:

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

ADD201_IN_AGA(s(T220), T221, s(X1112)) → ADD201_IN_AGA(T220, T221, X1112)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
ADD201_IN_AGA(x1, x2, x3)  =  ADD201_IN_AGA(x2)

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

(101) UsableRulesProof (EQUIVALENT transformation)

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

(102) Obligation:

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

ADD201_IN_AGA(s(T220), T221, s(X1112)) → ADD201_IN_AGA(T220, T221, X1112)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
ADD201_IN_AGA(x1, x2, x3)  =  ADD201_IN_AGA(x2)

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

(103) PiDPToQDPProof (SOUND transformation)

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

(104) Obligation:

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

ADD201_IN_AGA(T221) → ADD201_IN_AGA(T221)

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

(105) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = ADD201_IN_AGA(T221) evaluates to t =ADD201_IN_AGA(T221)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from ADD201_IN_AGA(T221) to ADD201_IN_AGA(T221).

(106) NO

(107) Obligation:

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

TIMES190_IN_GGA(s(T199), T200, X1082) → TIMES190_IN_GGA(T199, T200, X1081)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
TIMES190_IN_GGA(x1, x2, x3)  =  TIMES190_IN_GGA(x1, x2)

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

(108) UsableRulesProof (EQUIVALENT transformation)

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

(109) Obligation:

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

TIMES190_IN_GGA(s(T199), T200, X1082) → TIMES190_IN_GGA(T199, T200, X1081)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
TIMES190_IN_GGA(x1, x2, x3)  =  TIMES190_IN_GGA(x1, x2)

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

(110) PiDPToQDPProof (SOUND transformation)

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

(111) Obligation:

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

TIMES190_IN_GGA(s(T199), T200) → TIMES190_IN_GGA(T199, T200)

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

(112) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• TIMES190_IN_GGA(s(T199), T200) → TIMES190_IN_GGA(T199, T200)
  The graph contains the following edges 1 > 1, 2 >= 2

(113) YES

(114) Obligation:

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

P1397_IN_GG(s(T1603), T1602) → U52_GG(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_GG(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → P1397_IN_GG(T1603, T1602)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
P1397_IN_GG(x1, x2)  =  P1397_IN_GG(x1, x2)
U52_GG(x1, x2, x3)  =  U52_GG(x1, x2, x3)

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

(115) UsableRulesProof (EQUIVALENT transformation)

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

(116) Obligation:

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

P1397_IN_GG(s(T1603), T1602) → U52_GG(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_GG(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → P1397_IN_GG(T1603, T1602)

The TRS R consists of the following rules:

not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))

The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
0  =  0
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
P1397_IN_GG(x1, x2)  =  P1397_IN_GG(x1, x2)
U52_GG(x1, x2, x3)  =  U52_GG(x1, x2, x3)

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

(117) PiDPToQDPProof (SOUND transformation)

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

(118) Obligation:

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

P1397_IN_GG(s(T1603), T1602) → U52_GG(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_GG(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → P1397_IN_GG(T1603, T1602)

The TRS R consists of the following rules:

not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122))
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122))
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122))
div1402_in_gga(0, T1159) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169) → U103_gga(T1168, T1169, quot1419_in_gga(T1168, T1169))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122)) → not_divides1398_out_gg(T1122, T1123)
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122)) → U102_gg(T1122, T1123, neq227_in_ga(T1123))
U103_gga(T1168, T1169, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
times190_in_gga(0, T194) → times190_out_gga(0, T194)
times190_in_gga(s(T199), T200) → U3_gga(T199, T200, times190_in_gga(T199, T200))
times190_in_gga(s(T199), T200) → U4_gga(T199, T200, times190_in_gga(T199, T200))
U102_gg(T1122, T1123, neq227_out_ga(T1123)) → not_divides1398_out_gg(T1122, T1123)
quot1419_in_gga(0, s(T1176)) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193))) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210)))) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227))))) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244)))))) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261))))))) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271))))))) → U35_gga(T1270, T1271, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271)))))))))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0)))))) → U36_gga(T1368, quot1532_in_ga(T1368))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0))))) → U37_gga(T1419, quot1615_in_ga(T1419))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0)))) → U38_gga(T1464, quot1687_in_ga(T1464))
quot1419_in_gga(s(s(T1503)), s(s(0))) → U39_gga(T1503, quot1748_in_ga(T1503))
quot1419_in_gga(s(T1536), s(0)) → U40_gga(T1536, quot1798_in_ga(T1536))
quot1419_in_gga(T1563, 0) → U41_gga(T1563, quot1837_in_ga(T1563))
U3_gga(T199, T200, times190_out_gga(T199, T200)) → times190_out_gga(s(T199), T200)
U4_gga(T199, T200, times190_out_gga(T199, T200)) → U5_gga(T199, T200, add201_in_aga(T200))
neq227_in_ga(T258) → neq227_out_ga(T258)
neq227_in_ga(T263) → U49_ga(T263, neq236_in_ga(T263))
U35_gga(T1270, T1271, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U36_gga(T1368, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
U37_gga(T1419, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
U38_gga(T1464, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
U39_gga(T1503, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
U40_gga(T1536, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
U41_gga(T1563, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U5_gga(T199, T200, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200)
U49_ga(T263, neq236_out_ga(T263)) → neq227_out_ga(T263)
quot1481_in_ggga(0, s(T1287), T1288) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303) → U32_ggga(T1301, T1302, T1303, quot1481_in_ggga(T1301, T1302, T1303))
quot1481_in_ggga(0, 0, T1320) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347)) → U33_ggga(T1346, T1347, quot1419_in_gga(T1346, T1347))
quot1532_in_ga(0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0)) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0))) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0)))) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0))))) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0)))))) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0))))))) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409)))))))) → U43_ga(T1409, quot1532_in_ga(T1409))
quot1615_in_ga(0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0)) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0))) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0)))) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0))))) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0)))))) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455))))))) → U44_ga(T1455, quot1615_in_ga(T1455))
quot1687_in_ga(0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0)) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0))) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0)))) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0))))) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495)))))) → U45_ga(T1495, quot1687_in_ga(T1495))
quot1748_in_ga(0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0)) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0))) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0)))) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529))))) → U46_ga(T1529, quot1748_in_ga(T1529))
quot1798_in_ga(0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0)) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0))) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557)))) → U47_ga(T1557, quot1798_in_ga(T1557))
quot1837_in_ga(0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0)) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579))) → U48_ga(T1579, quot1837_in_ga(T1579))
add201_in_aga(T215) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(T221) → U6_aga(T221, add201_in_aga(T221))
neq236_in_ga(s(T271)) → neq236_out_ga(s(T271))
neq236_in_ga(0) → neq236_out_ga(0)
neq236_in_ga(s(T281)) → U7_ga(T281, neq236_in_ga(T281))
U32_ggga(T1301, T1302, T1303, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U33_ggga(T1346, T1347, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
U43_ga(T1409, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U44_ga(T1455, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U45_ga(T1495, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U46_ga(T1529, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U47_ga(T1557, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U48_ga(T1579, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U6_aga(T221, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U7_ga(T281, neq236_out_ga(T281)) → neq236_out_ga(s(T281))
quot1481_in_ggga(s(T1352), 0, 0) → U34_ggga(T1352, quot1514_in_ga(T1352))
U34_ggga(T1352, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
quot1514_in_ga(0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363)) → U42_ga(T1363, quot1514_in_ga(T1363))
U42_ga(T1363, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))

The set Q consists of the following terms:

not_divides1398_in_gg(x0, x1)
U98_gg(x0, x1, x2)
U99_gg(x0, x1, x2)
div1402_in_gga(x0, x1)
U100_gg(x0, x1, x2)
U101_gg(x0, x1, x2)
U103_gga(x0, x1, x2)
times190_in_gga(x0, x1)
U102_gg(x0, x1, x2)
quot1419_in_gga(x0, x1)
U3_gga(x0, x1, x2)
U4_gga(x0, x1, x2)
neq227_in_ga(x0)
U35_gga(x0, x1, x2)
U36_gga(x0, x1)
U37_gga(x0, x1)
U38_gga(x0, x1)
U39_gga(x0, x1)
U40_gga(x0, x1)
U41_gga(x0, x1)
U5_gga(x0, x1, x2)
U49_ga(x0, x1)
quot1481_in_ggga(x0, x1, x2)
quot1532_in_ga(x0)
quot1615_in_ga(x0)
quot1687_in_ga(x0)
quot1748_in_ga(x0)
quot1798_in_ga(x0)
quot1837_in_ga(x0)
add201_in_aga(x0)
neq236_in_ga(x0)
U32_ggga(x0, x1, x2, x3)
U33_ggga(x0, x1, x2)
U43_ga(x0, x1)
U44_ga(x0, x1)
U45_ga(x0, x1)
U46_ga(x0, x1)
U47_ga(x0, x1)
U48_ga(x0, x1)
U6_aga(x0, x1)
U7_ga(x0, x1)
U34_ggga(x0, x1)
quot1514_in_ga(x0)
U42_ga(x0, x1)

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

(119) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• U52_GG(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → P1397_IN_GG(T1603, T1602)
  The graph contains the following edges 1 >= 1, 3 > 1, 2 >= 2, 3 > 2

• P1397_IN_GG(s(T1603), T1602) → U52_GG(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
  The graph contains the following edges 1 > 1, 2 >= 2

(120) YES

(121) Obligation:

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

QUOT67_IN_GGA(s(T137), T138, X461) → QUOT67_IN_GGA(T137, T138, X461)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g(x1)
U104_g(x1, x2)  =  U104_g(x1, x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x1, x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x1, x2, x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x1, x2, x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x1, x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g(x1)
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x1, x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x1, x2, x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x1, x2, x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x2, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x2, x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x1, x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga(x1)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x1, x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x1, x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x1, x2, x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x1, x2, x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x1, x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g(x1)
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x1, x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x1, x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x1, x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x1, x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x1, x2, x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x1, x2, x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x1, x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g(x1)
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x1, x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x1, x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x1, x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x1, x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x1, x2, x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x1, x2, x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x1, x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g(x1)
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x1, x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x1, x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x1, x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x1, x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x1, x2, x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x1, x2, x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x1, x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g(x1)
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x1, x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x1, x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x1, x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x1, x2, x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x1, x2, x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x1, x2, x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x1, x2, x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x1, x2, x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x1, x2, x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x1, x2, x3, x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x1, x2, x3, x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x1, x2, x4)
U36_gga(x1, x2, x3)  =  U36_gga(x1, x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x1, x2)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U37_gga(x1, x2, x3)  =  U37_gga(x1, x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x1, x2)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U38_gga(x1, x2, x3)  =  U38_gga(x1, x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x1, x2)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U39_gga(x1, x2, x3)  =  U39_gga(x1, x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x1, x2)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
U40_gga(x1, x2, x3)  =  U40_gga(x1, x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x1, x2)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U41_gga(x1, x2, x3)  =  U41_gga(x1, x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x1, x2)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x1, x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x1, x2)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg(x1, x2)
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x1, x2, x3)
U101_gg(x1, x2, x3)  =  U101_gg(x1, x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x1, x2, x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg(x1, x2)
U51_gg(x1, x2)  =  U51_gg(x1, x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x1, x2, x3)
QUOT67_IN_GGA(x1, x2, x3)  =  QUOT67_IN_GGA(x1, x2)

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

(122) UsableRulesProof (EQUIVALENT transformation)

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

(123) Obligation:

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

QUOT67_IN_GGA(s(T137), T138, X461) → QUOT67_IN_GGA(T137, T138, X461)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT67_IN_GGA(x1, x2, x3)  =  QUOT67_IN_GGA(x1, x2)

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

(124) PiDPToQDPProof (SOUND transformation)

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

(125) Obligation:

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

QUOT67_IN_GGA(s(T137), T138) → QUOT67_IN_GGA(T137, T138)

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

(126) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT67_IN_GGA(s(T137), T138) → QUOT67_IN_GGA(T137, T138)
  The graph contains the following edges 1 > 1, 2 >= 2

(127) YES

(128) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
prime1_in: (b)
not_divides13_in: (b)
div17_in: (b,f)
quot67_in: (b,b,f)
times190_in: (b,b,f)
add201_in: (f,b,f)
neq191_in: (b,f)
neq227_in: (b,f)
neq236_in: (b,f)
not_divides259_in: (b)
div263_in: (b,f)
quot313_in: (b,b,f)
quot349_in: (f)
quot467_in: (f)
not_divides497_in: (b)
div501_in: (b,f)
quot551_in: (b,b,f)
quot595_in: (f)
quot740_in: (f)
not_divides770_in: (b)
div774_in: (b,f)
quot824_in: (b,b,f)
quot876_in: (f)
not_divides1072_in: (b)
div1076_in: (b,f)
quot1126_in: (b,b,f)
p1397_in: (b,b)
not_divides1398_in: (b,b)
div1402_in: (b,b,f)
quot1419_in: (b,b,f)
quot1481_in: (b,b,b,f)
quot1532_in: (b,f)
quot1615_in: (b,f)
quot1687_in: (b,f)
quot1748_in: (b,f)
quot1798_in: (b,f)
quot1837_in: (b,f)
quot1514_in: (b,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(129) Obligation:

Pi-finite rewrite system:
The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)

(130) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
Pi DP problem:
The TRS P consists of the following rules:

PRIME1_IN_G(s(s(s(T14)))) → U104_G(T14, not_divides13_in_g(T14))
PRIME1_IN_G(s(s(s(T14)))) → NOT_DIVIDES13_IN_G(T14)
NOT_DIVIDES13_IN_G(T20) → U54_G(T20, div17_in_ga(T20, X38))
NOT_DIVIDES13_IN_G(T20) → DIV17_IN_GA(T20, X38)
DIV17_IN_GA(s(s(s(s(s(s(T117)))))), X412) → U59_GA(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
DIV17_IN_GA(s(s(s(s(s(s(T117)))))), X412) → QUOT67_IN_GGA(T117, s(s(s(s(s(s(s(T117))))))), X412)
QUOT67_IN_GGA(s(T137), T138, X461) → U1_GGA(T137, T138, X461, quot67_in_gga(T137, T138, X461))
QUOT67_IN_GGA(s(T137), T138, X461) → QUOT67_IN_GGA(T137, T138, X461)
QUOT67_IN_GGA(0, 0, s(s(X565))) → U2_GGA(X565, quot88_in_a(X565))
QUOT67_IN_GGA(0, 0, s(s(X565))) → QUOT88_IN_A(X565)
DIV17_IN_GA(s(s(0)), s(X833)) → U60_GA(X833, quot143_in_a(X833))
DIV17_IN_GA(s(s(0)), s(X833)) → QUOT143_IN_A(X833)
DIV17_IN_GA(s(0), s(X910)) → U61_GA(X910, quot158_in_a(X910))
DIV17_IN_GA(s(0), s(X910)) → QUOT158_IN_A(X910)
DIV17_IN_GA(0, s(X987)) → U62_GA(X987, quot173_in_a(X987))
DIV17_IN_GA(0, s(X987)) → QUOT173_IN_A(X987)
NOT_DIVIDES13_IN_G(T20) → U55_G(T20, div17_in_ga(T20, T22))
U55_G(T20, div17_out_ga(T20, T22)) → U56_G(T20, times190_in_gga(T22, T20, X39))
U55_G(T20, div17_out_ga(T20, T22)) → TIMES190_IN_GGA(T22, T20, X39)
TIMES190_IN_GGA(s(T199), T200, X1082) → U3_GGA(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
TIMES190_IN_GGA(s(T199), T200, X1082) → TIMES190_IN_GGA(T199, T200, X1081)
TIMES190_IN_GGA(s(T199), T200, X1082) → U4_GGA(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_GGA(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_GGA(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
U4_GGA(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → ADD201_IN_AGA(T203, T200, X1082)
ADD201_IN_AGA(s(T220), T221, s(X1112)) → U6_AGA(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
ADD201_IN_AGA(s(T220), T221, s(X1112)) → ADD201_IN_AGA(T220, T221, X1112)
U55_G(T20, div17_out_ga(T20, T22)) → U57_G(T20, times190_in_gga(T22, T20, T187))
U57_G(T20, times190_out_gga(T22, T20, T187)) → U58_G(T20, neq191_in_ga(T20, T187))
U57_G(T20, times190_out_gga(T22, T20, T187)) → NEQ191_IN_GA(T20, T187)
NEQ191_IN_GA(T250, s(s(T251))) → U11_GA(T250, T251, neq227_in_ga(T250, T251))
NEQ191_IN_GA(T250, s(s(T251))) → NEQ227_IN_GA(T250, T251)
NEQ227_IN_GA(T263, s(T264)) → U49_GA(T263, T264, neq236_in_ga(T263, T264))
NEQ227_IN_GA(T263, s(T264)) → NEQ236_IN_GA(T263, T264)
NEQ236_IN_GA(s(T281), s(T282)) → U7_GA(T281, T282, neq236_in_ga(T281, T282))
NEQ236_IN_GA(s(T281), s(T282)) → NEQ236_IN_GA(T281, T282)
PRIME1_IN_G(s(s(s(0)))) → U105_G(not_divides13_in_g(0))
PRIME1_IN_G(s(s(s(0)))) → NOT_DIVIDES13_IN_G(0)
PRIME1_IN_G(s(s(s(s(T297))))) → U106_G(T297, not_divides13_in_g(s(T297)))
PRIME1_IN_G(s(s(s(s(T297))))) → NOT_DIVIDES13_IN_G(s(T297))
U106_G(T297, not_divides13_out_g(s(T297))) → U107_G(T297, not_divides259_in_g(T297))
U106_G(T297, not_divides13_out_g(s(T297))) → NOT_DIVIDES259_IN_G(T297)
NOT_DIVIDES259_IN_G(T303) → U63_G(T303, div263_in_ga(T303, X1231))
NOT_DIVIDES259_IN_G(T303) → DIV263_IN_GA(T303, X1231)
DIV263_IN_GA(s(s(s(s(s(s(T400)))))), X1605) → U68_GA(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
DIV263_IN_GA(s(s(s(s(s(s(T400)))))), X1605) → QUOT313_IN_GGA(T400, s(s(s(s(s(s(s(T400))))))), X1605)
QUOT313_IN_GGA(s(T420), T421, X1654) → U8_GGA(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
QUOT313_IN_GGA(s(T420), T421, X1654) → QUOT313_IN_GGA(T420, T421, X1654)
QUOT313_IN_GGA(0, s(0), s(s(X1808))) → U9_GGA(X1808, quot340_in_a(X1808))
QUOT313_IN_GGA(0, s(0), s(s(X1808))) → QUOT340_IN_A(X1808)
QUOT313_IN_GGA(0, 0, s(s(X1842))) → U10_GGA(X1842, quot349_in_a(X1842))
QUOT313_IN_GGA(0, 0, s(s(X1842))) → QUOT349_IN_A(X1842)
QUOT349_IN_A(s(X1937)) → U16_A(X1937, quot88_in_a(X1937))
QUOT349_IN_A(s(X1937)) → QUOT88_IN_A(X1937)
DIV263_IN_GA(s(0), s(X2493)) → U69_GA(X2493, quot446_in_a(X2493))
DIV263_IN_GA(s(0), s(X2493)) → QUOT446_IN_A(X2493)
DIV263_IN_GA(0, s(X2627)) → U70_GA(X2627, quot467_in_a(X2627))
DIV263_IN_GA(0, s(X2627)) → QUOT467_IN_A(X2627)
QUOT467_IN_A(s(X2776)) → U22_A(X2776, quot340_in_a(X2776))
QUOT467_IN_A(s(X2776)) → QUOT340_IN_A(X2776)
NOT_DIVIDES259_IN_G(T303) → U64_G(T303, div263_in_ga(T303, T305))
U64_G(T303, div263_out_ga(T303, T305)) → U65_G(T303, times190_in_gga(T305, T303, X1232))
U64_G(T303, div263_out_ga(T303, T305)) → TIMES190_IN_GGA(T305, T303, X1232)
U64_G(T303, div263_out_ga(T303, T305)) → U66_G(T303, times190_in_gga(T305, T303, T474))
U66_G(T303, times190_out_gga(T305, T303, T474)) → U67_G(T303, neq191_in_ga(s(T303), T474))
U66_G(T303, times190_out_gga(T305, T303, T474)) → NEQ191_IN_GA(s(T303), T474)
PRIME1_IN_G(s(s(s(s(0))))) → U108_G(not_divides13_in_g(s(0)))
PRIME1_IN_G(s(s(s(s(0))))) → NOT_DIVIDES13_IN_G(s(0))
U108_G(not_divides13_out_g(s(0))) → U109_G(not_divides259_in_g(0))
U108_G(not_divides13_out_g(s(0))) → NOT_DIVIDES259_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(T491)))))) → U110_G(T491, not_divides13_in_g(s(s(T491))))
PRIME1_IN_G(s(s(s(s(s(T491)))))) → NOT_DIVIDES13_IN_G(s(s(T491)))
U110_G(T491, not_divides13_out_g(s(s(T491)))) → U111_G(T491, not_divides259_in_g(s(T491)))
U110_G(T491, not_divides13_out_g(s(s(T491)))) → NOT_DIVIDES259_IN_G(s(T491))
U111_G(T491, not_divides259_out_g(s(T491))) → U112_G(T491, not_divides497_in_g(T491))
U111_G(T491, not_divides259_out_g(s(T491))) → NOT_DIVIDES497_IN_G(T491)
NOT_DIVIDES497_IN_G(T497) → U71_G(T497, div501_in_ga(T497, X2833))
NOT_DIVIDES497_IN_G(T497) → DIV501_IN_GA(T497, X2833)
DIV501_IN_GA(s(s(s(s(s(s(T594)))))), X3207) → U76_GA(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
DIV501_IN_GA(s(s(s(s(s(s(T594)))))), X3207) → QUOT551_IN_GGA(T594, s(s(s(s(s(s(s(T594))))))), X3207)
QUOT551_IN_GGA(s(T614), T615, X3256) → U12_GGA(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
QUOT551_IN_GGA(s(T614), T615, X3256) → QUOT551_IN_GGA(T614, T615, X3256)
QUOT551_IN_GGA(0, s(s(0)), s(s(X3450))) → U13_GGA(X3450, quot584_in_a(X3450))
QUOT551_IN_GGA(0, s(s(0)), s(s(X3450))) → QUOT584_IN_A(X3450)
QUOT551_IN_GGA(0, s(0), s(s(X3484))) → U14_GGA(X3484, quot173_in_a(X3484))
QUOT551_IN_GGA(0, s(0), s(s(X3484))) → QUOT173_IN_A(X3484)
QUOT551_IN_GGA(0, 0, s(s(X3508))) → U15_GGA(X3508, quot595_in_a(X3508))
QUOT551_IN_GGA(0, 0, s(s(X3508))) → QUOT595_IN_A(X3508)
QUOT595_IN_A(s(X3610)) → U23_A(X3610, quot349_in_a(X3610))
QUOT595_IN_A(s(X3610)) → QUOT349_IN_A(X3610)
DIV501_IN_GA(s(0), s(s(X4604))) → U77_GA(X4604, quot584_in_a(X4604))
DIV501_IN_GA(s(0), s(s(X4604))) → QUOT584_IN_A(X4604)
DIV501_IN_GA(0, s(X4627)) → U78_GA(X4627, quot740_in_a(X4627))
DIV501_IN_GA(0, s(X4627)) → QUOT740_IN_A(X4627)
QUOT740_IN_A(s(X4783)) → U30_A(X4783, quot173_in_a(X4783))
QUOT740_IN_A(s(X4783)) → QUOT173_IN_A(X4783)
NOT_DIVIDES497_IN_G(T497) → U72_G(T497, div501_in_ga(T497, T499))
U72_G(T497, div501_out_ga(T497, T499)) → U73_G(T497, times190_in_gga(T499, T497, X2834))
U72_G(T497, div501_out_ga(T497, T499)) → TIMES190_IN_GGA(T499, T497, X2834)
U72_G(T497, div501_out_ga(T497, T499)) → U74_G(T497, times190_in_gga(T499, T497, T674))
U74_G(T497, times190_out_gga(T499, T497, T674)) → U75_G(T497, neq191_in_ga(s(s(T497)), T674))
U74_G(T497, times190_out_gga(T499, T497, T674)) → NEQ191_IN_GA(s(s(T497)), T674)
PRIME1_IN_G(s(s(s(s(s(0)))))) → U113_G(not_divides13_in_g(s(s(0))))
PRIME1_IN_G(s(s(s(s(s(0)))))) → NOT_DIVIDES13_IN_G(s(s(0)))
U113_G(not_divides13_out_g(s(s(0)))) → U114_G(not_divides259_in_g(s(0)))
U113_G(not_divides13_out_g(s(s(0)))) → NOT_DIVIDES259_IN_G(s(0))
U114_G(not_divides259_out_g(s(0))) → U115_G(not_divides497_in_g(0))
U114_G(not_divides259_out_g(s(0))) → NOT_DIVIDES497_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(s(T691))))))) → U116_G(T691, not_divides13_in_g(s(s(s(T691)))))
PRIME1_IN_G(s(s(s(s(s(s(T691))))))) → NOT_DIVIDES13_IN_G(s(s(s(T691))))
U116_G(T691, not_divides13_out_g(s(s(s(T691))))) → U117_G(T691, not_divides259_in_g(s(s(T691))))
U116_G(T691, not_divides13_out_g(s(s(s(T691))))) → NOT_DIVIDES259_IN_G(s(s(T691)))
U117_G(T691, not_divides259_out_g(s(s(T691)))) → U118_G(T691, not_divides497_in_g(s(T691)))
U117_G(T691, not_divides259_out_g(s(s(T691)))) → NOT_DIVIDES497_IN_G(s(T691))
U118_G(T691, not_divides497_out_g(s(T691))) → U119_G(T691, not_divides770_in_g(T691))
U118_G(T691, not_divides497_out_g(s(T691))) → NOT_DIVIDES770_IN_G(T691)
NOT_DIVIDES770_IN_G(T697) → U79_G(T697, div774_in_ga(T697, X4847))
NOT_DIVIDES770_IN_G(T697) → DIV774_IN_GA(T697, X4847)
DIV774_IN_GA(s(s(s(s(s(s(T794)))))), X5221) → U84_GA(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
DIV774_IN_GA(s(s(s(s(s(s(T794)))))), X5221) → QUOT824_IN_GGA(T794, s(s(s(s(s(s(s(T794))))))), X5221)
QUOT824_IN_GGA(s(T814), T815, X5270) → U17_GGA(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
QUOT824_IN_GGA(s(T814), T815, X5270) → QUOT824_IN_GGA(T814, T815, X5270)
QUOT824_IN_GGA(0, s(s(s(0))), s(s(X5504))) → U18_GGA(X5504, quot863_in_a(X5504))
QUOT824_IN_GGA(0, s(s(s(0))), s(s(X5504))) → QUOT863_IN_A(X5504)
QUOT824_IN_GGA(0, s(s(0)), s(s(X5538))) → U19_GGA(X5538, quot158_in_a(X5538))
QUOT824_IN_GGA(0, s(s(0)), s(s(X5538))) → QUOT158_IN_A(X5538)
QUOT824_IN_GGA(0, s(0), s(s(X5562))) → U20_GGA(X5562, quot467_in_a(X5562))
QUOT824_IN_GGA(0, s(0), s(s(X5562))) → QUOT467_IN_A(X5562)
QUOT824_IN_GGA(0, 0, s(s(X5586))) → U21_GGA(X5586, quot876_in_a(X5586))
QUOT824_IN_GGA(0, 0, s(s(X5586))) → QUOT876_IN_A(X5586)
QUOT876_IN_A(s(X5688)) → U31_A(X5688, quot595_in_a(X5688))
QUOT876_IN_A(s(X5688)) → QUOT595_IN_A(X5688)
DIV774_IN_GA(s(s(0)), s(s(X6716))) → U85_GA(X6716, quot863_in_a(X6716))
DIV774_IN_GA(s(s(0)), s(s(X6716))) → QUOT863_IN_A(X6716)
DIV774_IN_GA(s(0), s(s(X6952))) → U86_GA(X6952, quot158_in_a(X6952))
DIV774_IN_GA(s(0), s(s(X6952))) → QUOT158_IN_A(X6952)
DIV774_IN_GA(0, s(s(X7138))) → U87_GA(X7138, quot467_in_a(X7138))
DIV774_IN_GA(0, s(s(X7138))) → QUOT467_IN_A(X7138)
NOT_DIVIDES770_IN_G(T697) → U80_G(T697, div774_in_ga(T697, T699))
U80_G(T697, div774_out_ga(T697, T699)) → U81_G(T697, times190_in_gga(T699, T697, X4848))
U80_G(T697, div774_out_ga(T697, T699)) → TIMES190_IN_GGA(T699, T697, X4848)
U80_G(T697, div774_out_ga(T697, T699)) → U82_G(T697, times190_in_gga(T699, T697, T880))
U82_G(T697, times190_out_gga(T699, T697, T880)) → U83_G(T697, neq191_in_ga(s(s(s(T697))), T880))
U82_G(T697, times190_out_gga(T699, T697, T880)) → NEQ191_IN_GA(s(s(s(T697))), T880)
PRIME1_IN_G(s(s(s(s(s(s(0))))))) → U120_G(not_divides13_in_g(s(s(s(0)))))
PRIME1_IN_G(s(s(s(s(s(s(0))))))) → NOT_DIVIDES13_IN_G(s(s(s(0))))
U120_G(not_divides13_out_g(s(s(s(0))))) → U121_G(not_divides259_in_g(s(s(0))))
U120_G(not_divides13_out_g(s(s(s(0))))) → NOT_DIVIDES259_IN_G(s(s(0)))
U121_G(not_divides259_out_g(s(s(0)))) → U122_G(not_divides497_in_g(s(0)))
U121_G(not_divides259_out_g(s(s(0)))) → NOT_DIVIDES497_IN_G(s(0))
U122_G(not_divides497_out_g(s(0))) → U123_G(not_divides770_in_g(0))
U122_G(not_divides497_out_g(s(0))) → NOT_DIVIDES770_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(s(s(T897)))))))) → U124_G(T897, not_divides13_in_g(s(s(s(s(T897))))))
PRIME1_IN_G(s(s(s(s(s(s(s(T897)))))))) → NOT_DIVIDES13_IN_G(s(s(s(s(T897)))))
U124_G(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_G(T897, not_divides259_in_g(s(s(s(T897)))))
U124_G(T897, not_divides13_out_g(s(s(s(s(T897)))))) → NOT_DIVIDES259_IN_G(s(s(s(T897))))
U125_G(T897, not_divides259_out_g(s(s(s(T897))))) → U126_G(T897, not_divides497_in_g(s(s(T897))))
U125_G(T897, not_divides259_out_g(s(s(s(T897))))) → NOT_DIVIDES497_IN_G(s(s(T897)))
U126_G(T897, not_divides497_out_g(s(s(T897)))) → U127_G(T897, not_divides770_in_g(s(T897)))
U126_G(T897, not_divides497_out_g(s(s(T897)))) → NOT_DIVIDES770_IN_G(s(T897))
U127_G(T897, not_divides770_out_g(s(T897))) → U128_G(T897, not_divides1072_in_g(T897))
U127_G(T897, not_divides770_out_g(s(T897))) → NOT_DIVIDES1072_IN_G(T897)
NOT_DIVIDES1072_IN_G(T903) → U88_G(T903, div1076_in_ga(T903, X7202))
NOT_DIVIDES1072_IN_G(T903) → DIV1076_IN_GA(T903, X7202)
DIV1076_IN_GA(s(s(s(s(s(s(T1000)))))), X7576) → U93_GA(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
DIV1076_IN_GA(s(s(s(s(s(s(T1000)))))), X7576) → QUOT1126_IN_GGA(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)
QUOT1126_IN_GGA(s(T1020), T1021, X7625) → U24_GGA(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
QUOT1126_IN_GGA(s(T1020), T1021, X7625) → QUOT1126_IN_GGA(T1020, T1021, X7625)
QUOT1126_IN_GGA(0, s(s(s(s(0)))), s(s(X7899))) → U25_GGA(X7899, quot1171_in_a(X7899))
QUOT1126_IN_GGA(0, s(s(s(s(0)))), s(s(X7899))) → QUOT1171_IN_A(X7899)
QUOT1126_IN_GGA(0, s(s(s(0))), s(s(X7933))) → U26_GGA(X7933, quot143_in_a(X7933))
QUOT1126_IN_GGA(0, s(s(s(0))), s(s(X7933))) → QUOT143_IN_A(X7933)
QUOT1126_IN_GGA(0, s(s(0)), s(s(X7957))) → U27_GGA(X7957, quot446_in_a(X7957))
QUOT1126_IN_GGA(0, s(s(0)), s(s(X7957))) → QUOT446_IN_A(X7957)
QUOT1126_IN_GGA(0, s(0), s(s(X7981))) → U28_GGA(X7981, quot740_in_a(X7981))
QUOT1126_IN_GGA(0, s(0), s(s(X7981))) → QUOT740_IN_A(X7981)
QUOT1126_IN_GGA(0, 0, s(s(s(X8107)))) → U29_GGA(X8107, quot876_in_a(X8107))
QUOT1126_IN_GGA(0, 0, s(s(s(X8107)))) → QUOT876_IN_A(X8107)
DIV1076_IN_GA(s(s(s(0))), s(s(X9055))) → U94_GA(X9055, quot1171_in_a(X9055))
DIV1076_IN_GA(s(s(s(0))), s(s(X9055))) → QUOT1171_IN_A(X9055)
DIV1076_IN_GA(s(s(0)), s(s(X9348))) → U95_GA(X9348, quot143_in_a(X9348))
DIV1076_IN_GA(s(s(0)), s(s(X9348))) → QUOT143_IN_A(X9348)
DIV1076_IN_GA(s(0), s(s(X9591))) → U96_GA(X9591, quot446_in_a(X9591))
DIV1076_IN_GA(s(0), s(s(X9591))) → QUOT446_IN_A(X9591)
DIV1076_IN_GA(0, s(s(X9777))) → U97_GA(X9777, quot740_in_a(X9777))
DIV1076_IN_GA(0, s(s(X9777))) → QUOT740_IN_A(X9777)
NOT_DIVIDES1072_IN_G(T903) → U89_G(T903, div1076_in_ga(T903, T905))
U89_G(T903, div1076_out_ga(T903, T905)) → U90_G(T903, times190_in_gga(T905, T903, X7203))
U89_G(T903, div1076_out_ga(T903, T905)) → TIMES190_IN_GGA(T905, T903, X7203)
U89_G(T903, div1076_out_ga(T903, T905)) → U91_G(T903, times190_in_gga(T905, T903, T1092))
U91_G(T903, times190_out_gga(T905, T903, T1092)) → U92_G(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U91_G(T903, times190_out_gga(T905, T903, T1092)) → NEQ191_IN_GA(s(s(s(s(T903)))), T1092)
PRIME1_IN_G(s(s(s(s(s(s(s(0)))))))) → U129_G(not_divides13_in_g(s(s(s(s(0))))))
PRIME1_IN_G(s(s(s(s(s(s(s(0)))))))) → NOT_DIVIDES13_IN_G(s(s(s(s(0)))))
U129_G(not_divides13_out_g(s(s(s(s(0)))))) → U130_G(not_divides259_in_g(s(s(s(0)))))
U129_G(not_divides13_out_g(s(s(s(s(0)))))) → NOT_DIVIDES259_IN_G(s(s(s(0))))
U130_G(not_divides259_out_g(s(s(s(0))))) → U131_G(not_divides497_in_g(s(s(0))))
U130_G(not_divides259_out_g(s(s(s(0))))) → NOT_DIVIDES497_IN_G(s(s(0)))
U131_G(not_divides497_out_g(s(s(0)))) → U132_G(not_divides770_in_g(s(0)))
U131_G(not_divides497_out_g(s(s(0)))) → NOT_DIVIDES770_IN_G(s(0))
U132_G(not_divides770_out_g(s(0))) → U133_G(not_divides1072_in_g(0))
U132_G(not_divides770_out_g(s(0))) → NOT_DIVIDES1072_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(s(s(s(T1109))))))))) → U134_G(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
PRIME1_IN_G(s(s(s(s(s(s(s(s(T1109))))))))) → NOT_DIVIDES13_IN_G(s(s(s(s(s(T1109))))))
U134_G(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_G(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U134_G(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → NOT_DIVIDES259_IN_G(s(s(s(s(T1109)))))
U135_G(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_G(T1109, not_divides497_in_g(s(s(s(T1109)))))
U135_G(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → NOT_DIVIDES497_IN_G(s(s(s(T1109))))
U136_G(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_G(T1109, not_divides770_in_g(s(s(T1109))))
U136_G(T1109, not_divides497_out_g(s(s(s(T1109))))) → NOT_DIVIDES770_IN_G(s(s(T1109)))
U137_G(T1109, not_divides770_out_g(s(s(T1109)))) → U138_G(T1109, not_divides1072_in_g(s(T1109)))
U137_G(T1109, not_divides770_out_g(s(s(T1109)))) → NOT_DIVIDES1072_IN_G(s(T1109))
U138_G(T1109, not_divides1072_out_g(s(T1109))) → U139_G(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
U138_G(T1109, not_divides1072_out_g(s(T1109))) → P1397_IN_GG(T1109, s(s(s(s(s(s(s(T1109))))))))
P1397_IN_GG(T1109, T1111) → U50_GG(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
P1397_IN_GG(T1109, T1111) → NOT_DIVIDES1398_IN_GG(T1109, T1111)
NOT_DIVIDES1398_IN_GG(T1122, T1123) → U98_GG(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
NOT_DIVIDES1398_IN_GG(T1122, T1123) → DIV1402_IN_GGA(T1123, T1122, X9845)
DIV1402_IN_GGA(s(T1168), T1169, X9960) → U103_GGA(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
DIV1402_IN_GGA(s(T1168), T1169, X9960) → QUOT1419_IN_GGA(T1168, T1169, X9960)
QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_GGA(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → QUOT1481_IN_GGGA(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)
QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303, X10279) → U32_GGGA(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303, X10279) → QUOT1481_IN_GGGA(T1301, T1302, T1303, X10279)
QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_GGGA(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347), s(X10388)) → QUOT1419_IN_GGA(T1346, T1347, X10388)
QUOT1419_IN_GGA(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_GGA(T1368, X10512, quot1532_in_ga(T1368, X10512))
QUOT1419_IN_GGA(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → QUOT1532_IN_GA(T1368, X10512)
QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_GA(T1409, X10864, quot1532_in_ga(T1409, X10864))
QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → QUOT1532_IN_GA(T1409, X10864)
QUOT1419_IN_GGA(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_GGA(T1419, X10901, quot1615_in_ga(T1419, X10901))
QUOT1419_IN_GGA(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → QUOT1615_IN_GA(T1419, X10901)
QUOT1615_IN_GA(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_GA(T1455, X11208, quot1615_in_ga(T1455, X11208))
QUOT1615_IN_GA(s(s(s(s(s(s(T1455)))))), s(X11208)) → QUOT1615_IN_GA(T1455, X11208)
QUOT1419_IN_GGA(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_GGA(T1464, X11242, quot1687_in_ga(T1464, X11242))
QUOT1419_IN_GGA(s(s(s(T1464))), s(s(s(0))), s(X11242)) → QUOT1687_IN_GA(T1464, X11242)
QUOT1687_IN_GA(s(s(s(s(s(T1495))))), s(X11504)) → U45_GA(T1495, X11504, quot1687_in_ga(T1495, X11504))
QUOT1687_IN_GA(s(s(s(s(s(T1495))))), s(X11504)) → QUOT1687_IN_GA(T1495, X11504)
QUOT1419_IN_GGA(s(s(T1503)), s(s(0)), s(X11535)) → U39_GGA(T1503, X11535, quot1748_in_ga(T1503, X11535))
QUOT1419_IN_GGA(s(s(T1503)), s(s(0)), s(X11535)) → QUOT1748_IN_GA(T1503, X11535)
QUOT1748_IN_GA(s(s(s(s(T1529)))), s(X11752)) → U46_GA(T1529, X11752, quot1748_in_ga(T1529, X11752))
QUOT1748_IN_GA(s(s(s(s(T1529)))), s(X11752)) → QUOT1748_IN_GA(T1529, X11752)
QUOT1419_IN_GGA(s(T1536), s(0), s(X11780)) → U40_GGA(T1536, X11780, quot1798_in_ga(T1536, X11780))
QUOT1419_IN_GGA(s(T1536), s(0), s(X11780)) → QUOT1798_IN_GA(T1536, X11780)
QUOT1798_IN_GA(s(s(s(T1557))), s(X11952)) → U47_GA(T1557, X11952, quot1798_in_ga(T1557, X11952))
QUOT1798_IN_GA(s(s(s(T1557))), s(X11952)) → QUOT1798_IN_GA(T1557, X11952)
QUOT1419_IN_GGA(T1563, 0, s(X11977)) → U41_GGA(T1563, X11977, quot1837_in_ga(T1563, X11977))
QUOT1419_IN_GGA(T1563, 0, s(X11977)) → QUOT1837_IN_GA(T1563, X11977)
QUOT1837_IN_GA(s(s(T1579)), s(X12104)) → U48_GA(T1579, X12104, quot1837_in_ga(T1579, X12104))
QUOT1837_IN_GA(s(s(T1579)), s(X12104)) → QUOT1837_IN_GA(T1579, X12104)
QUOT1481_IN_GGGA(s(T1352), 0, 0, s(s(X10408))) → U34_GGGA(T1352, X10408, quot1514_in_ga(T1352, X10408))
QUOT1481_IN_GGGA(s(T1352), 0, 0, s(s(X10408))) → QUOT1514_IN_GA(T1352, X10408)
QUOT1514_IN_GA(s(T1363), s(X10490)) → U42_GA(T1363, X10490, quot1514_in_ga(T1363, X10490))
QUOT1514_IN_GA(s(T1363), s(X10490)) → QUOT1514_IN_GA(T1363, X10490)
NOT_DIVIDES1398_IN_GG(T1122, T1123) → U99_GG(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_GG(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_GG(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U99_GG(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → TIMES190_IN_GGA(T1126, T1122, X9846)
U99_GG(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_GG(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_GG(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_GG(T1122, T1123, neq227_in_ga(T1123, T1586))
U101_GG(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → NEQ227_IN_GA(T1123, T1586)
P1397_IN_GG(0, T1597) → U51_GG(T1597, not_divides1398_in_gg(0, T1597))
P1397_IN_GG(0, T1597) → NOT_DIVIDES1398_IN_GG(0, T1597)
P1397_IN_GG(s(T1603), T1602) → U52_GG(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
P1397_IN_GG(s(T1603), T1602) → NOT_DIVIDES1398_IN_GG(s(T1603), T1602)
U52_GG(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_GG(T1603, T1602, p1397_in_gg(T1603, T1602))
U52_GG(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → P1397_IN_GG(T1603, T1602)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
PRIME1_IN_G(x1)  =  PRIME1_IN_G(x1)
U104_G(x1, x2)  =  U104_G(x2)
NOT_DIVIDES13_IN_G(x1)  =  NOT_DIVIDES13_IN_G(x1)
U54_G(x1, x2)  =  U54_G(x2)
DIV17_IN_GA(x1, x2)  =  DIV17_IN_GA(x1)
U59_GA(x1, x2, x3)  =  U59_GA(x3)
QUOT67_IN_GGA(x1, x2, x3)  =  QUOT67_IN_GGA(x1, x2)
U1_GGA(x1, x2, x3, x4)  =  U1_GGA(x4)
U2_GGA(x1, x2)  =  U2_GGA(x2)
QUOT88_IN_A(x1)  =  QUOT88_IN_A
U60_GA(x1, x2)  =  U60_GA(x2)
QUOT143_IN_A(x1)  =  QUOT143_IN_A
U61_GA(x1, x2)  =  U61_GA(x2)
QUOT158_IN_A(x1)  =  QUOT158_IN_A
U62_GA(x1, x2)  =  U62_GA(x2)
QUOT173_IN_A(x1)  =  QUOT173_IN_A
U55_G(x1, x2)  =  U55_G(x1, x2)
U56_G(x1, x2)  =  U56_G(x2)
TIMES190_IN_GGA(x1, x2, x3)  =  TIMES190_IN_GGA(x1, x2)
U3_GGA(x1, x2, x3, x4)  =  U3_GGA(x4)
U4_GGA(x1, x2, x3, x4)  =  U4_GGA(x2, x4)
U5_GGA(x1, x2, x3, x4)  =  U5_GGA(x4)
ADD201_IN_AGA(x1, x2, x3)  =  ADD201_IN_AGA(x2)
U6_AGA(x1, x2, x3, x4)  =  U6_AGA(x4)
U57_G(x1, x2)  =  U57_G(x1, x2)
U58_G(x1, x2)  =  U58_G(x2)
NEQ191_IN_GA(x1, x2)  =  NEQ191_IN_GA(x1)
U11_GA(x1, x2, x3)  =  U11_GA(x3)
NEQ227_IN_GA(x1, x2)  =  NEQ227_IN_GA(x1)
U49_GA(x1, x2, x3)  =  U49_GA(x3)
NEQ236_IN_GA(x1, x2)  =  NEQ236_IN_GA(x1)
U7_GA(x1, x2, x3)  =  U7_GA(x3)
U105_G(x1)  =  U105_G(x1)
U106_G(x1, x2)  =  U106_G(x1, x2)
U107_G(x1, x2)  =  U107_G(x2)
NOT_DIVIDES259_IN_G(x1)  =  NOT_DIVIDES259_IN_G(x1)
U63_G(x1, x2)  =  U63_G(x2)
DIV263_IN_GA(x1, x2)  =  DIV263_IN_GA(x1)
U68_GA(x1, x2, x3)  =  U68_GA(x3)
QUOT313_IN_GGA(x1, x2, x3)  =  QUOT313_IN_GGA(x1, x2)
U8_GGA(x1, x2, x3, x4)  =  U8_GGA(x4)
U9_GGA(x1, x2)  =  U9_GGA(x2)
QUOT340_IN_A(x1)  =  QUOT340_IN_A
U10_GGA(x1, x2)  =  U10_GGA(x2)
QUOT349_IN_A(x1)  =  QUOT349_IN_A
U16_A(x1, x2)  =  U16_A(x2)
U69_GA(x1, x2)  =  U69_GA(x2)
QUOT446_IN_A(x1)  =  QUOT446_IN_A
U70_GA(x1, x2)  =  U70_GA(x2)
QUOT467_IN_A(x1)  =  QUOT467_IN_A
U22_A(x1, x2)  =  U22_A(x2)
U64_G(x1, x2)  =  U64_G(x1, x2)
U65_G(x1, x2)  =  U65_G(x2)
U66_G(x1, x2)  =  U66_G(x1, x2)
U67_G(x1, x2)  =  U67_G(x2)
U108_G(x1)  =  U108_G(x1)
U109_G(x1)  =  U109_G(x1)
U110_G(x1, x2)  =  U110_G(x1, x2)
U111_G(x1, x2)  =  U111_G(x1, x2)
U112_G(x1, x2)  =  U112_G(x2)
NOT_DIVIDES497_IN_G(x1)  =  NOT_DIVIDES497_IN_G(x1)
U71_G(x1, x2)  =  U71_G(x2)
DIV501_IN_GA(x1, x2)  =  DIV501_IN_GA(x1)
U76_GA(x1, x2, x3)  =  U76_GA(x3)
QUOT551_IN_GGA(x1, x2, x3)  =  QUOT551_IN_GGA(x1, x2)
U12_GGA(x1, x2, x3, x4)  =  U12_GGA(x4)
U13_GGA(x1, x2)  =  U13_GGA(x2)
QUOT584_IN_A(x1)  =  QUOT584_IN_A
U14_GGA(x1, x2)  =  U14_GGA(x2)
U15_GGA(x1, x2)  =  U15_GGA(x2)
QUOT595_IN_A(x1)  =  QUOT595_IN_A
U23_A(x1, x2)  =  U23_A(x2)
U77_GA(x1, x2)  =  U77_GA(x2)
U78_GA(x1, x2)  =  U78_GA(x2)
QUOT740_IN_A(x1)  =  QUOT740_IN_A
U30_A(x1, x2)  =  U30_A(x2)
U72_G(x1, x2)  =  U72_G(x1, x2)
U73_G(x1, x2)  =  U73_G(x2)
U74_G(x1, x2)  =  U74_G(x1, x2)
U75_G(x1, x2)  =  U75_G(x2)
U113_G(x1)  =  U113_G(x1)
U114_G(x1)  =  U114_G(x1)
U115_G(x1)  =  U115_G(x1)
U116_G(x1, x2)  =  U116_G(x1, x2)
U117_G(x1, x2)  =  U117_G(x1, x2)
U118_G(x1, x2)  =  U118_G(x1, x2)
U119_G(x1, x2)  =  U119_G(x2)
NOT_DIVIDES770_IN_G(x1)  =  NOT_DIVIDES770_IN_G(x1)
U79_G(x1, x2)  =  U79_G(x2)
DIV774_IN_GA(x1, x2)  =  DIV774_IN_GA(x1)
U84_GA(x1, x2, x3)  =  U84_GA(x3)
QUOT824_IN_GGA(x1, x2, x3)  =  QUOT824_IN_GGA(x1, x2)
U17_GGA(x1, x2, x3, x4)  =  U17_GGA(x4)
U18_GGA(x1, x2)  =  U18_GGA(x2)
QUOT863_IN_A(x1)  =  QUOT863_IN_A
U19_GGA(x1, x2)  =  U19_GGA(x2)
U20_GGA(x1, x2)  =  U20_GGA(x2)
U21_GGA(x1, x2)  =  U21_GGA(x2)
QUOT876_IN_A(x1)  =  QUOT876_IN_A
U31_A(x1, x2)  =  U31_A(x2)
U85_GA(x1, x2)  =  U85_GA(x2)
U86_GA(x1, x2)  =  U86_GA(x2)
U87_GA(x1, x2)  =  U87_GA(x2)
U80_G(x1, x2)  =  U80_G(x1, x2)
U81_G(x1, x2)  =  U81_G(x2)
U82_G(x1, x2)  =  U82_G(x1, x2)
U83_G(x1, x2)  =  U83_G(x2)
U120_G(x1)  =  U120_G(x1)
U121_G(x1)  =  U121_G(x1)
U122_G(x1)  =  U122_G(x1)
U123_G(x1)  =  U123_G(x1)
U124_G(x1, x2)  =  U124_G(x1, x2)
U125_G(x1, x2)  =  U125_G(x1, x2)
U126_G(x1, x2)  =  U126_G(x1, x2)
U127_G(x1, x2)  =  U127_G(x1, x2)
U128_G(x1, x2)  =  U128_G(x2)
NOT_DIVIDES1072_IN_G(x1)  =  NOT_DIVIDES1072_IN_G(x1)
U88_G(x1, x2)  =  U88_G(x2)
DIV1076_IN_GA(x1, x2)  =  DIV1076_IN_GA(x1)
U93_GA(x1, x2, x3)  =  U93_GA(x3)
QUOT1126_IN_GGA(x1, x2, x3)  =  QUOT1126_IN_GGA(x1, x2)
U24_GGA(x1, x2, x3, x4)  =  U24_GGA(x4)
U25_GGA(x1, x2)  =  U25_GGA(x2)
QUOT1171_IN_A(x1)  =  QUOT1171_IN_A
U26_GGA(x1, x2)  =  U26_GGA(x2)
U27_GGA(x1, x2)  =  U27_GGA(x2)
U28_GGA(x1, x2)  =  U28_GGA(x2)
U29_GGA(x1, x2)  =  U29_GGA(x2)
U94_GA(x1, x2)  =  U94_GA(x2)
U95_GA(x1, x2)  =  U95_GA(x2)
U96_GA(x1, x2)  =  U96_GA(x2)
U97_GA(x1, x2)  =  U97_GA(x2)
U89_G(x1, x2)  =  U89_G(x1, x2)
U90_G(x1, x2)  =  U90_G(x2)
U91_G(x1, x2)  =  U91_G(x1, x2)
U92_G(x1, x2)  =  U92_G(x2)
U129_G(x1)  =  U129_G(x1)
U130_G(x1)  =  U130_G(x1)
U131_G(x1)  =  U131_G(x1)
U132_G(x1)  =  U132_G(x1)
U133_G(x1)  =  U133_G(x1)
U134_G(x1, x2)  =  U134_G(x1, x2)
U135_G(x1, x2)  =  U135_G(x1, x2)
U136_G(x1, x2)  =  U136_G(x1, x2)
U137_G(x1, x2)  =  U137_G(x1, x2)
U138_G(x1, x2)  =  U138_G(x1, x2)
U139_G(x1, x2)  =  U139_G(x2)
P1397_IN_GG(x1, x2)  =  P1397_IN_GG(x1, x2)
U50_GG(x1, x2, x3)  =  U50_GG(x3)
NOT_DIVIDES1398_IN_GG(x1, x2)  =  NOT_DIVIDES1398_IN_GG(x1, x2)
U98_GG(x1, x2, x3)  =  U98_GG(x3)
DIV1402_IN_GGA(x1, x2, x3)  =  DIV1402_IN_GGA(x1, x2)
U103_GGA(x1, x2, x3, x4)  =  U103_GGA(x4)
QUOT1419_IN_GGA(x1, x2, x3)  =  QUOT1419_IN_GGA(x1, x2)
U35_GGA(x1, x2, x3, x4)  =  U35_GGA(x4)
QUOT1481_IN_GGGA(x1, x2, x3, x4)  =  QUOT1481_IN_GGGA(x1, x2, x3)
U32_GGGA(x1, x2, x3, x4, x5)  =  U32_GGGA(x5)
U33_GGGA(x1, x2, x3, x4)  =  U33_GGGA(x4)
U36_GGA(x1, x2, x3)  =  U36_GGA(x3)
QUOT1532_IN_GA(x1, x2)  =  QUOT1532_IN_GA(x1)
U43_GA(x1, x2, x3)  =  U43_GA(x3)
U37_GGA(x1, x2, x3)  =  U37_GGA(x3)
QUOT1615_IN_GA(x1, x2)  =  QUOT1615_IN_GA(x1)
U44_GA(x1, x2, x3)  =  U44_GA(x3)
U38_GGA(x1, x2, x3)  =  U38_GGA(x3)
QUOT1687_IN_GA(x1, x2)  =  QUOT1687_IN_GA(x1)
U45_GA(x1, x2, x3)  =  U45_GA(x3)
U39_GGA(x1, x2, x3)  =  U39_GGA(x3)
QUOT1748_IN_GA(x1, x2)  =  QUOT1748_IN_GA(x1)
U46_GA(x1, x2, x3)  =  U46_GA(x3)
U40_GGA(x1, x2, x3)  =  U40_GGA(x3)
QUOT1798_IN_GA(x1, x2)  =  QUOT1798_IN_GA(x1)
U47_GA(x1, x2, x3)  =  U47_GA(x3)
U41_GGA(x1, x2, x3)  =  U41_GGA(x3)
QUOT1837_IN_GA(x1, x2)  =  QUOT1837_IN_GA(x1)
U48_GA(x1, x2, x3)  =  U48_GA(x3)
U34_GGGA(x1, x2, x3)  =  U34_GGGA(x3)
QUOT1514_IN_GA(x1, x2)  =  QUOT1514_IN_GA(x1)
U42_GA(x1, x2, x3)  =  U42_GA(x3)
U99_GG(x1, x2, x3)  =  U99_GG(x1, x2, x3)
U100_GG(x1, x2, x3)  =  U100_GG(x3)
U101_GG(x1, x2, x3)  =  U101_GG(x2, x3)
U102_GG(x1, x2, x3)  =  U102_GG(x3)
U51_GG(x1, x2)  =  U51_GG(x2)
U52_GG(x1, x2, x3)  =  U52_GG(x1, x2, x3)
U53_GG(x1, x2, x3)  =  U53_GG(x3)

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

(131) Obligation:

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

PRIME1_IN_G(s(s(s(T14)))) → U104_G(T14, not_divides13_in_g(T14))
PRIME1_IN_G(s(s(s(T14)))) → NOT_DIVIDES13_IN_G(T14)
NOT_DIVIDES13_IN_G(T20) → U54_G(T20, div17_in_ga(T20, X38))
NOT_DIVIDES13_IN_G(T20) → DIV17_IN_GA(T20, X38)
DIV17_IN_GA(s(s(s(s(s(s(T117)))))), X412) → U59_GA(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
DIV17_IN_GA(s(s(s(s(s(s(T117)))))), X412) → QUOT67_IN_GGA(T117, s(s(s(s(s(s(s(T117))))))), X412)
QUOT67_IN_GGA(s(T137), T138, X461) → U1_GGA(T137, T138, X461, quot67_in_gga(T137, T138, X461))
QUOT67_IN_GGA(s(T137), T138, X461) → QUOT67_IN_GGA(T137, T138, X461)
QUOT67_IN_GGA(0, 0, s(s(X565))) → U2_GGA(X565, quot88_in_a(X565))
QUOT67_IN_GGA(0, 0, s(s(X565))) → QUOT88_IN_A(X565)
DIV17_IN_GA(s(s(0)), s(X833)) → U60_GA(X833, quot143_in_a(X833))
DIV17_IN_GA(s(s(0)), s(X833)) → QUOT143_IN_A(X833)
DIV17_IN_GA(s(0), s(X910)) → U61_GA(X910, quot158_in_a(X910))
DIV17_IN_GA(s(0), s(X910)) → QUOT158_IN_A(X910)
DIV17_IN_GA(0, s(X987)) → U62_GA(X987, quot173_in_a(X987))
DIV17_IN_GA(0, s(X987)) → QUOT173_IN_A(X987)
NOT_DIVIDES13_IN_G(T20) → U55_G(T20, div17_in_ga(T20, T22))
U55_G(T20, div17_out_ga(T20, T22)) → U56_G(T20, times190_in_gga(T22, T20, X39))
U55_G(T20, div17_out_ga(T20, T22)) → TIMES190_IN_GGA(T22, T20, X39)
TIMES190_IN_GGA(s(T199), T200, X1082) → U3_GGA(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
TIMES190_IN_GGA(s(T199), T200, X1082) → TIMES190_IN_GGA(T199, T200, X1081)
TIMES190_IN_GGA(s(T199), T200, X1082) → U4_GGA(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_GGA(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_GGA(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
U4_GGA(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → ADD201_IN_AGA(T203, T200, X1082)
ADD201_IN_AGA(s(T220), T221, s(X1112)) → U6_AGA(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
ADD201_IN_AGA(s(T220), T221, s(X1112)) → ADD201_IN_AGA(T220, T221, X1112)
U55_G(T20, div17_out_ga(T20, T22)) → U57_G(T20, times190_in_gga(T22, T20, T187))
U57_G(T20, times190_out_gga(T22, T20, T187)) → U58_G(T20, neq191_in_ga(T20, T187))
U57_G(T20, times190_out_gga(T22, T20, T187)) → NEQ191_IN_GA(T20, T187)
NEQ191_IN_GA(T250, s(s(T251))) → U11_GA(T250, T251, neq227_in_ga(T250, T251))
NEQ191_IN_GA(T250, s(s(T251))) → NEQ227_IN_GA(T250, T251)
NEQ227_IN_GA(T263, s(T264)) → U49_GA(T263, T264, neq236_in_ga(T263, T264))
NEQ227_IN_GA(T263, s(T264)) → NEQ236_IN_GA(T263, T264)
NEQ236_IN_GA(s(T281), s(T282)) → U7_GA(T281, T282, neq236_in_ga(T281, T282))
NEQ236_IN_GA(s(T281), s(T282)) → NEQ236_IN_GA(T281, T282)
PRIME1_IN_G(s(s(s(0)))) → U105_G(not_divides13_in_g(0))
PRIME1_IN_G(s(s(s(0)))) → NOT_DIVIDES13_IN_G(0)
PRIME1_IN_G(s(s(s(s(T297))))) → U106_G(T297, not_divides13_in_g(s(T297)))
PRIME1_IN_G(s(s(s(s(T297))))) → NOT_DIVIDES13_IN_G(s(T297))
U106_G(T297, not_divides13_out_g(s(T297))) → U107_G(T297, not_divides259_in_g(T297))
U106_G(T297, not_divides13_out_g(s(T297))) → NOT_DIVIDES259_IN_G(T297)
NOT_DIVIDES259_IN_G(T303) → U63_G(T303, div263_in_ga(T303, X1231))
NOT_DIVIDES259_IN_G(T303) → DIV263_IN_GA(T303, X1231)
DIV263_IN_GA(s(s(s(s(s(s(T400)))))), X1605) → U68_GA(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
DIV263_IN_GA(s(s(s(s(s(s(T400)))))), X1605) → QUOT313_IN_GGA(T400, s(s(s(s(s(s(s(T400))))))), X1605)
QUOT313_IN_GGA(s(T420), T421, X1654) → U8_GGA(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
QUOT313_IN_GGA(s(T420), T421, X1654) → QUOT313_IN_GGA(T420, T421, X1654)
QUOT313_IN_GGA(0, s(0), s(s(X1808))) → U9_GGA(X1808, quot340_in_a(X1808))
QUOT313_IN_GGA(0, s(0), s(s(X1808))) → QUOT340_IN_A(X1808)
QUOT313_IN_GGA(0, 0, s(s(X1842))) → U10_GGA(X1842, quot349_in_a(X1842))
QUOT313_IN_GGA(0, 0, s(s(X1842))) → QUOT349_IN_A(X1842)
QUOT349_IN_A(s(X1937)) → U16_A(X1937, quot88_in_a(X1937))
QUOT349_IN_A(s(X1937)) → QUOT88_IN_A(X1937)
DIV263_IN_GA(s(0), s(X2493)) → U69_GA(X2493, quot446_in_a(X2493))
DIV263_IN_GA(s(0), s(X2493)) → QUOT446_IN_A(X2493)
DIV263_IN_GA(0, s(X2627)) → U70_GA(X2627, quot467_in_a(X2627))
DIV263_IN_GA(0, s(X2627)) → QUOT467_IN_A(X2627)
QUOT467_IN_A(s(X2776)) → U22_A(X2776, quot340_in_a(X2776))
QUOT467_IN_A(s(X2776)) → QUOT340_IN_A(X2776)
NOT_DIVIDES259_IN_G(T303) → U64_G(T303, div263_in_ga(T303, T305))
U64_G(T303, div263_out_ga(T303, T305)) → U65_G(T303, times190_in_gga(T305, T303, X1232))
U64_G(T303, div263_out_ga(T303, T305)) → TIMES190_IN_GGA(T305, T303, X1232)
U64_G(T303, div263_out_ga(T303, T305)) → U66_G(T303, times190_in_gga(T305, T303, T474))
U66_G(T303, times190_out_gga(T305, T303, T474)) → U67_G(T303, neq191_in_ga(s(T303), T474))
U66_G(T303, times190_out_gga(T305, T303, T474)) → NEQ191_IN_GA(s(T303), T474)
PRIME1_IN_G(s(s(s(s(0))))) → U108_G(not_divides13_in_g(s(0)))
PRIME1_IN_G(s(s(s(s(0))))) → NOT_DIVIDES13_IN_G(s(0))
U108_G(not_divides13_out_g(s(0))) → U109_G(not_divides259_in_g(0))
U108_G(not_divides13_out_g(s(0))) → NOT_DIVIDES259_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(T491)))))) → U110_G(T491, not_divides13_in_g(s(s(T491))))
PRIME1_IN_G(s(s(s(s(s(T491)))))) → NOT_DIVIDES13_IN_G(s(s(T491)))
U110_G(T491, not_divides13_out_g(s(s(T491)))) → U111_G(T491, not_divides259_in_g(s(T491)))
U110_G(T491, not_divides13_out_g(s(s(T491)))) → NOT_DIVIDES259_IN_G(s(T491))
U111_G(T491, not_divides259_out_g(s(T491))) → U112_G(T491, not_divides497_in_g(T491))
U111_G(T491, not_divides259_out_g(s(T491))) → NOT_DIVIDES497_IN_G(T491)
NOT_DIVIDES497_IN_G(T497) → U71_G(T497, div501_in_ga(T497, X2833))
NOT_DIVIDES497_IN_G(T497) → DIV501_IN_GA(T497, X2833)
DIV501_IN_GA(s(s(s(s(s(s(T594)))))), X3207) → U76_GA(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
DIV501_IN_GA(s(s(s(s(s(s(T594)))))), X3207) → QUOT551_IN_GGA(T594, s(s(s(s(s(s(s(T594))))))), X3207)
QUOT551_IN_GGA(s(T614), T615, X3256) → U12_GGA(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
QUOT551_IN_GGA(s(T614), T615, X3256) → QUOT551_IN_GGA(T614, T615, X3256)
QUOT551_IN_GGA(0, s(s(0)), s(s(X3450))) → U13_GGA(X3450, quot584_in_a(X3450))
QUOT551_IN_GGA(0, s(s(0)), s(s(X3450))) → QUOT584_IN_A(X3450)
QUOT551_IN_GGA(0, s(0), s(s(X3484))) → U14_GGA(X3484, quot173_in_a(X3484))
QUOT551_IN_GGA(0, s(0), s(s(X3484))) → QUOT173_IN_A(X3484)
QUOT551_IN_GGA(0, 0, s(s(X3508))) → U15_GGA(X3508, quot595_in_a(X3508))
QUOT551_IN_GGA(0, 0, s(s(X3508))) → QUOT595_IN_A(X3508)
QUOT595_IN_A(s(X3610)) → U23_A(X3610, quot349_in_a(X3610))
QUOT595_IN_A(s(X3610)) → QUOT349_IN_A(X3610)
DIV501_IN_GA(s(0), s(s(X4604))) → U77_GA(X4604, quot584_in_a(X4604))
DIV501_IN_GA(s(0), s(s(X4604))) → QUOT584_IN_A(X4604)
DIV501_IN_GA(0, s(X4627)) → U78_GA(X4627, quot740_in_a(X4627))
DIV501_IN_GA(0, s(X4627)) → QUOT740_IN_A(X4627)
QUOT740_IN_A(s(X4783)) → U30_A(X4783, quot173_in_a(X4783))
QUOT740_IN_A(s(X4783)) → QUOT173_IN_A(X4783)
NOT_DIVIDES497_IN_G(T497) → U72_G(T497, div501_in_ga(T497, T499))
U72_G(T497, div501_out_ga(T497, T499)) → U73_G(T497, times190_in_gga(T499, T497, X2834))
U72_G(T497, div501_out_ga(T497, T499)) → TIMES190_IN_GGA(T499, T497, X2834)
U72_G(T497, div501_out_ga(T497, T499)) → U74_G(T497, times190_in_gga(T499, T497, T674))
U74_G(T497, times190_out_gga(T499, T497, T674)) → U75_G(T497, neq191_in_ga(s(s(T497)), T674))
U74_G(T497, times190_out_gga(T499, T497, T674)) → NEQ191_IN_GA(s(s(T497)), T674)
PRIME1_IN_G(s(s(s(s(s(0)))))) → U113_G(not_divides13_in_g(s(s(0))))
PRIME1_IN_G(s(s(s(s(s(0)))))) → NOT_DIVIDES13_IN_G(s(s(0)))
U113_G(not_divides13_out_g(s(s(0)))) → U114_G(not_divides259_in_g(s(0)))
U113_G(not_divides13_out_g(s(s(0)))) → NOT_DIVIDES259_IN_G(s(0))
U114_G(not_divides259_out_g(s(0))) → U115_G(not_divides497_in_g(0))
U114_G(not_divides259_out_g(s(0))) → NOT_DIVIDES497_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(s(T691))))))) → U116_G(T691, not_divides13_in_g(s(s(s(T691)))))
PRIME1_IN_G(s(s(s(s(s(s(T691))))))) → NOT_DIVIDES13_IN_G(s(s(s(T691))))
U116_G(T691, not_divides13_out_g(s(s(s(T691))))) → U117_G(T691, not_divides259_in_g(s(s(T691))))
U116_G(T691, not_divides13_out_g(s(s(s(T691))))) → NOT_DIVIDES259_IN_G(s(s(T691)))
U117_G(T691, not_divides259_out_g(s(s(T691)))) → U118_G(T691, not_divides497_in_g(s(T691)))
U117_G(T691, not_divides259_out_g(s(s(T691)))) → NOT_DIVIDES497_IN_G(s(T691))
U118_G(T691, not_divides497_out_g(s(T691))) → U119_G(T691, not_divides770_in_g(T691))
U118_G(T691, not_divides497_out_g(s(T691))) → NOT_DIVIDES770_IN_G(T691)
NOT_DIVIDES770_IN_G(T697) → U79_G(T697, div774_in_ga(T697, X4847))
NOT_DIVIDES770_IN_G(T697) → DIV774_IN_GA(T697, X4847)
DIV774_IN_GA(s(s(s(s(s(s(T794)))))), X5221) → U84_GA(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
DIV774_IN_GA(s(s(s(s(s(s(T794)))))), X5221) → QUOT824_IN_GGA(T794, s(s(s(s(s(s(s(T794))))))), X5221)
QUOT824_IN_GGA(s(T814), T815, X5270) → U17_GGA(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
QUOT824_IN_GGA(s(T814), T815, X5270) → QUOT824_IN_GGA(T814, T815, X5270)
QUOT824_IN_GGA(0, s(s(s(0))), s(s(X5504))) → U18_GGA(X5504, quot863_in_a(X5504))
QUOT824_IN_GGA(0, s(s(s(0))), s(s(X5504))) → QUOT863_IN_A(X5504)
QUOT824_IN_GGA(0, s(s(0)), s(s(X5538))) → U19_GGA(X5538, quot158_in_a(X5538))
QUOT824_IN_GGA(0, s(s(0)), s(s(X5538))) → QUOT158_IN_A(X5538)
QUOT824_IN_GGA(0, s(0), s(s(X5562))) → U20_GGA(X5562, quot467_in_a(X5562))
QUOT824_IN_GGA(0, s(0), s(s(X5562))) → QUOT467_IN_A(X5562)
QUOT824_IN_GGA(0, 0, s(s(X5586))) → U21_GGA(X5586, quot876_in_a(X5586))
QUOT824_IN_GGA(0, 0, s(s(X5586))) → QUOT876_IN_A(X5586)
QUOT876_IN_A(s(X5688)) → U31_A(X5688, quot595_in_a(X5688))
QUOT876_IN_A(s(X5688)) → QUOT595_IN_A(X5688)
DIV774_IN_GA(s(s(0)), s(s(X6716))) → U85_GA(X6716, quot863_in_a(X6716))
DIV774_IN_GA(s(s(0)), s(s(X6716))) → QUOT863_IN_A(X6716)
DIV774_IN_GA(s(0), s(s(X6952))) → U86_GA(X6952, quot158_in_a(X6952))
DIV774_IN_GA(s(0), s(s(X6952))) → QUOT158_IN_A(X6952)
DIV774_IN_GA(0, s(s(X7138))) → U87_GA(X7138, quot467_in_a(X7138))
DIV774_IN_GA(0, s(s(X7138))) → QUOT467_IN_A(X7138)
NOT_DIVIDES770_IN_G(T697) → U80_G(T697, div774_in_ga(T697, T699))
U80_G(T697, div774_out_ga(T697, T699)) → U81_G(T697, times190_in_gga(T699, T697, X4848))
U80_G(T697, div774_out_ga(T697, T699)) → TIMES190_IN_GGA(T699, T697, X4848)
U80_G(T697, div774_out_ga(T697, T699)) → U82_G(T697, times190_in_gga(T699, T697, T880))
U82_G(T697, times190_out_gga(T699, T697, T880)) → U83_G(T697, neq191_in_ga(s(s(s(T697))), T880))
U82_G(T697, times190_out_gga(T699, T697, T880)) → NEQ191_IN_GA(s(s(s(T697))), T880)
PRIME1_IN_G(s(s(s(s(s(s(0))))))) → U120_G(not_divides13_in_g(s(s(s(0)))))
PRIME1_IN_G(s(s(s(s(s(s(0))))))) → NOT_DIVIDES13_IN_G(s(s(s(0))))
U120_G(not_divides13_out_g(s(s(s(0))))) → U121_G(not_divides259_in_g(s(s(0))))
U120_G(not_divides13_out_g(s(s(s(0))))) → NOT_DIVIDES259_IN_G(s(s(0)))
U121_G(not_divides259_out_g(s(s(0)))) → U122_G(not_divides497_in_g(s(0)))
U121_G(not_divides259_out_g(s(s(0)))) → NOT_DIVIDES497_IN_G(s(0))
U122_G(not_divides497_out_g(s(0))) → U123_G(not_divides770_in_g(0))
U122_G(not_divides497_out_g(s(0))) → NOT_DIVIDES770_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(s(s(T897)))))))) → U124_G(T897, not_divides13_in_g(s(s(s(s(T897))))))
PRIME1_IN_G(s(s(s(s(s(s(s(T897)))))))) → NOT_DIVIDES13_IN_G(s(s(s(s(T897)))))
U124_G(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_G(T897, not_divides259_in_g(s(s(s(T897)))))
U124_G(T897, not_divides13_out_g(s(s(s(s(T897)))))) → NOT_DIVIDES259_IN_G(s(s(s(T897))))
U125_G(T897, not_divides259_out_g(s(s(s(T897))))) → U126_G(T897, not_divides497_in_g(s(s(T897))))
U125_G(T897, not_divides259_out_g(s(s(s(T897))))) → NOT_DIVIDES497_IN_G(s(s(T897)))
U126_G(T897, not_divides497_out_g(s(s(T897)))) → U127_G(T897, not_divides770_in_g(s(T897)))
U126_G(T897, not_divides497_out_g(s(s(T897)))) → NOT_DIVIDES770_IN_G(s(T897))
U127_G(T897, not_divides770_out_g(s(T897))) → U128_G(T897, not_divides1072_in_g(T897))
U127_G(T897, not_divides770_out_g(s(T897))) → NOT_DIVIDES1072_IN_G(T897)
NOT_DIVIDES1072_IN_G(T903) → U88_G(T903, div1076_in_ga(T903, X7202))
NOT_DIVIDES1072_IN_G(T903) → DIV1076_IN_GA(T903, X7202)
DIV1076_IN_GA(s(s(s(s(s(s(T1000)))))), X7576) → U93_GA(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
DIV1076_IN_GA(s(s(s(s(s(s(T1000)))))), X7576) → QUOT1126_IN_GGA(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)
QUOT1126_IN_GGA(s(T1020), T1021, X7625) → U24_GGA(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
QUOT1126_IN_GGA(s(T1020), T1021, X7625) → QUOT1126_IN_GGA(T1020, T1021, X7625)
QUOT1126_IN_GGA(0, s(s(s(s(0)))), s(s(X7899))) → U25_GGA(X7899, quot1171_in_a(X7899))
QUOT1126_IN_GGA(0, s(s(s(s(0)))), s(s(X7899))) → QUOT1171_IN_A(X7899)
QUOT1126_IN_GGA(0, s(s(s(0))), s(s(X7933))) → U26_GGA(X7933, quot143_in_a(X7933))
QUOT1126_IN_GGA(0, s(s(s(0))), s(s(X7933))) → QUOT143_IN_A(X7933)
QUOT1126_IN_GGA(0, s(s(0)), s(s(X7957))) → U27_GGA(X7957, quot446_in_a(X7957))
QUOT1126_IN_GGA(0, s(s(0)), s(s(X7957))) → QUOT446_IN_A(X7957)
QUOT1126_IN_GGA(0, s(0), s(s(X7981))) → U28_GGA(X7981, quot740_in_a(X7981))
QUOT1126_IN_GGA(0, s(0), s(s(X7981))) → QUOT740_IN_A(X7981)
QUOT1126_IN_GGA(0, 0, s(s(s(X8107)))) → U29_GGA(X8107, quot876_in_a(X8107))
QUOT1126_IN_GGA(0, 0, s(s(s(X8107)))) → QUOT876_IN_A(X8107)
DIV1076_IN_GA(s(s(s(0))), s(s(X9055))) → U94_GA(X9055, quot1171_in_a(X9055))
DIV1076_IN_GA(s(s(s(0))), s(s(X9055))) → QUOT1171_IN_A(X9055)
DIV1076_IN_GA(s(s(0)), s(s(X9348))) → U95_GA(X9348, quot143_in_a(X9348))
DIV1076_IN_GA(s(s(0)), s(s(X9348))) → QUOT143_IN_A(X9348)
DIV1076_IN_GA(s(0), s(s(X9591))) → U96_GA(X9591, quot446_in_a(X9591))
DIV1076_IN_GA(s(0), s(s(X9591))) → QUOT446_IN_A(X9591)
DIV1076_IN_GA(0, s(s(X9777))) → U97_GA(X9777, quot740_in_a(X9777))
DIV1076_IN_GA(0, s(s(X9777))) → QUOT740_IN_A(X9777)
NOT_DIVIDES1072_IN_G(T903) → U89_G(T903, div1076_in_ga(T903, T905))
U89_G(T903, div1076_out_ga(T903, T905)) → U90_G(T903, times190_in_gga(T905, T903, X7203))
U89_G(T903, div1076_out_ga(T903, T905)) → TIMES190_IN_GGA(T905, T903, X7203)
U89_G(T903, div1076_out_ga(T903, T905)) → U91_G(T903, times190_in_gga(T905, T903, T1092))
U91_G(T903, times190_out_gga(T905, T903, T1092)) → U92_G(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U91_G(T903, times190_out_gga(T905, T903, T1092)) → NEQ191_IN_GA(s(s(s(s(T903)))), T1092)
PRIME1_IN_G(s(s(s(s(s(s(s(0)))))))) → U129_G(not_divides13_in_g(s(s(s(s(0))))))
PRIME1_IN_G(s(s(s(s(s(s(s(0)))))))) → NOT_DIVIDES13_IN_G(s(s(s(s(0)))))
U129_G(not_divides13_out_g(s(s(s(s(0)))))) → U130_G(not_divides259_in_g(s(s(s(0)))))
U129_G(not_divides13_out_g(s(s(s(s(0)))))) → NOT_DIVIDES259_IN_G(s(s(s(0))))
U130_G(not_divides259_out_g(s(s(s(0))))) → U131_G(not_divides497_in_g(s(s(0))))
U130_G(not_divides259_out_g(s(s(s(0))))) → NOT_DIVIDES497_IN_G(s(s(0)))
U131_G(not_divides497_out_g(s(s(0)))) → U132_G(not_divides770_in_g(s(0)))
U131_G(not_divides497_out_g(s(s(0)))) → NOT_DIVIDES770_IN_G(s(0))
U132_G(not_divides770_out_g(s(0))) → U133_G(not_divides1072_in_g(0))
U132_G(not_divides770_out_g(s(0))) → NOT_DIVIDES1072_IN_G(0)
PRIME1_IN_G(s(s(s(s(s(s(s(s(T1109))))))))) → U134_G(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
PRIME1_IN_G(s(s(s(s(s(s(s(s(T1109))))))))) → NOT_DIVIDES13_IN_G(s(s(s(s(s(T1109))))))
U134_G(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_G(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U134_G(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → NOT_DIVIDES259_IN_G(s(s(s(s(T1109)))))
U135_G(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_G(T1109, not_divides497_in_g(s(s(s(T1109)))))
U135_G(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → NOT_DIVIDES497_IN_G(s(s(s(T1109))))
U136_G(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_G(T1109, not_divides770_in_g(s(s(T1109))))
U136_G(T1109, not_divides497_out_g(s(s(s(T1109))))) → NOT_DIVIDES770_IN_G(s(s(T1109)))
U137_G(T1109, not_divides770_out_g(s(s(T1109)))) → U138_G(T1109, not_divides1072_in_g(s(T1109)))
U137_G(T1109, not_divides770_out_g(s(s(T1109)))) → NOT_DIVIDES1072_IN_G(s(T1109))
U138_G(T1109, not_divides1072_out_g(s(T1109))) → U139_G(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
U138_G(T1109, not_divides1072_out_g(s(T1109))) → P1397_IN_GG(T1109, s(s(s(s(s(s(s(T1109))))))))
P1397_IN_GG(T1109, T1111) → U50_GG(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
P1397_IN_GG(T1109, T1111) → NOT_DIVIDES1398_IN_GG(T1109, T1111)
NOT_DIVIDES1398_IN_GG(T1122, T1123) → U98_GG(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
NOT_DIVIDES1398_IN_GG(T1122, T1123) → DIV1402_IN_GGA(T1123, T1122, X9845)
DIV1402_IN_GGA(s(T1168), T1169, X9960) → U103_GGA(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
DIV1402_IN_GGA(s(T1168), T1169, X9960) → QUOT1419_IN_GGA(T1168, T1169, X9960)
QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_GGA(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → QUOT1481_IN_GGGA(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)
QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303, X10279) → U32_GGGA(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303, X10279) → QUOT1481_IN_GGGA(T1301, T1302, T1303, X10279)
QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_GGGA(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347), s(X10388)) → QUOT1419_IN_GGA(T1346, T1347, X10388)
QUOT1419_IN_GGA(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_GGA(T1368, X10512, quot1532_in_ga(T1368, X10512))
QUOT1419_IN_GGA(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → QUOT1532_IN_GA(T1368, X10512)
QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_GA(T1409, X10864, quot1532_in_ga(T1409, X10864))
QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → QUOT1532_IN_GA(T1409, X10864)
QUOT1419_IN_GGA(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_GGA(T1419, X10901, quot1615_in_ga(T1419, X10901))
QUOT1419_IN_GGA(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → QUOT1615_IN_GA(T1419, X10901)
QUOT1615_IN_GA(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_GA(T1455, X11208, quot1615_in_ga(T1455, X11208))
QUOT1615_IN_GA(s(s(s(s(s(s(T1455)))))), s(X11208)) → QUOT1615_IN_GA(T1455, X11208)
QUOT1419_IN_GGA(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_GGA(T1464, X11242, quot1687_in_ga(T1464, X11242))
QUOT1419_IN_GGA(s(s(s(T1464))), s(s(s(0))), s(X11242)) → QUOT1687_IN_GA(T1464, X11242)
QUOT1687_IN_GA(s(s(s(s(s(T1495))))), s(X11504)) → U45_GA(T1495, X11504, quot1687_in_ga(T1495, X11504))
QUOT1687_IN_GA(s(s(s(s(s(T1495))))), s(X11504)) → QUOT1687_IN_GA(T1495, X11504)
QUOT1419_IN_GGA(s(s(T1503)), s(s(0)), s(X11535)) → U39_GGA(T1503, X11535, quot1748_in_ga(T1503, X11535))
QUOT1419_IN_GGA(s(s(T1503)), s(s(0)), s(X11535)) → QUOT1748_IN_GA(T1503, X11535)
QUOT1748_IN_GA(s(s(s(s(T1529)))), s(X11752)) → U46_GA(T1529, X11752, quot1748_in_ga(T1529, X11752))
QUOT1748_IN_GA(s(s(s(s(T1529)))), s(X11752)) → QUOT1748_IN_GA(T1529, X11752)
QUOT1419_IN_GGA(s(T1536), s(0), s(X11780)) → U40_GGA(T1536, X11780, quot1798_in_ga(T1536, X11780))
QUOT1419_IN_GGA(s(T1536), s(0), s(X11780)) → QUOT1798_IN_GA(T1536, X11780)
QUOT1798_IN_GA(s(s(s(T1557))), s(X11952)) → U47_GA(T1557, X11952, quot1798_in_ga(T1557, X11952))
QUOT1798_IN_GA(s(s(s(T1557))), s(X11952)) → QUOT1798_IN_GA(T1557, X11952)
QUOT1419_IN_GGA(T1563, 0, s(X11977)) → U41_GGA(T1563, X11977, quot1837_in_ga(T1563, X11977))
QUOT1419_IN_GGA(T1563, 0, s(X11977)) → QUOT1837_IN_GA(T1563, X11977)
QUOT1837_IN_GA(s(s(T1579)), s(X12104)) → U48_GA(T1579, X12104, quot1837_in_ga(T1579, X12104))
QUOT1837_IN_GA(s(s(T1579)), s(X12104)) → QUOT1837_IN_GA(T1579, X12104)
QUOT1481_IN_GGGA(s(T1352), 0, 0, s(s(X10408))) → U34_GGGA(T1352, X10408, quot1514_in_ga(T1352, X10408))
QUOT1481_IN_GGGA(s(T1352), 0, 0, s(s(X10408))) → QUOT1514_IN_GA(T1352, X10408)
QUOT1514_IN_GA(s(T1363), s(X10490)) → U42_GA(T1363, X10490, quot1514_in_ga(T1363, X10490))
QUOT1514_IN_GA(s(T1363), s(X10490)) → QUOT1514_IN_GA(T1363, X10490)
NOT_DIVIDES1398_IN_GG(T1122, T1123) → U99_GG(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_GG(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_GG(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U99_GG(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → TIMES190_IN_GGA(T1126, T1122, X9846)
U99_GG(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_GG(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_GG(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_GG(T1122, T1123, neq227_in_ga(T1123, T1586))
U101_GG(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → NEQ227_IN_GA(T1123, T1586)
P1397_IN_GG(0, T1597) → U51_GG(T1597, not_divides1398_in_gg(0, T1597))
P1397_IN_GG(0, T1597) → NOT_DIVIDES1398_IN_GG(0, T1597)
P1397_IN_GG(s(T1603), T1602) → U52_GG(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
P1397_IN_GG(s(T1603), T1602) → NOT_DIVIDES1398_IN_GG(s(T1603), T1602)
U52_GG(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_GG(T1603, T1602, p1397_in_gg(T1603, T1602))
U52_GG(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → P1397_IN_GG(T1603, T1602)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
PRIME1_IN_G(x1)  =  PRIME1_IN_G(x1)
U104_G(x1, x2)  =  U104_G(x2)
NOT_DIVIDES13_IN_G(x1)  =  NOT_DIVIDES13_IN_G(x1)
U54_G(x1, x2)  =  U54_G(x2)
DIV17_IN_GA(x1, x2)  =  DIV17_IN_GA(x1)
U59_GA(x1, x2, x3)  =  U59_GA(x3)
QUOT67_IN_GGA(x1, x2, x3)  =  QUOT67_IN_GGA(x1, x2)
U1_GGA(x1, x2, x3, x4)  =  U1_GGA(x4)
U2_GGA(x1, x2)  =  U2_GGA(x2)
QUOT88_IN_A(x1)  =  QUOT88_IN_A
U60_GA(x1, x2)  =  U60_GA(x2)
QUOT143_IN_A(x1)  =  QUOT143_IN_A
U61_GA(x1, x2)  =  U61_GA(x2)
QUOT158_IN_A(x1)  =  QUOT158_IN_A
U62_GA(x1, x2)  =  U62_GA(x2)
QUOT173_IN_A(x1)  =  QUOT173_IN_A
U55_G(x1, x2)  =  U55_G(x1, x2)
U56_G(x1, x2)  =  U56_G(x2)
TIMES190_IN_GGA(x1, x2, x3)  =  TIMES190_IN_GGA(x1, x2)
U3_GGA(x1, x2, x3, x4)  =  U3_GGA(x4)
U4_GGA(x1, x2, x3, x4)  =  U4_GGA(x2, x4)
U5_GGA(x1, x2, x3, x4)  =  U5_GGA(x4)
ADD201_IN_AGA(x1, x2, x3)  =  ADD201_IN_AGA(x2)
U6_AGA(x1, x2, x3, x4)  =  U6_AGA(x4)
U57_G(x1, x2)  =  U57_G(x1, x2)
U58_G(x1, x2)  =  U58_G(x2)
NEQ191_IN_GA(x1, x2)  =  NEQ191_IN_GA(x1)
U11_GA(x1, x2, x3)  =  U11_GA(x3)
NEQ227_IN_GA(x1, x2)  =  NEQ227_IN_GA(x1)
U49_GA(x1, x2, x3)  =  U49_GA(x3)
NEQ236_IN_GA(x1, x2)  =  NEQ236_IN_GA(x1)
U7_GA(x1, x2, x3)  =  U7_GA(x3)
U105_G(x1)  =  U105_G(x1)
U106_G(x1, x2)  =  U106_G(x1, x2)
U107_G(x1, x2)  =  U107_G(x2)
NOT_DIVIDES259_IN_G(x1)  =  NOT_DIVIDES259_IN_G(x1)
U63_G(x1, x2)  =  U63_G(x2)
DIV263_IN_GA(x1, x2)  =  DIV263_IN_GA(x1)
U68_GA(x1, x2, x3)  =  U68_GA(x3)
QUOT313_IN_GGA(x1, x2, x3)  =  QUOT313_IN_GGA(x1, x2)
U8_GGA(x1, x2, x3, x4)  =  U8_GGA(x4)
U9_GGA(x1, x2)  =  U9_GGA(x2)
QUOT340_IN_A(x1)  =  QUOT340_IN_A
U10_GGA(x1, x2)  =  U10_GGA(x2)
QUOT349_IN_A(x1)  =  QUOT349_IN_A
U16_A(x1, x2)  =  U16_A(x2)
U69_GA(x1, x2)  =  U69_GA(x2)
QUOT446_IN_A(x1)  =  QUOT446_IN_A
U70_GA(x1, x2)  =  U70_GA(x2)
QUOT467_IN_A(x1)  =  QUOT467_IN_A
U22_A(x1, x2)  =  U22_A(x2)
U64_G(x1, x2)  =  U64_G(x1, x2)
U65_G(x1, x2)  =  U65_G(x2)
U66_G(x1, x2)  =  U66_G(x1, x2)
U67_G(x1, x2)  =  U67_G(x2)
U108_G(x1)  =  U108_G(x1)
U109_G(x1)  =  U109_G(x1)
U110_G(x1, x2)  =  U110_G(x1, x2)
U111_G(x1, x2)  =  U111_G(x1, x2)
U112_G(x1, x2)  =  U112_G(x2)
NOT_DIVIDES497_IN_G(x1)  =  NOT_DIVIDES497_IN_G(x1)
U71_G(x1, x2)  =  U71_G(x2)
DIV501_IN_GA(x1, x2)  =  DIV501_IN_GA(x1)
U76_GA(x1, x2, x3)  =  U76_GA(x3)
QUOT551_IN_GGA(x1, x2, x3)  =  QUOT551_IN_GGA(x1, x2)
U12_GGA(x1, x2, x3, x4)  =  U12_GGA(x4)
U13_GGA(x1, x2)  =  U13_GGA(x2)
QUOT584_IN_A(x1)  =  QUOT584_IN_A
U14_GGA(x1, x2)  =  U14_GGA(x2)
U15_GGA(x1, x2)  =  U15_GGA(x2)
QUOT595_IN_A(x1)  =  QUOT595_IN_A
U23_A(x1, x2)  =  U23_A(x2)
U77_GA(x1, x2)  =  U77_GA(x2)
U78_GA(x1, x2)  =  U78_GA(x2)
QUOT740_IN_A(x1)  =  QUOT740_IN_A
U30_A(x1, x2)  =  U30_A(x2)
U72_G(x1, x2)  =  U72_G(x1, x2)
U73_G(x1, x2)  =  U73_G(x2)
U74_G(x1, x2)  =  U74_G(x1, x2)
U75_G(x1, x2)  =  U75_G(x2)
U113_G(x1)  =  U113_G(x1)
U114_G(x1)  =  U114_G(x1)
U115_G(x1)  =  U115_G(x1)
U116_G(x1, x2)  =  U116_G(x1, x2)
U117_G(x1, x2)  =  U117_G(x1, x2)
U118_G(x1, x2)  =  U118_G(x1, x2)
U119_G(x1, x2)  =  U119_G(x2)
NOT_DIVIDES770_IN_G(x1)  =  NOT_DIVIDES770_IN_G(x1)
U79_G(x1, x2)  =  U79_G(x2)
DIV774_IN_GA(x1, x2)  =  DIV774_IN_GA(x1)
U84_GA(x1, x2, x3)  =  U84_GA(x3)
QUOT824_IN_GGA(x1, x2, x3)  =  QUOT824_IN_GGA(x1, x2)
U17_GGA(x1, x2, x3, x4)  =  U17_GGA(x4)
U18_GGA(x1, x2)  =  U18_GGA(x2)
QUOT863_IN_A(x1)  =  QUOT863_IN_A
U19_GGA(x1, x2)  =  U19_GGA(x2)
U20_GGA(x1, x2)  =  U20_GGA(x2)
U21_GGA(x1, x2)  =  U21_GGA(x2)
QUOT876_IN_A(x1)  =  QUOT876_IN_A
U31_A(x1, x2)  =  U31_A(x2)
U85_GA(x1, x2)  =  U85_GA(x2)
U86_GA(x1, x2)  =  U86_GA(x2)
U87_GA(x1, x2)  =  U87_GA(x2)
U80_G(x1, x2)  =  U80_G(x1, x2)
U81_G(x1, x2)  =  U81_G(x2)
U82_G(x1, x2)  =  U82_G(x1, x2)
U83_G(x1, x2)  =  U83_G(x2)
U120_G(x1)  =  U120_G(x1)
U121_G(x1)  =  U121_G(x1)
U122_G(x1)  =  U122_G(x1)
U123_G(x1)  =  U123_G(x1)
U124_G(x1, x2)  =  U124_G(x1, x2)
U125_G(x1, x2)  =  U125_G(x1, x2)
U126_G(x1, x2)  =  U126_G(x1, x2)
U127_G(x1, x2)  =  U127_G(x1, x2)
U128_G(x1, x2)  =  U128_G(x2)
NOT_DIVIDES1072_IN_G(x1)  =  NOT_DIVIDES1072_IN_G(x1)
U88_G(x1, x2)  =  U88_G(x2)
DIV1076_IN_GA(x1, x2)  =  DIV1076_IN_GA(x1)
U93_GA(x1, x2, x3)  =  U93_GA(x3)
QUOT1126_IN_GGA(x1, x2, x3)  =  QUOT1126_IN_GGA(x1, x2)
U24_GGA(x1, x2, x3, x4)  =  U24_GGA(x4)
U25_GGA(x1, x2)  =  U25_GGA(x2)
QUOT1171_IN_A(x1)  =  QUOT1171_IN_A
U26_GGA(x1, x2)  =  U26_GGA(x2)
U27_GGA(x1, x2)  =  U27_GGA(x2)
U28_GGA(x1, x2)  =  U28_GGA(x2)
U29_GGA(x1, x2)  =  U29_GGA(x2)
U94_GA(x1, x2)  =  U94_GA(x2)
U95_GA(x1, x2)  =  U95_GA(x2)
U96_GA(x1, x2)  =  U96_GA(x2)
U97_GA(x1, x2)  =  U97_GA(x2)
U89_G(x1, x2)  =  U89_G(x1, x2)
U90_G(x1, x2)  =  U90_G(x2)
U91_G(x1, x2)  =  U91_G(x1, x2)
U92_G(x1, x2)  =  U92_G(x2)
U129_G(x1)  =  U129_G(x1)
U130_G(x1)  =  U130_G(x1)
U131_G(x1)  =  U131_G(x1)
U132_G(x1)  =  U132_G(x1)
U133_G(x1)  =  U133_G(x1)
U134_G(x1, x2)  =  U134_G(x1, x2)
U135_G(x1, x2)  =  U135_G(x1, x2)
U136_G(x1, x2)  =  U136_G(x1, x2)
U137_G(x1, x2)  =  U137_G(x1, x2)
U138_G(x1, x2)  =  U138_G(x1, x2)
U139_G(x1, x2)  =  U139_G(x2)
P1397_IN_GG(x1, x2)  =  P1397_IN_GG(x1, x2)
U50_GG(x1, x2, x3)  =  U50_GG(x3)
NOT_DIVIDES1398_IN_GG(x1, x2)  =  NOT_DIVIDES1398_IN_GG(x1, x2)
U98_GG(x1, x2, x3)  =  U98_GG(x3)
DIV1402_IN_GGA(x1, x2, x3)  =  DIV1402_IN_GGA(x1, x2)
U103_GGA(x1, x2, x3, x4)  =  U103_GGA(x4)
QUOT1419_IN_GGA(x1, x2, x3)  =  QUOT1419_IN_GGA(x1, x2)
U35_GGA(x1, x2, x3, x4)  =  U35_GGA(x4)
QUOT1481_IN_GGGA(x1, x2, x3, x4)  =  QUOT1481_IN_GGGA(x1, x2, x3)
U32_GGGA(x1, x2, x3, x4, x5)  =  U32_GGGA(x5)
U33_GGGA(x1, x2, x3, x4)  =  U33_GGGA(x4)
U36_GGA(x1, x2, x3)  =  U36_GGA(x3)
QUOT1532_IN_GA(x1, x2)  =  QUOT1532_IN_GA(x1)
U43_GA(x1, x2, x3)  =  U43_GA(x3)
U37_GGA(x1, x2, x3)  =  U37_GGA(x3)
QUOT1615_IN_GA(x1, x2)  =  QUOT1615_IN_GA(x1)
U44_GA(x1, x2, x3)  =  U44_GA(x3)
U38_GGA(x1, x2, x3)  =  U38_GGA(x3)
QUOT1687_IN_GA(x1, x2)  =  QUOT1687_IN_GA(x1)
U45_GA(x1, x2, x3)  =  U45_GA(x3)
U39_GGA(x1, x2, x3)  =  U39_GGA(x3)
QUOT1748_IN_GA(x1, x2)  =  QUOT1748_IN_GA(x1)
U46_GA(x1, x2, x3)  =  U46_GA(x3)
U40_GGA(x1, x2, x3)  =  U40_GGA(x3)
QUOT1798_IN_GA(x1, x2)  =  QUOT1798_IN_GA(x1)
U47_GA(x1, x2, x3)  =  U47_GA(x3)
U41_GGA(x1, x2, x3)  =  U41_GGA(x3)
QUOT1837_IN_GA(x1, x2)  =  QUOT1837_IN_GA(x1)
U48_GA(x1, x2, x3)  =  U48_GA(x3)
U34_GGGA(x1, x2, x3)  =  U34_GGGA(x3)
QUOT1514_IN_GA(x1, x2)  =  QUOT1514_IN_GA(x1)
U42_GA(x1, x2, x3)  =  U42_GA(x3)
U99_GG(x1, x2, x3)  =  U99_GG(x1, x2, x3)
U100_GG(x1, x2, x3)  =  U100_GG(x3)
U101_GG(x1, x2, x3)  =  U101_GG(x2, x3)
U102_GG(x1, x2, x3)  =  U102_GG(x3)
U51_GG(x1, x2)  =  U51_GG(x2)
U52_GG(x1, x2, x3)  =  U52_GG(x1, x2, x3)
U53_GG(x1, x2, x3)  =  U53_GG(x3)

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

(132) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 17 SCCs with 245 less nodes.

(133) Complex Obligation (AND)

(134) Obligation:

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

QUOT1514_IN_GA(s(T1363), s(X10490)) → QUOT1514_IN_GA(T1363, X10490)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
QUOT1514_IN_GA(x1, x2)  =  QUOT1514_IN_GA(x1)

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

(135) UsableRulesProof (EQUIVALENT transformation)

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

(136) Obligation:

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

QUOT1514_IN_GA(s(T1363), s(X10490)) → QUOT1514_IN_GA(T1363, X10490)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1514_IN_GA(x1, x2)  =  QUOT1514_IN_GA(x1)

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

(137) PiDPToQDPProof (SOUND transformation)

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

(138) Obligation:

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

QUOT1514_IN_GA(s(T1363)) → QUOT1514_IN_GA(T1363)

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

(139) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1514_IN_GA(s(T1363)) → QUOT1514_IN_GA(T1363)
  The graph contains the following edges 1 > 1

(140) YES

(141) Obligation:

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

QUOT1837_IN_GA(s(s(T1579)), s(X12104)) → QUOT1837_IN_GA(T1579, X12104)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
QUOT1837_IN_GA(x1, x2)  =  QUOT1837_IN_GA(x1)

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

(142) UsableRulesProof (EQUIVALENT transformation)

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

(143) Obligation:

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

QUOT1837_IN_GA(s(s(T1579)), s(X12104)) → QUOT1837_IN_GA(T1579, X12104)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1837_IN_GA(x1, x2)  =  QUOT1837_IN_GA(x1)

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

(144) PiDPToQDPProof (SOUND transformation)

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

(145) Obligation:

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

QUOT1837_IN_GA(s(s(T1579))) → QUOT1837_IN_GA(T1579)

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

(146) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1837_IN_GA(s(s(T1579))) → QUOT1837_IN_GA(T1579)
  The graph contains the following edges 1 > 1

(147) YES

(148) Obligation:

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

QUOT1798_IN_GA(s(s(s(T1557))), s(X11952)) → QUOT1798_IN_GA(T1557, X11952)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
QUOT1798_IN_GA(x1, x2)  =  QUOT1798_IN_GA(x1)

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

(149) UsableRulesProof (EQUIVALENT transformation)

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

(150) Obligation:

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

QUOT1798_IN_GA(s(s(s(T1557))), s(X11952)) → QUOT1798_IN_GA(T1557, X11952)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1798_IN_GA(x1, x2)  =  QUOT1798_IN_GA(x1)

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

(151) PiDPToQDPProof (SOUND transformation)

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

(152) Obligation:

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

QUOT1798_IN_GA(s(s(s(T1557)))) → QUOT1798_IN_GA(T1557)

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

(153) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1798_IN_GA(s(s(s(T1557)))) → QUOT1798_IN_GA(T1557)
  The graph contains the following edges 1 > 1

(154) YES

(155) Obligation:

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

QUOT1748_IN_GA(s(s(s(s(T1529)))), s(X11752)) → QUOT1748_IN_GA(T1529, X11752)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
QUOT1748_IN_GA(x1, x2)  =  QUOT1748_IN_GA(x1)

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

(156) UsableRulesProof (EQUIVALENT transformation)

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

(157) Obligation:

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

QUOT1748_IN_GA(s(s(s(s(T1529)))), s(X11752)) → QUOT1748_IN_GA(T1529, X11752)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1748_IN_GA(x1, x2)  =  QUOT1748_IN_GA(x1)

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

(158) PiDPToQDPProof (SOUND transformation)

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

(159) Obligation:

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

QUOT1748_IN_GA(s(s(s(s(T1529))))) → QUOT1748_IN_GA(T1529)

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

(160) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1748_IN_GA(s(s(s(s(T1529))))) → QUOT1748_IN_GA(T1529)
  The graph contains the following edges 1 > 1

(161) YES

(162) Obligation:

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

QUOT1687_IN_GA(s(s(s(s(s(T1495))))), s(X11504)) → QUOT1687_IN_GA(T1495, X11504)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
QUOT1687_IN_GA(x1, x2)  =  QUOT1687_IN_GA(x1)

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

(163) UsableRulesProof (EQUIVALENT transformation)

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

(164) Obligation:

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

QUOT1687_IN_GA(s(s(s(s(s(T1495))))), s(X11504)) → QUOT1687_IN_GA(T1495, X11504)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1687_IN_GA(x1, x2)  =  QUOT1687_IN_GA(x1)

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

(165) PiDPToQDPProof (SOUND transformation)

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

(166) Obligation:

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

QUOT1687_IN_GA(s(s(s(s(s(T1495)))))) → QUOT1687_IN_GA(T1495)

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

(167) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1687_IN_GA(s(s(s(s(s(T1495)))))) → QUOT1687_IN_GA(T1495)
  The graph contains the following edges 1 > 1

(168) YES

(169) Obligation:

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

QUOT1615_IN_GA(s(s(s(s(s(s(T1455)))))), s(X11208)) → QUOT1615_IN_GA(T1455, X11208)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
QUOT1615_IN_GA(x1, x2)  =  QUOT1615_IN_GA(x1)

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

(170) UsableRulesProof (EQUIVALENT transformation)

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

(171) Obligation:

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

QUOT1615_IN_GA(s(s(s(s(s(s(T1455)))))), s(X11208)) → QUOT1615_IN_GA(T1455, X11208)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1615_IN_GA(x1, x2)  =  QUOT1615_IN_GA(x1)

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

(172) PiDPToQDPProof (SOUND transformation)

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

(173) Obligation:

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

QUOT1615_IN_GA(s(s(s(s(s(s(T1455))))))) → QUOT1615_IN_GA(T1455)

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

(174) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1615_IN_GA(s(s(s(s(s(s(T1455))))))) → QUOT1615_IN_GA(T1455)
  The graph contains the following edges 1 > 1

(175) YES

(176) Obligation:

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

QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → QUOT1532_IN_GA(T1409, X10864)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
QUOT1532_IN_GA(x1, x2)  =  QUOT1532_IN_GA(x1)

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

(177) UsableRulesProof (EQUIVALENT transformation)

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

(178) Obligation:

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

QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → QUOT1532_IN_GA(T1409, X10864)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1532_IN_GA(x1, x2)  =  QUOT1532_IN_GA(x1)

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

(179) PiDPToQDPProof (SOUND transformation)

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

(180) Obligation:

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

QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409)))))))) → QUOT1532_IN_GA(T1409)

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

(181) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1532_IN_GA(s(s(s(s(s(s(s(T1409)))))))) → QUOT1532_IN_GA(T1409)
  The graph contains the following edges 1 > 1

(182) YES

(183) Obligation:

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

QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → QUOT1481_IN_GGGA(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)
QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303, X10279) → QUOT1481_IN_GGGA(T1301, T1302, T1303, X10279)
QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347), s(X10388)) → QUOT1419_IN_GGA(T1346, T1347, X10388)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
QUOT1419_IN_GGA(x1, x2, x3)  =  QUOT1419_IN_GGA(x1, x2)
QUOT1481_IN_GGGA(x1, x2, x3, x4)  =  QUOT1481_IN_GGGA(x1, x2, x3)

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

(184) UsableRulesProof (EQUIVALENT transformation)

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

(185) Obligation:

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

QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → QUOT1481_IN_GGGA(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)
QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303, X10279) → QUOT1481_IN_GGGA(T1301, T1302, T1303, X10279)
QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347), s(X10388)) → QUOT1419_IN_GGA(T1346, T1347, X10388)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
0  =  0
QUOT1419_IN_GGA(x1, x2, x3)  =  QUOT1419_IN_GGA(x1, x2)
QUOT1481_IN_GGGA(x1, x2, x3, x4)  =  QUOT1481_IN_GGGA(x1, x2, x3)

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

(186) PiDPToQDPProof (SOUND transformation)

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

(187) Obligation:

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

QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271))))))) → QUOT1481_IN_GGGA(T1270, T1271, s(s(s(s(s(s(s(T1271))))))))
QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303) → QUOT1481_IN_GGGA(T1301, T1302, T1303)
QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347)) → QUOT1419_IN_GGA(T1346, T1347)

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

(188) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1481_IN_GGGA(s(s(T1346)), 0, s(T1347)) → QUOT1419_IN_GGA(T1346, T1347)
  The graph contains the following edges 1 > 1, 3 > 2

• QUOT1481_IN_GGGA(s(T1301), s(T1302), T1303) → QUOT1481_IN_GGGA(T1301, T1302, T1303)
  The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3

• QUOT1419_IN_GGA(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271))))))) → QUOT1481_IN_GGGA(T1270, T1271, s(s(s(s(s(s(s(T1271))))))))
  The graph contains the following edges 1 > 1, 2 > 2

(189) YES

(190) Obligation:

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

QUOT1126_IN_GGA(s(T1020), T1021, X7625) → QUOT1126_IN_GGA(T1020, T1021, X7625)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
QUOT1126_IN_GGA(x1, x2, x3)  =  QUOT1126_IN_GGA(x1, x2)

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

(191) UsableRulesProof (EQUIVALENT transformation)

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

(192) Obligation:

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

QUOT1126_IN_GGA(s(T1020), T1021, X7625) → QUOT1126_IN_GGA(T1020, T1021, X7625)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT1126_IN_GGA(x1, x2, x3)  =  QUOT1126_IN_GGA(x1, x2)

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

(193) PiDPToQDPProof (SOUND transformation)

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

(194) Obligation:

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

QUOT1126_IN_GGA(s(T1020), T1021) → QUOT1126_IN_GGA(T1020, T1021)

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

(195) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT1126_IN_GGA(s(T1020), T1021) → QUOT1126_IN_GGA(T1020, T1021)
  The graph contains the following edges 1 > 1, 2 >= 2

(196) YES

(197) Obligation:

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

QUOT824_IN_GGA(s(T814), T815, X5270) → QUOT824_IN_GGA(T814, T815, X5270)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
QUOT824_IN_GGA(x1, x2, x3)  =  QUOT824_IN_GGA(x1, x2)

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

(198) UsableRulesProof (EQUIVALENT transformation)

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

(199) Obligation:

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

QUOT824_IN_GGA(s(T814), T815, X5270) → QUOT824_IN_GGA(T814, T815, X5270)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT824_IN_GGA(x1, x2, x3)  =  QUOT824_IN_GGA(x1, x2)

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

(200) PiDPToQDPProof (SOUND transformation)

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

(201) Obligation:

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

QUOT824_IN_GGA(s(T814), T815) → QUOT824_IN_GGA(T814, T815)

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

(202) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT824_IN_GGA(s(T814), T815) → QUOT824_IN_GGA(T814, T815)
  The graph contains the following edges 1 > 1, 2 >= 2

(203) YES

(204) Obligation:

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

QUOT551_IN_GGA(s(T614), T615, X3256) → QUOT551_IN_GGA(T614, T615, X3256)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
QUOT551_IN_GGA(x1, x2, x3)  =  QUOT551_IN_GGA(x1, x2)

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

(205) UsableRulesProof (EQUIVALENT transformation)

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

(206) Obligation:

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

QUOT551_IN_GGA(s(T614), T615, X3256) → QUOT551_IN_GGA(T614, T615, X3256)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT551_IN_GGA(x1, x2, x3)  =  QUOT551_IN_GGA(x1, x2)

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

(207) PiDPToQDPProof (SOUND transformation)

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

(208) Obligation:

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

QUOT551_IN_GGA(s(T614), T615) → QUOT551_IN_GGA(T614, T615)

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

(209) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT551_IN_GGA(s(T614), T615) → QUOT551_IN_GGA(T614, T615)
  The graph contains the following edges 1 > 1, 2 >= 2

(210) YES

(211) Obligation:

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

QUOT313_IN_GGA(s(T420), T421, X1654) → QUOT313_IN_GGA(T420, T421, X1654)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
QUOT313_IN_GGA(x1, x2, x3)  =  QUOT313_IN_GGA(x1, x2)

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

(212) UsableRulesProof (EQUIVALENT transformation)

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

(213) Obligation:

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

QUOT313_IN_GGA(s(T420), T421, X1654) → QUOT313_IN_GGA(T420, T421, X1654)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT313_IN_GGA(x1, x2, x3)  =  QUOT313_IN_GGA(x1, x2)

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

(214) PiDPToQDPProof (SOUND transformation)

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

(215) Obligation:

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

QUOT313_IN_GGA(s(T420), T421) → QUOT313_IN_GGA(T420, T421)

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

(216) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT313_IN_GGA(s(T420), T421) → QUOT313_IN_GGA(T420, T421)
  The graph contains the following edges 1 > 1, 2 >= 2

(217) YES

(218) Obligation:

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

NEQ236_IN_GA(s(T281), s(T282)) → NEQ236_IN_GA(T281, T282)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
NEQ236_IN_GA(x1, x2)  =  NEQ236_IN_GA(x1)

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

(219) UsableRulesProof (EQUIVALENT transformation)

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

(220) Obligation:

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

NEQ236_IN_GA(s(T281), s(T282)) → NEQ236_IN_GA(T281, T282)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
NEQ236_IN_GA(x1, x2)  =  NEQ236_IN_GA(x1)

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

(221) PiDPToQDPProof (SOUND transformation)

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

(222) Obligation:

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

NEQ236_IN_GA(s(T281)) → NEQ236_IN_GA(T281)

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

(223) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• NEQ236_IN_GA(s(T281)) → NEQ236_IN_GA(T281)
  The graph contains the following edges 1 > 1

(224) YES

(225) Obligation:

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

ADD201_IN_AGA(s(T220), T221, s(X1112)) → ADD201_IN_AGA(T220, T221, X1112)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
ADD201_IN_AGA(x1, x2, x3)  =  ADD201_IN_AGA(x2)

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

(226) UsableRulesProof (EQUIVALENT transformation)

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

(227) Obligation:

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

ADD201_IN_AGA(s(T220), T221, s(X1112)) → ADD201_IN_AGA(T220, T221, X1112)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
ADD201_IN_AGA(x1, x2, x3)  =  ADD201_IN_AGA(x2)

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

(228) PiDPToQDPProof (SOUND transformation)

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

(229) Obligation:

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

ADD201_IN_AGA(T221) → ADD201_IN_AGA(T221)

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

(230) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = ADD201_IN_AGA(T221) evaluates to t =ADD201_IN_AGA(T221)

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from ADD201_IN_AGA(T221) to ADD201_IN_AGA(T221).

(231) NO

(232) Obligation:

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

TIMES190_IN_GGA(s(T199), T200, X1082) → TIMES190_IN_GGA(T199, T200, X1081)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
TIMES190_IN_GGA(x1, x2, x3)  =  TIMES190_IN_GGA(x1, x2)

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

(233) UsableRulesProof (EQUIVALENT transformation)

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

(234) Obligation:

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

TIMES190_IN_GGA(s(T199), T200, X1082) → TIMES190_IN_GGA(T199, T200, X1081)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
TIMES190_IN_GGA(x1, x2, x3)  =  TIMES190_IN_GGA(x1, x2)

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

(235) PiDPToQDPProof (SOUND transformation)

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

(236) Obligation:

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

TIMES190_IN_GGA(s(T199), T200) → TIMES190_IN_GGA(T199, T200)

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

(237) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• TIMES190_IN_GGA(s(T199), T200) → TIMES190_IN_GGA(T199, T200)
  The graph contains the following edges 1 > 1, 2 >= 2

(238) YES

(239) Obligation:

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

P1397_IN_GG(s(T1603), T1602) → U52_GG(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_GG(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → P1397_IN_GG(T1603, T1602)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
P1397_IN_GG(x1, x2)  =  P1397_IN_GG(x1, x2)
U52_GG(x1, x2, x3)  =  U52_GG(x1, x2, x3)

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

(240) UsableRulesProof (EQUIVALENT transformation)

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

(241) Obligation:

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

P1397_IN_GG(s(T1603), T1602) → U52_GG(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_GG(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → P1397_IN_GG(T1603, T1602)

The TRS R consists of the following rules:

not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))

The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
0  =  0
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
P1397_IN_GG(x1, x2)  =  P1397_IN_GG(x1, x2)
U52_GG(x1, x2, x3)  =  U52_GG(x1, x2, x3)

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

(242) PiDPToQDPProof (SOUND transformation)

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

(243) Obligation:

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

P1397_IN_GG(s(T1603), T1602) → U52_GG(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_GG(T1603, T1602, not_divides1398_out_gg) → P1397_IN_GG(T1603, T1602)

The TRS R consists of the following rules:

not_divides1398_in_gg(T1122, T1123) → U98_gg(div1402_in_gga(T1123, T1122))
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122))
U98_gg(div1402_out_gga(X9845)) → not_divides1398_out_gg
U99_gg(T1122, T1123, div1402_out_gga(T1126)) → U100_gg(times190_in_gga(T1126, T1122))
U99_gg(T1122, T1123, div1402_out_gga(T1126)) → U101_gg(T1123, times190_in_gga(T1126, T1122))
div1402_in_gga(0, T1159) → div1402_out_gga(0)
div1402_in_gga(s(T1168), T1169) → U103_gga(quot1419_in_gga(T1168, T1169))
U100_gg(times190_out_gga) → not_divides1398_out_gg
U101_gg(T1123, times190_out_gga) → U102_gg(neq227_in_ga(T1123))
U103_gga(quot1419_out_gga(X9960)) → div1402_out_gga(X9960)
times190_in_gga(0, T194) → times190_out_gga
times190_in_gga(s(T199), T200) → U3_gga(times190_in_gga(T199, T200))
times190_in_gga(s(T199), T200) → U4_gga(T200, times190_in_gga(T199, T200))
U102_gg(neq227_out_ga) → not_divides1398_out_gg
quot1419_in_gga(0, s(T1176)) → quot1419_out_gga(0)
quot1419_in_gga(s(0), s(s(T1193))) → quot1419_out_gga(0)
quot1419_in_gga(s(s(0)), s(s(s(T1210)))) → quot1419_out_gga(0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227))))) → quot1419_out_gga(0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244)))))) → quot1419_out_gga(0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261))))))) → quot1419_out_gga(0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271))))))) → U35_gga(quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271)))))))))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0)))))) → U36_gga(quot1532_in_ga(T1368))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0))))) → U37_gga(quot1615_in_ga(T1419))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0)))) → U38_gga(quot1687_in_ga(T1464))
quot1419_in_gga(s(s(T1503)), s(s(0))) → U39_gga(quot1748_in_ga(T1503))
quot1419_in_gga(s(T1536), s(0)) → U40_gga(quot1798_in_ga(T1536))
quot1419_in_gga(T1563, 0) → U41_gga(quot1837_in_ga(T1563))
U3_gga(times190_out_gga) → times190_out_gga
U4_gga(T200, times190_out_gga) → U5_gga(add201_in_aga(T200))
neq227_in_ga(T258) → neq227_out_ga
neq227_in_ga(T263) → U49_ga(neq236_in_ga(T263))
U35_gga(quot1481_out_ggga(X10230)) → quot1419_out_gga(X10230)
U36_gga(quot1532_out_ga(X10512)) → quot1419_out_gga(s(X10512))
U37_gga(quot1615_out_ga(X10901)) → quot1419_out_gga(s(X10901))
U38_gga(quot1687_out_ga(X11242)) → quot1419_out_gga(s(X11242))
U39_gga(quot1748_out_ga(X11535)) → quot1419_out_gga(s(X11535))
U40_gga(quot1798_out_ga(X11780)) → quot1419_out_gga(s(X11780))
U41_gga(quot1837_out_ga(X11977)) → quot1419_out_gga(s(X11977))
U5_gga(add201_out_aga(T203, X1082)) → times190_out_gga
U49_ga(neq236_out_ga) → neq227_out_ga
quot1481_in_ggga(0, s(T1287), T1288) → quot1481_out_ggga(0)
quot1481_in_ggga(s(T1301), s(T1302), T1303) → U32_ggga(quot1481_in_ggga(T1301, T1302, T1303))
quot1481_in_ggga(0, 0, T1320) → quot1481_out_ggga(s(0))
quot1481_in_ggga(s(0), 0, s(T1337)) → quot1481_out_ggga(s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347)) → U33_ggga(quot1419_in_gga(T1346, T1347))
quot1532_in_ga(0) → quot1532_out_ga(0)
quot1532_in_ga(s(0)) → quot1532_out_ga(0)
quot1532_in_ga(s(s(0))) → quot1532_out_ga(0)
quot1532_in_ga(s(s(s(0)))) → quot1532_out_ga(0)
quot1532_in_ga(s(s(s(s(0))))) → quot1532_out_ga(0)
quot1532_in_ga(s(s(s(s(s(0)))))) → quot1532_out_ga(0)
quot1532_in_ga(s(s(s(s(s(s(0))))))) → quot1532_out_ga(0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409)))))))) → U43_ga(quot1532_in_ga(T1409))
quot1615_in_ga(0) → quot1615_out_ga(0)
quot1615_in_ga(s(0)) → quot1615_out_ga(0)
quot1615_in_ga(s(s(0))) → quot1615_out_ga(0)
quot1615_in_ga(s(s(s(0)))) → quot1615_out_ga(0)
quot1615_in_ga(s(s(s(s(0))))) → quot1615_out_ga(0)
quot1615_in_ga(s(s(s(s(s(0)))))) → quot1615_out_ga(0)
quot1615_in_ga(s(s(s(s(s(s(T1455))))))) → U44_ga(quot1615_in_ga(T1455))
quot1687_in_ga(0) → quot1687_out_ga(0)
quot1687_in_ga(s(0)) → quot1687_out_ga(0)
quot1687_in_ga(s(s(0))) → quot1687_out_ga(0)
quot1687_in_ga(s(s(s(0)))) → quot1687_out_ga(0)
quot1687_in_ga(s(s(s(s(0))))) → quot1687_out_ga(0)
quot1687_in_ga(s(s(s(s(s(T1495)))))) → U45_ga(quot1687_in_ga(T1495))
quot1748_in_ga(0) → quot1748_out_ga(0)
quot1748_in_ga(s(0)) → quot1748_out_ga(0)
quot1748_in_ga(s(s(0))) → quot1748_out_ga(0)
quot1748_in_ga(s(s(s(0)))) → quot1748_out_ga(0)
quot1748_in_ga(s(s(s(s(T1529))))) → U46_ga(quot1748_in_ga(T1529))
quot1798_in_ga(0) → quot1798_out_ga(0)
quot1798_in_ga(s(0)) → quot1798_out_ga(0)
quot1798_in_ga(s(s(0))) → quot1798_out_ga(0)
quot1798_in_ga(s(s(s(T1557)))) → U47_ga(quot1798_in_ga(T1557))
quot1837_in_ga(0) → quot1837_out_ga(0)
quot1837_in_ga(s(0)) → quot1837_out_ga(0)
quot1837_in_ga(s(s(T1579))) → U48_ga(quot1837_in_ga(T1579))
add201_in_aga(T215) → add201_out_aga(0, s(s(T215)))
add201_in_aga(T221) → U6_aga(add201_in_aga(T221))
neq236_in_ga(s(T271)) → neq236_out_ga
neq236_in_ga(0) → neq236_out_ga
neq236_in_ga(s(T281)) → U7_ga(neq236_in_ga(T281))
U32_ggga(quot1481_out_ggga(X10279)) → quot1481_out_ggga(X10279)
U33_ggga(quot1419_out_gga(X10388)) → quot1481_out_ggga(s(X10388))
U43_ga(quot1532_out_ga(X10864)) → quot1532_out_ga(s(X10864))
U44_ga(quot1615_out_ga(X11208)) → quot1615_out_ga(s(X11208))
U45_ga(quot1687_out_ga(X11504)) → quot1687_out_ga(s(X11504))
U46_ga(quot1748_out_ga(X11752)) → quot1748_out_ga(s(X11752))
U47_ga(quot1798_out_ga(X11952)) → quot1798_out_ga(s(X11952))
U48_ga(quot1837_out_ga(X12104)) → quot1837_out_ga(s(X12104))
U6_aga(add201_out_aga(T220, X1112)) → add201_out_aga(s(T220), s(X1112))
U7_ga(neq236_out_ga) → neq236_out_ga
quot1481_in_ggga(s(T1352), 0, 0) → U34_ggga(quot1514_in_ga(T1352))
U34_ggga(quot1514_out_ga(X10408)) → quot1481_out_ggga(s(s(X10408)))
quot1514_in_ga(0) → quot1514_out_ga(0)
quot1514_in_ga(s(T1363)) → U42_ga(quot1514_in_ga(T1363))
U42_ga(quot1514_out_ga(X10490)) → quot1514_out_ga(s(X10490))

The set Q consists of the following terms:

not_divides1398_in_gg(x0, x1)
U98_gg(x0)
U99_gg(x0, x1, x2)
div1402_in_gga(x0, x1)
U100_gg(x0)
U101_gg(x0, x1)
U103_gga(x0)
times190_in_gga(x0, x1)
U102_gg(x0)
quot1419_in_gga(x0, x1)
U3_gga(x0)
U4_gga(x0, x1)
neq227_in_ga(x0)
U35_gga(x0)
U36_gga(x0)
U37_gga(x0)
U38_gga(x0)
U39_gga(x0)
U40_gga(x0)
U41_gga(x0)
U5_gga(x0)
U49_ga(x0)
quot1481_in_ggga(x0, x1, x2)
quot1532_in_ga(x0)
quot1615_in_ga(x0)
quot1687_in_ga(x0)
quot1748_in_ga(x0)
quot1798_in_ga(x0)
quot1837_in_ga(x0)
add201_in_aga(x0)
neq236_in_ga(x0)
U32_ggga(x0)
U33_ggga(x0)
U43_ga(x0)
U44_ga(x0)
U45_ga(x0)
U46_ga(x0)
U47_ga(x0)
U48_ga(x0)
U6_aga(x0)
U7_ga(x0)
U34_ggga(x0)
quot1514_in_ga(x0)
U42_ga(x0)

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

(244) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• U52_GG(T1603, T1602, not_divides1398_out_gg) → P1397_IN_GG(T1603, T1602)
  The graph contains the following edges 1 >= 1, 2 >= 2

• P1397_IN_GG(s(T1603), T1602) → U52_GG(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
  The graph contains the following edges 1 > 1, 2 >= 2

(245) YES

(246) Obligation:

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

QUOT67_IN_GGA(s(T137), T138, X461) → QUOT67_IN_GGA(T137, T138, X461)

The TRS R consists of the following rules:

prime1_in_g(s(s(0))) → prime1_out_g(s(s(0)))
prime1_in_g(s(s(s(T14)))) → U104_g(T14, not_divides13_in_g(T14))
not_divides13_in_g(T20) → U54_g(T20, div17_in_ga(T20, X38))
div17_in_ga(s(s(s(s(s(s(T117)))))), X412) → U59_ga(T117, X412, quot67_in_gga(T117, s(s(s(s(s(s(s(T117))))))), X412))
quot67_in_gga(s(T137), T138, X461) → U1_gga(T137, T138, X461, quot67_in_gga(T137, T138, X461))
quot67_in_gga(0, s(T164), s(0)) → quot67_out_gga(0, s(T164), s(0))
quot67_in_gga(0, 0, s(s(X565))) → U2_gga(X565, quot88_in_a(X565))
quot88_in_a(0) → quot88_out_a(0)
U2_gga(X565, quot88_out_a(X565)) → quot67_out_gga(0, 0, s(s(X565)))
U1_gga(T137, T138, X461, quot67_out_gga(T137, T138, X461)) → quot67_out_gga(s(T137), T138, X461)
U59_ga(T117, X412, quot67_out_gga(T117, s(s(s(s(s(s(s(T117))))))), X412)) → div17_out_ga(s(s(s(s(s(s(T117)))))), X412)
div17_in_ga(s(s(s(s(s(0))))), s(0)) → div17_out_ga(s(s(s(s(s(0))))), s(0))
div17_in_ga(s(s(s(s(0)))), s(0)) → div17_out_ga(s(s(s(s(0)))), s(0))
div17_in_ga(s(s(s(0))), s(0)) → div17_out_ga(s(s(s(0))), s(0))
div17_in_ga(s(s(0)), s(X833)) → U60_ga(X833, quot143_in_a(X833))
quot143_in_a(0) → quot143_out_a(0)
U60_ga(X833, quot143_out_a(X833)) → div17_out_ga(s(s(0)), s(X833))
div17_in_ga(s(0), s(X910)) → U61_ga(X910, quot158_in_a(X910))
quot158_in_a(0) → quot158_out_a(0)
U61_ga(X910, quot158_out_a(X910)) → div17_out_ga(s(0), s(X910))
div17_in_ga(0, s(X987)) → U62_ga(X987, quot173_in_a(X987))
quot173_in_a(0) → quot173_out_a(0)
U62_ga(X987, quot173_out_a(X987)) → div17_out_ga(0, s(X987))
U54_g(T20, div17_out_ga(T20, X38)) → not_divides13_out_g(T20)
not_divides13_in_g(T20) → U55_g(T20, div17_in_ga(T20, T22))
U55_g(T20, div17_out_ga(T20, T22)) → U56_g(T20, times190_in_gga(T22, T20, X39))
times190_in_gga(0, T194, 0) → times190_out_gga(0, T194, 0)
times190_in_gga(s(T199), T200, X1082) → U3_gga(T199, T200, X1082, times190_in_gga(T199, T200, X1081))
times190_in_gga(s(T199), T200, X1082) → U4_gga(T199, T200, X1082, times190_in_gga(T199, T200, T203))
U4_gga(T199, T200, X1082, times190_out_gga(T199, T200, T203)) → U5_gga(T199, T200, X1082, add201_in_aga(T203, T200, X1082))
add201_in_aga(0, T215, s(s(T215))) → add201_out_aga(0, T215, s(s(T215)))
add201_in_aga(s(T220), T221, s(X1112)) → U6_aga(T220, T221, X1112, add201_in_aga(T220, T221, X1112))
U6_aga(T220, T221, X1112, add201_out_aga(T220, T221, X1112)) → add201_out_aga(s(T220), T221, s(X1112))
U5_gga(T199, T200, X1082, add201_out_aga(T203, T200, X1082)) → times190_out_gga(s(T199), T200, X1082)
U3_gga(T199, T200, X1082, times190_out_gga(T199, T200, X1081)) → times190_out_gga(s(T199), T200, X1082)
U56_g(T20, times190_out_gga(T22, T20, X39)) → not_divides13_out_g(T20)
U55_g(T20, div17_out_ga(T20, T22)) → U57_g(T20, times190_in_gga(T22, T20, T187))
U57_g(T20, times190_out_gga(T22, T20, T187)) → U58_g(T20, neq191_in_ga(T20, T187))
neq191_in_ga(T232, 0) → neq191_out_ga(T232, 0)
neq191_in_ga(T245, s(0)) → neq191_out_ga(T245, s(0))
neq191_in_ga(T250, s(s(T251))) → U11_ga(T250, T251, neq227_in_ga(T250, T251))
neq227_in_ga(T258, 0) → neq227_out_ga(T258, 0)
neq227_in_ga(T263, s(T264)) → U49_ga(T263, T264, neq236_in_ga(T263, T264))
neq236_in_ga(s(T271), 0) → neq236_out_ga(s(T271), 0)
neq236_in_ga(0, s(T276)) → neq236_out_ga(0, s(T276))
neq236_in_ga(s(T281), s(T282)) → U7_ga(T281, T282, neq236_in_ga(T281, T282))
U7_ga(T281, T282, neq236_out_ga(T281, T282)) → neq236_out_ga(s(T281), s(T282))
U49_ga(T263, T264, neq236_out_ga(T263, T264)) → neq227_out_ga(T263, s(T264))
U11_ga(T250, T251, neq227_out_ga(T250, T251)) → neq191_out_ga(T250, s(s(T251)))
U58_g(T20, neq191_out_ga(T20, T187)) → not_divides13_out_g(T20)
U104_g(T14, not_divides13_out_g(T14)) → prime1_out_g(s(s(s(T14))))
prime1_in_g(s(s(s(0)))) → U105_g(not_divides13_in_g(0))
U105_g(not_divides13_out_g(0)) → prime1_out_g(s(s(s(0))))
prime1_in_g(s(s(s(s(T297))))) → U106_g(T297, not_divides13_in_g(s(T297)))
U106_g(T297, not_divides13_out_g(s(T297))) → U107_g(T297, not_divides259_in_g(T297))
not_divides259_in_g(T303) → U63_g(T303, div263_in_ga(T303, X1231))
div263_in_ga(s(s(s(s(s(s(T400)))))), X1605) → U68_ga(T400, X1605, quot313_in_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605))
quot313_in_gga(s(T420), T421, X1654) → U8_gga(T420, T421, X1654, quot313_in_gga(T420, T421, X1654))
quot313_in_gga(0, s(s(T451)), s(0)) → quot313_out_gga(0, s(s(T451)), s(0))
quot313_in_gga(0, s(0), s(s(X1808))) → U9_gga(X1808, quot340_in_a(X1808))
quot340_in_a(0) → quot340_out_a(0)
U9_gga(X1808, quot340_out_a(X1808)) → quot313_out_gga(0, s(0), s(s(X1808)))
quot313_in_gga(0, 0, s(s(X1842))) → U10_gga(X1842, quot349_in_a(X1842))
quot349_in_a(s(X1937)) → U16_a(X1937, quot88_in_a(X1937))
U16_a(X1937, quot88_out_a(X1937)) → quot349_out_a(s(X1937))
U10_gga(X1842, quot349_out_a(X1842)) → quot313_out_gga(0, 0, s(s(X1842)))
U8_gga(T420, T421, X1654, quot313_out_gga(T420, T421, X1654)) → quot313_out_gga(s(T420), T421, X1654)
U68_ga(T400, X1605, quot313_out_gga(T400, s(s(s(s(s(s(s(T400))))))), X1605)) → div263_out_ga(s(s(s(s(s(s(T400)))))), X1605)
div263_in_ga(s(s(s(s(s(0))))), s(0)) → div263_out_ga(s(s(s(s(s(0))))), s(0))
div263_in_ga(s(s(s(s(0)))), s(0)) → div263_out_ga(s(s(s(s(0)))), s(0))
div263_in_ga(s(s(s(0))), s(0)) → div263_out_ga(s(s(s(0))), s(0))
div263_in_ga(s(s(0)), s(0)) → div263_out_ga(s(s(0)), s(0))
div263_in_ga(s(0), s(X2493)) → U69_ga(X2493, quot446_in_a(X2493))
quot446_in_a(0) → quot446_out_a(0)
U69_ga(X2493, quot446_out_a(X2493)) → div263_out_ga(s(0), s(X2493))
div263_in_ga(0, s(X2627)) → U70_ga(X2627, quot467_in_a(X2627))
quot467_in_a(s(X2776)) → U22_a(X2776, quot340_in_a(X2776))
U22_a(X2776, quot340_out_a(X2776)) → quot467_out_a(s(X2776))
U70_ga(X2627, quot467_out_a(X2627)) → div263_out_ga(0, s(X2627))
U63_g(T303, div263_out_ga(T303, X1231)) → not_divides259_out_g(T303)
not_divides259_in_g(T303) → U64_g(T303, div263_in_ga(T303, T305))
U64_g(T303, div263_out_ga(T303, T305)) → U65_g(T303, times190_in_gga(T305, T303, X1232))
U65_g(T303, times190_out_gga(T305, T303, X1232)) → not_divides259_out_g(T303)
U64_g(T303, div263_out_ga(T303, T305)) → U66_g(T303, times190_in_gga(T305, T303, T474))
U66_g(T303, times190_out_gga(T305, T303, T474)) → U67_g(T303, neq191_in_ga(s(T303), T474))
U67_g(T303, neq191_out_ga(s(T303), T474)) → not_divides259_out_g(T303)
U107_g(T297, not_divides259_out_g(T297)) → prime1_out_g(s(s(s(s(T297)))))
prime1_in_g(s(s(s(s(0))))) → U108_g(not_divides13_in_g(s(0)))
U108_g(not_divides13_out_g(s(0))) → U109_g(not_divides259_in_g(0))
U109_g(not_divides259_out_g(0)) → prime1_out_g(s(s(s(s(0)))))
prime1_in_g(s(s(s(s(s(T491)))))) → U110_g(T491, not_divides13_in_g(s(s(T491))))
U110_g(T491, not_divides13_out_g(s(s(T491)))) → U111_g(T491, not_divides259_in_g(s(T491)))
U111_g(T491, not_divides259_out_g(s(T491))) → U112_g(T491, not_divides497_in_g(T491))
not_divides497_in_g(T497) → U71_g(T497, div501_in_ga(T497, X2833))
div501_in_ga(s(s(s(s(s(s(T594)))))), X3207) → U76_ga(T594, X3207, quot551_in_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207))
quot551_in_gga(s(T614), T615, X3256) → U12_gga(T614, T615, X3256, quot551_in_gga(T614, T615, X3256))
quot551_in_gga(0, s(s(s(T651))), s(0)) → quot551_out_gga(0, s(s(s(T651))), s(0))
quot551_in_gga(0, s(s(0)), s(s(X3450))) → U13_gga(X3450, quot584_in_a(X3450))
quot584_in_a(0) → quot584_out_a(0)
U13_gga(X3450, quot584_out_a(X3450)) → quot551_out_gga(0, s(s(0)), s(s(X3450)))
quot551_in_gga(0, s(0), s(s(X3484))) → U14_gga(X3484, quot173_in_a(X3484))
U14_gga(X3484, quot173_out_a(X3484)) → quot551_out_gga(0, s(0), s(s(X3484)))
quot551_in_gga(0, 0, s(s(X3508))) → U15_gga(X3508, quot595_in_a(X3508))
quot595_in_a(s(X3610)) → U23_a(X3610, quot349_in_a(X3610))
U23_a(X3610, quot349_out_a(X3610)) → quot595_out_a(s(X3610))
U15_gga(X3508, quot595_out_a(X3508)) → quot551_out_gga(0, 0, s(s(X3508)))
U12_gga(T614, T615, X3256, quot551_out_gga(T614, T615, X3256)) → quot551_out_gga(s(T614), T615, X3256)
U76_ga(T594, X3207, quot551_out_gga(T594, s(s(s(s(s(s(s(T594))))))), X3207)) → div501_out_ga(s(s(s(s(s(s(T594)))))), X3207)
div501_in_ga(s(s(s(s(s(0))))), s(0)) → div501_out_ga(s(s(s(s(s(0))))), s(0))
div501_in_ga(s(s(s(s(0)))), s(0)) → div501_out_ga(s(s(s(s(0)))), s(0))
div501_in_ga(s(s(s(0))), s(0)) → div501_out_ga(s(s(s(0))), s(0))
div501_in_ga(s(s(0)), s(0)) → div501_out_ga(s(s(0)), s(0))
div501_in_ga(s(0), s(s(X4604))) → U77_ga(X4604, quot584_in_a(X4604))
U77_ga(X4604, quot584_out_a(X4604)) → div501_out_ga(s(0), s(s(X4604)))
div501_in_ga(0, s(X4627)) → U78_ga(X4627, quot740_in_a(X4627))
quot740_in_a(s(X4783)) → U30_a(X4783, quot173_in_a(X4783))
U30_a(X4783, quot173_out_a(X4783)) → quot740_out_a(s(X4783))
U78_ga(X4627, quot740_out_a(X4627)) → div501_out_ga(0, s(X4627))
U71_g(T497, div501_out_ga(T497, X2833)) → not_divides497_out_g(T497)
not_divides497_in_g(T497) → U72_g(T497, div501_in_ga(T497, T499))
U72_g(T497, div501_out_ga(T497, T499)) → U73_g(T497, times190_in_gga(T499, T497, X2834))
U73_g(T497, times190_out_gga(T499, T497, X2834)) → not_divides497_out_g(T497)
U72_g(T497, div501_out_ga(T497, T499)) → U74_g(T497, times190_in_gga(T499, T497, T674))
U74_g(T497, times190_out_gga(T499, T497, T674)) → U75_g(T497, neq191_in_ga(s(s(T497)), T674))
U75_g(T497, neq191_out_ga(s(s(T497)), T674)) → not_divides497_out_g(T497)
U112_g(T491, not_divides497_out_g(T491)) → prime1_out_g(s(s(s(s(s(T491))))))
prime1_in_g(s(s(s(s(s(0)))))) → U113_g(not_divides13_in_g(s(s(0))))
U113_g(not_divides13_out_g(s(s(0)))) → U114_g(not_divides259_in_g(s(0)))
U114_g(not_divides259_out_g(s(0))) → U115_g(not_divides497_in_g(0))
U115_g(not_divides497_out_g(0)) → prime1_out_g(s(s(s(s(s(0))))))
prime1_in_g(s(s(s(s(s(s(T691))))))) → U116_g(T691, not_divides13_in_g(s(s(s(T691)))))
U116_g(T691, not_divides13_out_g(s(s(s(T691))))) → U117_g(T691, not_divides259_in_g(s(s(T691))))
U117_g(T691, not_divides259_out_g(s(s(T691)))) → U118_g(T691, not_divides497_in_g(s(T691)))
U118_g(T691, not_divides497_out_g(s(T691))) → U119_g(T691, not_divides770_in_g(T691))
not_divides770_in_g(T697) → U79_g(T697, div774_in_ga(T697, X4847))
div774_in_ga(s(s(s(s(s(s(T794)))))), X5221) → U84_ga(T794, X5221, quot824_in_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221))
quot824_in_gga(s(T814), T815, X5270) → U17_gga(T814, T815, X5270, quot824_in_gga(T814, T815, X5270))
quot824_in_gga(0, s(s(s(s(T857)))), s(0)) → quot824_out_gga(0, s(s(s(s(T857)))), s(0))
quot824_in_gga(0, s(s(s(0))), s(s(X5504))) → U18_gga(X5504, quot863_in_a(X5504))
quot863_in_a(0) → quot863_out_a(0)
U18_gga(X5504, quot863_out_a(X5504)) → quot824_out_gga(0, s(s(s(0))), s(s(X5504)))
quot824_in_gga(0, s(s(0)), s(s(X5538))) → U19_gga(X5538, quot158_in_a(X5538))
U19_gga(X5538, quot158_out_a(X5538)) → quot824_out_gga(0, s(s(0)), s(s(X5538)))
quot824_in_gga(0, s(0), s(s(X5562))) → U20_gga(X5562, quot467_in_a(X5562))
U20_gga(X5562, quot467_out_a(X5562)) → quot824_out_gga(0, s(0), s(s(X5562)))
quot824_in_gga(0, 0, s(s(X5586))) → U21_gga(X5586, quot876_in_a(X5586))
quot876_in_a(s(X5688)) → U31_a(X5688, quot595_in_a(X5688))
U31_a(X5688, quot595_out_a(X5688)) → quot876_out_a(s(X5688))
U21_gga(X5586, quot876_out_a(X5586)) → quot824_out_gga(0, 0, s(s(X5586)))
U17_gga(T814, T815, X5270, quot824_out_gga(T814, T815, X5270)) → quot824_out_gga(s(T814), T815, X5270)
U84_ga(T794, X5221, quot824_out_gga(T794, s(s(s(s(s(s(s(T794))))))), X5221)) → div774_out_ga(s(s(s(s(s(s(T794)))))), X5221)
div774_in_ga(s(s(s(s(s(0))))), s(0)) → div774_out_ga(s(s(s(s(s(0))))), s(0))
div774_in_ga(s(s(s(s(0)))), s(0)) → div774_out_ga(s(s(s(s(0)))), s(0))
div774_in_ga(s(s(s(0))), s(0)) → div774_out_ga(s(s(s(0))), s(0))
div774_in_ga(s(s(0)), s(s(X6716))) → U85_ga(X6716, quot863_in_a(X6716))
U85_ga(X6716, quot863_out_a(X6716)) → div774_out_ga(s(s(0)), s(s(X6716)))
div774_in_ga(s(0), s(s(X6952))) → U86_ga(X6952, quot158_in_a(X6952))
U86_ga(X6952, quot158_out_a(X6952)) → div774_out_ga(s(0), s(s(X6952)))
div774_in_ga(0, s(s(X7138))) → U87_ga(X7138, quot467_in_a(X7138))
U87_ga(X7138, quot467_out_a(X7138)) → div774_out_ga(0, s(s(X7138)))
U79_g(T697, div774_out_ga(T697, X4847)) → not_divides770_out_g(T697)
not_divides770_in_g(T697) → U80_g(T697, div774_in_ga(T697, T699))
U80_g(T697, div774_out_ga(T697, T699)) → U81_g(T697, times190_in_gga(T699, T697, X4848))
U81_g(T697, times190_out_gga(T699, T697, X4848)) → not_divides770_out_g(T697)
U80_g(T697, div774_out_ga(T697, T699)) → U82_g(T697, times190_in_gga(T699, T697, T880))
U82_g(T697, times190_out_gga(T699, T697, T880)) → U83_g(T697, neq191_in_ga(s(s(s(T697))), T880))
U83_g(T697, neq191_out_ga(s(s(s(T697))), T880)) → not_divides770_out_g(T697)
U119_g(T691, not_divides770_out_g(T691)) → prime1_out_g(s(s(s(s(s(s(T691)))))))
prime1_in_g(s(s(s(s(s(s(0))))))) → U120_g(not_divides13_in_g(s(s(s(0)))))
U120_g(not_divides13_out_g(s(s(s(0))))) → U121_g(not_divides259_in_g(s(s(0))))
U121_g(not_divides259_out_g(s(s(0)))) → U122_g(not_divides497_in_g(s(0)))
U122_g(not_divides497_out_g(s(0))) → U123_g(not_divides770_in_g(0))
U123_g(not_divides770_out_g(0)) → prime1_out_g(s(s(s(s(s(s(0)))))))
prime1_in_g(s(s(s(s(s(s(s(T897)))))))) → U124_g(T897, not_divides13_in_g(s(s(s(s(T897))))))
U124_g(T897, not_divides13_out_g(s(s(s(s(T897)))))) → U125_g(T897, not_divides259_in_g(s(s(s(T897)))))
U125_g(T897, not_divides259_out_g(s(s(s(T897))))) → U126_g(T897, not_divides497_in_g(s(s(T897))))
U126_g(T897, not_divides497_out_g(s(s(T897)))) → U127_g(T897, not_divides770_in_g(s(T897)))
U127_g(T897, not_divides770_out_g(s(T897))) → U128_g(T897, not_divides1072_in_g(T897))
not_divides1072_in_g(T903) → U88_g(T903, div1076_in_ga(T903, X7202))
div1076_in_ga(s(s(s(s(s(s(T1000)))))), X7576) → U93_ga(T1000, X7576, quot1126_in_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576))
quot1126_in_gga(s(T1020), T1021, X7625) → U24_gga(T1020, T1021, X7625, quot1126_in_gga(T1020, T1021, X7625))
quot1126_in_gga(0, s(s(s(s(s(T1069))))), s(0)) → quot1126_out_gga(0, s(s(s(s(s(T1069))))), s(0))
quot1126_in_gga(0, s(s(s(s(0)))), s(s(X7899))) → U25_gga(X7899, quot1171_in_a(X7899))
quot1171_in_a(0) → quot1171_out_a(0)
U25_gga(X7899, quot1171_out_a(X7899)) → quot1126_out_gga(0, s(s(s(s(0)))), s(s(X7899)))
quot1126_in_gga(0, s(s(s(0))), s(s(X7933))) → U26_gga(X7933, quot143_in_a(X7933))
U26_gga(X7933, quot143_out_a(X7933)) → quot1126_out_gga(0, s(s(s(0))), s(s(X7933)))
quot1126_in_gga(0, s(s(0)), s(s(X7957))) → U27_gga(X7957, quot446_in_a(X7957))
U27_gga(X7957, quot446_out_a(X7957)) → quot1126_out_gga(0, s(s(0)), s(s(X7957)))
quot1126_in_gga(0, s(0), s(s(X7981))) → U28_gga(X7981, quot740_in_a(X7981))
U28_gga(X7981, quot740_out_a(X7981)) → quot1126_out_gga(0, s(0), s(s(X7981)))
quot1126_in_gga(0, 0, s(s(s(X8107)))) → U29_gga(X8107, quot876_in_a(X8107))
U29_gga(X8107, quot876_out_a(X8107)) → quot1126_out_gga(0, 0, s(s(s(X8107))))
U24_gga(T1020, T1021, X7625, quot1126_out_gga(T1020, T1021, X7625)) → quot1126_out_gga(s(T1020), T1021, X7625)
U93_ga(T1000, X7576, quot1126_out_gga(T1000, s(s(s(s(s(s(s(T1000))))))), X7576)) → div1076_out_ga(s(s(s(s(s(s(T1000)))))), X7576)
div1076_in_ga(s(s(s(s(s(0))))), s(0)) → div1076_out_ga(s(s(s(s(s(0))))), s(0))
div1076_in_ga(s(s(s(s(0)))), s(0)) → div1076_out_ga(s(s(s(s(0)))), s(0))
div1076_in_ga(s(s(s(0))), s(s(X9055))) → U94_ga(X9055, quot1171_in_a(X9055))
U94_ga(X9055, quot1171_out_a(X9055)) → div1076_out_ga(s(s(s(0))), s(s(X9055)))
div1076_in_ga(s(s(0)), s(s(X9348))) → U95_ga(X9348, quot143_in_a(X9348))
U95_ga(X9348, quot143_out_a(X9348)) → div1076_out_ga(s(s(0)), s(s(X9348)))
div1076_in_ga(s(0), s(s(X9591))) → U96_ga(X9591, quot446_in_a(X9591))
U96_ga(X9591, quot446_out_a(X9591)) → div1076_out_ga(s(0), s(s(X9591)))
div1076_in_ga(0, s(s(X9777))) → U97_ga(X9777, quot740_in_a(X9777))
U97_ga(X9777, quot740_out_a(X9777)) → div1076_out_ga(0, s(s(X9777)))
U88_g(T903, div1076_out_ga(T903, X7202)) → not_divides1072_out_g(T903)
not_divides1072_in_g(T903) → U89_g(T903, div1076_in_ga(T903, T905))
U89_g(T903, div1076_out_ga(T903, T905)) → U90_g(T903, times190_in_gga(T905, T903, X7203))
U90_g(T903, times190_out_gga(T905, T903, X7203)) → not_divides1072_out_g(T903)
U89_g(T903, div1076_out_ga(T903, T905)) → U91_g(T903, times190_in_gga(T905, T903, T1092))
U91_g(T903, times190_out_gga(T905, T903, T1092)) → U92_g(T903, neq191_in_ga(s(s(s(s(T903)))), T1092))
U92_g(T903, neq191_out_ga(s(s(s(s(T903)))), T1092)) → not_divides1072_out_g(T903)
U128_g(T897, not_divides1072_out_g(T897)) → prime1_out_g(s(s(s(s(s(s(s(T897))))))))
prime1_in_g(s(s(s(s(s(s(s(0)))))))) → U129_g(not_divides13_in_g(s(s(s(s(0))))))
U129_g(not_divides13_out_g(s(s(s(s(0)))))) → U130_g(not_divides259_in_g(s(s(s(0)))))
U130_g(not_divides259_out_g(s(s(s(0))))) → U131_g(not_divides497_in_g(s(s(0))))
U131_g(not_divides497_out_g(s(s(0)))) → U132_g(not_divides770_in_g(s(0)))
U132_g(not_divides770_out_g(s(0))) → U133_g(not_divides1072_in_g(0))
U133_g(not_divides1072_out_g(0)) → prime1_out_g(s(s(s(s(s(s(s(0))))))))
prime1_in_g(s(s(s(s(s(s(s(s(T1109))))))))) → U134_g(T1109, not_divides13_in_g(s(s(s(s(s(T1109)))))))
U134_g(T1109, not_divides13_out_g(s(s(s(s(s(T1109))))))) → U135_g(T1109, not_divides259_in_g(s(s(s(s(T1109))))))
U135_g(T1109, not_divides259_out_g(s(s(s(s(T1109)))))) → U136_g(T1109, not_divides497_in_g(s(s(s(T1109)))))
U136_g(T1109, not_divides497_out_g(s(s(s(T1109))))) → U137_g(T1109, not_divides770_in_g(s(s(T1109))))
U137_g(T1109, not_divides770_out_g(s(s(T1109)))) → U138_g(T1109, not_divides1072_in_g(s(T1109)))
U138_g(T1109, not_divides1072_out_g(s(T1109))) → U139_g(T1109, p1397_in_gg(T1109, s(s(s(s(s(s(s(T1109)))))))))
p1397_in_gg(T1109, T1111) → U50_gg(T1109, T1111, not_divides1398_in_gg(T1109, T1111))
not_divides1398_in_gg(T1122, T1123) → U98_gg(T1122, T1123, div1402_in_gga(T1123, T1122, X9845))
div1402_in_gga(0, T1159, 0) → div1402_out_gga(0, T1159, 0)
div1402_in_gga(s(T1168), T1169, X9960) → U103_gga(T1168, T1169, X9960, quot1419_in_gga(T1168, T1169, X9960))
quot1419_in_gga(0, s(T1176), 0) → quot1419_out_gga(0, s(T1176), 0)
quot1419_in_gga(s(0), s(s(T1193)), 0) → quot1419_out_gga(s(0), s(s(T1193)), 0)
quot1419_in_gga(s(s(0)), s(s(s(T1210))), 0) → quot1419_out_gga(s(s(0)), s(s(s(T1210))), 0)
quot1419_in_gga(s(s(s(0))), s(s(s(s(T1227)))), 0) → quot1419_out_gga(s(s(s(0))), s(s(s(s(T1227)))), 0)
quot1419_in_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0) → quot1419_out_gga(s(s(s(s(0)))), s(s(s(s(s(T1244))))), 0)
quot1419_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0) → quot1419_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T1261)))))), 0)
quot1419_in_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230) → U35_gga(T1270, T1271, X10230, quot1481_in_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230))
quot1481_in_ggga(0, s(T1287), T1288, 0) → quot1481_out_ggga(0, s(T1287), T1288, 0)
quot1481_in_ggga(s(T1301), s(T1302), T1303, X10279) → U32_ggga(T1301, T1302, T1303, X10279, quot1481_in_ggga(T1301, T1302, T1303, X10279))
quot1481_in_ggga(0, 0, T1320, s(0)) → quot1481_out_ggga(0, 0, T1320, s(0))
quot1481_in_ggga(s(0), 0, s(T1337), s(0)) → quot1481_out_ggga(s(0), 0, s(T1337), s(0))
quot1481_in_ggga(s(s(T1346)), 0, s(T1347), s(X10388)) → U33_ggga(T1346, T1347, X10388, quot1419_in_gga(T1346, T1347, X10388))
quot1419_in_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512)) → U36_gga(T1368, X10512, quot1532_in_ga(T1368, X10512))
quot1532_in_ga(0, 0) → quot1532_out_ga(0, 0)
quot1532_in_ga(s(0), 0) → quot1532_out_ga(s(0), 0)
quot1532_in_ga(s(s(0)), 0) → quot1532_out_ga(s(s(0)), 0)
quot1532_in_ga(s(s(s(0))), 0) → quot1532_out_ga(s(s(s(0))), 0)
quot1532_in_ga(s(s(s(s(0)))), 0) → quot1532_out_ga(s(s(s(s(0)))), 0)
quot1532_in_ga(s(s(s(s(s(0))))), 0) → quot1532_out_ga(s(s(s(s(s(0))))), 0)
quot1532_in_ga(s(s(s(s(s(s(0)))))), 0) → quot1532_out_ga(s(s(s(s(s(s(0)))))), 0)
quot1532_in_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864)) → U43_ga(T1409, X10864, quot1532_in_ga(T1409, X10864))
U43_ga(T1409, X10864, quot1532_out_ga(T1409, X10864)) → quot1532_out_ga(s(s(s(s(s(s(s(T1409))))))), s(X10864))
U36_gga(T1368, X10512, quot1532_out_ga(T1368, X10512)) → quot1419_out_gga(s(s(s(s(s(T1368))))), s(s(s(s(s(0))))), s(X10512))
quot1419_in_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901)) → U37_gga(T1419, X10901, quot1615_in_ga(T1419, X10901))
quot1615_in_ga(0, 0) → quot1615_out_ga(0, 0)
quot1615_in_ga(s(0), 0) → quot1615_out_ga(s(0), 0)
quot1615_in_ga(s(s(0)), 0) → quot1615_out_ga(s(s(0)), 0)
quot1615_in_ga(s(s(s(0))), 0) → quot1615_out_ga(s(s(s(0))), 0)
quot1615_in_ga(s(s(s(s(0)))), 0) → quot1615_out_ga(s(s(s(s(0)))), 0)
quot1615_in_ga(s(s(s(s(s(0))))), 0) → quot1615_out_ga(s(s(s(s(s(0))))), 0)
quot1615_in_ga(s(s(s(s(s(s(T1455)))))), s(X11208)) → U44_ga(T1455, X11208, quot1615_in_ga(T1455, X11208))
U44_ga(T1455, X11208, quot1615_out_ga(T1455, X11208)) → quot1615_out_ga(s(s(s(s(s(s(T1455)))))), s(X11208))
U37_gga(T1419, X10901, quot1615_out_ga(T1419, X10901)) → quot1419_out_gga(s(s(s(s(T1419)))), s(s(s(s(0)))), s(X10901))
quot1419_in_gga(s(s(s(T1464))), s(s(s(0))), s(X11242)) → U38_gga(T1464, X11242, quot1687_in_ga(T1464, X11242))
quot1687_in_ga(0, 0) → quot1687_out_ga(0, 0)
quot1687_in_ga(s(0), 0) → quot1687_out_ga(s(0), 0)
quot1687_in_ga(s(s(0)), 0) → quot1687_out_ga(s(s(0)), 0)
quot1687_in_ga(s(s(s(0))), 0) → quot1687_out_ga(s(s(s(0))), 0)
quot1687_in_ga(s(s(s(s(0)))), 0) → quot1687_out_ga(s(s(s(s(0)))), 0)
quot1687_in_ga(s(s(s(s(s(T1495))))), s(X11504)) → U45_ga(T1495, X11504, quot1687_in_ga(T1495, X11504))
U45_ga(T1495, X11504, quot1687_out_ga(T1495, X11504)) → quot1687_out_ga(s(s(s(s(s(T1495))))), s(X11504))
U38_gga(T1464, X11242, quot1687_out_ga(T1464, X11242)) → quot1419_out_gga(s(s(s(T1464))), s(s(s(0))), s(X11242))
quot1419_in_gga(s(s(T1503)), s(s(0)), s(X11535)) → U39_gga(T1503, X11535, quot1748_in_ga(T1503, X11535))
quot1748_in_ga(0, 0) → quot1748_out_ga(0, 0)
quot1748_in_ga(s(0), 0) → quot1748_out_ga(s(0), 0)
quot1748_in_ga(s(s(0)), 0) → quot1748_out_ga(s(s(0)), 0)
quot1748_in_ga(s(s(s(0))), 0) → quot1748_out_ga(s(s(s(0))), 0)
quot1748_in_ga(s(s(s(s(T1529)))), s(X11752)) → U46_ga(T1529, X11752, quot1748_in_ga(T1529, X11752))
U46_ga(T1529, X11752, quot1748_out_ga(T1529, X11752)) → quot1748_out_ga(s(s(s(s(T1529)))), s(X11752))
U39_gga(T1503, X11535, quot1748_out_ga(T1503, X11535)) → quot1419_out_gga(s(s(T1503)), s(s(0)), s(X11535))
quot1419_in_gga(s(T1536), s(0), s(X11780)) → U40_gga(T1536, X11780, quot1798_in_ga(T1536, X11780))
quot1798_in_ga(0, 0) → quot1798_out_ga(0, 0)
quot1798_in_ga(s(0), 0) → quot1798_out_ga(s(0), 0)
quot1798_in_ga(s(s(0)), 0) → quot1798_out_ga(s(s(0)), 0)
quot1798_in_ga(s(s(s(T1557))), s(X11952)) → U47_ga(T1557, X11952, quot1798_in_ga(T1557, X11952))
U47_ga(T1557, X11952, quot1798_out_ga(T1557, X11952)) → quot1798_out_ga(s(s(s(T1557))), s(X11952))
U40_gga(T1536, X11780, quot1798_out_ga(T1536, X11780)) → quot1419_out_gga(s(T1536), s(0), s(X11780))
quot1419_in_gga(T1563, 0, s(X11977)) → U41_gga(T1563, X11977, quot1837_in_ga(T1563, X11977))
quot1837_in_ga(0, 0) → quot1837_out_ga(0, 0)
quot1837_in_ga(s(0), 0) → quot1837_out_ga(s(0), 0)
quot1837_in_ga(s(s(T1579)), s(X12104)) → U48_ga(T1579, X12104, quot1837_in_ga(T1579, X12104))
U48_ga(T1579, X12104, quot1837_out_ga(T1579, X12104)) → quot1837_out_ga(s(s(T1579)), s(X12104))
U41_gga(T1563, X11977, quot1837_out_ga(T1563, X11977)) → quot1419_out_gga(T1563, 0, s(X11977))
U33_ggga(T1346, T1347, X10388, quot1419_out_gga(T1346, T1347, X10388)) → quot1481_out_ggga(s(s(T1346)), 0, s(T1347), s(X10388))
quot1481_in_ggga(s(T1352), 0, 0, s(s(X10408))) → U34_ggga(T1352, X10408, quot1514_in_ga(T1352, X10408))
quot1514_in_ga(0, 0) → quot1514_out_ga(0, 0)
quot1514_in_ga(s(T1363), s(X10490)) → U42_ga(T1363, X10490, quot1514_in_ga(T1363, X10490))
U42_ga(T1363, X10490, quot1514_out_ga(T1363, X10490)) → quot1514_out_ga(s(T1363), s(X10490))
U34_ggga(T1352, X10408, quot1514_out_ga(T1352, X10408)) → quot1481_out_ggga(s(T1352), 0, 0, s(s(X10408)))
U32_ggga(T1301, T1302, T1303, X10279, quot1481_out_ggga(T1301, T1302, T1303, X10279)) → quot1481_out_ggga(s(T1301), s(T1302), T1303, X10279)
U35_gga(T1270, T1271, X10230, quot1481_out_ggga(T1270, T1271, s(s(s(s(s(s(s(T1271))))))), X10230)) → quot1419_out_gga(s(s(s(s(s(s(T1270)))))), s(s(s(s(s(s(T1271)))))), X10230)
U103_gga(T1168, T1169, X9960, quot1419_out_gga(T1168, T1169, X9960)) → div1402_out_gga(s(T1168), T1169, X9960)
U98_gg(T1122, T1123, div1402_out_gga(T1123, T1122, X9845)) → not_divides1398_out_gg(T1122, T1123)
not_divides1398_in_gg(T1122, T1123) → U99_gg(T1122, T1123, div1402_in_gga(T1123, T1122, T1126))
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U100_gg(T1122, T1123, times190_in_gga(T1126, T1122, X9846))
U100_gg(T1122, T1123, times190_out_gga(T1126, T1122, X9846)) → not_divides1398_out_gg(T1122, T1123)
U99_gg(T1122, T1123, div1402_out_gga(T1123, T1122, T1126)) → U101_gg(T1122, T1123, times190_in_gga(T1126, T1122, T1586))
U101_gg(T1122, T1123, times190_out_gga(T1126, T1122, T1586)) → U102_gg(T1122, T1123, neq227_in_ga(T1123, T1586))
U102_gg(T1122, T1123, neq227_out_ga(T1123, T1586)) → not_divides1398_out_gg(T1122, T1123)
U50_gg(T1109, T1111, not_divides1398_out_gg(T1109, T1111)) → p1397_out_gg(T1109, T1111)
p1397_in_gg(0, T1597) → U51_gg(T1597, not_divides1398_in_gg(0, T1597))
U51_gg(T1597, not_divides1398_out_gg(0, T1597)) → p1397_out_gg(0, T1597)
p1397_in_gg(s(T1603), T1602) → U52_gg(T1603, T1602, not_divides1398_in_gg(s(T1603), T1602))
U52_gg(T1603, T1602, not_divides1398_out_gg(s(T1603), T1602)) → U53_gg(T1603, T1602, p1397_in_gg(T1603, T1602))
U53_gg(T1603, T1602, p1397_out_gg(T1603, T1602)) → p1397_out_gg(s(T1603), T1602)
U139_g(T1109, p1397_out_gg(T1109, s(s(s(s(s(s(s(T1109))))))))) → prime1_out_g(s(s(s(s(s(s(s(s(T1109)))))))))

The argument filtering Pi contains the following mapping:
prime1_in_g(x1)  =  prime1_in_g(x1)
s(x1)  =  s(x1)
0  =  0
prime1_out_g(x1)  =  prime1_out_g
U104_g(x1, x2)  =  U104_g(x2)
not_divides13_in_g(x1)  =  not_divides13_in_g(x1)
U54_g(x1, x2)  =  U54_g(x2)
div17_in_ga(x1, x2)  =  div17_in_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x3)
quot67_in_gga(x1, x2, x3)  =  quot67_in_gga(x1, x2)
U1_gga(x1, x2, x3, x4)  =  U1_gga(x4)
quot67_out_gga(x1, x2, x3)  =  quot67_out_gga(x3)
U2_gga(x1, x2)  =  U2_gga(x2)
quot88_in_a(x1)  =  quot88_in_a
quot88_out_a(x1)  =  quot88_out_a(x1)
div17_out_ga(x1, x2)  =  div17_out_ga(x2)
U60_ga(x1, x2)  =  U60_ga(x2)
quot143_in_a(x1)  =  quot143_in_a
quot143_out_a(x1)  =  quot143_out_a(x1)
U61_ga(x1, x2)  =  U61_ga(x2)
quot158_in_a(x1)  =  quot158_in_a
quot158_out_a(x1)  =  quot158_out_a(x1)
U62_ga(x1, x2)  =  U62_ga(x2)
quot173_in_a(x1)  =  quot173_in_a
quot173_out_a(x1)  =  quot173_out_a(x1)
not_divides13_out_g(x1)  =  not_divides13_out_g
U55_g(x1, x2)  =  U55_g(x1, x2)
U56_g(x1, x2)  =  U56_g(x2)
times190_in_gga(x1, x2, x3)  =  times190_in_gga(x1, x2)
times190_out_gga(x1, x2, x3)  =  times190_out_gga
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
U4_gga(x1, x2, x3, x4)  =  U4_gga(x2, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
add201_in_aga(x1, x2, x3)  =  add201_in_aga(x2)
add201_out_aga(x1, x2, x3)  =  add201_out_aga(x1, x3)
U6_aga(x1, x2, x3, x4)  =  U6_aga(x4)
U57_g(x1, x2)  =  U57_g(x1, x2)
U58_g(x1, x2)  =  U58_g(x2)
neq191_in_ga(x1, x2)  =  neq191_in_ga(x1)
neq191_out_ga(x1, x2)  =  neq191_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
neq227_in_ga(x1, x2)  =  neq227_in_ga(x1)
neq227_out_ga(x1, x2)  =  neq227_out_ga
U49_ga(x1, x2, x3)  =  U49_ga(x3)
neq236_in_ga(x1, x2)  =  neq236_in_ga(x1)
neq236_out_ga(x1, x2)  =  neq236_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U105_g(x1)  =  U105_g(x1)
U106_g(x1, x2)  =  U106_g(x1, x2)
U107_g(x1, x2)  =  U107_g(x2)
not_divides259_in_g(x1)  =  not_divides259_in_g(x1)
U63_g(x1, x2)  =  U63_g(x2)
div263_in_ga(x1, x2)  =  div263_in_ga(x1)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
quot313_in_gga(x1, x2, x3)  =  quot313_in_gga(x1, x2)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
quot313_out_gga(x1, x2, x3)  =  quot313_out_gga(x3)
U9_gga(x1, x2)  =  U9_gga(x2)
quot340_in_a(x1)  =  quot340_in_a
quot340_out_a(x1)  =  quot340_out_a(x1)
U10_gga(x1, x2)  =  U10_gga(x2)
quot349_in_a(x1)  =  quot349_in_a
U16_a(x1, x2)  =  U16_a(x2)
quot349_out_a(x1)  =  quot349_out_a(x1)
div263_out_ga(x1, x2)  =  div263_out_ga(x2)
U69_ga(x1, x2)  =  U69_ga(x2)
quot446_in_a(x1)  =  quot446_in_a
quot446_out_a(x1)  =  quot446_out_a(x1)
U70_ga(x1, x2)  =  U70_ga(x2)
quot467_in_a(x1)  =  quot467_in_a
U22_a(x1, x2)  =  U22_a(x2)
quot467_out_a(x1)  =  quot467_out_a(x1)
not_divides259_out_g(x1)  =  not_divides259_out_g
U64_g(x1, x2)  =  U64_g(x1, x2)
U65_g(x1, x2)  =  U65_g(x2)
U66_g(x1, x2)  =  U66_g(x1, x2)
U67_g(x1, x2)  =  U67_g(x2)
U108_g(x1)  =  U108_g(x1)
U109_g(x1)  =  U109_g(x1)
U110_g(x1, x2)  =  U110_g(x1, x2)
U111_g(x1, x2)  =  U111_g(x1, x2)
U112_g(x1, x2)  =  U112_g(x2)
not_divides497_in_g(x1)  =  not_divides497_in_g(x1)
U71_g(x1, x2)  =  U71_g(x2)
div501_in_ga(x1, x2)  =  div501_in_ga(x1)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
quot551_in_gga(x1, x2, x3)  =  quot551_in_gga(x1, x2)
U12_gga(x1, x2, x3, x4)  =  U12_gga(x4)
quot551_out_gga(x1, x2, x3)  =  quot551_out_gga(x3)
U13_gga(x1, x2)  =  U13_gga(x2)
quot584_in_a(x1)  =  quot584_in_a
quot584_out_a(x1)  =  quot584_out_a(x1)
U14_gga(x1, x2)  =  U14_gga(x2)
U15_gga(x1, x2)  =  U15_gga(x2)
quot595_in_a(x1)  =  quot595_in_a
U23_a(x1, x2)  =  U23_a(x2)
quot595_out_a(x1)  =  quot595_out_a(x1)
div501_out_ga(x1, x2)  =  div501_out_ga(x2)
U77_ga(x1, x2)  =  U77_ga(x2)
U78_ga(x1, x2)  =  U78_ga(x2)
quot740_in_a(x1)  =  quot740_in_a
U30_a(x1, x2)  =  U30_a(x2)
quot740_out_a(x1)  =  quot740_out_a(x1)
not_divides497_out_g(x1)  =  not_divides497_out_g
U72_g(x1, x2)  =  U72_g(x1, x2)
U73_g(x1, x2)  =  U73_g(x2)
U74_g(x1, x2)  =  U74_g(x1, x2)
U75_g(x1, x2)  =  U75_g(x2)
U113_g(x1)  =  U113_g(x1)
U114_g(x1)  =  U114_g(x1)
U115_g(x1)  =  U115_g(x1)
U116_g(x1, x2)  =  U116_g(x1, x2)
U117_g(x1, x2)  =  U117_g(x1, x2)
U118_g(x1, x2)  =  U118_g(x1, x2)
U119_g(x1, x2)  =  U119_g(x2)
not_divides770_in_g(x1)  =  not_divides770_in_g(x1)
U79_g(x1, x2)  =  U79_g(x2)
div774_in_ga(x1, x2)  =  div774_in_ga(x1)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
quot824_in_gga(x1, x2, x3)  =  quot824_in_gga(x1, x2)
U17_gga(x1, x2, x3, x4)  =  U17_gga(x4)
quot824_out_gga(x1, x2, x3)  =  quot824_out_gga(x3)
U18_gga(x1, x2)  =  U18_gga(x2)
quot863_in_a(x1)  =  quot863_in_a
quot863_out_a(x1)  =  quot863_out_a(x1)
U19_gga(x1, x2)  =  U19_gga(x2)
U20_gga(x1, x2)  =  U20_gga(x2)
U21_gga(x1, x2)  =  U21_gga(x2)
quot876_in_a(x1)  =  quot876_in_a
U31_a(x1, x2)  =  U31_a(x2)
quot876_out_a(x1)  =  quot876_out_a(x1)
div774_out_ga(x1, x2)  =  div774_out_ga(x2)
U85_ga(x1, x2)  =  U85_ga(x2)
U86_ga(x1, x2)  =  U86_ga(x2)
U87_ga(x1, x2)  =  U87_ga(x2)
not_divides770_out_g(x1)  =  not_divides770_out_g
U80_g(x1, x2)  =  U80_g(x1, x2)
U81_g(x1, x2)  =  U81_g(x2)
U82_g(x1, x2)  =  U82_g(x1, x2)
U83_g(x1, x2)  =  U83_g(x2)
U120_g(x1)  =  U120_g(x1)
U121_g(x1)  =  U121_g(x1)
U122_g(x1)  =  U122_g(x1)
U123_g(x1)  =  U123_g(x1)
U124_g(x1, x2)  =  U124_g(x1, x2)
U125_g(x1, x2)  =  U125_g(x1, x2)
U126_g(x1, x2)  =  U126_g(x1, x2)
U127_g(x1, x2)  =  U127_g(x1, x2)
U128_g(x1, x2)  =  U128_g(x2)
not_divides1072_in_g(x1)  =  not_divides1072_in_g(x1)
U88_g(x1, x2)  =  U88_g(x2)
div1076_in_ga(x1, x2)  =  div1076_in_ga(x1)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
quot1126_in_gga(x1, x2, x3)  =  quot1126_in_gga(x1, x2)
U24_gga(x1, x2, x3, x4)  =  U24_gga(x4)
quot1126_out_gga(x1, x2, x3)  =  quot1126_out_gga(x3)
U25_gga(x1, x2)  =  U25_gga(x2)
quot1171_in_a(x1)  =  quot1171_in_a
quot1171_out_a(x1)  =  quot1171_out_a(x1)
U26_gga(x1, x2)  =  U26_gga(x2)
U27_gga(x1, x2)  =  U27_gga(x2)
U28_gga(x1, x2)  =  U28_gga(x2)
U29_gga(x1, x2)  =  U29_gga(x2)
div1076_out_ga(x1, x2)  =  div1076_out_ga(x2)
U94_ga(x1, x2)  =  U94_ga(x2)
U95_ga(x1, x2)  =  U95_ga(x2)
U96_ga(x1, x2)  =  U96_ga(x2)
U97_ga(x1, x2)  =  U97_ga(x2)
not_divides1072_out_g(x1)  =  not_divides1072_out_g
U89_g(x1, x2)  =  U89_g(x1, x2)
U90_g(x1, x2)  =  U90_g(x2)
U91_g(x1, x2)  =  U91_g(x1, x2)
U92_g(x1, x2)  =  U92_g(x2)
U129_g(x1)  =  U129_g(x1)
U130_g(x1)  =  U130_g(x1)
U131_g(x1)  =  U131_g(x1)
U132_g(x1)  =  U132_g(x1)
U133_g(x1)  =  U133_g(x1)
U134_g(x1, x2)  =  U134_g(x1, x2)
U135_g(x1, x2)  =  U135_g(x1, x2)
U136_g(x1, x2)  =  U136_g(x1, x2)
U137_g(x1, x2)  =  U137_g(x1, x2)
U138_g(x1, x2)  =  U138_g(x1, x2)
U139_g(x1, x2)  =  U139_g(x2)
p1397_in_gg(x1, x2)  =  p1397_in_gg(x1, x2)
U50_gg(x1, x2, x3)  =  U50_gg(x3)
not_divides1398_in_gg(x1, x2)  =  not_divides1398_in_gg(x1, x2)
U98_gg(x1, x2, x3)  =  U98_gg(x3)
div1402_in_gga(x1, x2, x3)  =  div1402_in_gga(x1, x2)
div1402_out_gga(x1, x2, x3)  =  div1402_out_gga(x3)
U103_gga(x1, x2, x3, x4)  =  U103_gga(x4)
quot1419_in_gga(x1, x2, x3)  =  quot1419_in_gga(x1, x2)
quot1419_out_gga(x1, x2, x3)  =  quot1419_out_gga(x3)
U35_gga(x1, x2, x3, x4)  =  U35_gga(x4)
quot1481_in_ggga(x1, x2, x3, x4)  =  quot1481_in_ggga(x1, x2, x3)
quot1481_out_ggga(x1, x2, x3, x4)  =  quot1481_out_ggga(x4)
U32_ggga(x1, x2, x3, x4, x5)  =  U32_ggga(x5)
U33_ggga(x1, x2, x3, x4)  =  U33_ggga(x4)
U36_gga(x1, x2, x3)  =  U36_gga(x3)
quot1532_in_ga(x1, x2)  =  quot1532_in_ga(x1)
quot1532_out_ga(x1, x2)  =  quot1532_out_ga(x2)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U37_gga(x1, x2, x3)  =  U37_gga(x3)
quot1615_in_ga(x1, x2)  =  quot1615_in_ga(x1)
quot1615_out_ga(x1, x2)  =  quot1615_out_ga(x2)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U38_gga(x1, x2, x3)  =  U38_gga(x3)
quot1687_in_ga(x1, x2)  =  quot1687_in_ga(x1)
quot1687_out_ga(x1, x2)  =  quot1687_out_ga(x2)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U39_gga(x1, x2, x3)  =  U39_gga(x3)
quot1748_in_ga(x1, x2)  =  quot1748_in_ga(x1)
quot1748_out_ga(x1, x2)  =  quot1748_out_ga(x2)
U46_ga(x1, x2, x3)  =  U46_ga(x3)
U40_gga(x1, x2, x3)  =  U40_gga(x3)
quot1798_in_ga(x1, x2)  =  quot1798_in_ga(x1)
quot1798_out_ga(x1, x2)  =  quot1798_out_ga(x2)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U41_gga(x1, x2, x3)  =  U41_gga(x3)
quot1837_in_ga(x1, x2)  =  quot1837_in_ga(x1)
quot1837_out_ga(x1, x2)  =  quot1837_out_ga(x2)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U34_ggga(x1, x2, x3)  =  U34_ggga(x3)
quot1514_in_ga(x1, x2)  =  quot1514_in_ga(x1)
quot1514_out_ga(x1, x2)  =  quot1514_out_ga(x2)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
not_divides1398_out_gg(x1, x2)  =  not_divides1398_out_gg
U99_gg(x1, x2, x3)  =  U99_gg(x1, x2, x3)
U100_gg(x1, x2, x3)  =  U100_gg(x3)
U101_gg(x1, x2, x3)  =  U101_gg(x2, x3)
U102_gg(x1, x2, x3)  =  U102_gg(x3)
p1397_out_gg(x1, x2)  =  p1397_out_gg
U51_gg(x1, x2)  =  U51_gg(x2)
U52_gg(x1, x2, x3)  =  U52_gg(x1, x2, x3)
U53_gg(x1, x2, x3)  =  U53_gg(x3)
QUOT67_IN_GGA(x1, x2, x3)  =  QUOT67_IN_GGA(x1, x2)

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

(247) UsableRulesProof (EQUIVALENT transformation)

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

(248) Obligation:

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

QUOT67_IN_GGA(s(T137), T138, X461) → QUOT67_IN_GGA(T137, T138, X461)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
QUOT67_IN_GGA(x1, x2, x3)  =  QUOT67_IN_GGA(x1, x2)

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

(249) PiDPToQDPProof (SOUND transformation)

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

(250) Obligation:

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

QUOT67_IN_GGA(s(T137), T138) → QUOT67_IN_GGA(T137, T138)

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

(251) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• QUOT67_IN_GGA(s(T137), T138) → QUOT67_IN_GGA(T137, T138)
  The graph contains the following edges 1 > 1, 2 >= 2

(252) YES